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## Material Information- Title:
- Design issues for minimum mean square error (MMSE) receiver-based CDMA systems
- Creator:
- Almutairi, Ali Faisal, 1970-
- Publication Date:
- 2000
- Language:
- English
- Physical Description:
- vii, 114 leaves : ill. ; 29 cm.
## Subjects- Subjects / Keywords:
- Bandwidth ( jstor )
Binary phase shift keying ( jstor ) Code division multiple access ( jstor ) Communication systems ( jstor ) Multiple access ( jstor ) Receivers ( jstor ) Signal fading ( jstor ) Signals ( jstor ) Simulations ( jstor ) Transmitters ( jstor ) Code division multiple access ( fast ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Thesis:
- Thesis (Ph. D.)--University of Florida, 2000.
- Bibliography:
- Includes bibliographical references (leaves 109-113).
- General Note:
- Printout.
- General Note:
- Vita.
- Statement of Responsibility:
- by Ali Faisal Almutairi.
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- University of Florida
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- Resource Identifier:
- 45068139 ( OCLC )
ocm45068139
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DESIGN ISSUES FOR MINIMUM MEAN SQUARE ERROR (MMSE) RECEIVER-BASED CDMA SYSTEMS By ALI FAISAL ALMUTAIRI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2000 I dedicate this work to my wife, Aisha, my daughters, Bashayer and Ohood, my mother and the rest of my family members. ACKNOWLEDGMENTS I would like to thank Professor William Edmonson and Professor Ulrich H. Kurzweg for serving as members of my committee. I would like to express my appreciation to Professor Tan Wong for his fruitful suggestions. I extend special thanks to my adviser, Professor Haniph A. Latchman, not only for his time, but also for his guidance throughout my studies with respect to both to research issues and to professional issues. I would like to express my greatest appreciation to my adviser, Professor Scott L. Miller, for introducing me to this topic and advising me in the early stages of this project. I thank my family, my wife, Aisha, my lovely daughters, Bashayer and Ohood, my mother, and the rest of my family members, for their support, patience and encouragement throughout my studies. I also wish to acknowledge all of my friends at the University of Florida and elsewhere, especially my colleagues Dr. Brad Rainbolt and Dr. Ron F. Smith. I would like to thank Dave Tingling, Yassine Cherkaoui, and Sid Hassan for proofreading my dissertation. I would like to thank my friends at the LIST lab for their cooperation. I am grateful to many of my friends in Gainesville for their support. Finally, I acknowledge with gratitude the financial support and encouragement of Kuwait University. ill TABLE OF CONTENTS page ACKNOWLEDGMENTS ................ ........... iii ABSTRACT ............ .... ... . ............... vi CHAPTERS 1 INTRODUCTION ......................... 1 1.1 Direct Sequence Code-Division Multiple-Access Systems . .. 1 1.2 IS-95 CDMA Standard ................... .. 7 1.2.1 Channel Structure . .................. . 7 1.2.2 Modulation and Coding . ................ 8 1.2.3 Power Control ................... ... 12 1.3 The MMSE Receiver .... .................. 14 1.4 Motivation and An Overview of the Dissertation and Literature Review ................ ........ 16 2 SYSTEM MODEL ....... ............. ...... 24 2.1 The Transmitter ............. ............ 24 2.2 The Receiver ............. .......... .. ..25 3 MULTILEVEL MODULATION IN AWGN CHANNEL ... ..... 30 3.1 Performance in A Gaussian Channel . ............. 30 3.2 Results ........... . ........ ...... . 35 3.3 Summary. ............... .......... 38 4 MULTILEVEL MODULATION IN A FADING CHANNEL .... 40 4.1 Performance Analysis ... ................... 40 4.2 The Effect of Phase Offsets on the Performance of the System 46 4.3 Summary .......... ................... 57 5 FADING PROCESS ESTIMATION ............ .. .... 58 5.1 The MMSE Receiver Behavior in A Fading Channel .... . 58 5.2 Tracking Techniques in A Fading Channel . .......... 63 5.3 The Effect of the Fading Estimation Error on the Performance of the System ................... .. ... . 69 iv 5.4 The Effect of Pilot Symbol Rates on the Performance of the System ......... ...... .. ........... 77 5.5 The Effect of the Linear Predictor Length on the Performance of the System ............. ......... .. 82 5.6 Summary .................. ......... .. 83 6 POWER CONTROL .............. .......... ..87 6.1 Fully Distributed Power Control Algorithm ...... .... 87 6.2 Numerical Results . . . ........ ......... ...... 89 6.3 Summary ......... . ................. ..103 7 CONCLUSION AND FUTURE WORK . .............. 104 7.1 Conclusion .................. .......... 104 7.2 Future Work ...... .. ....... .. .......... 106 REFERENCES .......................... ............ 109 BIOGRAPHICAL SKETCH ................. .. ......... 114 v Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DESIGN ISSUES FOR MINIMUM MEAN SQUARE ERROR (MMSE) RECEIVER-BASED CDMA SYSTEMS By Ali Faisal Almutairi May 2000 Chairman: Dr. Haniph A. Latchman Major Department: Electrical and Computer Engineering Code-division multiple-access (CDMA) technology has been the subject of a great deal of practical and theoretical research over the last decade. The adoption of the IS-95 standard, which is based on CDMA technology, has boosted research interest in this area. The minimum mean squared error (MMSE) receiver is a nearfar resistant receiver that has attracted the interest of many researchers over the years. The popularity of the MMSE receiver is due to the fact that its performance is comparable to many complex multiuser receivers while its complexity is comparable to the conventional matched filter based receiver. This dissertation examines the benefits of using the MMSE receiver for the next generation of CDMA systems and how some aspects of the system can be redesigned or modified to improve the performance of the CDMA system in terms of bit error rate (BER) and capacity. This research will be targeting two areas of improvements, namely multilevel modulation and power control. vi The use of higher order modulation formats, like 16 Quadrature amplitude modulation (16-QAM) and quadrature phase shift keying (QPSK), is investigated and compared to a binary phase shift keying (BPSK) based system in both additive white Gaussian noise (AWGN) and fading channels. One drawback was the inability of the MMSE receiver to perform properly in a more realistic wireless environment where fading is considered. This problem was investigated and a general MMSE receiver structure, which is capable of demodulating a wide range of digital modulation formats, is proposed. It is shown that, in an MMSE based CDMA system, modulation format choice has a significant effect on the capacity of the system. The performance of such a system with the three different modulation formats mentioned previously was investigated. It is found that the 16-QAM outperforms BPSK and QPSK in AWGN and fading channels when the fading estimation error is very low for a highly loaded system. On the other hand, if the fading estimation error is high, QPSK modulation should be used since it is more robust for high estimation errors. The other area for improvement of the proposed system that has been investigated is the use of power control. It was found that the use of power control improves the performance of the MMSE receiver based CDMA system despite the fact the MMSE is known to resist interference by other users. A power control algorithm (PCA) which is based on the desired MMSE value of the user and which is capable of equalizing the output signal to interference and noise ratio (SINR) is proposed. The convergence of the algorithm in terms of SINR and total power is investigated. The implementation of the proposed PCA was found to improve the capacity of the system substantially. For example, The proposed PCA was shown to yield on average a capacity improvement of more than 20% over an MMSE based CDMA system with perfect power control where all users are received at the same power. vii CHAPTER 1 INTRODUCTION Code-division multiple access (CDMA) has been the subject of extensive attention by the research community in the last two decades. Due to the existence of multiuser interference in CDMA systems, near-far resistant receiver structures for direct sequence (DS) spread spectrum (SS) have been investigated thoroughly by the CDMA research community. The minimum mean-square error (MMSE) receiver is a near-far resistant receiver structure known for its acceptable performance and low complexity. In this research, the MMSE receiver is chosen to be the underlying receiver structure for our study of DS CDMA systems. IS-95 has been developed by QUALCOMM and adapted by the US Telecommunications Industry Association (TIA) as a standard for cellular CDMA systems. This dissertation revolves around the following idea: If the MMSE receiver is used as the underlying receiver for the next generation CDMA system, how can we redesign some aspects of the system and modify the current MMSE receiver to improve its performance as measured by bit error rate (BER), Signal to Interference plus Noise Ratio (SINR), and capacity? 1.1 Direct Sequence Code-Division Multiple-Access Systems Unlike other multiple-access techniques such as frequency division multiple-access (FDMA) and time division multiple-access (TDMA) where the channel is divided into subchannels and each user is assigned to one of the available subchannels, CDMA is a digital communication multiple access technique in which the channel is not partitioned in frequency or time but each user is assigned a distinct spreading sequence to access the channel. In general, in CDMA systems, spreading is accomplished by 1 either direct sequence (DS) or frequency-hopping (FH). In this work, we have chosen the first method as a means of spreading. The literature is rich in many outstanding papers about CDMA systems like ( [1], [2], [3],and [4]), to mention just a few. In DS CDMA, the data symbols of duration Ts of each user are multiplied by unique narrow chips of duration T,. The chip rate is N times the symbol rate where N is the spreading gain. Figure 1.1 illustrates the DS-SS concept. In this figure, an unspread binary phaseshift keying (BPSK) signal of square pulses of duration Tb is shown. The signal has been spread by a spreading sequence of length N = 7. The result of the spreading is a signal with pulses of duration Tc = Tb/N rather than Tb. The power spectral densities (PSD) of the unspread and spread signal are shown here to illustrate the effect of the spreading on the signal bandwidth. The first null bandwidth of the unspread signal has expanded by a factor N as a result of the spreading process. It is desirable for the spreading sequences of all users to be approximately orthogonal to minimize the multiple access interference (MAI) and hence enhance the receiver performance. This orthogonality is unachievable in practice for asynchronous communication systems. Due to their important role in the performance of CDMA systems, spreading sequences and their correlation properties are studied heavily in the literature. M-sequences [5] are known for their autocorrelation properties. Gold [6] and Kasami [5] sequences represent a tradeoff of the desirable autocorrelation properties of M-sequences for improved cross-correlation properties. Kasami sequences are superior to Gold sequences in cross-correlation performance but are fewer in number for a given sequence length. The cellular concept introduces the idea of replacing high-power large single cell systems with low-power small multiple cell systems that have the same coverage area and can support a much larger user population compared to the single cell systems with the same system bandwidth. Based on this concept, each base station is assigned 3 E CU C Tb E R C, NTc PSD Unspread PSD Spread PSD 0 1/Tb 1/Tc=NiTb Figure 1.1: Illustration of DS spread spectrum concept. 4 a set of radio channels which represents a portion of the total channels available to the entire system. Different sets of channels are assigned to the neighboring base stations. The same set of channels can be assigned to another base station provided that the co-channel interference is at a tolerable level. The use of the same frequency channels by several cells introduces interference to the signals that share this spectrum. This kind of interference is called co-channel interference. Unlike other type of channel impairments (thermal noise, fading and shadowing), the co-channel interference can not be overcome by increasing the transmitted power since this action will increase the co-channel interference for the other users. The use of the same channel set in another base station has resulted in a substantial increase in the capacity of the entire system. The concept of using the same channel sets at different cells is called frequency reuse. The design process by which channel sets are assigned to all the cells in the cellular system is called frequency planning. The frequency reuse factor represents the fraction of the total channels available in the system that may be used by an individual cell. A frequency reuse design which has 7 channel sets and a frequency reuse factor of 1/7, which is shown in Figure 1.2, is commonly used to describe these concepts. The channel sets are labeled A, B, C, D, E, F and G. The base station coverage areas are shown as hexagonal for simplicity. A cluster is a group of all channel sets and is shown in bold in the figure. The cluster in Figure 1.2 includes 7 cells. From the figure, one can see that the capacity of the system, which can be defined as the total number of active mobiles the system can support at a given time, is directly proportional to the number of times the cluster has been repeated in a coverage area. Therefore, the main objective of the designers of TDMA-based and FDMA-based cellular systems is to maximize the system capacity by providing spectral and geographical separations, through the use of frequency reuse and frequency planning 5 B F D A E Figure 1.2: Illustration of the frequency reuse concept. concepts. These separations will guarantee the reduction of the interference level and hence improve the system capacity. From the previous presentation, we see that in a traditional narrowband system based on TDMA and FDMA multiple access techniques, capacity is limited by the number of time slots or frequency channels available in the system for a given cell. In CDMA-based cellular systems, channel access is granted through codes, not frequency channels or time slots. Therefore, the loading of the system in terms of active users is not determined by the available frequency channels or time slots but rather by the level of interference the receivers at the base station can tolerate. Each mobile contributes a certain amount to the total interference experienced at the base station receivers. The amount of interference introduced by each mobile depends on the power level at which the signal is received at the base station and the cross-correlation value of its spreading sequence with the other users' spreading sequences. A fundamental difference between CDMA-based cellular systems on one hand, and FDMA-based and TDMA-based cellular systems on the other hand, is that of interference elimination strategies. In CDMA based cellular systems, interference elimination is achieved through the choice of spreading codes with low cross-correlation, the use of very 6 tight power control, and the design of the receiver rather than the implementation of geographical and spectral separation as in FDMA-based and TDMA-based cellular systems. In this section, we have discussed some major aspects of the cellular concept that are relevant to the work presented in this dissertation. Other aspects of the cellular concept like handoff, channel assignment, and cell splitting are not discussed here and the interested reader is referred to [7] and [8]. From the previous presentation, it is clear that Multiple Access Interference (MAI) is the major limiting factor in the capacity of a CDMA based cellular system. Therefore, the capacity can be improved by reducing the interference level. We will discuss some of the improvements that can be adopted to reduce the interference level and how they are related to the work presented in this dissertation. Due to the presence of the interference caused by other users, the matched-filter type receiver (which is optimum for a single user in an additive white Gaussian noise (AWGN) channel) performance degrades substantially. The performance of the conventional receiver was analyzed in [9] and [10]. The major problem of the conventional receiver is its inability to mitigate what is called the near-far problem. The near-far problem occurs when the received signal of the desired user is overwhelmed by the interfering signals of the other users. To minimize the effect of the near-far problem in CDMA systems, researchers introduced what are called near-far resistant receivers. Among this class of receivers, the MMSE receiver has attracted the attention of many researchers due to its low complexity and superior performance. This receiver structure, as discussed in Section 1.3, can greatly affect the capacity of the CDMA system. The MMSE receiver can be described to a certain degree, as a near-far-resistant receiver. This capability of the MMSE receiver will substantially increase the CDMA system capacity. The MMSE receiver is an essential component in this research and is discussed in Section 1.3. 7 As it has been pointed out before, power control can greatly reduce interference and improve the system capacity by adjusting the transmitted power of the mobile users. In IS-95, power control is used so that the received signal strengths are about the same for all mobiles at the base stations. In this dissertation, we have introduced a power control algorithm that is capable of equalizing the output SINR and reducing the transmitted power for all the CDMA system users. The proposed power control algorithm is discussed in Chapter 6. Another avenue we have explored for reducing the interference is the idea of increasing the CDMA system dimension, by choosing a higher level modulation format without increasing the bandwidth. This was accomplished by increasing the processing gain (# of chips per symbol). This subject is treated in Chapters 3, 4, and 5 of this dissertation. 1.2 IS-95 CDMA Standard A CDMA cellular system was developed by QUALCOMM and adopted by the Telecommunications Industry Association (TIA) as a standard for digital cellular systems in 1992 under the name IS-95. We will study some aspects of IS-95 that are relevant to the work presented in this dissertation. Namely, we will discuss the channel structure, power control, and modulation and coding issues that are adopted in the IS-95. 1.2.1 Channel Structure The IS-95 CDMA system operates on the same frequency band as the Advanced Mobile Phone Systems (AMPS) with a 25 MHz channel bandwidth for the uplink (mobile to base station) and downlink (base station to mobile). The uplink uses the frequencies from 869 to 894 MHz, while the downlink uses the frequencies from 824 to 849 MHz. Sixty-four Walsh codes are used to identify the downlink channels. Long PN code sequences are used to identify the uplink channels. The forward CDMA channel, shown in Figure 1.3, consists of 64 channels of which, 1 is a pilot channel, 1 is a synchronization (sync) channel, up to 7 are paging channels, and the rest are forward traffic channels. The pilot channel helps the mobile in clock recovery, provides phase reference for coherent demodulation, and helps in handoff decisions. The sync channel is used to provide frame synchronization. The paging channels are used to transmit control and paging messages to the mobile stations. The forward traffic channels are used by the base to transmit voice or data traffic to the mobile. The reverse CDMA shown in Figure 1.4 consists of access channels and reverse traffic channels. The access channels are used by the mobile to initiate a call with the base station. The reverse traffic channel transmits voice and data from the mobile to the base station. The blocks in Figures 1.3 and 1.4 will be discussed in the next subsection. 1.2.2 Modulation and Coding In this subsection, we will discuss the modulation and coding processes in the forward and reverse traffic channels as represented by the blocks shown in Figures 1.3 and 1.4 respectively. In IS-95, the modulation process is performed in stages. For the forward traffic channel, the data is grouped into 20 ms frames. The data then is convolutionally encoded by a rate 1/2 code. The code generators for the convolutional codes [11] and [12] are: 90o = [111101011] (1.1) gl = [101110001] If the data rate is less than 9600 bps, the encoded bits are repeated until a rate of 19.2 Ksps is achieved. After convolutional encoding and repetition, interleaving is performed on the data. The main purpose of interleaving, as in any communication 9 Wo 1.2288 Mcps Pilot Channel: All O's To quadrature spreading W32 1.2288 Sync channel Mcps data rate 1/2 Convolutional 4.8 ksps 1.2 kbps Encoder and Block Interleaver + Repetition To quadrature spreading Wp 1.2288 Mcps rate 1/2 Convolutional19.2 ksps S Encoder and Block Interleaver + + Paging Channel Repetition quadrature Data spreading 9.6 kbps 19.2 ksps 4.8 kbps 2.4 kbps 1.2288 Paging channel p Pong ann Long Code Generator Decimator Wt Power 1.2288 Data Control bit Mcps Forward scrambling Traffic rate1/2 19.2 Ch nn Convolutional lo ksps I-C e Pilo k Encoder and Inteaver To 4.8 kbps Repetition quadrature 2.4 kbps 19.2 ksps 4 spreading 1.2 kbps User k long Long Code Generator _ Decimator Decimator code mask 1.2288 Mcps Sequences Filter Quadrature Spreading N s(t) Baseband Filter Q(t) (b) QUADRATURE SPREADING Figure 1.3: Forward CDMA channel structure. 10 Access channel Convolutional To Encoder (rate 1/3) Block 64-ary Orthogonal + quadrature and Symbol Interleaver Modulator spreading Repetition 4.8 kbps 28.8 ksps 28.8 ksps 307.2 kcps o2 )8 Long Code Generator (a) REVERSE CDMA ACCESS CHANNEL Primary, User k Long secondary CodeMask and signaling reverse traffic channel data Convolutional 64-ary To Encoder (rate 13 1 0 Block P Data Burst 9.6 kb and Symbol Interleaver Orthogonal Randomzer ad 4.8 kbps 4. kbps Repetition Modulator srai 2.4 kbps 28.8 28.8 307.2 (1.2288 1.2 kbps ksps ksps kcps Mcps) Long Code Generator (b) REVERSE CDMA TRAFFIC CHANNEL User k Long CodeMask Figure 1.4: Reverse CDMA channel structure. system operating in a radio channel, is to eliminate the occurrence of blocks of error due to the fading effects on the transmitted signal. Because of interleaving, no adjacent bits are transmitted near each other. This will result in different effects of the radio channel fading on these bits and therefore will randomize the errors caused by fading. In the forward traffic channel, a long pseudo-noise (PN) sequence is used to scramble the data output of the interleaver. After data scrambling, a power control bit is inserted every 1.25 ms. This represent 2 modulation symbols in every 24 modulation symbols (about 8%). If a 0 is transmitted, the mobile is instructed to increase its transmitted power by 1 dB. If a 1 is transmitted, the mobile is instructed to lower its transmitted power by 1 dB. After these stages, the data stream is spread using 1 of 64 Walsh codes. These codes are orthogonal to each other and of length 64. Walsh 11 codes are generated based on a recursive generation of a Hadamard matrix as follows: 0 0 001011 H4 = H2N = H 0 0 1 1 HN HN 0110 In the forward channel we need a 64 x 64 Hadamard matrix to provide the needed 64 Walsh codes to label the channels. Each row of this matrix represents a Walsh code. Each channel has a unique Walsh code. The all-Zero Walsh code is assigned to the pilot channel. The synchronization channel is assigned Walsh code number 32 (row # 32 in the H matrix). The lowest code numbers are assigned to the paging channel and the rest of the codes are assigned to the forward traffic channels. The I and Q signals of the data stream are spread by different PN spreading sequences. This procedure is called quadrature spreading and the spreading sequences are called pilot PN sequences. The binary outputs of the quadrature spreading are mapped to QPSK modulation where 00 maps to ir/4, 10 maps to 3-r/4, 11 maps to -3r/4 and 01 maps to -7r/4. The reverse channel modulation process is shown in Figure 1.4. Many of the blocks in Figure 1.4 are the same as the ones shown in Figure 1.3 and will not be discussed again. The reverse channel uses a convolutional code at a rate 1/3 with code generators given by go = [101101111] gl = [110110011] (1.2) g2 = [111001001] 12 The 64-ary orthogonal modulation is a block of 64 Walsh codes. These are the same as the Walsh codes used in forward channel modulation but here they are used differently. Walsh codes in the reverse traffic channel are used to modulate the data stream out of the interleaver. Each six bits of data are mapped to one of the Walsh codes as shown in the following: 47 53 101111 110101 ---> (CODE47)(CODE53) The role of the randomizer block is to remove the redundant data introduced by the code repetition block. The same pilot PN sequences used in the forward modulation and coding are used in the reverse channel to modulate the data in the I and Q channels. The data spread in the Q channel is delayed by 1/2 of a chip resulting in an offset quadrature phase shift keying(OQPSK) modulation. In this dissertation, we have compared the performance of BPSK, QPSK, and 16QAM modulation formats in an MMSE receiver-based CDMA system in terms BER. We simply modulate the data stream using BPSK, QPSK, and 16-QAM modulation formats for comparison. Then the modulated signal is spread using a random spreading sequence. In IS-95, the data is processed before sending them in the channel as shown in Figures 1.3 and 1.4. 1.2.3 Power Control To eliminate the near-far problem and to reduce the interference level in a CDMA system, a fine power control is necessary for acceptable operation of the CDMA system. IS-95 supports open-loop power control and closed-loop power control. In open-loop power control, the mobile user attempts to control its transmitted power based on the received signal strength. In closed-loop power control, the base station sends power control messages to the mobile user to adjust its transmitted power once every 1.25 ms. The base station transmits power control bits for every mobile user 13 in the forward traffic channel. When a mobile user receives a power control bit it increases or decreases its power by 1 dB according to the value of the power control bit (O=increase, l=decrease). For the mobile user to access the reverse channel, it must do so with the following initial power in the access channel: Paccess(dBm) = Pmean + Pnom + Pcorr - 73 (1.3) where Paccess = The initial access power in the access channel, Pmean = The mean input power of the mobile transmitter (dBm), Pnom = The nominal correction factor for the base station (dB), Pcorr = The correction factor for the base station from partial path loss (dB). Power in dB = 10 log0 (actual power in watts). Power in dBm = 10 logo0 (actual ) = 30 + Power in dB If the mobile user attempting to access the reverse channel is unsuccessful, the mobile will increase its transmitted power by a defined increment called the Power Step (Ptep) and try again. This process continues until the access attempt is successful or the mobile reaches the maximum allowed number of attempts. When granted access to the reverse traffic channel, the mobile station transmits with initial power P1(dBm) = Paccess + Sum of all access corrections (1.4) When the communication with the base station is established, the base station sends a power control bit to adjust the power of the mobile station transmitted signal. These adjustments are in increments of 1dB. When the power control bit is 0, the mobile station transmitted power increases by 1 dB. When the power control bit is 1, the mobile station transmitted power decreases by 1 dB. After these closed-loop 14 power updates, the mobile station transmitted power is given by Preverse(dBm) = PI + The sum of the closed loop updates (1.5) The maximum value of the sum of the closed-loop updates is ï¿½24dB. A typical set of ranges and values for the parameters in the previous equations are -8 < Pnom < 7dB (1.6) A typical value of Pom is 0 dB. -16 < Porr < 15dB (1.7) A typical value of Po,. is 0 dB. The values of these parameters for each base station are transmitted on the forward channel in a message called the access parameters message. In Chapter 6, we introduce a power control algorithm that can be used to adjust the mobile station transmitted power in a closed loop power control fashion. The power control presented in Chapter 6 does not update the transmitter power in constant steps of ï¿½1 dB like the IS-95 but with variable steps that are dependent on the channel condition and the MMSE receiver filter coefficients. Chapter 6 of this dissertation has been devoted to the power control issue in MMSE receiver based CDMA. 1.3 The MMSE Receiver To improve the performance of the CDMA system in the presence of MAI, and to mitigate the near-far problem, several receivers with different degrees of complexity and performance have been developed. For example, an optimum multi-user receiver is presented in [13]. The complexity of this receiver increases exponentially with the number of users. A suboptimal class of detectors with linear complexity are 15 t=nlc r(t) f. dt T I t=nT Update Weights Adaptive Algorithm Error Signal Training Figure 1.5: The MMSE receiver. presented in [14], [15],and [16]. Although they show linear complexity, these suboptimum receivers still require a great deal of side information. The MMSE receiver is a suboptimum receiver which is known to be near-far resistant. In addition, the MMSE receiver does not need to know certain side information like the code sequence and the carrier frequency of the desired user. This information can be obtained through adequate training if the MMSE is implemented in its adaptive form. Adaptive algorithms such as the least-mean-square (LMS) and recursive least-square (RLS) can be used to obtain the tap weights of the filter. The performance of the MMSE receiver in an AWGN is presented in [17], [18], [19], [20],and [21] and in a fading channel in [22], [23], [24], [25] and [26] for multiuser and [27] for a single user environment. To understand the advantages of the MMSE receiver, we need to describe briefly how it works. The MMSE receiver is shown in Figure 1.5. The received signal which consists of the desired user's signal, MAI, and Gaussian noise is fed at the chip rate into the equalizer until the N-tap delay line becomes full. After one symbol time, the equalizer content is correlated with the tap weights, a, and the result of this correlation is used 16 to make a decision about which symbol was sent. These tap weights are updated every symbol interval to minimize the mean square error between the output of the filter and the desired output. In practice, the filter is trained for a reasonable period of time by a known training sequence to reach a tap weight vector that is close to the optimum weights. After the training period, the receiver switches to decision feedback mode. It has been shown in [22] that the decision directed mode proves to be troublesome in a fading channel. In deep fades, with the MMSE structure shown in Figure 1.5, incorrect decisions being fed back to the receiver cause the MMSE receiver to lose track of the desired signal. A modified MMSE receiver structure to overcome this problem was described in [22] for a BPSK modulation format and it has been generalized in [24]. It should be noted that the IS-95 standard uses a conventional matched filter based receiver where the coefficients of the filter are matched to the desired user's spreading sequence. The matched filter structure is optimum for a single user environment. When this structure is employed in a multiuser system, it degrades rapidly due to the presents of MAI. 1.4 Motivation and An Overview of the Dissertation and Literature Review This section presents a review of the design issues that we are researching and a layout of motivations for our research in this dissertation. As has been stated before, this research project revolves around the following question: If the MMSE receiver is used as the underlying receiver for the next generation CDMA system, how can we redesign some aspects of the system and modify the current MMSE structure to improve the performance of the CDMA system in terms of the system capacity, SINR, and BER? The motivation behind this research is that given the advantages of the MMSE receiver presented in the previous section, one would expect superior performance of a CDMA system based on the MMSE in comparison to that of a CDMA system based on the current conventional receiver, and hence, the MMSE 17 receiver could be a good candidate to be implemented in the next generation of CDMA systems. This research will be targeting two areas of improvements. The first is multilevel-modulation and the second is power control . The first area to be investigated in this research is multilevel modulation. Traditionally, higher level modulation has been used to achieve higher bandwidth efficiency (# of information bits transmitted in a given bandwidth). The price for the higher bandwidth efficiency is paid in terms of the required SINR to achieve the same error probability. In cellular systems, the main objective of the system designers is to increase the system capacity for a given quality of service and limited resources such as bandwidth. In the literature, BPSK and sometimes QPSK are used as modulation formats for the MMSE receiver. As noted in [18], if BPSK is used, the MMSE receiver becomes interference limited when the loading of the system becomes high enough and close to the processing gain. This threshold is reached because of the imperfect cancellation of the Multiple Access Interference (MAI) due to the lack of dimensions in the system. One way to improve the performance of the system is to introduce more dimensions while keeping the bandwidth the same to help in suppressing the MAI. To achieve that, one can choose a higher order modulation format like MPSK or 16-QAM to increase the processing gain (# of chips per symbols). The justification for increasing the processing gain for the system employing higher order modulation is presented in the following example. In an unspread system, for the same bit rate, using QPSK will result in using half the bandwidth required of a BPSK system, while using a 16-QAM will result in using one fourth of the bandwidth required by a BPSK system. In a CDMA system, to utilize the total available bandwidth when higher order mosulation formats are used, the spreading gain of the QPSK system should be twice that of the BPSK system and the spreading gain of the 16-QAM system should be 4 times that spreading gain of the BPSK system. 18 Throughout this dissertation, we have used random sequences with spreading gains of 31 for the BPSK system, 62 for the QPSK system, and 124 for the 16-QAM system to utilize the whole available bandwidth. If m- , Gold, or Kasami sequences were used, we would not be able to choose a processing gains of 62 and 124 since the processing gain of these sequences is given by 2" - 1 where n is the number of stages of the shift register used to generate such sequences. By adopting a higher order modulation and increasing the processing gain , the MMSE receiver has been moved out of the interference limited region and can restore its ability to suppress more interference than the original system. Since the receiver now is operating in the interference resistant region, one can increase the transmitted power to obtain a higher SINR for acceptable performance. Increasing the transmitted power will increase the interference level and hence will degrade the performance of a conventional receiver-based CDMA system. On the other hand, the MMSE receiver, with the increased processing gain, will perform as a near-far resistant receiver and the increased interference level will be alleviated. Furthermore, if increasing the transmitted power is not desirable, one can resort to combined modulation and coding in the form of trellis-coded modulation (TCM). Milstein and Shamain studied the performance of QPSK and 16-QAM modulation formats in a multipath and narrowband Gaussian interference (NGI) environment, in [25] and [26] for single or two user systems. They show that when the multipaths cause significant interstmbol interference (ISI), with or without NGI, the 16-QAM system outperforms the QPSK system. In both papers, the desired user's fading is assumed to be known and an optimum MMSE receiver is used. In our research, we have shown the improvement of the system performance in terms of BER and capacity when higher order modulation is used. In addition, we have investigated the performance of the system in a fading environment with optimum or adaptive implementation of the MMSE receiver for different system loadings. Furthermore, we 19 have investigated the case when the desired user's fading is unknown to the receiver or it has been estimated inaccurately. The details of our results in this area are presented in [24], [23], and Chapter 3, 4, and 5 of this dissertation. In Chapter 3, the performance, in terms of BER and system loading, of an MMSE receiver based CDMA system with different modulation formats, namely, BPSK, QPSK, and 16-QAM, was investigated in AWGN channels. Based on BER performance, it has been found that for a lightly loaded system BPSK outperforms QPSK and 16-QAM. For a moderately loaded system QPSK outperforms BPSK and 16QAM. For a highly loaded system, 16-QAM outperforms BPSK and QPSK. These results are shown in [23]. The use of multi-level modulation formats, like 16-QAM, leads to some interesting research problems. As with unspread systems, any time a multilevel modulation format is used in a fading channel, it becomes necessary to carefully track the phase and amplitude of the desired user's fading process in order for the receiver to demodulate the desired user's signal successfully. Channel tracking through the use of pilot symbol assisted modulation (PSAM) has been proposed, in single user system, as a mean to estimate the fading process and mitigate its effects at the receiver by several authors [28], [29], [30], and [31]. In PSAM, pilot symbols are inserted periodically into the data stream. Channel estimates are obtained using Gaussian interpolation [30], Wiener filtering interpolation [28] , or sinc interpolation [31]. One needs to notice that there is always a delay associated with the use of PSAM since the demodulator has to receive a certain number of pilot symbols to estimate the fading process. This estimation technique can not apply directly to the MMSE receiver since this receiver updates its tap weights every symbol based on the demodulation of the previous symbol. Furthermore, linear prediction has been used to obtain estimates of a fading process for a single user system in [32] and for multiuser systems in [22] and [24]. As 20 described in [22], Linear prediction of the desired user's fading is performed by using the outputs of the MMSE filter from past symbol intervals. This technique can lose track of the fading process due to the aburst of decision errors as pointed out in [33] and [24]. In [24], we have shown that a combination of PSAM and linear prediction can effectively track the fading process of the desired user. The use of pilot symbols has been proven to be beneficial in preventing the MMSE receiver from feeding back unreliable decisions when it is operating in its decision directed mode while the desired user signal is going into a deep fade. Traditionally, pilot symbols are used in a single user environment to obtain an estimate of the fading process, but there is a delay associated with their use since the detector needs to detect many pilot symbols to form an estimate of the fading process. In this research, the main reason for using pilot symbols is to prevent the MMSE receiver from feeding back the unreliable decisions. In Chapters 4 and 5, the study of the performance of the system in Chapter 3, for which an AWGN channel model was used, is extended to a fading channel to represent a more realistic model for wireless communication systems. The use of multilevel modulation, like 16-QAM, in a fading environment introduced an interesting problem, namely, tracking the channel variation to be able to demodulate the desired user signal. The behavior of the MMSE receiver structure, shown in Figure 1.5, in a fading channel with 16-QAM modulation was studied. It was found that the MMSE receiver's present structure performs poorly in a fading channel. A general MMSE receiver structure which can be used in a fading environment to demodulate the desired user's signal effectively was proposed. The performance of the different modulation formats in terms of BER was analyzed and theoretical BER bounds for, BPSK, QPSK, and 16-QAM in multiuser systems operating in a fading environment were derived. The performance in terms of BER under different loads of the three modulation formats were compared in a fading environment. 21 To improve the poor performance of the MMSE receiver in a fading channel, we proposed a tracking scheme which is based on the use of both periodic pilot symbols (PPS) and linear prediction. The introduction of PPS helps to improve the performance of the MMSE receiver in two ways. First, and more important, the pilot symbols provide the receiver with a reliable reference when it operates in a decision directed mode. Second, the pilot symbols might be used to get channel estimates. The effect of the estimation errors, which results from inaccurate estimation of the fading process, on the performance of the 16-QAM and QPSK systems is investigated. Theoretical bounds based on the BER when there is a phase offset due to imperfect estimation of the desired signal phase were derived. The effects of the PSAM rate and the linear predictor length (L) values on the estimation error and on the performance of the system in terms of BER were investigated. In Chapter 6, The power control improvement area was investigated in AWGN and fading channels. The main reason for using power control in a conventional receiver based DS-CDMA system is to combat the near-far problem which occurs when an undesired user's signal over-powers the desired user's signal. The MMSE receiver is known to be near-far resistant but power control can still be used to reduce multiuser interference, increase the system capacity, compensate for channel loss, reduce the transmitted power and hence prolong the battery life. As shown in [20], the MMSE receiver can achieve many of the performance measures of other multi-user receivers performance without the need for side information like user sequences, clock offsets, and the received powers of all the interfering signals. This receiver offers a strong potential for capacity improvement over a conventional receiver-based CDMA system. In a conventional receiver based system, the transmitted power of the mobile user must be tightly controlled so that the received powers of all users are very close to be equal. This type of power control which equalizes the received powers does not guarantee the equalization of the SINRs at the output 22 of the matched filter receiver and hence, users may experience an unequal quality of service (QoS). On the other hand, consider the MMSE receiver based CDMA system. Since the MMSE receiver is near-far resistant, the SINR at the output of the MMSE receiver is largely independent of the variation of the received powers of the other users. Therefore, a mobile unit can adjust its transmitted power to achieve a target output SINR without affecting the other users' output SINRs. For example, a receiver experiencing a low SINR can instruct the corresponding transmitter to increase its transmitted power without having much effect on the other users' output SINRs. Likewise, a receiver enjoying a high SINR can instruct the corresponding transmitter to decrease its transmitted power to conserve battery life without having much of an effect on the other users' output SINRs. Our results in Chapter 6 and in [34] show that the blockage based system capacity of an MMSE receiver based CDMA system can be improved substantially by applying such a power control algorithm. The major problem with many of the power control techniques presented in the literature is their need, with varying degree, for side information such as channel gains, spread sequences, bit error rate, received powers and the SINRs of all users. The power control algorithm (PCA) proposed in [35] uses measurements of the meansquared error (MSE) which require knowledge of the actual transmitted symbols. This makes it hard to implement in a fading channel since in deep fades the symbol estimates out of the decision device of the receiver are unreliable [22] and [24]. Both the power algorithms proposed in this paper and the one proposed in [36], do not use the MSE measurements. To implement the algorithm presented in [36], a sample average of the the output of the MMSE receiver is required to provide an estimate of the interference to update the power. In addition, the channel gain of the desired user needs to be estimated. The PCA proposed in Chapter 6 does not require knowledge of the interference caused by other users. Indeed, only one parameter which includes the channel gain of the desired user needs to be estimated.' Additionally, in contrast 23 to the algorithms presented in [35] and [36], the proposed PCA does not require the use of pilot symbols if a constant envelope modulation is used. The PCAs presented in this paper and the ones presented in [35] and [36] converge to the same transmitted power solution. The first task in this area of the research is to design a power control algorithm that can achieve a target SINR at the output of the receiver. A power control algorithm which updates the power to converge to a target SINR value is proposed in Section 6.1. This algorithm is compared to two other algorithms based on the MMSE receiver presented in [36] and [35] respectively, in terms of the convergence of SINR and the total transmitted power. The capacity improvement realized by a system implementing the proposed PCA was compared to the theoretical bounds presented in [37] and [38] and was found to be in agreement with these capacity bounds for a large range of target SINR values. CHAPTER 2 SYSTEM MODEL In this chapter, a general CDMA system model, shown in Figure 2.1, based on the MMSE receiver is described. The model here will be flexible and easy to modify to accommodate the study of different issues concerning the MMSE receiver based CDMA system design. For example, when we study the performance of the system in AWGN channel, we can simplify the model by setting the fading amplitude to 1 and the fading phase to zero. The system consists of K users transmitting asynchronously over an AWGN channel or Rayleigh fading channel. The received signal, which consists of the desired user signal, interference from other user signals, and AWGN, is demodulated using the MMSE reciever. In the following sections, the transmitter and the receiver, shown in Figures 2.1 and 2.2, will be described. 2.1 The Transmitter There are K transmitters, one for each user, in this system. In this dissertation, the transmitter, shown in Figure 2.2, uses either a BPSK, QPSK, or 16-QAM. Each user is assigned a unique random spreading waveform ci(t). The modulated signal of the jth user can be written as sj(t) = Re { V2pdj(t)cj(t)ejwot} (2.1) = Re {gj(t)ejwot} where wo is the carrier frequency which is the same for all users, gj (t) is the complex envelope of sj(t), pj is the transmitted power, and dj(t) is a complex baseband signalling format with symbol interval T,. The waveform cj (t) is assumed to be in the polar form with chip interval Tc. Therefore, the processing gain N is equal to 24 25 Tx. Channel n(t) . i Figure 2.1: System Model C j(t) jcos( tI) r (t) d .j(t) Fading dj (+ Channel d (t) (t) -(t) - 2 sin(wt) Figure 2.2: Transmitter of the jth user Ts/Tc. Throughout this dissertation, user 1 is considered the desired user unless specified otherwise. We are interested in demodulating its signal and the other users are treated as multiple access interefernce. 2.2 The Receiver After going through the communication channel, the bandpass received signal at the receiver corresponding to the jth user is given by K r(t) = Re { l hijaj(t)e'(t)gj(t - Tj)ejwoi} + n(t) (2.2) j=1 26 2cos(wt) T, t=nT r, (n) r(t) m)MMSE 0 + Receiver r(n) t .r,(n) c -T, - = mT, -2sin(wt) Figure 2.3: The receiver where hij is the channel gain of user j to the assigned base station of user i. The variables rj, aj, 0, are the propagation delay, and the amplitude and phase of the fading process for the jth user respectively. The process n(t) is a real AWGN process with a spectral density of No/2. The fading amplitude is Rayleigh distributed while the fading phase is uniformly distributed. The desired user propagation delay is assumed to be 0. In addition, it is assumed that the fading process of each user varies at a slow rate so that the amplitude and the phase of the fading process can be assumed constant over the duration of a symbol. The front-end part of the receiver, which is shown in Figure 2.3, consists of an in-phase (I) and a quadrature (Q) components. First, the bandpass received signal is shifted to baseband. Then, each component goes through a chip-matched filter with a scale factor of v'Tc. The output of the chip-matched filter is sampled every Tc seconds. At the nth chip time, the output of the receiver front end consists of the received complex signal sample of r(n) = ri(n) + rQ (n). These samples are fed at the chip rate to the MMSE receiver (the receiver is shown in Figure 1.5) until the N-tap delay line becomes full after one symbol time. The contents of the equalizer are given by 27 K ri (m) = a pj(m) h-jaj(m)ejei(m)dj (m)fj(1, 6) j=1 (2.3) + Vp(m - 1) ija (m) ej(m)di(m- 1)(1, 6)1 + n(m) In the above equation, 7j = 1jTc + 6j where Ij is an integer and 0 < 6j < Tc. The vectors f, and ( are defined as follows fj(1, 6) =T f(N - 1 - 1) + 1 - f(N - 1) (1,6)= gj(N -1- 1) + 1 - j gj(N - 1) where fj(1) = (c(.1) + i))/2 gj(l) = (') - t))/2 ) (Cj,N-1, Cj,N-l+1, ..., Cj,N-1, Cj,O, Cj,1, ..., Cj,N-l-1)T l) = (-Cj,N-1, -Cj,N-I+1, ... -Cj,N-1 -Cj),O CJ,1 ..., Cj,N-1-1)T Equation 2.3 can be written in a compact form as ri(m) = pi(m) hiaj(m)eei(m)di(m)ci + MAI + n(m) (2.4) and K MAI= E aj(m)eio(m) [ p(n) hijdj(n)j(l,6) + pj(n- 1)/ hjdj(n- 1)(, 6)] ji In eqn. (2.4), n(m) is a vector of independent complex Gaussian random variables with zero mean and the variances of the in-phase and the quadrature components are 28 equal to No/2Tc. The output of the MMSE receiver filter corresponding to the jth user is zi(m) = wi(m)Hry(m) (2.5) where wi is the filter coefficients that correspond to ith user received signal. These coefficients are adjusted by an adaptive algorithm, like the LMS and RLS algorithms, to minimize the mean squar error J(w) which is given by J(w) = E[|e(m)|2] (2.6) Initially, the MMSE receiver works in a training mode. In this mode of operation, a known data squence is sent by the transmitter and this sequnce is used as a reference for demodulated desired user's data. When the variable J reaches an acceptable value, the MMSE receiver switches to decision directed mode. The error, e(m), in a training mode is given by e(m) = di(m) - zi(m) (2.7) In a decision directed mode di(m) is substituted by the decision ds(m). The mean square error, J is shown in [39] to be a quadratic function of the filter coefficients and is given by J(w) = E[di(m)2] - pHw - wHPi + WHRw (2.8) Where R is the autocorrelation matrix of the equalizer contents, R = E [r(m)r(m)H] and Pi is a correlation between the desired user response and the received signal and given by Pi = E [d*(m)r(m)]. The minimum mean square error, Jmin, is achieved when the tap weights are the optimum weights. These optimum weights are obtained by differentiating equation 2.8 with respect to w and equating the result to zero. This will result in a form of 29 the Wiener Hopf equation and the optimum vector of the filter coefficients is given by wi = R-1Pi (2.9) The value of Jmim can be obtained by substituting the optimum vector of the filter coefficients given by Eqn. 2.9 in Eqn. 2.8. This will result in Jmin = 0o. - pHR-'Pi (2.10) where 0o is the variance of the data symbols. di Although the optimum tap weights force the MMSE receiver to operate at Jmin, these weights are hard to obtain in practice due to the unavailability of the autoccorelation matrix. Adaptive algorithms like the Least- Mean-Square (LMS) and the Recursive Least-Square (RLS) are used to drive the filter coefficients close to the optimum tap weights. In this dissertation, the LMS will be used as the adaptive algorithm in the MMSE receiver unless specified otherwise. CHAPTER 3 MULTILEVEL MODULATION IN AWGN CHANNEL The goal of this chapter is to investigate the performance of the MMSE receiver with BPSK, QPSK, and 16-QAM modulations in an AWGN channel. These different modulation formats were compared based on their BER performance at different loadings of the MMSE based CDMA system. It should be noted that in this dissertation, we simply modulate the data stream using BPSK, QPSK, or 16-QAM modulation formats for comparison. Then the modulated signal is spread using a random spreading sequence. We do not use any type of channel coding. In IS-95, the data is processed (by coding and interleaving) and then modulated using a QPSK as shown in Figures 1.3 and 1.4. 3.1 Performance in A Gaussian Channel In this section, we modify the model presented in Chapter 2 to study the performance of the CDMA system using different modulation formats in a Gaussian channel. This can be done by setting the amplitude and phase of the fading process to 1 and zero in Equation (2.3) respectively. In addition, assume hik = 1 and that user 1 is the desired user and the integrator in front of the MMSE receiver has a scale factor of v2pTc associated with it. Based on these assumptions, we can rewrite Equation (2.3) as K r(m)= di(m)c+ Z +[dj(m)fj(1, 6) j=2 (3.1) + dj(m - 1)j (1, 6)] + n(m) Where n(m) consists of independent zero-mean complex Gaussian random variables whose real and imaginary parts have variances of , where E, is the average 30 31 energy per symbol. The probabilities of error for 16-QAM, QPSK, and BPSK are derived below. r(m) can be written in the form r(m) = di(m)c1 + f(m) (3.2) Since E [did*] = 1, the correlation vector P, the autocorrelation matrix R, and the tap weights vector a can be written as follows (dropping the dependence on m for convenience): P = E [dfr] = E [d1 2] C1 (3.3) = C1 R = E [Id112] C1CT + (3.4) = PPH + 1 and the tap weights vector, a, given in terms P and R by a = R-1P (3.5) where R = E [ffH].The output of the filter can be written as z = aHr (3.6) = dPHR-1p + pHR-ip (3.7) = dPHR-P + ii (3.8) Now we need to find the value of PHR-1P and the variance of fi. Using the matrixinversion lemma, we can find the inverse of R as follows: R-1 = + Ri-P(1 + pHf-lp)-1pHft-1 (3.9) - + -i(3.1ppH-0) (1 + PH- )- (3.10) 32 If we multiply both sides of eqn. (3.10) from the left by PH and the left by P and simplify the result we will get pHfj-1p pHR-1p = (3.11) 1 + pHR-IP Now, we need to find the variance of the term i! fi = pHR-1' (3.12) E[iiiiH] = pHR-1E[ffH]R-1P (3.13) = pHR-1ftR-'P (3.14) We can find pHR-1 by multiplying both sides of eqn. (3.10) by pH. This results in pHR-1 pHt-1 (3.15) (1+ PHy-1P) in a similar manner, we can find R-1P by multiplying both sides of Eqn. (3.10) by P. This result in R-1P =- p (3.16) (1+ PH-1p) Substituting Eqns. (3.15) and (3.16) into (3.14), E[iiiiH pHip E[ii [ + pH-ip]2 (3.17) [1 + PHft-1p]2 Then Eqn. 3.8 can be written as pH ft-i z = dl [ i 1 + pHR-1p SN 02 [1+ pHI-lp] (3.18) ( 1 PHR-IP] + NQ0, O 1 pHft-I P1 2 2 [1 ï¿½ pHR-1p12 33 Having the output of the filter z in this form, it is straightforward to show that the probability of symbol error is given by [40] Pel6QAM 3I - 4P (3.19) where PQ( PH lP (3.20) where the Q-function is defined as 00 1 u2 Q(x) = exp(- ) du (3.21) Equation (3.19) implicitly depends on the interfering users codes, delays, and transmitted powers, through the matrix II. To obtain an average value for SER, one would average Eqn. (3.19) over these quantities. The symbol error rate (SER) can be related to J,min by recalling (2.10) and recognizing that a = 1. Jmin = 1 - pHR-1P (3.22) substituting (3.11) into (3.22) pHlt-lp Jmin =11 + pHI -lp 1 H P (3.23) 1 + pHt-lp Eqn. 3.23 can be written as pH-lp - Jmin (3.24) Jmin then P can be written as ( 1- Jin (3.25) 34 The symbol error rate for 16-QAM in terms of Jmin is obtained by substituting (3.25) into (4.13). It is straightforward to show that for BPSK and QPSK we have PeBPSK Q (V2PH-1P) (3.26) PeQPSK m 2Q ( pH,-1P) (3.27) by substituting Eqn. (3.24) in Eqns. (3.26) and (3.27). The probabilities of error for BPSK and QPSK in terms of Jmin are given as PeBPSK 2(1 Jmin)) (3.28) PeQPSK - 2Q ( 1 J (3.29) For a single user case, these results reduce to the well known results given below which are the same as the results shown in many digital communications books like [40] and [11]. PeBPSK =Q( Q 2E (3.30) PeQPSK 2Q( E (3.31) For 16-QAM P = Q( E (3.32) Assuming that the system is using Gray coding, the bit error rate (BER) is given by SER BER SER (3.33) log2M 35 100 * = BPSK o = QPSK x = 16-QAM 10 10-2 10-3 10 10-5 10-6 10-7 0 5 10 15 Eb/No (dB) Figure 3.1: Theoretical performance of BPSK, QPSK, and 16-QAM in a Gaussian channel with one user. where M is the number of points in the constellation. For BPSK, QPSK, and 16QAM, M equals 2, 4, and 16, respectively. The justification for the Gaussian approximation is based on the central limit theorem by noting that the output of the filter is a sum of random variables with different probability density functions (pdfs). Therefore, the sum of these random variables at the output of the filter can be considered a Gaussian random variable. This approximation is widely used in evaluating conventional receivers [9]. This approximation is more accurate with the MMSE receiver since we have less interference at the output of the filter and more Gaussian noise [20]. Poor and Verdu in [41] have studied the behavior of the output of the MMSE receiver and found that the output is approximately Gaussian in many cases. 3.2 Results Figures 3.1, 3.2, and 3.3 show the performance of the MMSE receiver with BPSK, 36 100 10 10-2 10-3 rn 0-4 10-S solid =theoretical dash = simulation 10- * = BPSK o=QPSK x=16-QAM 10-7 0 5 10 15 Eb/No (dB) Figure 3.2: Theoretical and simulation performances of BPSK, QPSK, and 16-QAM in a Gaussian channel with 20 users. QPSK, and 16-QAM in a Gaussian channel for 1-, 20-, and 50- user CDMA systems. The theoretical results are based on the BER equations obtained in the previous section. The processing gains are 31, 62, 124 for BPSK, QPSK, and 16-QAM respectively. These processing gains were chosen to ensure the full use of the available bandwidth by these systems. We will use these values of processing gains for the modulation formats for the rest of the dissertation. For the single user case the results are the same as the results found in the digital communication literature, for example [11]. For a single user system, the bit error rate is the same for BPSK and QPSK and lower than that of 16-QAM for a given E. When the load of the system increases to 20, the QPSK-based CDMA systems outperforms the BPSK and the 16-QAM systems. The rate of improvement is faster for QPSK than for BPSK as the - increases. On the other hand, the 16-QAM sysNo tem starts about 1 dB worse than BPSK but at about = 12 dB the 16-QAM BER No becomes lower than that of BPSK for a given E-. With the load further increased to 37 100 10 10-2 10-3 0C . 10-4 10-5 10-6 *BPSK o=QPSK x=16-QAM 10-7 0 5 10 15 20 25 Eb/No (dB) Figure 3.3: Theoretical performance of BPSK, QPSK, and 16-QAM in a Gaussian channel with 50 users. 50 users, both BPSK and QPSK will reach a point at which the bit error rate will become invariant to the increase in E. That basically means we can increase the load of the system by increasing the length of the processing gain but not increasing the bandwidth or information rate by simply going to a higher order modulation. Therefore, there is a tradeoff between the information rate and higher load for multilevel modulation. We can explain the behavior of the MMSE in these figures as follows: When the CDMA system is using BPSK, at some loading point, the MMSE will not have enough dimension, provided by the processing gain, to suppress all the interfering users. At this point, the MMSE receiver becomes interference limited, like the conventional matched filter receiver, and the performance cannot be increased by simply increasing the transmitted power. One way to overcome this is to increase the processing gain. To do so while keeping the bandwidth and information rate the same, one should choose a higher order modulation. In our case, QPSK would be 38 the choice for a moderately-loaded system and 16-QAM would be the choice for a highly-loaded system. Figure 3.2 compares an LMS based MMSE receiver system performance for 20 users with the theoretical results given in the previous section. The figure shows a very good agreement between the simulation and the analytical BER for the different modulation schemes. Figure 3.4 shows how the different modulation format systems deal with the nearfar problem. The interfering signal received powers were modeled as lognormal distribution. In this case, the standard deviation oa (dB) of the interfering signal received powers is varied while Ek is 5 dB for 30 users load. It is clear from the figure that, at this load, The MMSE receiver with the BPSK modulation format is not near-far resistant anymore. The QPSK and 16-QAM based MMSE receiver systems are acting as near-far resistant. Clearly, at this level of loading, one should choose a higher order modulation format to restore the near-far resistance of the MMSE reviver. If the system loading is increased to a higher level, one would expect the QPSK based system to lose its near-far resistant property. 3.3 Summary This chapter examines the effect of using higher order modulation formats in the performance of MMSE receiver based CDMA systems in terms of bit error rate (BER) at different loading levels in (AWGN). The performance of BPSK, QPSK, and 16QAM modulation formats are compared and analysed. In addition, simulation results are presented in terms of the bit error rates for these different modulation formats. A comparison of the rejection of the near-far effects for each modulation scheme is also presented. Under a very high loading level, 16-QAM outperforms QPSK and BPSK for identical bandwidth and information rate while, at a moderate loading levels, QPSK represents the best option. 39 10 0 3 6 9 12 15 18 x (dB) oo O=BPSK *=QPSK X=16QAM 10-2 I I , I I 0 3 6 9 12 15 18 0o(dB) Figure 3.4: BER of QPSK, BPSK, and 16-QAM as a function of near-far ratio for 30 users. CHAPTER 4 MULTILEVEL MODULATION IN A FADING CHANNEL In this chapter, we will extend the work of the previous chapter by investigating the performance of the 3 modulation formats, namely, BPSK, QPSK, and 16-QAM, in a fading channel. These different modulation formats are compared based on their BER performance at different loadings of the MMSE based CDMA system. The results presented in this chapter are based on the assumption the the optimum implementation of the MMSE filter has been used. 4.1 Performance Analysis In this section, we will provide a performance analysis, both analytically and through simulation when a multilevel modulation schemes, like QPSK and 16-QAM, are used in a fading channel. In this section, the optimum MMSE filter is used and hence all the users' fading processes are assumed to be known to the receiver. In the next chapter, the performance of the system, where an adaptive MMSE filter implementation is used, will be investigated in detail. We modify the model presented in Chapter 2 to study the performance of the CDMA system using different modulation formats in a fading channel. This can be done by setting hik = 1 and assuming that user 1 is the desired user and the integrator in front of the MMSE receiver has a scale factor of -2pTc associated with it. Based 40 41 on these assumptions, we can rewrite the received vector given in Equation (2.3) as K r(m) = di(m)a,(m)ejl(m)c1 + Ey(m) eim) dj (m)fj(l, 6) j=2 P(4.1) + dj(m- 1)(1, 6) +n(m) Assuming the desired user's phase is known exactly, the input to the MMSE receiver can be written as y(m) = e3-jmr(m) (4.2) where 01,m is the estimated phase of the desired user's fading and here we assumed 01,m = 01,m. Substituting Eqn. 4.1 into Eqn. 4.2, the input to the MMSE receiver, y(m), can be written as y(m) = di(m)a,mc + Pj,meejoj,m dj(m)Y(1, 6) j=2 + dj (m - 1)gj (1, 6) + n(m)e-jii, (4.3) = di(m)al,mcl + here AOj,m = 0j,m - 81,m. Next, the real and imaginary part of the variable y(m) are taken and processed to find the I and Q channels desired user data. To find the desired user signal, we need to calculate the optimum tap weights for the I and Q channels. It is straightforward to show that the optimum tap weights for the I and Q channel filters are the same. Let the autocorrelation matrices for the I and Q channels received vectors (yl and Y2) at the input of the MMSE filters be R1 and R2 and the steering vectors be P1 and P2, respectively. We have E [Re [dl] Re [d]] = . In addition, the correlation vector Pi, the autocorrelation matrix R1, and the tap weights vector a, can be written as follows (dropping the dependence on m for convenience): P1 = E [Re [d*]yl] 1 (4.4) S2al,mC = P2 42 1 2 H R1 = 2al,mClc + R = 2PPH + (4.5) = R2 al = a2 Rl-lP1 = a (4.6) where R1 = E [37171H]. The output of the filter can be written as zl = aHyl (4.7) = 2 Re [dl]P1HRl-'P1 + p1HR1-1 1 (4.8) = 2 Re [dl]P1 "Rl-P1 + hi (4.9) Now we need to find the value of P1HR1-lP1 and the variance of nl. Using the matrix-inversion lemma, we can find the inverse of R as follows f-1 R - 1 + (4.10) 1 + 2P, Rjll P1 It can be shown that the variance of the term il is IE [ii iiH P p 2 (4.11) E lf = [1 + 2P1H 1P1]2 Then the output of the modified MMSE z = di [ p 1 + 2pHft-lp ( PH -1 + N, 0, o[i t-lp (4.12) + pH.-2p 9 +[1 + 2H-1P] 2) 43 Having the output of the filter z in this form, it is straightforward to show that the probability of symbol error conditioned in al is given by [40] Pe/alm 31e/, 1 - 4 Pe/o1 (4.13) / Q 2 5 10)=( 121H -1 (4.14) Averaging 1e/a, over the probability density function (pdf) of the desired user's fading amplitude,al, gives the expression for P as P fam()Q 10 dclc) (4.15) fa,,m(a) = 2a exp (-a2) (4.16) where fa,m(a) is the probability density function (pdf) of the desired user fading amplitude. A closed form solution for this integral can be obtained by performing the integration and changing variables, and is given as follows: - U2 jP c j a exp (-a2) exp du, do (4.17) a=o 1 = 1 xa2,H c 2 using the polar coordinates, we can write the previous equation as 2 f 0 0 a n - ( H 1t1n P15 2 : f f (V r2 exp (-r2) sin(0), dr, dO (4.18) V Jr=0 JO =0 Performing this integration will result in p 1 1 - (4.19) 220 + cHiH-1c For a single user, the previous result reduces to 1V N 1 -N (4.20) 44 The probability of symbol error for the 16-QAM is given by P16QAM , 3k [1- 3 (4.21) For BPSK and QPSK modulation, the average symbol error rates can be derived in the same manner and they are given, respectively, by 1( ccH1C1 PBPSK ( 1 -- -c-i (4.22) 2 R2 clH -lci PQPSK 1 - C(4.23) 4 + c1H -1c1 Assuming that the system is using Gray coding, the bit error rate (BER) is given by SER BER ~ (4.24) log2M These equations implicitly depend on the interfering user codes, delays, transmitted powers, and fading amplitudes through the matrix ft. To obtain an average value for SER or BER, one would average over these quantities. For the single user case, it is easy to show that these results reduce to the well known results shown in the digital communications literature [42] and [11]. To obtain these results, we have used the Gaussian approximation for the output of the filter due to interference and noise. The justification for the Gaussian approximation is based on the central limit theorem by noting that the output of the filter is a sum of random variables with different probability density functions (pdfs). Therefore, the sum of these random variables at the output of the filter can be considered a Gaussian random variable. This approximation is widely used in evaluating conventional receivers [9]. Moreover this approximation is more accurate with the MMSE receiver since we have less interference at the output of the filter and more Gaussian noise [20]. Poor and Verdu in [41] have studied the behavior of the 45 output of the MMSE receiver and found that the output is approximately Gaussian in many cases. To show the improvements of the systems employing higher order modulation formats, Figures 4.1, 4.2, and 4.3 illustrate the performance, in terms of BER, of MMSE receiver based systems with BPSK, QPSK, or 16-QAM modulation formats in a fading channel. These figures are based on the theoretical results obtained in the previous section. The received powers were modeled as a lognormal distribution with zero mean and 1.5 dB standard deviation. The BER performance of the 3-user system as a function of E is shown in FigNo ure 4.1 for the different modulation formats. The theoretical and simulation based performances are in agreement. The simulation results are based on modeling the fading as a complex Gaussian process. The performance of the 16-QAM worse by few dBs than that of the QPSK or the BPSK performance. on the other hand, the BPSK and QPSK have the same performance for such load. In this case there is no advantage of using 16-QAM since using this higher modulation format will require more transmitted power to achieve the same BER. When the load of the the system increases to 30 users, as shown in Figure 4.2, The performance of the system that is based on a BPSK modulation degrades rapidly. In this case, an error floor is introduced and the performance of the system cannot be improved by increasing -. This behavior can be explained as follows. The MMSE receiver is overwhelmed by this load and the system does not have enough dimension to overcome the interference introduced by such a high load. In addition, the QPSK and 16-QAM based systems do not develop an error floor and they outperform the BPSK based system. This basically means that we can increase the capacity of the system by increasing the processing gain, without increasing the bandwidth or the information rate by simply adapting a higher order modulation format. Using higher order modulation formats provided the MMSE receiver with enough dimensions to 46 100 10 10 10-3 10-4 * = theoretical o = simulation , solid = 16-QAM dash = QPSK dot-dash B 10-5 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 4.1: The performance of BPSK, QPSK, and 16-QAM in a fading channel with 3 users with optimum MMSE receiver implementation. suppress the interfering signals. The 16-QAM system outperforms the QPSK system for - greater than 18 dB. When the system loading was further increased to 60 users as shown in Figure 4.3, the QPSK based system would lose its ability to to suppress the new level of interference and would introduce an error floor while the 16-QAM system still operating effectively. 4.2 The Effect of Phase Offsets on the Performance of the System As it will be pointed in Section (5.1), the phase variations are more severe on degrading the system performance because the errors that are caused by phase variation often are not localized to the deep fade periods but rather propagate due to the loss of lock on the desired signal phase by the receiver. In this section, we will study the effect of the phase offsets, due to imperfect estimation of the desired user's fading on the performance of the system. Symbol 47 100 10-1 10 -2 . 10-3 10-5 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 4.2: The theoretical performance of BPSK, QPSK, and 16-QAM in a fading channel with 30 users with optimum MMSE receiver implementation 100 10 - -2 m 10 10-3 theoretical *= 16-QAM o= QPSK 10-4 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 4.3: The theoretical performance of QPSK , and 16-QAM in a fading channel with 60 users with optimum MMSE receiver implementation. 48 error rate (SER) bounds for QPSK and 16-QAM systems are derived when there is an imperfect phase reference. The SER for a QPSK and the 16-QAM systems can be derived as follows. We try to eliminate the phase variation in the desired signal by multiplying the received vector by the estimated phase as follows: y(m) = e-jelmr(m) (4.25) where 01 is the estimated value of the desired user's fading phase, the vector y(m) can be written as y(m) = di(m)a,mciej(O,m-,m) + aj,,mej(e-9 1,m) dj(m)f(1, 6) j=2 + d,(m - 1)g(l, 6)] + n(m)e-i,m (4.26) = dl(m)al,meJem c1 + k(m) where AO1,m = 01,m - 01,m. A01,m is assumed to be IA01,m < l for QPSK and |A01,m < El for 16-QAM because otherwise there are errors even without MAI and noise. Taking the real and imaginary parts of the vector y(m) results in Yl = R[y(m)] = [duicos(AO1,m) - dQlsin(AOl,m)]al,,cl + 51(m) (4.27) Y2 = I[y(m)] = [dlsin(AOl,m) - dQlCOS(AOl,m)] al,mCl + y2(m) (4.28) To find the optimum weights of the MMSE filter, al and a2 the autocorrelation matrices R1 and R2 and the correlation vectors P1 and P2 corresponding to the received vectors yl and Y2, respectively, need to be found. It can be shown that R1 = R2 and P1 = P2. The optimum filter weights can be found as follows. P1= E [R[dj]y] 1 (4.29) = 2cos(AOi,m)al,mcl = P2 2 49 The correlation matrix is given by R1= E [yi(m)yH(m)] 1 2 H = ~2a,mc1i 2 am [i' + p + 3,2M (4.30) j=2 2 P1PH + it = R2 COS2 ( ,m) The MMSE filters optimum weights are given in terms Rl' and P1 by al = a2 = Rl1P1 (4.31) The output of the MMSE filters can be written as z1 =- a Y1 = a[R 1] Hy P= PR-1dllCOs(601,m) - dQlsin(601,m)] al,mcl + PfR 1 1 (4.32) Z2 = aHY2 = [R1P1] HY2 = PR1 [dQlcos(601,m) + drisin(608,m)]al,mcl + P l R12 (4.33) Define il = PHR- 1i and fi2 = P HRL-'2 which consist of the contribution of MAI and the AWGN at the output of the MMSE filters. Substituting the value for al,mcl from Eqn. (4.29) into Eqn. (4.32) Eqn. (4.32) results in the outputs of the MMSE filters, zl and z2, written as 2 zl = P H R1Pl [dilcos(AO1,m) - dQlsin(AOl,m)] + 8l (4.34) cos(AO, 1 1 50 Z2 = P HR P1 [dQlCOS(AOl,m) + dnsin(AOl,m)] + i2 (4.35) cos(A01,m) Making use of the matrix-inversion lemma; R1 can be shown to be equal R-1 = R- + Rit1P(cOS2(01,m) + pHfR P1)-PHf-1 (4.36) 1co2 11,m)1 11 Cos2 ( AOl ,) Rl 1 (4.37) coS2(AOi,m) + 2PHi R P The variances of il and i2 are equal and are given as follows: a E [ijIjH] (4.38) 1= PrR1E [1] RI1P1 (4.39) = PfR-'1RIR P1 (4.40) Substituting the value of R-1 from Equation (4.37) into Equation (4.40) results in o2 given by 2 = Oim)1P (4.41) (Cos2(AO0,m) + 2P R1 I1) The output of MMSE filters, zl and z2, can be written in terms of R- as z, = Kcos(AOl,m)dl - Ksin(AOl,m)dQl + i1 (4.42) z2 = Kcos(AO9,m)dQ1 + Ksin(AOl,m)dll + i2 (4.43) where hl and 2 are assumed to be N(0, ao2) and K is given by 2Cos(AO1,m)PRf1Pi K 2cs 1 1 (4.44) cos2(AOB,m) + 2PjR-'P Since zl and z2 represent the statistics of drn and dQ1, zl and z2 can be written as zl = Kcos(AOl,m)doi + i1, (4.45) 51 z2 = Kcos(AOl,m)dQ1 + ffi2 (4.46) where ii = N(-Ksin(AO,m)dQ1, an2) (4.47) m2 = N(Ksin(AOl,m)dl, O'n2) (4.48) Having the statistics in the form of zl and z2, one can easily calculate the probability of symbol error conditioned on al,Ps ,,, for QPSK an 16-QAM system. After ignoring the double Q-function terms, the Ps/,l of the QPSK system can be approximated by K (cos(601,m) - sin(601,m))) + Q(K (cos(601,m) + sin(601,m)) (449) Q)+Q( ) (4.49) The value of - can be simplified to K _ K2 -m -m2 4Cos2(61,m) (pHrR-iP1)2 (cos2(601,m) + 2P R P1)2 S(co2(601,m) + 2P 'Pi) cos2(S 1,m)pH ilP1 = 4pH1 - IP1 (4.50) Let L1 = cos(AO1,m) - sin(AOi,m) (4.51) L2 = cos( A1,m) + sin(AO,m) (4.52) Then P,lI can be written as Ps/, - Q( 2L~P -'iP1) + Q(V2L~PR i-P1) (4.53) 52 Recalling P1 from Equation (4.29) 1 P1 = -cos(AOi,m)a,mCi (4.54) 2 Then P/1,, can be written in terms of A01,m, al,m, cl, and R1 as Ps ai Q(/ La 2,mcoS2 (AOI,m)CHI-1C) + Q( L2a,mCOS2( AO,m)CHR1i) (4.55) Averaging Ps/,, over the probability density function (pdf) of the desired user's fading amplitude, a1, gives the expression for the symbol error rate, P,, as P, = fi,m(a)P,,,da (4.56) a=o fa,m (a) = 2a exp(-a2) (4.57) where f1,m (a) is the pdf of the desired user's fading amplitude which is assumed to be Rayleigh distributed Ps = fa,m (o ( 2L~ ,mCos2(AO1,m)CH 11C1)da + j fal,m (a)Q( - La2,mCOS2(AOl,m)CHIfl1C1)da (4.58) 0=o 2 Where Q is the Q-function which is defined as (z) exp(- )dA (4.59) Let h = COS2(AOl,m)C1Hf-11 (4.60) 53 P, 1 - a exp (-a2) exp 2 dul da af=0 t1=al,m, h -U 2 + a exp (-a2) exp 2 du2 da (4.61) a=0 2=al,m 2 2 By setting vi =L and v2 = - Equation (4.61)can be written as f2 0 -00 P,= 2 o ,1o a exp(-( 2 + v ))dv1, da Or Ja=0 vi=a,m Lh 2 fOO "" + a exp(-(a2 + v2))dv2, da (4.62) V a=0 V2=al,m 2 Using the polar coordinates, we have r2 = 2 + v (4.63) 0 = tan-1 = tan' (4.64) v L h (4.64) Ps 2 i00 tan-1 sqrtT4 =00 O tan- sqrt 4+ 2 I L2h r2 exp(-r 2)dr2d02 [2 o4+L h= 1 Lh I + - [ -] 21 4+L h 1 Lc2h = [1- 2 4 + L2~h] 1 (L 2cos2 (Al,m)C1H-1Cl 1 L2cos2(AOI,)cHRI:ICl - RC ) (4.65) 2 4 + Lcos2 (el,m)ClH -ll1 If there is no phase offset, AO1,m = 0, Equation (4.65) reduces to Equation (4.23). For the 16-QAM system the probability of symbol error conditioned on al, Ps/al, can be approximated by the following equation after ignoring the terms that have 54 doubled or squared Q-functions and defining L1 = cos(AO,m) - sin(AOi,m) (4.66) L2 = cos(A01,m) + sin(AO,m) (4.67) L3 = cos(AO1,m) - 3sin(AOl,m) (4.68) L4 = cos(AOl,m) + 3sin(AO,m) (4.69) Thus Ps/l, can be written as Ps/,I,, l6QAM < Q 1 a ,go1,mCOS2 (Ao1,m)CH I-11c) + Q 0 l',mCOS2(AO1,m)CHl C1 3 I(L 2c c + Q( 02 mCOS2(A1,m)CHI11C1) (4.70) 4 10 1 '' Averaging Ps/,, over the Rayleigh pdf of the desired user's fading amplitude, the symbol error rate for 16-QAM system can be approximated as P, - 1 2\ - 20$ Lcos2(AOl,m)c H ic1 ) 1 LCOS2(AO1,m)CHft1 + -1 (- L20+L 2(AO 1l) (4.71) +3- /20 L2cos2(AOi,m)cHrRI7lC ) 3 LjcOS2 1,m)CH -101 8 -4 1 20 + L2CO2(Aom)CH lc ) (4.72) 3 +LCS2(AO1,m)CHR -1 + - 1 -1 (4.72) 8( 20 + L4cG2 1 1,m)CH 1 55 Assuming that the system is using Gray coding, the bit error rate (BER) is given by SER BEER (4.73) log2M Where M is the number of points in the constellation. For BPSK, QPSK, and 16QAM, M equals 2, 4, and 16, respectively. These equations implicitly depend on the interfering user codes, delays, transmitted powers, and fading amplitudes through the matrix R. To obtain an average value for SER or BER, one would average over these quantities. Figures 4.4 and 4.5 show the performance in terms of BER by using the theoretical error bounds presented in this section for different values of phase offsets (AO). In these figures, the AO values are 00, 50, and 150 for the 16-QAM case and 00, 50, 150, and 300 for the QPSK case. We did not include the case where AO = 30' for the 16-QAM because with such phase offset the 16-QAM system will not be operational even in the absence of MAI and noise effects. The curves, with the phase offsets, are obtained by using Eqn. (4.72) for the 16-QAM systems and Eqn. (4.65) for the QPSK systems. When the phase offset is 00, the theoretical results presented in this chapter in the form of Eqn. (4.72) and Eqn. (4.65) are in agreement with the results of the previous chapter given by Eqn. (4.21) and Eqn. (4.23). Comparing Figures 4.4 and 4.5, one notices that the 3 and 30-users 16-QAM systems have a very close BER performance while this is not true for the QPSK systems. This means that the 16QAM is more resistant to the multiple access interference caused by the other users. From Figure 4.4, for the 3 users case, we see that the performance of the 16-QAM system with phase offset of 150 is worst than the QPSK system with phase offset of 300 by 5 dB for BER less than 1 x 10-2. For this load, the QPSK system has a better performance than that of 16-QAM. On the other hand, for the 30 users system, the 16-QAM system performs better when the phase offsets are 00 and 50 56 100 10 103 solid =16-QAM dash= QPSK 10-4 phase offsets o = 0 + = 5 *=15 .=30 degrees 10-5 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 4.4: BER of QPSK and 16-QAM where (o, +, *,.) are based on Eqn. (4.72) and Eqn. (4.65) for 3 users. 100 10 10-2 10-3 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 4.5: BER of QPSK and 16-QAM where o, QPSK, ,) are based on Eqn. (4.72) and Eqn. (4.65) for 30 users. 57 4.3 Summary In this chapter, we have investigated the performance of an MMSE receiver based CDMA system in a fading channel with BPSK, QPSK, and 16-QAM modulation formats. It has been found that for the same bandwidth and bit rate, the 16-QAM system outperforms the BPSK and QPSK system when the loading of the system is high compared to the processing gain (pg) of the BPSK or QPSK systems. This performance improvement is made possible by increasing the ability of the MMSE receiver to suppress the multiple access interference by using a higher processing gain. In this context, for MMSE receiver based CDMA systems, one should look at the higher order modulation as a means to increase the system efficiency by allowing more users to access the available bandwidth. The estimation of the desired user's fading process plays an essential role in determining how much capacity improvement can be gained by using the different modulation formats. In the next chapter, the performance of such systems is investigated when the desired user's fading is estimated. CHAPTER 5 FADING PROCESS ESTIMATION In Chapters 3 and 4, we have shown that the use of multilevel modulation can improve the performance of the system in terms of BER and capacity. In Chapter 3, the AWGN channel model was used while in Chapter 4, a fading channel model and an optimum MMSE receiver implementation were used. The optimum receiver is impractical and hard to construct because it assumes that the powers, the fading processes, the time delays, and the spreading sequences of all users are known. An adaptive MMSE receiver based on the LMS algorithm can be used as a practical alternative to implement the MMSE receiver. In this chapter, a practical situation is considered where an adaptive implementation of the MMSE receiver based on the LMS algorithm is used. In addition the desired user's fading process is estimated to provide the receiver with a reference phase and amplitude to demodulate the desired user signal. The estimation of the desired user's fading process is accomplished through the use of a technique based on linear prediction and pilot symbols which will be described shortly. For most of this chapter, only the performance of QPSK and 16-QAM modulation will be investigated since, as we have seen in the previous chapter, the BPSK system is not able to perform effectively even when an optimum implementation of the MMSE filter is used when the system has 30 users. 5.1 The MMSE Receiver Behavior in A Fading Channel In this section, we study the behavior of the MMSE receiver in a fading channel when a multilevel modulation format is used. Since tracking the phase and magnitude of the fading is essential for successful demodulation of a multilevel modulation format 58 59 15 Error Indicator 10 Channel Phase 10 C Channel Amplitude 5 ' 0 0 -5 Error S-10 Estimated phase . -15 Estimated -20- Amplitude -25 0 200 400 600 800 1000 symbol number Figure 5.1: The MMSE behavior in a fading channel in decision directed mode. like 16-QAM, we will study the ability of the present structure of the MMSE receiver to track these fading parameters. In [22], the performance of the MMSE receiver in a frequency nonselective fading channel has been evaluated when a BPSK modulation format is used. It has been shown that the MMSE has a difficult time tracking the channel variation due to the fact that during deep fades, unreliable decisions are fed back to the LMS algorithm. This will cause the MMSE receiver to lose lock on the desired signal or it may lock onto another interfering signal. In this section, we assume a slow fading environment with a processing gain of 124 chips/symbol, a 16-QAM modulation format, a mobile speed of 5 mph, a frequency band of 900 MHz, and a data rate of 9600 bps. This will result in a normalized Doppler rate, fdT, of 0.0028. Figure 5.1 demonstrates the behavior of the present MMSE structure in a slowly varying Rayleigh fading channel for a single user using 16-QAM modulation. As expected, the figure shows the inability of the receiver to 60 track the magnitude and phase of the fading process when the desired user goes into deep fades. The phase estimate in Figure 5.1 represents the MMSE receiver estimate of the phase based on the receiver coefficients. In a single user case, if the MMSE is doing its job of tracking the channel variation, the phase of the MMSE filter coefficients is equal to the opposite value of the phase of the channel. The amplitude estimate is calculated from the value of the filter output. It is clear from Figure 5.1 that the MMSE receiver does a good job in tracking the amplitude variation of the fading channel except during the deep fade period. On the other hand, the receiver does a poor job in tracking the phase of the fading process. In fact, the receiver ends up locked 1800 out of phase to the desired user after the deep fade period is over. Differential detection may be considered to solve this problem, but differential encoding will not solve the more practical problem, when the MMSE receiver locks on to other interfering signals. Figure 5.2 shows that in a training mode, the MMSE receiver always tracks phase and amplitude of the fading channel well. This shows that the decision-directed mode of operation of the MMSE receiver is a disadvantage to its performance in this environment. Therefore, if there is a technique by which we can feed back reliable decisions to the adaptive algorithm, the LMS in this case, then the MMSE will perform in an acceptable manner. This is part of the motivation for using periodic pilot symbols to provide a reliable feedback for the LMS and this will be discussed in the next section. In Figure 5.3, the effect of the phase variation while the amplitude is kept constant is shown in the top graphe and the effect of the amplitude variation while the phase is kept constant is shown in the bottom graph. It seems that when the phase is held constant, the amplitude variation leads to errors only in the deep fade periods. This is due to the fact that during deep fades the desired user's signal to noise ratio value decreases to a low level at which the receiver can not demodulate the signal correctly. In addition, it can be concluded from the figure that the effect of phase 61 10 Channel Phase 5- Channel Amplitude b 0 -5 Estimated 0 Phase -10 Error Estimated -15 Amplitude -15 -20 0 200 400 600 800 1000 symbol number Figure 5.2: The MMSE behavior in a fading channel in a training mode variations is more severe because the errors in this case are not made just in deep fades but they propagate due to the loss of lock on the desired signal phase by the receiver. Having shown the inability of the present MMSE structure to work in a fading environment described in the previous section, we now consider modification of the MMSE receiver to be capable of demodulating multilevel modulation schemes in a fading environment. In [22], a modified MMSE structure for one-dimensional (BPSK) modulation is presented. We will present a more general modified MMSE structure capable of demodulating a wide range of digital modulation formats. First, since the errors due to the phase of the fading process are dominant, we need to eliminate this phase variation from the input to the adaptive filter. In addition, to eliminate the problem of the MMSE receiver locking to other user's phases, we need to take the real and imaginary part of the input to the adaptive filter. The modified 62 Constant fading amplitude 15 1 0 Error Indicator 0 Channel Phase oo 0 -5 Estimated phase -10 ' ' 0 200 400 600 800 1000 Constant fading phase 20 10 Error Indicator 0 0 Channel Amplitude Estimated -20 - Amplitude -30 0 200 400 600 800 1000 symbol number Figure 5.3: The behavior of the MMSE when the the amplitude or the phase of the fading is held constant. 63 Channel estimator a,. Re[d,(m)] e, (m) LMS + x Y7 (m) Adaptive filter zz(m) Re[ da (m)] (mr(m) - -- - + + IlAdaptive filter Decision y2(m) W(m) (2) Im[d,(m)] LMS 2 a., Im[d, (m)] Figure 5.4: The modified MMSE structure. structure is shown in Figure 5.4. This structure assumes an estimate of the amplitude and phase of the fading process are available at the receiver. 5.2 Tracking Techniques in A Fading Channel In the previous chapter, the exact fading process of the desired user is assumed to be known and the MMSE filter weights are assumed to be optimum. In this section, the case where the desired user fading is estimated, rather than assumed to be known, is investigated. In addition, the adaptive LMS algorithm is used to update the MMSE filters coefficients. For the rest of this section, we assume a slow fading environment with a processing gain of 124 chips/symbol, a 16-QAM modulation format, a mobile speed of 5 mph, a frequency band of 900 MHz, and a data rate of 9600 bps. This will result in a normalized Doppler rate, fdTs of 0.0028. There are 3 users in the 64 15 10 Error Indicator 10 D 5 e o S-5 A 10 Channel Estimated S-Channel Error S -15 Phase MEstimated -20 Amplitude -25 0 200 400 600 800 1000 symbol number Figure 5.5: Channel tracking using linear prediction. system. It has been shown by [22] that phase compensation is an effective method of improving the MMSE receiver performance in a fading channel. In [22] a phase estimate is obtained by using a linear predictor. In our case, since we are dealing with multilevel modulation, 16-QAM, amplitude and phase compensation are needed to improve the performance of the MMSE receiver. We studied the capabilities of three techniques in tracking the fading amplitude and phase. These techniques are based on pilot symbols and/or linear prediction. The first tracking technique uses the decision out of the MMSE to form an estimate of the desired user's fading parameters using linear prediction. The channel estimation based on this technique is shown in Figure 5.5. This technique is presented in some detail in [22] for a CDMA system with BPSK modulation. It worked fairly well for BPSK modulation but not in the case here, where 16-QAM modulation is 65 used. This has motivated the search for a better tracking method. We will now summarize the procedure used to obtain channel estimates using linear prediction. The tracking of the desired user's fading process can be accomplished as follows. From Figure 5.4, the output of the filter output, z(m), when r(m) is the input, is given by z(m) = di(m)a l,meJeimaTc + !i (5.1) A noisy estimate of the fading process can be given by z(m) dl(m)aTc1 (5.2) In a decision-directed mode, di(m) is replaced by di(m). The linear prediction can be formulated by the following. As has been shown in [22] , the L th order linear prediction of the fading channel is given by L p(m) = i:P(m - i) (5.3) i=1 The optimum coefficients of the linear predictor which minimize the mean-square error between the actual fading process and its estimates are given by a = C-1v (5.4) The expressions for C and v for the single user case are given in [22] as C = B + (E, (5.5) No where B is a L x L matrix whose elements are given by [B]i,j = Rc((i - j)T,) (5.6) [v]i = R,(iT) (5.7) 66 15 Error Indicator 10 I I 00 Channel Phase Channel - Amplitude -5 S 0 -5o -S S-Estimated lz r Etiaed Error . -10_ Estimated phase Amplitude -15 -20 0 200 400 600 800 1000 symbol number Figure 5.6: Channel tracking using pilot symbols. and R,(r) is the autocorrelation function of the fading process and is approximated by R,(r) = 1 - (7rfDr)2 (5.8) The estimates of the fading process out of the linear predictor are then used to remove the phase of the desired user fading from the input of the modified MMSE receiver and to scale the decisions in the modified MMSE receiver, respectively. The second tracking technique is based on pilot symbols. The result of tracking the fading channel using this technique is shown in Figure 5.6. In this technique, pilot symbols, known by the receiver, are sent periodically (every 10th symbol for the case reported in Figure 5.6). The MMSE receiver uses these pilots to obtain an estimate for the fading process in the same manner as in Eqn. 5.2. The fading parameters 67 15 Error Indicator Channel Phase S 5 - Estimated phase 0 - -Channel Amplitude Error -10 be Estimated E -1 5 Amplitude -20 0 200 400 600 800 1000 symbol number Figure 5.7: Channel tracking using pilot symbols and linear prediction obtained by this estimate are used in demodulating the desired user's signal until the next pilot symbol is received and a new estimate is made. We propose the use of pilot symbols for two reasons. First, pilot symbols can be used to periodically train the MMSE and prevent the MMSE filter from feeding back wrong decisions. The second reason for using pilot symbols is to aid the receiver in estimating the channel fading condition. The fading parameters obtained by this estimate are used in demodulating the desired user's signal until the next pilot symbol is received and a new estimate is made. Obviously, this technique is suitable for a slowly fading channel and may not work well for a rapidly fading channel. We propose a third approach which consists of a combination of the first and second techniques. The tracking of the fading channel using this technique is shown in Figure 5.7. In this case, channel estimates are made by feeding back a linear prediction of the previous channel estimates. 68 By comparing Figures 5.5, 5.6, and 5.7, one can conclude that the third technique has better tracking capabilities than those of the other techniques. The good performance of the third technique can be attributed to three reasons. First, the use of pilot symbols provides the MMSE receiver with a reference that helps the receiver not to lose lock on the desired user. Second, using the linear predictor, estimates are made for every received symbol. This gives the linear predictor recent past channel estimates to predict the channel conditions. Third, pilot symbols can help the linear predictor not to lose track of the fading process by interrupting the propagation of decision errors. Figure 5.6 demonstrates that the MMSE receiver can be updated based on pilot symbols only. This is interesting since the poor performance of the MMSE receiver in a fading channel is often due to the feeding back of unreliable decisions to the adaptive algorithm during deep fades. To show the improvements of the systems, which are based in different modulation formats, Figures 5.8, 5.9, and 5.10 illustrate the BER performance of an MMSE receiver base systems with BPSK, QPSK, or 16-QAM modulation formats in a slowly fading channel for a 3 and 30-user CDMA systems. To generate these figures, the following simulation environment was chosen. The mobile speed was 5 mph, the mobile operates at the 900 MHZ band, the bit rate was 9600 bps, a pilot symbol was sent every 10th symbol. This corresponds to f,T, of 0.0028, 0.0014, 0.007 for 16-QAM, QPSK, and BPSK, respectively. The received powers were modeled as a lognormal distribution with zero mean and 1.5 dB standard deviation. The receiver structure shown in Figure 5.4 has been used. The BER performance of the 3-user system as a function of Eb/No is shown in Figure 5.8 for the different modulation formats. As expected, the CDMA system which based in a BPSK modulation outperforms the other systems. In this case there is no advantage of using higher order modulation since using higher order modulation will require more transmitted power to achieve the same BER. 69 100 10 cc 2 Lw 1010 solid = 16QAM dash = QPSK dot-dash = B'PSK 10 ' ' ' ' ' ' ' \ 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.8: The performance of BPSK, QPSK, and 16-QAM in a slow fading channel with 3 users, fading estimated. When the load of the the system increases to 30 users, as shown in Figure 5.9, The performance of the system that is based on a BPSK modulation degrades rapidly. In this case, an error floor is introduced and the performance of the system can not be improved by increasing Eb/No. When the system loading further increased to 60 users as shown in Figure 5.10, the QPSK based system would lose its ability to to suppress the new level of interference and would introduced an error floor. In the next section, we will be examining the third tracking technique that we have proposed in this section in some details. For example, we examine the effect of the predictor length and the pilot symbol rates on the performance of the QPSK and 16-QAM systems. 5.3 The Effect of the Fading Estimation Error on the Performance of the System In coherent detection of a desired signal, the fading process of the desired user need to be estimated. The estimate of the fading of the desired user's fading is given 70 100 10 10-3 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.9: The performance of BPSK, QPSK, and 16-QAM in a slow fading channel with 30 users, fading estimated. 100 10-1 dot-dash = 16QAM known fading 10-2 solid = 16QAM estimated fading dash = QPSK known fading 10-3 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.10: The performance QPSK (known fading), and 16-QAM (known and estimated fading) in a slow fading channel with 60 users. 71 in Eqn. 5.2 as z(m) dl(m)aTc (5.9) ^ (1 ej01,m where the variables &1,m and O1,m are the estimated amplitude and phase of the desired user's fading process. As has been shown in [22] , the Lth order linear prediction of the fading channel is given by L ^(m) = 0/P(m - i) (5.10) i=1 Let y(m) be the exact desired user fading process. Then fading estimation error is defined as e(m) = y(m) - /(m) = X + jY (5.11) Since y(m) was modeled as a complex zero mean Gaussian random process, the estimate of the fading can be assumed a Gaussian process since it is produced by a linear operation on a Gaussian process. Therefore, the estimation error is a complex Gaussian process. If the estimator is unbiased, the mean of the estimation error is zero. The real and imaginary parts of the estimation error have a zero mean Gaussian distribution and the amplitude has a Rayleigh distribution while the phase has a uniform distribution from -7r to ir. Figure 5.11 shows the distributions of the real and imaginary parts, X and Y, of the estimation error. Figure 5.12 shows the distributions of the amplitude and the phase of the estimation error. The figures are in agreement with our observation that the estimation error represents a zero mean complex random process. The figures are obtained from a simulation of a 3 users, 16-QAM system with fdT, = 0.0028 at Eb/No = 20 dB It is interesting to see how the system performs if the estimation error is modeled as a complex Gaussian process which its real and imaginary parts modeled as a zero mean Gaussian process 72 15 mean = -3.311 e-004 variance = 1.560e-003 x 10 05 0 5' - - Fn---R -0.2 -0.1 0 0.1 0.2 0.3 x 15 mean = 1.563e-004 variance = 1.594e-003 >- 10L5 0 , -0.2 -0.1 0 0.1 0.2 0.3 Y Figure 5.11: The distributions of the real and imaginary parts of the estimation error for a 16-QAM system; PSAM rate = 0.2, 3 users, pg= 124, fdT = 0.0028, Eb/No = 20 dB 20 -0 mean = 4.5014e-002 variance = 1.1283e-003 L 15 210 C5 -0.2 0 0.2 0.4 0.2 mean = 2.125e-001 variance = 1.887e+002 . 0.15 0. 0 - 0.05 '0 -4 -3 -2 -1 0 1 2 3 4 Figure 5.12: The distributions of the amplitude and the phase of the estimation error for a 16-QAM system; PSAM rate = 0.2, 3 users, pg= 124, fdT, = 0.0028, Eb/No = 20 dB 73 with variance a2. The estimation error can be represented as e = X + jY where X = N(0, a2) and Y = N(0, a2). Where N stands for normal (Gaussian) distribution. Figures 5.13 and 5.14 show the performance of a 16-QAM system, when the estimation was modeled as a zero mean complex Gaussian process. The variance, a2, varies from 0 to 0.1. The loading for the results in Figures 5.13 and 5.14 are 3 and 30 respectively. For comparison, the cases where the desired user's fading process is known or estimated with a normalized Doppler rate of 0.0028 and 0.0355, respectively, are also shown in the figures. As can be seen from these figures, if a2 of X and Y are 1 x 10-6 the performance of the system will be the same as if the process is known. If the a2 is increased to 1 x 10-4 the performance is very close to the case when the fading process is known for E less than 30 dB, then it degrades. N. If a2 is increased further to 1 x 10-3, the performance in terms of BER is very close to the known fading case for - less than 20 dB and then the BER becomes constant N0 and the performance does not improve at higher - for the 3 users case. For the N. 30 users case, the performance degrades substantially for E greater than 25 dB for a2 = 1 x 10-3 . Increasing a2 to 1 x 10-1 will introduce an error floor at BER 0.3 which makes the system ineffective. An interesting result to see from Figures 5.13 and 5.14 is to compare the performance of the 16-QAM system when the fading is estimated to the cases when X and Y are modeled as zero mean Gaussian with different variances. For example, for the estimated fading system with fdT = 0.0028 the BER curves cross over the BER curve of a2 = 1 x 10-3 at E = 27 dB for 3 users and 33 dB for 30 users. This No cross over can be attributed to the fact that the estimation of the fading improves by increasing - These figures can serve as figures of merit for a system designer. By No checking the variances of the real and imaginary parts of the estimation error, one can have a good idea what the system BER would be. 74 100 10-2 Sx = var.= le-1 + = var. = le-3 10-3 o= var. = le-4 = var.= le-6 solid = known fading 10 dash = estimated fading Norm. Dopp. = 0.003 . = estimated fading Norm. Dopp. = 0.0335 10-5 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.13: BER of 16-QAM with different estimation error variances for 3 users. For the estimated case PSAM rate =.2, L= 3 , pg= 124, 100 10 10-2 X = var. = le-1 + = var. = le-3 o = var. = le-4 = var.= le-6 10-3 solid = known fading dash = estimated fading Norm. Doppp.= 0.003 = estimated fading Norm. Doppp.= 0.0335 10-4 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.14: BER of 16-QAM with different estimation error variances for 30 users. For the estimated case PSAM rate =.2, L= 3 , pg= 124, 75 100 10 10-3 x= var.=le-1 +=var.=l e-3 o var.=le-4" * = var.=le-6 10-4 solid = known fading dash = fading estimated Norm. Dopp =0.0014 = fading estimated Norm. Dopp =0.017 10-5 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.15: BER of QPSK with different estimation error variances for 3 users. For the estimated case PSAM rate =.2, L= 3 , pg= 62, respectively, Figures 5.15 and 5.16 show the performance of 3 and 30 user QPSK systems when the estimation error is modeled as a zero mean complex Gaussian. These figures are to be compared to the 16-QAM Figures 5.13 and 5.14. From these figures, one can compare the sensitivity of the BER performances of the 16-QAM and the QPSK systems to the estimation error. This can be demonstrated clearly by comparing the 16-QAM and QPSK systems when the system load is 30 users. For the QPSK case, with a2 as high as 1 x 10-3, the system performance in terms of BER is the same as for the known fading case. On the other hand, for the 16-QAM case, for a2 = 1 x 10-3 the system performance in terms of BER degrades substantially when compared to the known fading case. This result is expected since the 16QAM modulation constellation is more crowded than than the QPSK constellation. By comparing Figure 5.14 and 5.16 for the 16-QAM and QPSK systems, one can conclude that if the estimation error is high, for example here a2 = 1 x 10-3, there is no justification for using 16-QAM modulation. 76 100 10-x UJ m x = var. = le-1 +=var.= le-3 10-2 o = var. = le-4 * = var. = 1 e-6 solid = known fading dash = estimated fading Norm. Dopp. = 0.0014 . = estimated fading Norm. Dopp. = 0.017 10-3 1 1 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.16: BER of QPSK with different estimation error variances for 30 users. For the estimated case PSAM rate =.2, L= 3 , pg= 62, Another observation to be made from these figures is that the performance of the system in terms of BER becomes less sensitive to the increase of the real and imaginary parts of the estimation error variances at high load. This becomes clear by comparing the 3 and 30 user systems for 16-QAM or QPSK systems. For example, when a2 = 1 x 10-4, the 30 user 16-QAM based system performs very close to the system with known desired user fading while the 3 user system degrades substantially. This is more clear in the QPSK system, where in the 30 user case the system performance is almost the same as that of a known fading case while for 3 users there is a loss of about 5 dB for BER more than 1 x 10-4. One can expect these results because when the system load is low, the multiple access interference is not a major factor on the BER, while the estimation error is. At high loads, the multiple access interference is a major factor in the BER performance of the system and its effects are more dominant than the effect of the estimation error. This suggests that for 77 Table 5.1: The estimation error statistics for 16-QAM system with L = 3, PSAM = .2, 3 users and fdT, = 0.0028 b(dB) 2 0 9.984 x 10-2 9.865 x 10-2 5 4.763 x 10-2 4.890 x 10-2 10 1.673 x 10-2 1.672 x 10-2 15 5.129 x 10-3 4.989 x 10-3 20 1.560 x 10-3 1.594 x 10-3 25 6.238 x 10-4 6.273 x 10-4 30 3.082 x 10-4 3.123 x 10-4 35 1.690 x 10-4 1.675 x 10-4 40 1.036 x 10-4 1.068 x 10-4 high load systems, the estimation of the error does not have to be as accurate as for the low load systems. Table 5.1 shows the values of the variances of the real and imaginary parts of the estimation error based on simulating a 3 user 16-QAM system. The PSAM rate is 0.2, the predictor length L = 3 and the normalized Doppler rate, fdT, is 0.0028. This table is to be compared to Figure 5.13. In Figure 5.13 a cross over between the BER's curve corresponding to the system where the fading has been estimated and the BER's curve corresponding to o2 = 1 x 103 at about -E = 27 dB. This can be N. seen from 5.1 that at -E = 25 dB, a = 1.56 x 10-3 and a = 1.5944 x 10-3 while at E - 30 dB, oa = 6.2376 x 10-4 and = 6.2731 x 10-4. This is in agreement with Figure 5.13 in which we see that the 3 user 16-QAM system with PSAM=0.2 and L=3 and fdT, of 0.0028 operating between the curves corresponding to a2 = 1 x 10-3 and a2 = 1 x 10-4 for - = 27 dB. No 5.4 The Effect of Pilot Symbol Rates on the Performance of the System The effect of a pilot symbol assisted modulation (PSAM) rate on the BER performance of the system is compared for different Doppler rates and system loadings in 78 Figures 5.17 to 5.20. PSAM rates of 0.2, 0.1, 0.05, and 0.02 were used. As expected, the higher the PSAM rate the better the performance. This is more evident at high Doppler rates. The performance improvement due to the high PSAM rate in terms of BER came at the expense of the bandwidth efficiency of the system. For example, in the case of a PSAM rate of 0.2, 20% of the available bandwidth is used for sending pilot symbols where at a PSAM rate of 0.05, only 5% of the available bandwidth is used for pilot symbols. The system designer needs to balance the tradeoff between the bandwidth efficiency and the performance of the system in terms of BER. Based on these figures, we see that at low Doppler rate, independent of the loading of the system, a small penalty in - is paid if a PSAM rate of 0.1 is used instead of 0.2. For example; in the case of a system employing a 16-QAM modulation with a load of 30 users and the mobile speed of 5 mph which corresponds to a normalized Doppler frequency of 0.0028, the difference in performance when a PSAM rate of 0.2 and 0.1 is about 2 dB and the use of the lower PSAM rate is attractive in this situation. The use of lower than 0.1 PSAM rate even at low Doppler rates will degrade the performance substantially as shown in Figure 5.17, 5.18, and 5.21. On the other hand, At a higher Doppler rate as shown in Figures 5.22 the penalty in -is about 5 dB when a PSAM rate of 0.1 is used instead of 0.2 and this penalty widens substantially when a lower PSAM rate is used. For 16-QAM system with normalized Doppler frequency, fdTs, 0.0335 which is shown in figure 5.22 there is a substantial improvement due to the use of higher rate PSAM but the system is still not attractive since an error floor develops at high BER. The improvement in the performance of the system due to the use of higher PSAM rate is due to the fact that sending PSAM frequently will improve the estimation of the fading process which translate to an improvement to the system BER performance. This can be seen from Table (5.1) and Table (5.2). By comparing the variances of the real and imaginary parts of the error process for the system with PSAM rate 79 100 10 i0 10-3 PSAM rate *=0.2 x=0.1 0=0.05 +=0.02 10-4 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.17: BER of 16-QAM with different PSAM rates; L= 3 , 3 users, pg= 124, fdT, = 0.0028. 100 10-1 10 PSAM rate: = 0.2 x=0.1 = 0.05 += 0.02 10-3 0 5 10 15 20 25 30 35 40 Eb/No Figure 5.18: BER of 16-QAM with different PSAM rates; L= 3 , 30 users, pg= 124, fdT = 0.0028. 80 100 -r1 w 10 PSAM rate *=0.2 x=0.1 o=0.05 +=0.02 10-2 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.19: BER of 16-QAM with different PSAM rates; L= 3 , 30 users, pg= 124, fdT, = 0.017. 100 w 10 PSAM rate: * = 0.2 x=0.1 o =0.05 + =0.02 10-2 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.20: BER of 16-QAM with different PSAM rates; L= 3 , 30 users, pg= 124, fdT, = 0.0335. 81 100 10 10 PSAM rate: *=0.2 x=0.1 o0= 0.05 += 0.02 103 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.21: BER of QPSK with different PSAM rates; L= 3 , 30 users, pg= 62, speed= 5 mph fdTs = 0.0014. 100 Lu 10 PSAM rate: * = 0.2 x=0.1 o = 0.05 + =0.02 10-2 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.22: BER of QPSK with different PSAM rates; L= 3 , 30 users, pg= 62, speed= 60 mph fdT, = 0.017. 82 Table 5.2: The estimation error statistics for 16-QAM system with L = 3, PSAM = 0.02, 3 users and fdT, = 0.0028 S(dB) U2 0 5.1563 x 10-1 5.196 x 10-1 5 5.207 x 10-1 5.389 x 10-1 10 3.498 x 10-1 3.708 x 10-1 15 2.541 x 10-1 2.388 x 10-1 20 2.041 x 10-1 2.413 x 10-1 25 1.457 x 10-2 1.306 x 10-2 30 4.205 x 10-3 3.534 x 10-3 35 2.333 x 10-3 1.930 x 10-3 40 1.439 x 10-3 2.2858 x 10-3 of 0.2 and the system with PSAM rate of 0.02, we notice that the variances for the former system are lower than that of the later system. These improvements in the estimation due to use of higher PSAM rates translate to a better BER performances. 5.5 The Effect of the Linear Predictor Length on the Performance of the System Figures 5.23 to 5.24 show the BER performance of the 16-QAM system for a certain normalized Doppler rate and number of users while the linear estimator length, L, has different values, namely; 1, 2, 3, 10, and 50. The BERs are the same independent of these values of L at high j. This is due to the fact that the length of the linear estimator has a small effect on the value of the estimation error. Tables (5.1) and (5.3) show that values of a2 and ,2 for different values of for a simulation environment of a mobile speed of 5 mph, which corresponds to fdTs = 0.0028 in a system with 3 users employing 16-QAM and PSAM rate of 0.2. The information in these tables need to be compared to the results in Figure (5.23) for E > 30, the values of o, and ,2 for L = 3, and 50 are very close. For these values No - l of E we see no change in the BER as shown in Figure (5.23). For Eb < 30, the No' No values of a 2and a2 for L = 3, and 50 are not as close as before and this is translated vaue o x aY 83 Table 5.3: The estimation error statistics for 16-QAM system with L = 50, PSAM = 0.02, 3 users and fdT, = 0.0028 S2 2 k(dB) 01202 0 5.1563 x 10-2 5.196 x 10-2 5 5.207 x 10-2 5.389 x 10-2 10 3.498 x 10-3 3.708 x 10-3 15 2.541 x 10-3 2.388 x 10-3 20 2.041 x 10-4 2.413 x 10-4 25 1.457 x 10-4 1.306 x 10-4 30 4.205 x 10-4 3.534 x 10-4 35 2.333 x 10-4 1.930 x 10-4 40 1.439 x 10-4 2.2858 x 10-4 to a small difference in BER performance in Figure (5.23). The performances of the QPSK with different values of L are shown in Figures (5.25) to (5.26). As in the case for 16-QAM, there is no improvements in terms of BER for high values of E N" We notice from these figures that the BERs for system with L = 3 and L = 50 are very close. therefore; going to higher than L = 3 is not justified. 5.6 Summary In this chapter, we have investigated the performance of an adaptive MMSE receiver based CDMA system in a fading channel with QPSK, and 16-QAM modulation formats when the fading of the desired user is estimated. By using the estimator presented in Section 5.2, the capacity is improved when a 16-QAM system is used as shown in Figures 5.9 and 5.10 at a low Doppler rate but not at high Doppler rate. A system designer can make a decision about what modulation format should be used based on the quality of the estimate of the desired user's fading process and employing Figures 5.13 to 5.16 to help in deciding whether a 16-QAM or a QPSK is to be used. If the fading process is known or the fading estimation error is very low, 16-QAM modulation should be employed to improve the system capacity . On the 84 100 L:.=1 +=2 *=3 x=10 0=50 10-1 w 10 10-3 10-4 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.23: BER of 16-QAM with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg = 124, and fdT, = 0.0028 100 -T 1 w 10 L:.=1 +=2 *=3 x=10 o=50 10-2 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.24: BER of 16-QAM with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg= 124, and fdT = 0.0335. 85 10 L: *3 x=10 0=50 10-1 -2 w 10 10-3 10-4 0 5 10 15 20 25 30 35 40 Eb/No (dB) Figure 5.25: BER of QPSK with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg= 62, and fdT = 0.0014. 100 L: +=1 .=2 *=3 x=10 o=50 -1 w 10 10-2 0 5 10 15 20 25 30 35 40 Eb/No(dB) Figure 5.26: BER of QPSK with different predictor lengths (L); PSAM rate = 0.2, 30 users, pg= 62, and fdT. = 0.017. 86 other hand, if the fading error estimation is high, QPSK modulation should be used since it is more robust for high estimation errors. CHAPTER 6 POWER CONTROL In this chapter, a fully distributed power control algorithm is presented that is based on the MSE. We study the capacity improvements that can be gained by an MMSE receiver-based CDMA system implementing this power control algorithm. We investigate the performance of this power control algorithm when the MMSE receiver filter coefficients are obtained through the Weiner solution or adaptive algorithms like the LMS and the RLS. We also look at the convergence of the SINR and the total transmitted power in the in AWGN and fading channels. In this chapter, we propose a power control algorithm that can be used to adjust the mobile station transmitted power in a closed loop power control fashion. The power control presented here does not update the transmitter power in constant steps of ï¿½1 dB like the IS-95 but with variable steps that are dependent on the channel condition and the MMSE receiver filter coefficients. 6.1 Fully Distributed Power Control Algorithm Power control algorithms are based on the fact that the SINR at the receiver is directly proportional to the desired user's transmitted power and inversely proportional to the sum of the interfering signals' transmitted powers. The goal of power control algorithms is to equalize the SINR to reduce the total transmitted power in the system. This reduces the interference level in the CDMA system and hence increases the capacity. In general, power control algorithms are classified as centralized or distributed power control algorithms. In a centralized algorithm, there is a controller that has complete knowledge of all active radio links and their terminal powers [43] and is responsible for adjusting the transmitted powers at the transmitting terminals. 87 88 On the other hand, in a distributed power control algorithm, each radio link adjusts its own transmitted power based on its own measurements [44]. For the ith user, SINRi at the output of the MMSE filter is given in [19] as pihii ayci I2 SINRi = (6.1) |(aH I)12 + 2a2(afai) where the variables, pi is the transmitted power, ci is the spreading of user i with a period N, hij is the channel gain of user j to the assigned base station of user i, ai is the filter coefficient vector that correspond to the ith user, I is the multiple access interference presents in the received signal, and a2 is the noise variance. For the ith user, define the desired MMSE ( MMSEi ) as the value of the MMSE which corresponds to the desired SINR (SINRi). The relation between SINRi and MMSEi is given in [19] as SINRi = 1 (6.2) MMSEi The MMSEi is obtained by the Wiener solution for the tap weights as described in [39], [20], [18], [19]. For the ith user, the MMSEi is given by MMSEi = 1 - / a apaiiaci (6.3) From Eqn. 6.3, we can write the transmitted power in terms of MMSE, the tap wieghts, and the spreading sequence as follows (1 - MMSE)2 Pi = h I(ac2 (6.4) We propose to update the transmitted power at the (n + 1) iteration according to the following algorithm (1 - MMSE)2 pi(n + 1) = ( (6.5) hii I (af (n)ci)12 89 It is clear that the transmitter needs to know (a(n)Hci) and hii to update its power. The value of these terms can be calculated by the receiver and then sent to the transmitter. The denominator of eqn.(6.5) estimation can be approached as follows. The transmitter sends a pilot symbol at the beginning of each transmission period. The receiver uses the output of the MMSE receiver that corresponds to these pilot symbols to get a noisy estimate of the the denominator of Eqn.(6.5) as follows zi = diV,/-i haci + fi (6.6) where i consists of the output of the filter due to the noise and the multiuser interference and di is the data symbol. A noisy estimate the denominator of eqn.(6.5) is obtained from hi I (a (n)ci) 2 := (n) ) (6.7) The value of d is sent from the receiver to the transmitter which divides it by the last transmitted power value to find r(n). The transmitter then uses this value of r(n) to update its transmitted power according to eqn. (6.5). Furthermore, when constant envelope modulation is used, no pilot symbols need to be sent since the value of Idi| is constant. 6.2 Numerical Results To show the improvements that can be realized for the system, in this section, we present some simulation results for an MMSE receiver-based DS-CDMA system using the MMSE-based PCA proposed in the previous section. In all the results in this section, a BPSK modulation format is used. To evaluate the advantage of implementing the proposed PCA, our results are compared to an MMSE receiver based system with perfect power control as well as the theoretic bounds using optimal spreading sequences [38] or asymptotic analysis (using 90 large number of users and large processing gain) [37]. To facilitate comparison for the system with perfect power control, we assume that each user transmits with a constant power of - the average total transmitted power obtain from the proposed PCA. The proposed PCA based system was found to yield on average a capacity improvement of more than 20% over the system with perfect power control. The simulated capacity results, shown in Figure 6.1, were obtained by varying the number of the CDMA system users to find the maximum number of users that can be supported by the system using a blocking probability criterion of 0.01 . Blocking is defined as a scenario in which the converged value of the SINR of any user, was less than 98% of the desired SINR; so that the capacity of the system is given by the maximum number of users that could be present in the system while satisfying the following performance criterion Pr(SINR < 0.98SINR) < 0.01 (6.8) The simulation results shown in Figure 6.1 are found to be in agreement with the theoretical capacity upper bound given in [38] and [37] by K < N(1 + (6.9) SINR despite the fact that, for the results shown in this section, short random sequences are used rather than optimal sequences as used in [38] or as asymptotic analysis using large number of users and large processing gain as in [37]. Figure 6.1 shows that for a practical system as considered in the simulation study (with finite number of users and reasonable length of processing gain) , it is possible to attain the same capacity as the MMSE system with optimal signature sequence [38] or that with large spreading gain [37] for a wide range of SINR but at the expense of transmitting more power. This is further illustrated in Table 6.1 which shows the average total transmitted power, Pt, required to attain the capacities obtained by 91 * = theoretical bound 50- o = MMSE based PCA + = perfect power control 45 40 . o 35 30 25 20 0 2 4 6 8 10 12 14 Target SINR(dB) Figure 6.1: The capacity improvement due to the use of the proposed power control algorithm as compared to the capacity of a system with perfect power control and theoretical bound the proposed algorithm (6.8) for different values SINR. It is clear that while the capacities attained by the proposed algorithm are close to the theoretical capacity bounds, the associated total transmitted powers required by the proposed algorithm are somewhat higher than that for the total power given in [37] by Pt = INR, (6.10) N 1+saNR For the capacity simulation results, we use a normalized channel gain of 1, a processing gain of 31, a noise variance of 0.1, the power is updated every symbol, and we set the initial transmitted power of all users to 0.1. Figures 6.2 and 6.3 show the total transmitted power and the SINR convergence for the system using the PCA proposed in the previous sections. There are 33 users in the system and SINR of 10 dB. The SINRs of the users would converge to a value less than SINR if the number of users were more than 33. While we assume in previous results that all users have the same target SINR, the proposed PCA can 92 Table 6.1: Simulation capacity and average total transmitted powers corresponding to different SINR requirements SINR(dB) Capacity eqn. 6.8 Pt (simulation) Pt eqn. 6.10 1 55 637.4 617 3 46 850.7 796 6 38 1037.1 746 8 35 1453.3 869 10 33 2219.7 1023 12 31 1631.4 827 14 29 800.9 726 10 103 102 I 10, F 100 0 50 100 150 Iteration Figure 6.2: A typical total transmitted power for MMSE receiver based CDMA system with for 33 users and SINR = 10 dB. 93 12 :6 z 4 2 0 20 40 60 80 100 Iteration Figure 6.3: A typical SINR convergence SINR = 10 dB for 33 users. support different target SINRs without any modification. In Figure 6.4, W show the convergence of the SINR and the total transmitted power of a system with 6 users if there are two different target SINR values. Three of these users have a target SINR of 6 dB while the other 3 users have a target SINR of 10 dB. We see from the figure that each user converges to its desired target SINR. The SINR of the user with the low target SINR (6 dB) converges faster than the SINR of the users with higher target SINR. The power control algorithm performance with adaptive implemintation of the MMSE receiver in which the LMS and RLS algorithm are used to update the filter weights was studied and the results are shown in Figure 6.5, 6.6, 6.7, and 6.8. In these figures, the power has been updated every 100 iterations of the adaptive algorithm and the transmitted powers of all users where initilize to 1. As expected, the convergence of the SINR and the convergence of the total transmitted power in the adaptive cases are slower than when the receiver filter tap weights are obtained by the Weiner solution. The SINR converges to a value close to, but not exactly equal to, the target SINR due to the fact that the proposed power control algorithm has |

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It is clear that the transmitter needs to know (a(n)fc) and ha to update its power. The value of these terms can be calculated by the receiver and then sent to the transmitter. The denominator of eqn.(6.5) estimation can be approached as follows. The transmitter sends a pilot symbol at the beginning of each transmission period. The receiver uses the output of the MMSE receiver that corresponds to these pilot symbols to get a noisy estimate of the the denominator of Eqn.(6.5) as follows Zi = Ci + (6.6) where fi consists of the output of the filter due to the noise and the multiuser inter ference and di is the data symbol. A noisy estimate the denominator of eqn.(6.5) is obtained from ha |(af (n)Cj)|2 := rÂ¡(n) Pi(n) (6.7) The value of ^ is sent from the receiver to the transmitter which divides it by the last transmitted power value to find r](n). The transmitter then uses this value of rj(n) to update its transmitted power according to eqn. (6.5). Furthermore, when constant envelope modulation is used, no pilot symbols need to be sent since the value of \di\ is constant. 6.2 Numerical Results To show the improvements that can be realized for the system, in this section, we present some simulation results for an MMSE receiver-based DS-CDMA system using the MMSE-based PCA proposed in the previous section. In all the results in this section, a BPSK modulation format is used. To evaluate the advantage of implementing the proposed PCA, our results are compared to an MMSE receiver based system with perfect power control as well as the theoretic bounds using optimal spreading sequences [38] or asymptotic analysis (using 12 The 64-ary orthogonal modulation is a block of 64 Walsh codes. These are the same as the Walsh codes used in forward channel modulation but here they are used differently. Walsh codes in the reverse traffic channel are used to modulate the data stream out of the interleaver. Each six bits of data are mapped to one of the Walsh codes as shown in the following: 47 53 TTT TToT > (code47)(code53) The role of the randomizer block is to remove the redundant data introduced by the code repetition block. The same pilot PN sequences used in the forward modulation and coding are used in the reverse channel to modulate the data in the I and Q channels. The data spread in the Q channel is delayed by 1/2 of a chip resulting in an offset quadrature phase shift keying(OQPSK) modulation. In this dissertation, we have compared the performance of BPSK, QPSK, and 16- QAM modulation formats in an MMSE receiver-based CDMA system in terms BER. We simply modulate the data stream using BPSK, QPSK, and 16-QAM modulation formats for comparison. Then the modulated signal is spread using a random spread ing sequence. In IS-95, the data is processed before sending them in the channel as shown in Figures 1.3 and 1.4. 1.2.3 Power Control To eliminate the near-far problem and to reduce the interference level in a CDMA system, a fine power control is necessary for acceptable operation of the CDMA system. IS-95 supports open-loop power control and closed-loop power control. In open-loop power control, the mobile user attempts to control its transmitted power based on the received signal strength. In closed-loop power control, the base station sends power control messages to the mobile user to adjust its transmitted power once every 1.25 ms. The base station transmits power control bits for every mobile user 15 Figure 1.5: The MMSE receiver. presented in [14], [15],and [16]. Although they show linear complexity, these subopti mum receivers still require a great deal of side information. The MMSE receiver is a suboptimum receiver which is known to be near-far resistant. In addition, the MMSE receiver does not need to know certain side information like the code sequence and the carrier frequency of the desired user. This information can be obtained through adequate training if the MMSE is implemented in its adaptive form. Adaptive algo rithms such as the least-mean-square (LMS) and recursive least-square (RLS) can be used to obtain the tap weights of the filter. The performance of the MMSE receiver in an AWGN is presented in [17], [18], [19], [20],and [21] and in a fading channel in [22], [23], [24], [25] and [26] for multiuser and [27] for a single user environment. To understand the advantages of the MMSE receiver, we need to describe briefly how it works. The MMSE receiver is shown in Figure 1.5. The received signal which consists of the desired users signal, MAI, and Gaussian noise is fed at the chip rate into the equalizer until the N-tap delay line becomes full. After one symbol time, the equalizer content is correlated with the tap weights, a, and the result of this correlation is used 84 Figure 5.23: BER of 16-QAM with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg = 124, and fTs = 0.0028 Figure 5.24: BER of 16-QAM with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg= 124, and fdTs = 0.0335. I dedicate this work to my wife, Aisha, my daughters, Bashayer and Ohood, my mother and the rest of my family members. 54 doubled or squared Q-functions and defining cos(A9hm) sin(A9itTn) (4.66) cos(A9itm) + sin(^A9i^m') (4.67) Z/3 cosiyA9\rn^j 3sin( A9irn) (4.68) LA = cos(A0i,m) + 3sin(A9itTn) (4.69) Thus P4/Ql can be written as Ps/ai16QAM < q(^J^almcos2(A0i,m)cf + <3 (y/ Yof,mc052(A^i,m)cf + \q[]J ^lmCOS^ehm)c^C^ + ^ symbol error rate for 16-QAM system can be approximated as p l_(l_ I Afcos2 (A^lim)cfRf1Ci \ 2\ y 2O + L?cos2(A01,m)cfRT1c1/ l/j_ j L\cosi{Ag1,m)cfR1~1c1~\ 4\ y 20 + A2COs2(A01,m)cf Rr'ci / 3 / / L|cos2(Ag1,m)cfRf1c1 \ 8 V V 20 + Â£lcos2(A0lim)c? R^ci / 3/_ / Tjcos^A^Jcf^ \ 8 \ y 20 + L|cos2(A0i,m)cf R^Ci / 34 The symbol error rate for 16-QAM in terms of is obtained by substituting (3.25) into (4.13). It is straightforward to show that for BPSK and QPSK we have PeBPSK ~ Q^ptfR-ip) (3.26) PeQPSK ~ 2q(Vp"R-ip) (3.27) by substituting Eqn. (3.24) in Eqns. (3.26) and (3.27). The probabilities of error for BPSK and QPSK in terms of Jmn are given as PeBPSK ~ Q (\/ j(3.28) \ y Jmin / PeQPSK ~ 2Q ((3.29) \ V Jmin J For a single user case, these results reduce to the well known results given below which are the same as the results shown in many digital communications books like [40] and [11]. pBpsK=Q{\fW) PeQPSK = For 16-QAM Am Assuming that the system is using Gray coding, the bit error rate (BER) is given by SER (3.30) (3.31) (3.32) BER log^M (3.33) 102 Figure 6.15: SINR and Total transmitted power of the PCA proposed in a slowly fading channel for 5 users, SINR = 10 dB, and power update every 10 symbols. Figure 6.16: SINR and Total transmitted power of the PCA proposed in a slowly fading channel for 5 users, SINR = 10 dB, and power update every 20 symbols. 105 process of the desired user fading need to be estimated. A tracking technique based on periodic pilot symbols and linear prediction was proposed to estimate the fading process of the desired user. The main reason for introducing pilot symbols here is to prevent the MMSE filter from feeding back the wrong decisions when the desired sig nal goes through a deep fade while the MMSE filter operating in the decision directed mode. In AWGN channel, 16-QAM modulation system was suggested to be the best choice out of the 3 modulation formats because of its ability to support more users. However, in a fading channel, if the fading process is known or the fading estimation error is very low, 16-QAM modulation should be employed. On the other hand, if the fading error estimation is high, QPSK modulation should be used since it is more robust for high estimation errors. The performance of the system in a fading channel with the previous modulation formats was investigated in Chapters 4 and 5. The inability of the present MMSE receiver structure to operate in a fading channel for one- and two-dimension was demonstrated. A general structure of the MMSE receiver which can perform effec tively for a wide range of modulation formats in a fading channel was proposed. For successful detection of the desired users signal, the phase and amplitude of the fading process of the desired user fading need to be estimated. A tracking technique based on periodic pilot symbols and linear prediction was proposed to estimate the fading process of the desired user. Theoretical BER performance bound for AWGN and fading channels for these modulation formats were presented. These bounds for a single user CDMA system found to be in agreement with the well know single user BER bounds in these en vironments. In addition BER bounds for the case when there is a phase offset in the desired user signal were derived and found to be in a greement with the previous results. 85 Figure 5.25: BER of QPSK with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg= 62, and fdTs = 0.0014. Figure 5.26: BER of QPSK with different predictor lengths (L); PSAM rate = 0.2, 30 users, pg= 62, and /Ts = 0.017. 23 to the algorithms presented in [35] and [36], the proposed PCA does not require the use of pilot symbols if a constant envelope modulation is used. The PCAs presented in this paper and the ones presented in [35] and [36] converge to the same transmitted power solution. The first task in this area of the research is to design a power control algorithm that can achieve a target SINR at the output of the receiver. A power control al gorithm which updates the power to converge to a target SINR value is proposed in Section 6.1. This algorithm is compared to two other algorithms based on the MMSE receiver presented in [36] and [35] respectively, in terms of the convergence of SINR and the total transmitted power. The capacity improvement realized by a system implementing the proposed PCA was compared to the theoretical bounds presented in [37] and [38] and was found to be in agreement with these capacity bounds for a large range of target SINR values. 47 Figure 4.2: The theoretical performance of BPSK, QPSK, and 16-QAM in a fading channel with 30 users with optimum MMSE receiver implementation Figure 4.3: The theoretical performance of QPSK and 16-QAM in a fading channel with 60 users with optimum MMSE receiver implementation. 90 large number of users and large processing gain) [37]. To facilitate comparison for the system with perfect power control, we assume that each user transmits with a constant power of A the average total transmitted power obtain from the proposed PCA. The proposed PCA based system was found to yield on average a capacity improvement of more than 20% over the system with perfect power control. The simulated capacity results, shown in Figure 6.1, were obtained by varying the number of the CDMA system users to find the maximum number of users that can be supported by the system using a blocking probability criterion of 0.01 Blocking is defined as a scenario in which the converged value of the SINR of any user, was less than 98% of the desired SINR; so that the capacity of the system is given by the maximum number of users that could be present in the system while satisfying the following performance criterion Pr(SINR < 0.98SINR) < 0.01 (6.8) The simulation results shown in Figure 6.1 are found to be in agreement with the theoretical capacity upper bound given in [38] and [37] by K < N(l + SINR; (6.9) despite the fact that, for the results shown in this section, short random sequences are used rather than optimal sequences as used in [38] or as asymptotic analysis using large number of users and large processing gain as in [37]. Figure 6.1 shows that for a practical system as considered in the simulation study (with finite number of users and reasonable length of processing gain) it is possible to attain the same capacity as the MMSE system with optimal signature sequence [38] or that with large spreading gain [37] for a wide range of SINR but at the expense of transmitting more power. This is further illustrated in Table 6.1 which shows the average total transmitted power, Pt, required to attain the capacities obtained by 44 The probability of symbol error for the 16-QAM is given by Pwqam ~ 3p 1 -p (4.21) For BPSK and QPSK modulation, the average symbol error rates can be derived in the same manner and they are given, respectively, by (4.22) (4.23) Assuming that the system is using Gray coding, the bit error rate (BER) is given by (4.24) These equations implicitly depend on the interfering user codes, delays, transmit ted powers, and fading amplitudes through the matrix R. To obtain an average value for SER or BER, one would average over these quantities. For the single user case, it is easy to show that these results reduce to the well known results shown in the digital communications literature [42] and [11]. To obtain these results, we have used the Gaussian approximation for the out put of the filter due to interference and noise. The justification for the Gaussian approximation is based on the central limit theorem by noting that the output of the filter is a sum of random variables with different probability density functions (pdfs). Therefore, the sum of these random variables at the output of the filter can be considered a Gaussian random variable. This approximation is widely used in evaluating conventional receivers [9]. Moreover this approximation is more accurate with the MMSE receiver since we have less interference at the output of the filter and more Gaussian noise [20]. Poor and Verdu in [41] have studied the behavior of the spread waveform unspread waveform 3 * t Tb * t Figure 1.1: Illustration of DS spread spectrum concept. 56 Figure 4.4: BER of QPSK and 16-QAM where (o, +, *,.) are based on Eqn. (4.72) and Eqn. (4.65) for 3 users. Figure 4.5: BER of QPSK and 16-QAM where (o, +, *,.) are based on Eqn. (4.72) and Eqn. (4.65) for 30 users. DESIGN ISSUES FOR MINIMUM MEAN SQUARE ERROR (MMSE) RECEIVER-BASED CDMA SYSTEMS By ALI FAISAL ALMUTAIRI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2000 I dedicate this work to my wife, Aisha, my daughters, Bashayer and Ohood, my mother and the rest of my family members. ACKNOWLEDGMENTS I would like to thank Professor William Edmonson and Professor Ulrich H. Kurzweg for serving as members of my committee. I would like to express my appreciation to Professor Tan Wong for his fruitful suggestions. I extend special thanks to my adÂ¬ viser, Professor Haniph A. Latchman, not only for his time, but also for his guidance throughout my studies with respect to both to research issues and to professional isÂ¬ sues. I would like to express my greatest appreciation to my adviser, Professor Scott L. Miller, for introducing me to this topic and advising me in the early stages of this project. I thank my family, my wife, Aisha, my lovely daughters, Bashayer and Ohood, my mother, and the rest of my family members, for their support, patience and encouragement throughout my studies. I also wish to acknowledge all of my friends at the University of Florida and elsewhere, especially my colleagues Dr. Brad Rainbolt and Dr. Ron F. Smith. I would like to thank Dave Tingling, Yassine Cherkaoui, and Sid Hassan for proofreading my dissertation. I would like to thank my friends at the LIST lab for their cooperation. I am grateful to many of my friends in Gainesville for their support. Finally, I acknowledge with gratitude the financial support and encouragement of iii Kuwait University. TABLE OF CONTENTS gage ACKNOWLEDGMENTS iii ABSTRACT vi CHAPTERS 1 INTRODUCTION 1 1.1 Direct Sequence Code-Division Multiple-Access Systems ... 1 1.2 IS-95 CDMA Standard 7 1.2.1 Channel Structure 7 1.2.2 Modulation and Coding 8 1.2.3 Power Control 12 1.3 The MMSE Receiver 14 1.4 Motivation and An Overview of the Dissertation and LiteraÂ¬ ture Review 16 2 SYSTEM MODEL 24 2.1 The Transmitter 24 2.2 The Receiver 25 3 MULTILEVEL MODULATION IN AWGN CHANNEL 30 3.1 Performance in A Gaussian Channel 30 3.2 Results 35 3.3 Summary 38 4 MULTILEVEL MODULATION IN A FADING CHANNEL .... 40 4.1 Performance Analysis 40 4.2 The Effect of Phase Offsets on the Performance of the System 46 4.3 Summary 57 5 FADING PROCESS ESTIMATION 58 5.1 The MMSE Receiver Behavior in A Fading Channel 58 5.2 Tracking Techniques in A Fading Channel 63 5.3 The Effect of the Fading Estimation Error on the Performance of the System 69 IV 5.4 The Effect of Pilot Symbol Rates on the Performance of the System 77 5.5 The Effect of the Linear Predictor Length on the Performance of the System 82 5.6 Summary 83 6 POWER CONTROL 87 6.1 Fully Distributed Power Control Algorithm 87 6.2 Numerical Results 89 6.3 Summary 103 7 CONCLUSION AND FUTURE WORK 104 7.1 Conclusion 104 7.2 Future Work 106 REFERENCES 109 BIOGRAPHICAL SKETCH 114 v Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DESIGN ISSUES FOR MINIMUM MEAN SQUARE ERROR (MMSE) RECEIVER-BASED CDMA SYSTEMS By Ali Faisal Almutairi May 2000 Chairman: Dr. Haniph A. Latchman Major Department: Electrical and Computer Engineering Code-division multiple-access (CDMA) technology has been the subject of a great deal of practical and theoretical research over the last decade. The adoption of the IS-95 standard, which is based on CDMA technology, has boosted research interest in this area. The minimum mean squared error (MMSE) receiver is a near- far resistant receiver that has attracted the interest of many researchers over the years. The popularity of the MMSE receiver is due to the fact that its performance is comparable to many complex multiuser receivers while its complexity is comparable to the conventional matched filter based receiver. This dissertation examines the benefits of using the MMSE receiver for the next generation of CDMA systems and how some aspects of the system can be redesigned or modified to improve the performance of the CDMA system in terms of bit error rate (BER) and capacity. This research will be targeting two areas of improvements, namely multilevel modulation and power control. vi The use of higher order modulation formats, like 16 Quadrature amplitude modÂ¬ ulation (16-QAM) and quadrature phase shift keying (QPSK), is investigated and compared to a binary phase shift keying (BPSK) based system in both additive white Gaussian noise (AWGN) and fading channels. One drawback was the inability of the MMSE receiver to perform properly in a more realistic wireless environment where fading is considered. This problem was investigated and a general MMSE receiver structure, which is capable of demodulating a wide range of digital modulation forÂ¬ mats, is proposed. It is shown that, in an MMSE based CDMA system, modulation format choice has a significant effect on the capacity of the system. The performance of such a system with the three different modulation formats mentioned previously was investigated. It is found that the 16-QAM outperforms BPSK and QPSK in AWGN and fading channels when the fading estimation error is very low for a highly loaded system. On the other hand, if the fading estimation error is high, QPSK modulation should be used since it is more robust for high estimation errors. The other area for improvement of the proposed system that has been investigated is the use of power control. It was found that the use of power control improves the performance of the MMSE receiver based CDMA system despite the fact the MMSE is known to resist interference by other users. A power control algorithm (PCA) which is based on the desired MMSE value of the user and which is capable of equalizing the output signal to interference and noise ratio (SINR) is proposed. The convergence of the algorithm in terms of SINR and total power is investigated. The implementation of the proposed PCA was found to improve the capacity of the system substantially. For example, The proposed PCA was shown to yield on average a capacity improvement of more than 20% over an MMSE based CDMA system with perfect power control where all users are received at the same power. Vll CHAPTER 1 INTRODUCTION Code-division multiple access (CDMA) has been the subject of extensive attenÂ¬ tion by the research community in the last two decades. Due to the existence of multiuser interference in CDMA systems, near-far resistant receiver structures for diÂ¬ rect sequence (DS) spread spectrum (SS) have been investigated thoroughly by the CDMA research community. The minimum mean-square error (MMSE) receiver is a near-far resistant receiver structure known for its acceptable performance and low complexity. In this research, the MMSE receiver is chosen to be the underlying receiver structure for our study of DS CDMA systems. IS-95 has been developed by QUALCOMM and adapted by the US Telecommunications Industry Association (TIA) as a standard for cellular CDMA systems. This dissertation revolves around the following idea: If the MMSE receiver is used as the underlying receiver for the next generation CDMA system, how can we redesign some aspects of the system and modify the current MMSE receiver to improve its performance as measured by bit error rate (BER), Signal to Interference plus Noise Ratio (SINR), and capacity? 1.1 Direct Sequence Code-Division Multiple-Access Systems Unlike other multiple-access techniques such as frequency division multiple-access (FDMA) and time division multiple-access (TDMA) where the channel is divided into subchannels and each user is assigned to one of the available subchannels, CDMA is a digital communication multiple access technique in which the channel is not partitioned in frequency or time but each user is assigned a distinct spreading sequence to access the channel. In general, in CDMA systems, spreading is accomplished by 1 2 either direct sequence (DS) or frequency-hopping (FH). In this work, we have chosen the first method as a means of spreading. The literature is rich in many outstanding papers about CDMA systems like ( [1], [2], [3],and [4]), to mention just a few. In DS CDMA, the data symbols of duration Ts of each user are multiplied by unique narrow chips of duration Tc. The chip rate is N times the symbol rate where N is the spreading gain. Figure 1.1 illustrates the DS-SS concept. In this figure, an unspread binary phase- shift keying (BPSK) signal of square pulses of duration Tb is shown. The signal has been spread by a spreading sequence of length N = 7. The result of the spreading is a signal with pulses of duration Tc = Tb/N rather than Tb. The power spectral densities (PSD) of the unspread and spread signal are shown here to illustrate the effect of the spreading on the signal bandwidth. The first null bandwidth of the unspread signal has expanded by a factor N as a result of the spreading process. It is desirable for the spreading sequences of all users to be approximately orthogoÂ¬ nal to minimize the multiple access interference (MAI) and hence enhance the receiver performance. This orthogonality is unachievable in practice for asynchronous commuÂ¬ nication systems. Due to their important role in the performance of CDMA systems, spreading sequences and their correlation properties are studied heavily in the literÂ¬ ature. M-sequences [5] are known for their autocorrelation properties. Gold [6] and Kasami [5] sequences represent a tradeoff of the desirable autocorrelation properties of M-sequences for improved cross-correlation properties. Kasami sequences are suÂ¬ perior to Gold sequences in cross-correlation performance but are fewer in number for a given sequence length. The cellular concept introduces the idea of replacing high-power large single cell systems with low-power small multiple cell systems that have the same coverage area and can support a much larger user population compared to the single cell systems with the same system bandwidth. Based on this concept, each base station is assigned spread waveform unspread waveform 3 â–² * t â–º Tb *â€¢ t NTc PSD Figure 1.1: Illustration of DS spread spectrum concept. 4 a set of radio channels which represents a portion of the total channels available to the entire system. Different sets of channels are assigned to the neighboring base stations. The same set of channels can be assigned to another base station provided that the co-channel interference is at a tolerable level. The use of the same frequency channels by several cells introduces interference to the signals that share this spectrum. This kind of interference is called co-channel interference. Unlike other type of channel impairments (thermal noise, fading and shadowing), the co-channel interference can not be overcome by increasing the transmitted power since this action will increase the co-channel interference for the other users. The use of the same channel set in another base station has resulted in a substantial increase in the capacity of the entire system. The concept of using the same channel sets at different cells is called frequency reuse. The design process by which channel sets are assigned to all the cells in the cellular system is called frequency planning. The frequency reuse factor represents the fraction of the total channels available in the system that may be used by an individual cell. A frequency reuse design which has 7 channel sets and a frequency reuse factor of 1/7, which is shown in Figure 1.2, is commonly used to describe these concepts. The channel sets are labeled A, B, C, D, E, F and G. The base station coverage areas are shown as hexagonal for simplicity. A cluster is a group of all channel sets and is shown in bold in the figure. The cluster in Figure 1.2 includes 7 cells. From the figure, one can see that the capacity of the system, which can be defined as the total number of active mobiles the system can support at a given time, is directly proportional to the number of times the cluster has been repeated in a coverage area. Therefore, the main objective of the designers of TDMA-based and FDMA-based cellular systems is to maximize the system capacity by providing spectral and geÂ¬ ographical separations, through the use of frequency reuse and frequency planning 5 Figure 1.2: Illustration of the frequency reuse concept. concepts. These separations will guarantee the reduction of the interference level and hence improve the system capacity. From the previous presentation, we see that in a traditional narrowband system based on TDMA and FDMA multiple access techniques, capacity is limited by the number of time slots or frequency channels available in the system for a given cell. In CDMA-based cellular systems, channel access is granted through codes, not frequency channels or time slots. Therefore, the loading of the system in terms of active users is not determined by the available frequency channels or time slots but rather by the level of interference the receivers at the base station can tolerate. Each mobile contributes a certain amount to the total interference experienced at the base station receivers. The amount of interference introduced by each mobile depends on the power level at which the signal is received at the base station and the cross-correlation value of its spreading sequence with the other usersâ€™ spreading sequences. A fundamental difference between CDMA-based cellular systems on one hand, and FDMA-based and TDMA-based cellular systems on the other hand, is that of interference elimination strategies. In CDMA based cellular systems, interference elimination is achieved through the choice of spreading codes with low cross-correlation, the use of very 6 tight power control, and the design of the receiver rather than the implementation of geographical and spectral separation as in FDMA-based and TDMA-based cellular systems. In this section, we have discussed some major aspects of the cellular concept that are relevant to the work presented in this dissertation. Other aspects of the cellular concept like handoff, channel assignment, and cell splitting are not discussed here and the interested reader is referred to [7] and [8]. From the previous presentation, it is clear that Multiple Access Interference (MAI) is the major limiting factor in the capacity of a CDMA based cellular system. ThereÂ¬ fore, the capacity can be improved by reducing the interference level. We will discuss some of the improvements that can be adopted to reduce the interference level and how they are related to the work presented in this dissertation. Due to the presence of the interference caused by other users, the matched-filter type receiver (which is optimum for a single user in an additive white Gaussian noise (AWGN) channel) performance degrades substantially. The performance of the conÂ¬ ventional receiver was analyzed in [9] and [10]. The major problem of the conventional receiver is its inability to mitigate what is called the near-far problem. The near-far problem occurs when the received signal of the desired user is overwhelmed by the interfering signals of the other users. To minimize the effect of the near-far problem in CDMA systems, researchers introduced what are called near-far resistant receivers. Among this class of receivers, the MMSE receiver has attracted the attention of many researchers due to its low complexity and superior performance. This receiver strucÂ¬ ture, as discussed in Section 1.3, can greatly affect the capacity of the CDMA system. The MMSE receiver can be described to a certain degree, as a near-far-resistant reÂ¬ ceiver. This capability of the MMSE receiver will substantially increase the CDMA system capacity. The MMSE receiver is an essential component in this research and is discussed in Section 1.3. 7 As it has been pointed out before, power control can greatly reduce interference and improve the system capacity by adjusting the transmitted power of the mobile users. In IS-95, power control is used so that the received signal strengths are about the same for all mobiles at the base stations. In this dissertation, we have introduced a power control algorithm that is capable of equalizing the output SINR and reducing the transmitted power for all the CDMA system users. The proposed power control algorithm is discussed in Chapter 6. Another avenue we have explored for reducing the interference is the idea of inÂ¬ creasing the CDMA system dimension, by choosing a higher level modulation format without increasing the bandwidth. This was accomplished by increasing the processÂ¬ ing gain (# of chips per symbol). This subject is treated in Chapters 3, 4, and 5 of this dissertation. 1.2 IS-95 CDMA Standard A CDMA cellular system was developed by QUALCOMM and adopted by the Telecommunications Industry Association (TIA) as a standard for digital cellular systems in 1992 under the name IS-95. We will study some aspects of IS-95 that are relevant to the work presented in this dissertation. Namely, we will discuss the channel structure, power control, and modulation and coding issues that are adopted in the IS-95. 1.2.1 Channel Structure The IS-95 CDMA system operates on the same frequency band as the Advanced Mobile Phone Systems (AMPS) with a 25 MHz channel bandwidth for the uplink (mobile to base station) and downlink (base station to mobile). The uplink uses the frequencies from 869 to 894 MHz, while the downlink uses the frequencies from 824 to 849 MHz. Sixty-four Walsh codes are used to identify the downlink channels. Long PN code sequences are used to identify the uplink channels. 8 The forward CDMA channel, shown in Figure 1.3, consists of 64 channels of which, 1 is a pilot channel, 1 is a synchronization (sync) channel, up to 7 are paging channels, and the rest are forward traffic channels. The pilot channel helps the mobile in clock recovery, provides phase reference for coherent demodulation, and helps in handoff decisions. The sync channel is used to provide frame synchronization. The paging channels are used to transmit control and paging messages to the mobile stations. The forward traffic channels are used by the base to transmit voice or data traffic to the mobile. The reverse CDMA shown in Figure 1.4 consists of access channels and reverse traffic channels. The access channels are used by the mobile to initiate a call with the base station. The reverse traffic channel transmits voice and data from the mobile to the base station. The blocks in Figures 1.3 and 1.4 will be discussed in the next subsection. 1.2.2 Modulation and Coding In this subsection, we will discuss the modulation and coding processes in the forward and reverse traffic channels as represented by the blocks shown in Figures 1.3 and 1.4 respectively. In IS-95, the modulation process is performed in stages. For the forward traffic channel, the data is grouped into 20 ms frames. The data then is convolutionally encoded by a rate 1/2 code. The code generators for the convolutional codes [11] and [12] are: g0 = [111101011] gi = [101110001] If the data rate is less than 9600 bps, the encoded bits are repeated until a rate of 19.2 Ksps is achieved. After convolutional encoding and repetition, interleaving is performed on the data. The main purpose of interleaving, as in any communication 9 Wo Pilot Channel: All 0â€™s 1.2288 Mops quadrature spreading W32 spreading Wp Wt Mops (a) MODULATION cos{2Tfct ) Sequence sin(2;z/c/) (b) QUADRATURE SPREADING Figure 1.3: Forward CDMA channel structure. 10 Access Primary, User k Long secondary CodeMask and To quadrature spreading User k Long CodeMask Figure 1.4: Reverse CDMA channel structure. system operating in a radio channel, is to eliminate the occurrence of blocks of error due to the fading effects on the transmitted signal. Because of interleaving, no adjaÂ¬ cent bits are transmitted near each other. This will result in different effects of the radio channel fading on these bits and therefore will randomize the errors caused by fading. In the forward traffic channel, a long pseudo-noise (PN) sequence is used to scramble the data output of the interleaver. After data scrambling, a power control bit is inserted every 1.25 ms. This represent 2 modulation symbols in every 24 moduÂ¬ lation symbols (about 8%). If a 0 is transmitted, the mobile is instructed to increase its transmitted power by 1 dB. If a 1 is transmitted, the mobile is instructed to lower its transmitted power by 1 dB. After these stages, the data stream is spread using 1 of 64 Walsh codes. These codes are orthogonal to each other and of length 64. Walsh 11 codes are generated based on a recursive generation of a Hadamard matrix as follows: Hi = 0 H2 = 0 0 0 1 h4 = 0 0 0 0 0 10 1 0 0 11 H2JV â€” Hjv Hjy nN Hjv 0 110 In the forward channel we need a 64 x 64 Hadamard matrix to provide the needed 64 Walsh codes to label the channels. Each row of this matrix represents a Walsh code. Each channel has a unique Walsh code. The all-Zero Walsh code is assigned to the pilot channel. The synchronization channel is assigned Walsh code number 32 (row # 32 in the H matrix). The lowest code numbers are assigned to the paging channel and the rest of the codes are assigned to the forward traffic channels. The I and Q signals of the data stream are spread by different PN spreading sequences. This procedure is called quadrature spreading and the spreading sequences are called pilot PN sequences. The binary outputs of the quadrature spreading are mapped to QPSK modulation where 00 maps to tt/4, 10 maps to 37r/4, 11 maps to â€”37t/4 and 01 maps to â€”7t/4. The reverse channel modulation process is shown in Figure 1.4. Many of the blocks in Figure 1.4 are the same as the ones shown in Figure 1.3 and will not be discussed again. The reverse channel uses a convolutional code at a rate 1/3 with code generators given by g0 = [101101111] gi = [110110011] g2 = [111001001] (1.2) 12 The 64-ary orthogonal modulation is a block of 64 Walsh codes. These are the same as the Walsh codes used in forward channel modulation but here they are used differently. Walsh codes in the reverse traffic channel are used to modulate the data stream out of the interleaver. Each six bits of data are mapped to one of the Walsh codes as shown in the following: 47 53 TÃ“ÃÃTT ÃToÃÃ“l > (CODE47) (CODE53) The role of the randomizer block is to remove the redundant data introduced by the code repetition block. The same pilot PN sequences used in the forward modulation and coding are used in the reverse channel to modulate the data in the I and Q channels. The data spread in the Q channel is delayed by 1/2 of a chip resulting in an offset quadrature phase shift keying(OQPSK) modulation. In this dissertation, we have compared the performance of BPSK, QPSK, and 16- QAM modulation formats in an MMSE receiver-based CDMA system in terms BER. We simply modulate the data stream using BPSK, QPSK, and 16-QAM modulation formats for comparison. Then the modulated signal is spread using a random spreadÂ¬ ing sequence. In IS-95, the data is processed before sending them in the channel as shown in Figures 1.3 and 1.4. 1.2.3 Power Control To eliminate the near-far problem and to reduce the interference level in a CDMA system, a fine power control is necessary for acceptable operation of the CDMA system. IS-95 supports open-loop power control and closed-loop power control. In open-loop power control, the mobile user attempts to control its transmitted power based on the received signal strength. In closed-loop power control, the base station sends power control messages to the mobile user to adjust its transmitted power once every 1.25 ms. The base station transmits power control bits for every mobile user 13 in the forward traffic channel. When a mobile user receives a power control bit it increases or decreases its power by 1 dB according to the value of the power control bit (0=increase, l=decrease). For the mobile user to access the reverse channel, it must do so with the following initial power in the access channel: Paccess [dBvn) â€” Pmean T Pnom, T Pcorr 73 (13) where Paccess = The initial access power in the access channel, Pmean = The mean input power of the mobile transmitter (dBm), Pnom = The nominal correction factor for the base station (dB), Pcorr = The correction factor for the base station from partial path loss (dB). Power in dB = 10log10(actual power in watts). Power in dBm = 10 log10 (actual power in watts) = 3Q + power in dB If the mobile user attempting to access the reverse channel is unsuccessful, the mobile will increase its transmitted power by a defined increment called the Power Step (Pstep) and try again. This process continues until the access attempt is successÂ¬ ful or the mobile reaches the maximum allowed number of attempts. When granted access to the reverse traffic channel, the mobile station transmits with initial power Pj(dBm) = Paccess + Sum of all access corrections (1.4) When the communication with the base station is established, the base station sends a power control bit to adjust the power of the mobile station transmitted signal. These adjustments are in increments of ldB. When the power control bit is 0, the mobile station transmitted power increases by 1 dB. When the power control bit is 1, the mobile station transmitted power decreases by 1 dB. After these closed-loop 14 power updates, the mobile station transmitted power is given by Preverse {dBm) â€” Pj + The sum of the closed loop updates (1.5) The maximum value of the sum of the closed-loop updates is Â±24dB. A typical set of ranges and values for the parameters in the previous equations are -8 < Pnom < 7dB (1.6) A typical value of Pn0m is 0 dB. -16 < Pcorr < 15dB (1.7) A typical value of PCOrr is 0 dB. The values of these parameters for each base station are transmitted on the forÂ¬ ward channel in a message called the access parameters message. In Chapter 6, we introduce a power control algorithm that can be used to adjust the mobile station transmitted power in a closed loop power control fashion. The power control presented in Chapter 6 does not update the transmitter power in conÂ¬ stant steps of Â±1 dB like the IS-95 but with variable steps that are dependent on the channel condition and the MMSE receiver filter coefficients. Chapter 6 of this dissertation has been devoted to the power control issue in MMSE receiver based CDMA. 1.3 The MMSE Receiver To improve the performance of the CDMA system in the presence of MAI, and to mitigate the near-far problem, several receivers with different degrees of complexity and performance have been developed. For example, an optimum multi-user receiver is presented in [13]. The complexity of this receiver increases exponentially with the number of users. A suboptimal class of detectors with linear complexity are 15 Figure 1.5: The MMSE receiver. presented in [14], [15],and [16]. Although they show linear complexity, these suboptiÂ¬ mum receivers still require a great deal of side information. The MMSE receiver is a suboptimum receiver which is known to be near-far resistant. In addition, the MMSE receiver does not need to know certain side information like the code sequence and the carrier frequency of the desired user. This information can be obtained through adequate training if the MMSE is implemented in its adaptive form. Adaptive algoÂ¬ rithms such as the least-mean-square (LMS) and recursive least-square (RLS) can be used to obtain the tap weights of the filter. The performance of the MMSE receiver in an AWGN is presented in [17], [18], [19], [20],and [21] and in a fading channel in [22], [23], [24], [25] and [26] for multiuser and [27] for a single user environment. To understand the advantages of the MMSE receiver, we need to describe briefly how it works. The MMSE receiver is shown in Figure 1.5. The received signal which consists of the desired userâ€™s signal, MAI, and Gaussian noise is fed at the chip rate into the equalizer until the N-tap delay line becomes full. After one symbol time, the equalizer content is correlated with the tap weights, a, and the result of this correlation is used 16 to make a decision about which symbol was sent. These tap weights are updated every symbol interval to minimize the mean square error between the output of the filter and the desired output. In practice, the filter is trained for a reasonable period of time by a known training sequence to reach a tap weight vector that is close to the optimum weights. After the training period, the receiver switches to decision feedback mode. It has been shown in [22] that the decision directed mode proves to be troublesome in a fading channel. In deep fades, with the MMSE structure shown in Figure 1.5, incorrect decisions being fed back to the receiver cause the MMSE receiver to lose track of the desired signal. A modified MMSE receiver structure to overcome this problem was described in [22] for a BPSK modulation format and it has been generalized in [24], It should be noted that the IS-95 standard uses a conventional matched filter based receiver where the coefficients of the filter are matched to the desired userâ€™s spreading sequence. The matched filter structure is optimum for a single user environment. When this structure is employed in a multiuser system, it degrades rapidly due to the presents of MAI. 1.4 Motivation and An Overview of the Dissertation and Literature Review This section presents a review of the design issues that we are researching and a layout of motivations for our research in this dissertation. As has been stated before, this research project revolves around the following question: If the MMSE receiver is used as the underlying receiver for the next generation CDMA system, how can we redesign some aspects of the system and modify the current MMSE structure to improve the performance of the CDMA system in terms of the system capacity, SINR, and BER? The motivation behind this research is that given the advantages of the MMSE receiver presented in the previous section, one would expect superior performance of a CDMA system based on the MMSE in comparison to that of a CDMA system based on the current conventional receiver, and hence, the MMSE 17 receiver could be a good candidate to be implemented in the next generation of CDMA systems. This research will be targeting two areas of improvements. The first is multilevel-modulation and the second is power control . The first area to be investigated in this research is multilevel modulation. TradiÂ¬ tionally, higher level modulation has been used to achieve higher bandwidth efficiency (# of information bits transmitted in a given bandwidth). The price for the higher bandwidth efficiency is paid in terms of the required SINR to achieve the same error probability. In cellular systems, the main objective of the system designers is to inÂ¬ crease the system capacity for a given quality of service and limited resources such as bandwidth. In the literature, BPSK and sometimes QPSK are used as modulation formats for the MMSE receiver. As noted in [18], if BPSK is used, the MMSE receiver becomes interference limited when the loading of the system becomes high enough and close to the processing gain. This threshold is reached because of the imperfect cancellation of the Multiple Access Interference (MAI) due to the lack of dimensions in the system. One way to improve the performance of the system is to introduce more dimensions while keeping the bandwidth the same to help in suppressing the MAI. To achieve that, one can choose a higher order modulation format like MPSK or 16-QAM to increase the processing gain (# of chips per symbols). The justification for increasing the processing gain for the system employing higher order modulation is presented in the following example. In an unspread system, for the same bit rate, using QPSK will result in using half the bandwidth required of a BPSK system, while using a 16-QAM will result in using one fourth of the bandwidth required by a BPSK system. In a CDMA system, to utilize the total available bandwidth when higher order mosulation formats are used, the spreading gain of the QPSK system should be twice that of the BPSK system and the spreading gain of the 16-QAM system should be 4 times that spreading gain of the BPSK system. 18 Throughout this dissertation, we have used random sequences with spreading gains of 31 for the BPSK system, 62 for the QPSK system, and 124 for the 16-QAM system to utilize the whole available bandwidth. If m- , Gold, or Kasami sequences were used, we would not be able to choose a processing gains of 62 and 124 since the processing gain of these sequences is given by 2â€ â€” 1 where n is the number of stages of the shift register used to generate such sequences. By adopting a higher order modulation and increasing the processing gain , the MMSE receiver has been moved out of the interference limited region and can restore its ability to suppress more interference than the original system. Since the receiver now is operating in the interference resistant region, one can increase the transmitted power to obtain a higher SINR for acceptable performance. Increasing the transmitted power will increase the interference level and hence will degrade the performance of a conventional receiver-based CDMA system. On the other hand, the MMSE receiver, with the increased processing gain, will perform as a near-far resistant receiver and the increased interference level will be alleviated. Furthermore, if increasing the transmitted power is not desirable, one can resort to combined modulation and coding in the form of trellis-coded modulation (TCM). Milstein and Shamain studied the performance of QPSK and 16-QAM modulation formats in a multipath and narrowband Gaussian interference (NGI) environment, in [25] and [26] for single or two user systems. They show that when the multipaths cause significant interstmbol interference (ISI), with or without NGI, the 16-QAM system outperforms the QPSK system. In both papers, the desired userâ€™s fading is assumed to be known and an optimum MMSE receiver is used. In our research, we have shown the improvement of the system performance in terms of BER and capacity when higher order modulation is used. In addition, we have investigated the performance of the system in a fading environment with optimum or adaptive implementation of the MMSE receiver for different system loadings. Furthermore, we 19 have investigated the case when the desired userâ€™s fading is unknown to the receiver or it has been estimated inaccurately. The details of our results in this area are presented in [24], [23], and Chapter 3, 4, and 5 of this dissertation. In Chapter 3, the performance, in terms of BER and system loading, of an MMSE receiver based CDMA system with different modulation formats, namely, BPSK, QPSK, and 16-QAM, was investigated in AWGN channels. Based on BER perforÂ¬ mance, it has been found that for a lightly loaded system BPSK outperforms QPSK and 16-QAM. For a moderately loaded system QPSK outperforms BPSK and 16- QAM. For a highly loaded system, 16-QAM outperforms BPSK and QPSK. These results are shown in [23]. The use of multi-level modulation formats, like 16-QAM, leads to some interestÂ¬ ing research problems. As with unspread systems, any time a multilevel modulation format is used in a fading channel, it becomes necessary to carefully track the phase and amplitude of the desired userâ€™s fading process in order for the receiver to demodÂ¬ ulate the desired userâ€™s signal successfully. Channel tracking through the use of pilot symbol assisted modulation (PSAM) has been proposed, in single user system, as a mean to estimate the fading process and mitigate its effects at the receiver by several authors [28], [29], [30], and [31]. In PSAM, pilot symbols are inserted periodically into the data stream. Channel estimates are obtained using Gaussian interpolation [30], Wiener filtering interpolation [28] , or sine interpolation [31]. One needs to notice that there is always a delay associated with the use of PSAM since the demodulator has to receive a certain number of pilot symbols to estimate the fading process. This estimation technique can not apply directly to the MMSE receiver since this receiver updates its tap weights every symbol based on the demodulation of the previous symbol. Furthermore, linear prediction has been used to obtain estimates of a fading proÂ¬ cess for a single user system in [32] and for multiuser systems in [22] and [24]. As 20 described in [22], Linear prediction of the desired userâ€™s fading is performed by using the outputs of the MMSE filter from past symbol intervals. This technique can lose track of the fading process due to the aburst of decision errors as pointed out in [33] and [24]. In [24], we have shown that a combination of PSAM and linear prediction can effectively track the fading process of the desired user. The use of pilot symbols has been proven to be beneficial in preventing the MMSE receiver from feeding back unreliable decisions when it is operating in its decision directed mode while the desired user signal is going into a deep fade. Traditionally, pilot symbols are used in a single user environment to obtain an estimate of the fading process, but there is a delay associated with their use since the detector needs to detect many pilot symbols to form an estimate of the fading process. In this research, the main reason for using pilot symbols is to prevent the MMSE receiver from feeding back the unreliable decisions. In Chapters 4 and 5, the study of the performance of the system in Chapter 3, for which an AWGN channel model was used, is extended to a fading channel to represent a more realistic model for wireless communication systems. The use of mulÂ¬ tilevel modulation, like 16-QAM, in a fading environment introduced an interesting problem, namely, tracking the channel variation to be able to demodulate the deÂ¬ sired user signal. The behavior of the MMSE receiver structure, shown in Figure 1.5, in a fading channel with 16-QAM modulation was studied. It was found that the MMSE receiverâ€™s present structure performs poorly in a fading channel. A general MMSE receiver structure which can be used in a fading environment to demodulate the desired userâ€™s signal effectively was proposed. The performance of the different modulation formats in terms of BER was analyzed and theoretical BER bounds for, BPSK, QPSK, and 16-QAM in multiuser systems operating in a fading environment were derived. The performance in terms of BER under different loads of the three modulation formats were compared in a fading environment. 21 To improve the poor performance of the MMSE receiver in a fading channel, we proposed a tracking scheme which is based on the use of both periodic pilot symbols (PPS) and linear prediction. The introduction of PPS helps to improve the performance of the MMSE receiver in two ways. First, and more important, the pilot symbols provide the receiver with a reliable reference when it operates in a decision directed mode. Second, the pilot symbols might be used to get channel estimates. The effect of the estimation errors, which results from inaccurate estimation of the fading process, on the performance of the 16-QAM and QPSK systems is investigated. Theoretical bounds based on the BER when there is a phase offset due to imperfect estimation of the desired signal phase were derived. The effects of the PSAM rate and the linear predictor length (L) values on the estimation error and on the performance of the system in terms of BER were investigated. In Chapter 6, The power control improvement area was investigated in AWGN and fading channels. The main reason for using power control in a conventional receiver based DS-CDMA system is to combat the near-far problem which occurs when an undesired userâ€™s signal over-powers the desired userâ€™s signal. The MMSE receiver is known to be near-far resistant but power control can still be used to reduce multiuser interference, increase the system capacity, compensate for channel loss, reduce the transmitted power and hence prolong the battery life. As shown in [20], the MMSE receiver can achieve many of the performance meaÂ¬ sures of other multi-user receivers performance without the need for side information like user sequences, clock offsets, and the received powers of all the interfering signals. This receiver offers a strong potential for capacity improvement over a conventional receiver-based CDMA system. In a conventional receiver based system, the transmitÂ¬ ted power of the mobile user must be tightly controlled so that the received powers of all users are very close to be equal. This type of power control which equalizes the received powers does not guarantee the equalization of the SINRs at the output 22 of the matched filter receiver and hence, users may experience an unequal quality of service (QoS). On the other hand, consider the MMSE receiver based CDMA system. Since the MMSE receiver is near-far resistant, the SINR at the output of the MMSE receiver is largely independent of the variation of the received powers of the other users. Therefore, a mobile unit can adjust its transmitted power to achieve a target output SINR without affecting the other usersâ€™ output SINRs. For example, a reÂ¬ ceiver experiencing a low SINR can instruct the corresponding transmitter to increase its transmitted power without having much effect on the other usersâ€™ output SINRs. Likewise, a receiver enjoying a high SINR can instruct the corresponding transmitter to decrease its transmitted power to conserve battery life without having much of an effect on the other usersâ€™ output SINRs. Our results in Chapter 6 and in [34] show that the blockage based system capacity of an MMSE receiver based CDMA system can be improved substantially by applying such a power control algorithm. The major problem with many of the power control techniques presented in the literature is their need, with varying degree, for side information such as channel gains, spread sequences, bit error rate, received powers and the SINRs of all users. The power control algorithm (PCA) proposed in [35] uses measurements of the mean- squared error (MSE) which require knowledge of the actual transmitted symbols. This makes it hard to implement in a fading channel since in deep fades the symbol estimates out of the decision device of the receiver are unreliable [22] and [24]. Both the power algorithms proposed in this paper and the one proposed in [36], do not use the MSE measurements. To implement the algorithm presented in [36], a sample average of the the output of the MMSE receiver is required to provide an estimate of the interference to update the power. In addition, the channel gain of the desired user needs to be estimated. The PCA proposed in Chapter 6 does not require knowledge of the interference caused by other users. Indeed, only one parameter which includes the channel gain of the desired user needs to be estimated.'Additionally, in contrast 23 to the algorithms presented in [35] and [36], the proposed PCA does not require the use of pilot symbols if a constant envelope modulation is used. The PCAs presented in this paper and the ones presented in [35] and [36] converge to the same transmitted power solution. The first task in this area of the research is to design a power control algorithm that can achieve a target SINR at the output of the receiver. A power control alÂ¬ gorithm which updates the power to converge to a target SINR value is proposed in Section 6.1. This algorithm is compared to two other algorithms based on the MMSE receiver presented in [36] and [35] respectively, in terms of the convergence of SINR and the total transmitted power. The capacity improvement realized by a system implementing the proposed PCA was compared to the theoretical bounds presented in [37] and [38] and was found to be in agreement with these capacity bounds for a large range of target SINR values. CHAPTER 2 SYSTEM MODEL In this chapter, a general CDMA system model, shown in Figure 2.1, based on the MMSE receiver is described. The model here will be flexible and easy to modify to accommodate the study of different issues concerning the MMSE receiver based CDMA system design. For example, when we study the performance of the system in AWGN channel, we can simplify the model by setting the fading amplitude to 1 and the fading phase to zero. The system consists of K users transmitting asynchronously over an AWGN channel or Rayleigh fading channel. The received signal, which consists of the desired user signal, interference from other user signals, and AWGN, is demodulated using the MMSE reciever. In the following sections, the transmitter and the receiver, shown in Figures 2.1 and 2.2, will be described. 2.1 The Transmitter There are K transmitters, one for each user, in this system. In this dissertation, the transmitter, shown in Figure 2.2, uses either a BPSK, QPSK, or 16-QAM. Each user is assigned a unique random spreading waveform cÂ¿(Ã). The modulated signal of the jth user can be written as Sj(t) = Re {y/2pjdj(t)cj(t)e*Wot} (2.1) = Re {9j{t)eJWot} where w0 is the carrier frequency which is the same for all users, gj(t) is the comÂ¬ plex envelope of Sj(t), Pj is the transmitted power, and dj(t) is a complex baseband signalling format with symbol interval Ts. The waveform Cj(t) is assumed to be in the polar form with chip interval Tc. Therefore, the processing gain N is equal to 24 25 Figure 2.1: System Model Cj(t) -fipjÃ±nÃ.wj) Figure 2.2: Transmitter of the jth user Ts/Tc. Throughout this dissertation, user 1 is considered the desired user unless specÂ¬ ified otherwise. We are interested in demodulating its signal and the other users are treated as multiple access interefernce. 2.2 The Receiver After going through the communication channel, the bandpass received signal at the receiver corresponding to the jth user is given by K r(t) = Re{J2 VKjOijity6^ gj(t - Tj)e]Wot} + n{t) j=i (2,2) 26 2cos(w0p -2sin (wat) Figure 2.3: The receiver where is the channel gain of user j to the assigned base station of user i. The variables rÂ¿, aq, 9j are the propagation delay, and the amplitude and phase of the fading process for the jth user respectively. The process n(t) is a real AWGN process with a spectral density of Na/2. The fading amplitude is Rayleigh distributed while the fading phase is uniformly distributed. The desired user propagation delay is assumed to be 0. In addition, it is assumed that the fading process of each user varies at a slow rate so that the amplitude and the phase of the fading process can be assumed constant over the duration of a symbol. The front-end part of the receiver, which is shown in Figure 2.3, consists of an in-phase (I) and a quadrature (Q) components. First, the bandpass received signal is shifted to baseband. Then, each component goes through a chip-matched filter with a scale factor of V2TC. The output of the chip-matched filter is sampled every Tc seconds. At the nth chip time, the output of the receiver front end consists of the received complex signal sample of r(n) = rÂ¡(n) + rq(n). These samples are fed at the chip rate to the MMSE receiver (the receiver is shown in Figure 1.5) until the N-tap delay line becomes full after one symbol time. The contents of the equalizer are given by 27 K r 'i{m) = ^2 yjPj(m) \fhijOLj(m)eJ^'(m)dj6) j=i (2.3) + n(m) In the above equation, t,- = ljTc + where lj is an integer and 0 < 6j < Tc. The vectors f) and g) are defined as follows fj{U) 1 c i - i) + (i <5 ' TÂ¿. W-t) i)(l,S) = i(N - l - 1) + (l - T) gj(JV - I) where tj(0 = (cf +if )/2 g,(i) = (c<'>-cf)/2 (l) / \'J \Cj,Nâ€”li Cj,Nâ€”l+1) Cj,Nâ€”1) Cj, 1) â€¢â€¢â€¢> Cj,Nâ€”lâ€”1/ Cj ( Cj,Nâ€”h Cjtpjâ€”i+i) Cj,Nâ€”l i ^j,0) Cjji, C^jvâ€”Ãâ€”l) Equation 2.3 can be written in a compact form as rÂ¿(m) = y/pi(m) \[h~aOLj (m)e8j (m) dÂ¿(m)cÂ¿ + MAI + n(m) (2.4) and MAI = y^aj(m)eJA(^) y/Pj(Â«)y/h^dj(n)fj(l, S) + ^(n - l)y^dj(n - l)gÂ¿(/,Â¿) L In eqn. (2.4), n(m) is a vector of independent complex Gaussian random variables with zero mean and the variances of the in-phase and the quadrature components are 28 equal to N0/2TC. The output of the MMSE receiver filter corresponding to the _?th user is Zi(m) = wÂ¿(m)jfÃrÂ¿(m) (2.5) where wÂ¿ is the filter coefficients that correspond to *th user received signal. These coefficients are adjusted by an adaptive algorithm, like the LMS and RLS algorithms, to minimize the mean squar error J(w) which is given by J(w) = E[\e{m)\2] (2.6) Initially, the MMSE receiver works in a training mode. In this mode of operation, a known data squence is sent by the transmitter and this sequnce is used as a reference for demodulated desired userâ€™s data. When the variable J reaches an acceptable value, the MMSE receiver switches to decision directed mode. The error, e(m), in a training mode is given by e(m) = di(m) â€” Zi(m) (2.7) In a decision directed mode di(m) is substituted by the decision di(m). The mean square error, J is shown in [39] to be a quadratic function of the filter coefficients and is given by J(w) = E[di(m)2] - Pf w - w^Pj + whRw (2.8) Where R is the autocorrelation matrix of the equalizer contents, R = E [r(m)r(m)Hj and PÂ¿ is a correlation between the desired user response and the received signal and given by Pi = E [d*(m)r(m)]. The minimum mean square error, JmÂ¿n, is achieved when the tap weights are the optimum weights. These optimum weights are obtained by differentiating equation 2.8 with respect to w and equating the result to zero. This will result in a form of 29 the Wiener Hopf equation and the optimum vector of the filter coefficients is given by Wj = R_1PÂ¿ (2.9) The value of Jmjm can be obtained by substituting the optimum vector of the filter coefficients given by Eqn. 2.9 in Eqn. 2.8. This will result in Jmin = - PfR_1Pj (2.10) where a2~ is the variance of the data symbols. Although the optimum tap weights force the MMSE receiver to operate at Jmin, these weights are hard to obtain in practice due to the unavailability of the autoc- corelation matrix. Adaptive algorithms like the Least- Mean-Square (LMS) and the Recursive Least-Square (RLS) are used to drive the filter coefficients close to the optimum tap weights. In this dissertation, the LMS will be used as the adaptive algorithm in the MMSE receiver unless specified otherwise. CHAPTER 3 MULTILEVEL MODULATION IN AWGN CHANNEL The goal of this chapter is to investigate the performance of the MMSE receiver with BPSK, QPSK, and 16-QAM modulations in an AWGN channel. These different modulation formats were compared based on their BER performance at different loadings of the MMSE based CDMA system. It should be noted that in this dissertation, we simply modulate the data stream using BPSK, QPSK, or 16-QAM modulation formats for comparison. Then the modÂ¬ ulated signal is spread using a random spreading sequence. We do not use any type of channel coding. In IS-95, the data is processed (by coding and interleaving) and then modulated using a QPSK as shown in Figures 1.3 and 1.4. 3.1 Performance in A Gaussian Channel In this section, we modify the model presented in Chapter 2 to study the perÂ¬ formance of the CDMA system using different modulation formats in a Gaussian channel. This can be done by setting the amplitude and phase of the fading process to 1 and zero in Equation (2.3) respectively. In addition, assume hik = 1 and that user 1 is the desired user and the integrator in front of the MMSE receiver has a scale factor of y/2piTc associated with it. Based on these assumptions, we can rewrite Equation (2.3) as K r(m) = dx(m) Ci + 3=2 dj(m)ij{l,S) + dj(m - l)gj(Â¿,Â¿) n(m) (3.1) Where n(m) consists of independent zero-mean complex Gaussian random variables whose real and imaginary parts have variances of plsf/No) â€™ w^ere IS the average 30 31 energy per symbol. The probabilities of error for 16-QAM, QPSK, and BPSK are derived below. r(m) can be written in the form r(m) = di(m)ci + ?(m) (3.2) Since E [did{] = 1, the correlation vector P, the autocorrelation matrix R, and the tap weights vector a can be written as follows (dropping the dependence on m for convenience): P = E [djr] = E[\d1\2]cl (3.3) = Ci R = E[\d1\2] Clc[ + R h ~ (3-4) = pph + r and the tap weights vector, a, given in terms P and R by a = R-1P (3.5) where R â€” E [r?H] .The output of the filter can be written as 2 = afir (3.6) = diP^R^P + PHR-1r (3.7) = dx P^R-'P + Ã± (3.8) Now we need to find the value of P^R^P and the variance of Ã±. Using the matrix- inversion lemma, we can find the inverse of R as follows: R"1 RT1 + R_1P(1 + PiiR-1P)_1PiiR_1 - . R_1PPhR_1 R1 + = (1 -bP^R-iP)-1 (3.9) (3.10) 32 If we multiply both sides of eqn. (3.10) from the left by and the left by P and simplify the result we will get PhR-1P pffR-ip l + ptfRip (3.11) Now, we need to find the variance of the term Ã± Ã± = P^R-1? (3.12) E[Ã±Ã±H] = P^R^Efrf^jR^P (3.13) = PhR_1RR_1P (3.14) We can find P^R 1 by multiplying both sides of eqn. (3.10) by PH. This results in P^R1 P^R'1 = 1 + PifR1P (3.15) in a similar manner, we can find R *P by multiplying both sides of Eqn. (3.10) by P. This result in R-1P - R-*P l + P^Rip Substituting Eqns. (3.15) and (3.16) into (3.14), p/ip-ip E [Ã±Ã±H] [1 + P*R-1P]â€˜ Then Eqn. 3.8 can be written as r P^R^P n 2 1L i nffp-ipJ + iV/(^0, + Nq fo, 1 + PHR_1P 1 P^R^P 2 [1 + pffR-ip]2 1 P^R^P 2 [l + P^R-ip]: (3.16) (3.17) (3.18) 33 Having the output of the filter z in this form, it is straightforward to show that the probability of symbol error is given by [40] PeUQAM where p ~ Q pffR-ip where the Q-function is defined as OO X (3.19) (3.20) (3.21) Equation (3.19) implicitly depends on the interfering users codes, delays, and transÂ¬ mitted powers, through the matrix R. To obtain an average value for SER, one would average Eqn. (3.19) over these quantities. The symbol error rate (SER) can be related to Jmin by recalling (2.10) and recognizing that cr2- = 1. di Jmin = 1 - P^R XP (3.22) substituting (3.11) into (3.22) Jmin Eqn. 3.23 can be written as 1 PgR~1P l + P^R-T 1 l + P^R XP P^R^P 1 Jmir Jmin then P can be written as P q( 1 Jmin 5 Jmin (3.23) (3.24) (3.25) 34 The symbol error rate for 16-QAM in terms of is obtained by substituting (3.25) into (4.13). It is straightforward to show that for BPSK and QPSK we have PeBPSK ~ Q (3.26) PeQPSK ~ 2q(Vp"R-ip) (3.27) by substituting Eqn. (3.24) in Eqns. (3.26) and (3.27). The probabilities of error for BPSK and QPSK in terms of JmÂ¿n are given as PeBPSK ~q(\â€”â€”jâ€”(3.28) PeQPSK ~ 2Q (m^N) (3.29) For a single user case, these results reduce to the well known results given below which are the same as the results shown in many digital communications books like [40] and [11]. pâ€™BpsK=Q{\fW) PeQPSK = For 16-QAM -Â«m Assuming that the system is using Gray coding, the bit error rate (BER) is given by SER (3.30) (3.31) (3.32) BER log^M (3.33) 35 Figure 3.1: Theoretical performance of BPSK, QPSK, and 16-QAM in a Gaussian channel with one user. where M is the number of points in the constellation. For BPSK, QPSK, and 16- QAM, M equals 2, 4, and 16, respectively. The justification for the Gaussian approximation is based on the central limit theorem by noting that the output of the filter is a sum of random variables with different probability density functions (pdfs). Therefore, the sum of these random variables at the output of the filter can be considered a Gaussian random variable. This approximation is widely used in evaluating conventional receivers [9]. This apÂ¬ proximation is more accurate with the MMSE receiver since we have less interference at the output of the filter and more Gaussian noise [20]. Poor and Verdu in [41] have studied the behavior of the output of the MMSE receiver and found that the output is approximately Gaussian in many cases. 3.2 Results Figures 3.1, 3.2, and 3.3 show the performance of the MMSE receiver with BPSK, 36 Figure 3.2: Theoretical and simulation performances of BPSK, QPSK, and 16-QAM in a Gaussian channel with 20 users. QPSK, and 16-QAM in a Gaussian channel for 1-, 20-, and 50- user CDMA systems. The theoretical results are based on the BER equations obtained in the previous section. The processing gains are 31, 62, 124 for BPSK, QPSK, and 16-QAM reÂ¬ spectively. These processing gains were chosen to ensure the full use of the available bandwidth by these systems. We will use these values of processing gains for the modulation formats for the rest of the dissertation. For the single user case the results are the same as the results found in the digital communication literature, for example [11]. For a single user system, the bit error rate is the same for BPSK and QPSK and lower than that of 16-QAM for a given ^. When the load of the system increases to 20, the QPSK-based CDMA systems outperforms the BPSK and the 16-QAM systems. The rate of improvement is faster for QPSK than for BPSK as the ^ increases. On the other hand, the 16-QAM sysÂ¬ tem starts about 1 dB worse than BPSK but at about ^ = 12 dB the 16-QAM BER becomes lower than that of BPSK for a given With the load further increased to 37 Figure 3.3: Theoretical performance of BPSK, QPSK, and 16-QAM in a Gaussian channel with 50 users. 50 users, both BPSK and QPSK will reach a point at which the bit error rate will become invariant to the increase in That basically means we can increase the load of the system by increasing the length of the processing gain but not increasing the bandwidth or information rate by simply going to a higher order modulation. Therefore, there is a tradeoff between the information rate and higher load for mulÂ¬ tilevel modulation. We can explain the behavior of the MMSE in these figures as follows: When the CDMA system is using BPSK, at some loading point, the MMSE will not have enough dimension, provided by the processing gain, to suppress all the interfering users. At this point, the MMSE receiver becomes interference limited, like the conventional matched filter receiver, and the performance cannot be increased by simply increasing the transmitted power. One way to overcome this is to increase the processing gain. To do so while keeping the bandwidth and information rate the same, one should choose a higher order modulation. In our case, QPSK would be 38 the choice for a moderately-loaded system and 16-QAM would be the choice for a highly-loaded system. Figure 3.2 compares an LMS based MMSE receiver system performance for 20 users with the theoretical results given in the previous section. The figure shows a very good agreement between the simulation and the analytical BER for the different modulation schemes. Figure 3.4 shows how the different modulation format systems deal with the near- far problem. The interfering signal received powers were modeled as lognormal distriÂ¬ bution. In this case, the standard deviation ap (dB) of the interfering signal received powers is varied while ^ is 5 dB for 30 users load. It is clear from the figure that, at this load, The MMSE receiver with the BPSK modulation format is not near-far resistant anymore. The QPSK and 16-QAM based MMSE receiver systems are actÂ¬ ing as near-far resistant. Clearly, at this level of loading, one should choose a higher order modulation format to restore the near-far resistance of the MMSE reviver. If the system loading is increased to a higher level, one would expect the QPSK based system to lose its near-far resistant property. 3.3 Summary This chapter examines the effect of using higher order modulation formats in the performance of MMSE receiver based CDMA systems in terms of bit error rate (BER) at different loading levels in (AWGN). The performance of BPSK, QPSK, and 16- QAM modulation formats are compared and analysed. In addition, simulation results are presented in terms of the bit error rates for these different modulation formats. A comparison of the rejection of the near-far effects for each modulation scheme is also presented. Under a very high loading level, 16-QAM outperforms QPSK and BPSK for identical bandwidth and information rate while, at a moderate loading levels, QPSK represents the best option. 39 (X LU m 10 -2 I X o X o * Â» o X * * * * * 0=BPSK *=QPSK X=16QAM 0 3 6 9 12 15 18 opm Figure 3.4: BER of QPSK, BPSK, and 16-QAM as a function of near-far ratio for 30 users. CHAPTER 4 MULTILEVEL MODULATION IN A FADING CHANNEL In this chapter, we will extend the work of the previous chapter by investigating the performance of the 3 modulation formats, namely, BPSK, QPSK, and 16-QAM, in a fading channel. These different modulation formats are compared based on their BER performance at different loadings of the MMSE based CDMA system. The results presented in this chapter are based on the assumption the the optimum implementation of the MMSE filter has been used. 4.1 Performance Analysis In this section, we will provide a performance analysis, both analytically and through simulation when a multilevel modulation schemes, like QPSK and 16-QAM, are used in a fading channel. In this section, the optimum MMSE filter is used and hence all the usersâ€™ fading processes are assumed to be known to the receiver. In the next chapter, the perforÂ¬ mance of the system, where an adaptive MMSE filter implementation is used, will be investigated in detail. We modify the model presented in Chapter 2 to study the performance of the CDMA system using different modulation formats in a fading channel. This can be done by setting = 1 and assuming that user 1 is the desired user and the integrator in front of the MMSE receiver has a scale factor of \/2piTc associated with it. Based 40 41 on these assumptions, we can rewrite the received vector given in Equation (2.3) as K r(m) = di(m)ai(m)e-?e^m)c1 + ^ , ^-otj(m)e:â€™ej^ j=2 Â» Pl dj(m)fj(l, 6) + dj(m - l)gj(l,6) (4.1) + n(m) Assuming the desired userâ€™s phase is known exactly, the input to the MMSE receiver can be written as y(m) = e i'fll,mr(m) (4.2) where 9itin is the estimated phase of the desired userâ€™s fading and here we assumed 9iiTn = Substituting Eqn. 4.1 into Eqn. 4.2, the input to the MMSE receiver, y (m), can be written as K y(m) = di(m)ari,mCi + ^ i=2 dj(m)ij(l, 6) + dj (m l)gj(l,8) + n(m)e ^1â€™m = di(m)o;i,mCi + y (4.3) here A9j user signal, we need to calculate the optimum tap weights for the I and Q channels. It is straightforward to show that the optimum tap weights for the I and Q channel filters are the same. Let the autocorrelation matrices for the I and Q channels received vectors (yi and y2) at the input of the MMSE filters be Ri and R2 and the steering- vectors be Pi and P2, respectively. We have E [Re [dx] Re [d{]] = |. In addition, the correlation vector Px, the autocorrelation matrix Rx, and the tap weights vector ax can be written as follows (dropping the dependence on m for convenience): Pi â€” E [Re [c?i]yi] - = P 2 (4.4) 42 Rl = + R = 2PP = R2 H R (4.5) ai = a2 = Ri Pi = a where Ri = E [yiyi^]. The output of the filter can be written as zi = aHyi = 2Re[d1]P1iiRr1P1+P1HRr1yi = 2 Re [dijPi^Ri-1?! + Ã±i (4.6) (4.7) (4.8) (4.9) Now we need to find the value of Pi^Ri *Pi and the variance of Ã±\. Using the matrix-inversion lemma, we can find the inverse of R as follows Rr1 Ri -i 1 + 2P1hR1 P, It can be shown that the variance of the term Ã±i is p/Rr'Pi - -i. (4.10) ^[Ã±iÃ±f] = [n-2P1HR1-1Pi]i Then the output of the modified MMSE , , 2PhR1P , z = d\\ = L1 + 2P/iR-1PJ pi/^-rp (4.11) + Nt 10, + Nq(o, [l + 2PfrR"1P] PhR-1P [l + 2PffR-1P]: (4.12) 43 Having the output of the filter z in this form, it is straightforward to show that the probability of symbol error conditioned in a?i is given by [40] Pe/ai ~ 3pe/cci 1 ^Pe/ai (4.13) Pe/ai ~ Q ( 2 Pi^R^P i) = Q ,cvi2CiiiR1 xCi (4.14) 5 J V V 10 Averaging pe/ai over the probability density function (pdf) of the desired userâ€™s fading amplitude,Â«i, gives the expression for P as POO P ~ / fa\,m{p^)Q Jo 'Ql2CiiiR1 1c1 10 da faum(a) = 2a exp (â€”a2) (4.15) (4.16) where /Ql,m(a;) is the probability density function (pdf) of the desired user fading amplitude. A closed form solution for this integral can be obtained by performing the integration and changing variables, and is given as follows: Ã2 fÂ°Â° -u2 P~\ â€” / a exp (â€”a2) exp â€”â€” du,da (4-17) V 7T Ja=0 Jj^ajCiÃÃR,Â¡â€œ1ci 2 using the polar coordinates, we can write the previous equation as oo />tan' P 2 rÂ°Â° r \Ar Jr=o Je. I I / 20 â– h R.r i c =1 1 C1 ' r2 exp (â€”r2) sin($), dr, dd Performing this integration will result in (4.18) e~1(i i/ 2 V V 20 + Ci^Rf'c, For a single user, the previous result reduces to . 1 (4.19) v~Eâ€˜!N- P~2V V 10 + Es/N0 (4.20) 44 The probability of symbol error for the 16-QAM is given by Pwqam ~ 3p 1 - -p (4.21) For BPSK and QPSK modulation, the average symbol error rates can be derived in the same manner and they are given, respectively, by (4.22) (4.23) Assuming that the system is using Gray coding, the bit error rate (BER) is given by (4.24) These equations implicitly depend on the interfering user codes, delays, transmitÂ¬ ted powers, and fading amplitudes through the matrix R. To obtain an average value for SER or BER, one would average over these quantities. For the single user case, it is easy to show that these results reduce to the well known results shown in the digital communications literature [42] and [11]. To obtain these results, we have used the Gaussian approximation for the outÂ¬ put of the filter due to interference and noise. The justification for the Gaussian approximation is based on the central limit theorem by noting that the output of the filter is a sum of random variables with different probability density functions (pdfs). Therefore, the sum of these random variables at the output of the filter can be considered a Gaussian random variable. This approximation is widely used in evaluating conventional receivers [9]. Moreover this approximation is more accurate with the MMSE receiver since we have less interference at the output of the filter and more Gaussian noise [20]. Poor and Verdu in [41] have studied the behavior of the 45 output of the MMSE receiver and found that the output is approximately Gaussian in many cases. To show the improvements of the systems employing higher order modulation formats, Figures 4.1, 4.2, and 4.3 illustrate the performance, in terms of BER, of MMSE receiver based systems with BPSK, QPSK, or 16-QAM modulation formats in a fading channel. These figures are based on the theoretical results obtained in the previous section. The received powers were modeled as a lognormal distribution with zero mean and 1.5 dB standard deviation. The BER performance of the 3-user system as a function of is shown in FigÂ¬ ure 4.1 for the different modulation formats. The theoretical and simulation based performances are in agreement. The simulation results are based on modeling the fading as a complex Gaussian process. The performance of the 16-QAM worse by few dBs than that of the QPSK or the BPSK performance, on the other hand, the BPSK and QPSK have the same performance for such load. In this case there is no advantage of using 16-QAM since using this higher modulation format will require more transmitted power to achieve the same BER. When the load of the the system increases to 30 users, as shown in Figure 4.2, The performance of the system that is based on a BPSK modulation degrades rapidly. In this case, an error floor is introduced and the performance of the system cannot be improved by increasing This behavior can be explained as follows. The MMSE receiver is overwhelmed by this load and the system does not have enough dimension to overcome the interference introduced by such a high load. In addition, the QPSK and 16-QAM based systems do not develop an error floor and they outperform the BPSK based system. This basically means that we can increase the capacity of the system by increasing the processing gain, without increasing the bandwidth or the information rate by simply adapting a higher order modulation format. Using higher order modulation formats provided the MMSE receiver with enough dimensions to 46 Figure 4.1: The performance of BPSK, QPSK, and 16-QAM in a fading channel with 3 users with optimum MMSE receiver implementation. suppress the interfering signals. The 16-QAM system outperforms the QPSK system for ^ greater than 18 dB. When the system loading was further increased to 60 users as shown in Figure 4.3, the QPSK based system would lose its ability to to suppress the new level of interÂ¬ ference and would introduce an error floor while the 16-QAM system still operating effectively. 4.2 The Effect of Phase Offsets on the Performance of the System As it will be pointed in Section (5.1), the phase variations are more severe on degrading the system performance because the errors that are caused by phase variaÂ¬ tion often are not localized to the deep fade periods but rather propagate due to the loss of lock on the desired signal phase by the receiver. In this section, we will study the effect of the phase offsets, due to imperfect estimation of the desired userâ€™s fading on the performance of the system. Symbol 47 Figure 4.2: The theoretical performance of BPSK, QPSK, and 16-QAM in a fading channel with 30 users with optimum MMSE receiver implementation Figure 4.3: The theoretical performance of QPSK , and 16-QAM in a fading channel with 60 users with optimum MMSE receiver implementation. 48 error rate (SER) bounds for QPSK and 16-QAM systems are derived when there is an imperfect phase reference. The SER for a QPSK and the 16-QAM systems can be derived as follows. We try to eliminate the phase variation in the desired signal by multiplying the received vector by the estimated phase as follows: y (m) = e-jÂ§imT(m) (4.25) where 9i is the estimated value of the desired userâ€™s fading phase, the vector y(ra) can be written as K y(m) = di(m)ai,mcie + dj(m - l)gj(l,S) = d1(m)ai,TOe,il>mc1 + y(m) j(.0l ,m $l,m) + E ,m) 3=2 + n(m)e~^l>n dj{m)fj(l,S) (4.26) where A0ltTn = 9i]Tn â€” 9i^m. A(?li7n is assumed to be |A9i^m < || for QPSK and \A9itTn < f | for 16-QAM because otherwise there are errors even without MAI and noise. Taking the real and imaginary parts of the vector y (m) results in yi = &[i/(m)] = [d/xcos(A0i>m) - dQ1sin(A9hm)\aitmc1 + yi(m) (4.27) y2 = 9f[j/(m)] = [dnsin{A9hm) - dQ1cos(A9hm)]ahmc1 + y2(m) (4.28) To find the optimum weights of the MMSE filter, ai and a2 the autocorrelation matrices Ri and R2 and the correlation vectors Pi and P2 corresponding to the received vectors yi and y2, respectively, need to be found. It can be shown that R: = R2 and Pi = P2. The optimum filter weights can be found as follows. Pi = E[Â»[dI]y] = ^cos(A9hm)ahmc1 = P2 (4.29) 49 The correlation matrix is given by Ri = E [yi(m)y?(m)] 1 â€” 2 al,mClCi K Pi _,2 2^ J=2 a fiff + gjgj + 2 P xPf + Ri â€” R2 (4.30) cos2(A<9i,m)â€˜ The MMSE filters optimum weights are given in terms Rf1 and Pi by ax = a2 = Rx xPi (4.31) The output of the MMSE filters can be written as Zi = aHy1 = = Pf Rf1 [dnco8{59i,m) - dQ1**n(Â£0lim)]alifBc1 + PfR^yi (4.32) 22 = a.Hy2 = [Rrlpi]Hy2 = Pf Rf1 [dQicos(59itm) + dnsin(59itm)] ai,mCi + Pf Râ€œxy2 (4.33) Define Ã±x = Pf R^xyi and Ã±2 = Pf Rf xy2 which consist of the contribution of MAI and the AWGN at the output of the MMSE filters. Substituting the value for aiimCi from Eqn. (4.29) into Eqn. (4.32) Eqn. (4.32) results in the outputs of the MMSE filters, Z\ and z2, written as z\ = 2 cos( A01Â¡m) Pf Rx XPx [d/icos(A0lim) - dQ1sin(A9ltm)\ + (4.34) 50 z2 = Pf Ri :Pi [dQ1cos(A9hm) + dnsin(A9hm)\ + Ã±2 (4.35) cos(A6^m)' Making use of the matrix-inversion lemma; Rf1 can be shown to be equal Rr1 = R-1 + r-'p^cos2^^) + pfRr'po'pf Ã±r1 cos2(A^iim)Rj)1 cos2(A^1,m) + 2PfRr1Pi The variances of Ã±i and Ã±2 are equal and are given as follows: (4.36) (4.37) ol = E[Ã± iÃ±f] = PfBÃ^IyiyflBÃ'Pi = PfR^RxR^Pi (4.38) (4.39) (4.40) Substituting the value of R: 1 from Equation (4.37) into Equation (4.40) results in On Siven by cos2(A01,m)PfR71P1 = (cos2(A0lim) + 2Pf R^Pr) The output of MMSE filters, Z\ and z2, can be written in terms of Rr1 as zi = Kcos{A9^m)dn - Ksin(A6hm)dQi + (4.41) (4.42) 22 = Kcos(A9liTn)dQi + K sin(A9lfm)dn + Ã±2 (4.43) where fi\ and Ã±2 are assumed to be N(0, an2) and K is given by K= (444) cos2(A01â€ž) + 2PfR-'P Since Z\ and z2 represent the statistics of dn and dQi, z\ and z2 can be written as z\ â€” Kcos(A9i^m)dn + rhi (4.45) 51 z2 = Kcos(A9ltm)dQ1 + rh2 (4.46) where mi = N(â€”Ksin(A9i'm)d,Qi, an2) (4.47) rh2 = N(Ksin(A9hm)dn, an2) (4.48) Having the statistics in the form of z\ and z2, one can easily calculate the probability of symbol error conditioned on oti,Ps/ai, for QPSK an 16-QAM system. After ignoring the double Q-function terms, the Ps/ai of the QPSK system can be approximated by P, s/a i Q( K (cos(69ijjn) â€” sin(69ijTn)) % , K (cos(S9iiTn) + sin(59i ,m)) V2 -) + Q( V2 ) (4-49) The value of â€” can be simplified to <7m ^ K K2 4cos2(^1,m)(PfRr1P1)2 (cos2(59itm) + 2PfR^1P1)2 (cos2(69hm) + 2PfRj'1P1) cos*(66ltm)P? R^Pi 4PfR^Pi (4.50) Let L, = cos(A6hm) - sm(ASim) (4.51) = cos(A0iâ€ž) + sin( (4.52) Then Ps/ai can be written as Ps/ai ~ Q(\/ 2L\P^1Pl) + Q(^2L2 PfR^PQ (4.53) 52 Recalling Pi from Equation (4.29) Pi = ^cos(A0iim)aq,mCi Then Ps/ai can be written in terms of A#i!m, aq)m, Ci, and Ri as (4.54) Ps/oci Ã³Â¿?a?,mCOs2(A^l,m)cf Ri XCX) + Q{ ^2Q!l,mCOs2(A0l,m)cf R-i XCi) (4.55) Averaging Ps/ai over the probability density function (pdf) of the desired userâ€™s fading amplitude, aq, gives the expression for the symbol error rate, Ps, as POO Ps â€” / /ai,m (Â®)Ps,a\dOi (4.56) Ja-0 fcn,m(a) = 2aexp(â€”a2) (4.57) where fai m (a) is the pdf of the desired userâ€™s fading amplitude which is assumed to be Rayleigh distributed ps = J fai,m{a)Q(^\Llalmcos2{^i,m)c?Ri1Ci)da + J fai,m (a)Q()J\Ll(A,mcos2(/\elyTn)c^'k^1Cx)da (4.58) Where Q is the Q-function which is defined as OO Q(z) = -j= J exp(-y)dA (4.59) Z Let h = cos2 (A0i,m)ciHR1 xci (4.60) 53 + Ã2 V 7T Ja=o Jui = roo r J a=0 J U\ -U a exp (â€”a2) exp dui da ui-ai a exp (â€”a2) exp â€”â€” du2 da (4.61) ' U2=a\,m\J\Ã\h 2 By setting V\ = and t>2 = ^ Equation (4.61)can be written as 2 roo roo â€” / / aexp(â€”(a2 -f vf))dvi, da V7r Ja=0 Jvi ' Â«i=ai,m-\/\L\h r>00 roo roo roo J a=0 JD2=o 1 V2 â€”&l,m 4 Using the polar coordinates, we have aexp(â€”(a2 + vl))dv2, da (4-62) 2 2,2 r{ = a +v{ (4.63) . .Ãœ 0 - tan 1 â€” v (4.64) Ps - + + r\ exp(â€”r\)dridOi r% ex-p(â€”rl)dr2dd2 I L\cos2{A6>iim)ciiJR1 \ 2 \ V 4 + L\cos2 (A#x im) Ci 1 ci) If I L22cos2(Ag1;m)ciifR^1Ci \ 2 V y 4 + L%cos2(A0iÂ¡m)ciHRi lc1 / (4.65) If there is no phase offset, A0i)in = 0, Equation (4.65) reduces to Equation (4.23). For the 16-QAM system the probability of symbol error conditioned on ax, Ps/ai, can be approximated by the following equation after ignoring the terms that have 54 doubled or squared Q-functions and defining cos(A6>i,m) - stn(A0i,m) (4.66) cos(A6,ijm) + sin(^A9i^m') (4.67) Z/3 â€” cos(A9 i,m) 3sin( A9irn) (4.68) L4 = cos(A0i,m) + 3sin(A9itTn) (4.69) Thus Ps/ai can be written as Ps/ai16QAM < Q ai,mcos2 (AOi>m)cf Rj"1 c4^ + \q (j/^ symbol error rate for 16-QAM system can be approximated as p l_(l_ I Llcos2{Aehm)c^R^c~\ 2\ y 2O + L2cos2(A01,m)cfRT1c1/ l(1_ I L\cosi{ Ag1,m)cfR1~1c1~\ 4\ y 20 + T2Cos2(A01,m)cf Rr'ci / 3 / _ / L|cos2(A^i 3/_ / L|cos2(Aglim)cf \ 2 8 V y 20 + L|cos2(A0i,m)cf R^Ci / 55 Assuming that the system is using Gray coding, the bit error rate (BER) is given by BER SER log2M (4.73) Where M is the number of points in the constellation. For BPSK, QPSK, and 16- QAM, M equals 2, 4, and 16, respectively. These equations implicitly depend on the interfering user codes, delays, transmitÂ¬ ted powers, and fading amplitudes through the matrix R. To obtain an average value for SER or BER, one would average over these quantities. Figures 4.4 and 4.5 show the performance in terms of BER by using the theoretical error bounds presented in this section for different values of phase offsets (A9). In these figures, the A9 values are 0Â°, 5Â°, and 15Â° for the 16-QAM case and 0Â°, 5Â°, 15Â°, and 30Â° for the QPSK case. We did not include the case where A9 â€” 30Â° for the 16-QAM because with such phase offset the 16-QAM system will not be operational even in the absence of MAI and noise effects. The curves, with the phase offsets, are obtained by using Eqn. (4.72) for the 16-QAM systems and Eqn. (4.65) for the QPSK systems. When the phase offset is 0Â°, the theoretical results presented in this chapter in the form of Eqn. (4.72) and Eqn. (4.65) are in agreement with the results of the previous chapter given by Eqn. (4.21) and Eqn. (4.23). Comparing Figures 4.4 and 4.5, one notices that the 3 and 30-users 16-QAM systems have a very close BER performance while this is not true for the QPSK systems. This means that the 16- QAM is more resistant to the multiple access interference caused by the other users. From Figure 4.4, for the 3 users case, we see that the performance of the 16-QAM system with phase offset of 15Â° is worst than the QPSK system with phase offset of 30Â° by 5 dB for BER less than 1 x 10-2. For this load, the QPSK system has a better performance than that of 16-QAM. On the other hand, for the 30 users system, the 16-QAM system performs better when the phase offsets are 0Â° and 5Â°. 56 Figure 4.4: BER of QPSK and 16-QAM where (o, +, *,.) are based on Eqn. (4.72) and Eqn. (4.65) for 3 users. Figure 4.5: BER of QPSK and 16-QAM where (o, +, *,.) are based on Eqn. (4.72) and Eqn. (4.65) for 30 users. 57 4.3 Summary In this chapter, we have investigated the performance of an MMSE receiver based CDMA system in a fading channel with BPSK, QPSK, and 16-QAM modulation formats. It has been found that for the same bandwidth and bit rate, the 16-QAM system outperforms the BPSK and QPSK system when the loading of the system is high compared to the processing gain (pg) of the BPSK or QPSK systems. This performance improvement is made possible by increasing the ability of the MMSE receiver to suppress the multiple access interference by using a higher processing gain. In this context, for MMSE receiver based CDMA systems, one should look at the higher order modulation as a means to increase the system efficiency by allowing more users to access the available bandwidth. The estimation of the desired userâ€™s fading process plays an essential role in deterÂ¬ mining how much capacity improvement can be gained by using the different moduÂ¬ lation formats. In the next chapter, the performance of such systems is investigated when the desired userâ€™s fading is estimated. CHAPTER 5 FADING PROCESS ESTIMATION In Chapters 3 and 4, we have shown that the use of multilevel modulation can improve the performance of the system in terms of BER and capacity. In Chapter 3, the AWGN channel model was used while in Chapter 4, a fading channel model and an optimum MMSE receiver implementation were used. The optimum receiver is impractical and hard to construct because it assumes that the powers, the fading processes, the time delays, and the spreading sequences of all users are known. An adaptive MMSE receiver based on the LMS algorithm can be used as a practical alternative to implement the MMSE receiver. In this chapter, a practical situation is considered where an adaptive implemenÂ¬ tation of the MMSE receiver based on the LMS algorithm is used. In addition the desired userâ€™s fading process is estimated to provide the receiver with a reference phase and amplitude to demodulate the desired user signal. The estimation of the desired userâ€™s fading process is accomplished through the use of a technique based on linear prediction and pilot symbols which will be described shortly. For most of this chapter, only the performance of QPSK and 16-QAM modulation will be invesÂ¬ tigated since, as we have seen in the previous chapter, the BPSK system is not able to perform effectively even when an optimum implementation of the MMSE filter is used when the system has 30 users. 5.1 The MMSE Receiver Behavior in A Fading Channel In this section, we study the behavior of the MMSE receiver in a fading channel when a multilevel modulation format is used. Since tracking the phase and magnitude of the fading is essential for successful demodulation of a multilevel modulation format 58 59 Figure 5.1: The MMSE behavior in a fading channel in decision directed mode. like 16-QAM, we will study the ability of the present structure of the MMSE receiver to track these fading parameters. In [22], the performance of the MMSE receiver in a frequency nonselective fading channel has been evaluated when a BPSK modulation format is used. It has been shown that the MMSE has a difficult time tracking the channel variation due to the fact that during deep fades, unreliable decisions are fed back to the LMS algorithm. This will cause the MMSE receiver to lose lock on the desired signal or it may lock onto another interfering signal. In this section, we assume a slow fading environment with a processing gain of 124 chips/symbol, a 16-QAM modulation format, a mobile speed of 5 mph, a frequency band of 900 MHz, and a data rate of 9600 bps. This will result in a normalized Doppler rate, fÂ¿Ts of 0.0028. Figure 5.1 demonstrates the behavior of the present MMSE structure in a slowly varying Rayleigh fading channel for a single user using 16-QAM modulation. As expected, the figure shows the inability of the receiver to 60 track the magnitude and phase of the fading process when the desired user goes into deep fades. The phase estimate in Figure 5.1 represents the MMSE receiver estimate of the phase based on the receiver coefficients. In a single user case, if the MMSE is doing its job of tracking the channel variation, the phase of the MMSE filter coefficients is equal to the opposite value of the phase of the channel. The amplitude estimate is calculated from the value of the filter output. It is clear from Figure 5.1 that the MMSE receiver does a good job in tracking the amplitude variation of the fading channel except during the deep fade period. On the other hand, the receiver does a poor job in tracking the phase of the fading process. In fact, the receiver ends up locked 180Â° out of phase to the desired user after the deep fade period is over. Differential detection may be considered to solve this problem, but differential encoding will not solve the more practical problem, when the MMSE receiver locks on to other interfering signals. Figure 5.2 shows that in a training mode, the MMSE receiver always tracks phase and amplitude of the fading channel well. This shows that the decision-directed mode of operation of the MMSE receiver is a disadvantage to its performance in this environment. Therefore, if there is a technique by which we can feed back reliable decisions to the adaptive algorithm, the LMS in this case, then the MMSE will perform in an acceptable manner. This is part of the motivation for using periodic pilot symbols to provide a reliable feedback for the LMS and this will be discussed in the next section. In Figure 5.3, the effect of the phase variation while the amplitude is kept constant is shown in the top graphe and the effect of the amplitude variation while the phase is kept constant is shown in the bottom graph. It seems that when the phase is held constant, the amplitude variation leads to errors only in the deep fade periods. This is due to the fact that during deep fades the desired userâ€™s signal to noise ratio value decreases to a low level at which the receiver can not demodulate the signal correctly. In addition, it can be concluded from the figure that the effect of phase 61 variations is more severe because the errors in this case are not made just in deep fades but they propagate due to the loss of lock on the desired signal phase by the receiver. Having shown the inability of the present MMSE structure to work in a fading environment described in the previous section, we now consider modification of the MMSE receiver to be capable of demodulating multilevel modulation schemes in a fading environment. In [22], a modified MMSE structure for one-dimensional (BPSK) modulation is presented. We will present a more general modified MMSE structure capable of demodulating a wide range of digital modulation formats. First, since the errors due to the phase of the fading process are dominant, we need to eliminate this phase variation from the input to the adaptive filter. In addition, to eliminate the problem of the MMSE receiver locking to other userâ€™s phases, we need to take the real and imaginary part of the input to the adaptive filter. The modified 62 Constant fading amplitude Constant fading phase Figure 5.3: The behavior of the MMSE when the the amplitude or the phase of the fading is held constant. 63 Figure 5.4: The modified MMSE structure. structure is shown in Figure 5.4. This structure assumes an estimate of the amplitude and phase of the fading process are available at the receiver. 5.2 Tracking Techniques in A Fading Channel In the previous chapter, the exact fading process of the desired user is assumed to be known and the MMSE filter weights are assumed to be optimum. In this section, the case where the desired user fading is estimated, rather than assumed to be known, is investigated. In addition, the adaptive LMS algorithm is used to update the MMSE filters coefficients. For the rest of this section, we assume a slow fading environment with a processing gain of 124 chips/symbol, a 16-QAM modulation format, a mobile speed of 5 mph, a frequency band of 900 MHz, and a data rate of 9600 bps. This will result in a normalized Doppler rate, fdTs of 0.0028. There are 3 users in the 64 system. It has been shown by [22] that phase compensation is an effective method of improving the MMSE receiver performance in a fading channel. In [22] a phase estimate is obtained by using a linear predictor. In our case, since we are dealing with multilevel modulation, 16-QAM, amplitude and phase compensation are needed to improve the performance of the MMSE receiver. We studied the capabilities of three techniques in tracking the fading amplitude and phase. These techniques are based on pilot symbols and/or linear prediction. The first tracking technique uses the decision out of the MMSE to form an esÂ¬ timate of the desired userâ€™s fading parameters using linear prediction. The channel estimation based on this technique is shown in Figure 5.5. This technique is presented in some detail in [22] for a CDMA system with BPSK modulation. It worked fairly well for BPSK modulation but not in the case here, where 16-QAM modulation is 65 used. This has motivated the search for a better tracking method. We will now sumÂ¬ marize the procedure used to obtain channel estimates using linear prediction. The tracking of the desired userâ€™s fading process can be accomplished as follows. From Figure 5.4, the output of the filter output, z(m), when r(m) is the input, is given by z(m) = di(m)Â«iime-?6,1â€™marci + Ã± (5.1) A noisy estimate of the fading process can be given by z(m) P(m) = <Â¿i(m)aTCi Qi.me'*1'â€ (5.2) In a decision-directed mode, di(m) is replaced by di(m). The linear prediction can be formulated by the following. As has been shown in [22] , the L th order linear prediction of the fading channel is given by L $(m) = ^2 - *) (5.3) t=i The optimum coefficients of the linear predictor which minimize the mean-square error between the actual fading process and its estimates are given by Ã¡ = c_1v (5.4) The expressions for C and v for the single user case are given in [22] as C = B+(|)-1I (5.5) where B is a L x L matrix whose elements are given by â€” Redi j)Ts) (5.6) (5.7) [v]i = Rc(iT,) 66 and Rc(r) is the autocorrelation function of the fading process and is approximated by Rc(t) = 1 - (7TfDr)2 (5.8) The estimates of the fading process out of the linear predictor are then used to remove the phase of the desired user fading from the input of the modified MMSE receiver and to scale the decisions in the modified MMSE receiver, respectively. The second tracking technique is based on pilot symbols. The result of tracking the fading channel using this technique is shown in Figure 5.6. In this technique, pilot symbols, known by the receiver, are sent periodically (every 10th symbol for the case reported in Figure 5.6). The MMSE receiver uses these pilots to obtain an estimate for the fading process in the same manner as in Eqn. 5.2. The fading parameters 67 obtained by this estimate are used in demodulating the desired userâ€™s signal until the next pilot symbol is received and a new estimate is made. We propose the use of pilot symbols for two reasons. First, pilot symbols can be used to periodically train the MMSE and prevent the MMSE filter from feeding back wrong decisions. The second reason for using pilot symbols is to aid the receiver in estimating the channel fading condition. The fading parameters obtained by this estimate are used in demodulating the desired userâ€™s signal until the next pilot symbol is received and a new estimate is made. Obviously, this technique is suitable for a slowly fading channel and may not work well for a rapidly fading channel. We propose a third approach which consists of a combination of the first and second techniques. The tracking of the fading channel using this technique is shown in Figure 5.7. In this case, channel estimates are made by feeding back a linear prediction of the previous channel estimates. 68 By comparing Figures 5.5, 5.6, and 5.7, one can conclude that the third technique has better tracking capabilities than those of the other techniques. The good perÂ¬ formance of the third technique can be attributed to three reasons. First, the use of pilot symbols provides the MMSE receiver with a reference that helps the receiver not to lose lock on the desired user. Second, using the linear predictor, estimates are made for every received symbol. This gives the linear predictor recent past channel estimates to predict the channel conditions. Third, pilot symbols can help the linear predictor not to lose track of the fading process by interrupting the propagation of decision errors. Figure 5.6 demonstrates that the MMSE receiver can be updated based on pilot symbols only. This is interesting since the poor performance of the MMSE receiver in a fading channel is often due to the feeding back of unreliable decisions to the adaptive algorithm during deep fades. To show the improvements of the systems, which are based in different modulation formats, Figures 5.8, 5.9, and 5.10 illustrate the BER performance of an MMSE receiver base systems with BPSK, QPSK, or 16-QAM modulation formats in a slowly fading channel for a 3 and 30-user CDMA systems. To generate these figures, the following simulation environment was chosen. The mobile speed was 5 mph, the mobile operates at the 900 MHZ band, the bit rate was 9600 bps, a pilot symbol was sent every 10th symbol. This corresponds to fsTs of 0.0028, 0.0014, 0.007 for 16-QAM, QPSK, and BPSK, respectively. The received powers were modeled as a lognormal distribution with zero mean and 1.5 dB standard deviation. The receiver structure shown in Figure 5.4 has been used. The BER performance of the 3-user system as a function of Eb/N0 is shown in Figure 5.8 for the different modulation formats. As expected, the CDMA system which based in a BPSK modulation outperforms the other systems. In this case there is no advantage of using higher order modulation since using higher order modulation will require more transmitted power to achieve the same BER. 69 Figure 5.8: The performance of BPSK, QPSK, and 16-QAM in a slow fading channel with 3 users, fading estimated. When the load of the the system increases to 30 users, as shown in Figure 5.9, The performance of the system that is based on a BPSK modulation degrades rapidly. In this case, an error floor is introduced and the performance of the system can not be improved by increasing Eb/N0. When the system loading further increased to 60 users as shown in Figure 5.10, the QPSK based system would lose its ability to to suppress the new level of interference and would introduced an error floor. In the next section, we will be examining the third tracking technique that we have proposed in this section in some details. For example, we examine the effect of the predictor length and the pilot symbol rates on the performance of the QPSK and 16-QAM systems. 5.3 The Effect of the Fading Estimation Error on the Performance of the System In coherent detection of a desired signal, the fading process of the desired user need to be estimated. The estimate of the fading of the desired userâ€™s fading is given 70 Figure 5.9: The performance of BPSK, QPSK, and 16-QAM in a slow fading channel with 30 users, fading estimated. Figure 5.10: The performance QPSK (known fading), and 16-QAM (known and estimated fading) in a slow fading channel with 60 users. 71 in Eqn. 5.2 as (5.9) where the variables Ã¡ijm and are the estimated amplitude and phase of the desired userâ€™s fading process. As has been shown in [22] , the Lth order linear prediction of the fading channel is given by L (5.10) Let 7(77i) be the exact desired user fading process. Then fading estimation error is defined as e(m) â€” 7 (m) â€” /3(m) = X + jY (5.11) Since 7(m) was modeled as a complex zero mean Gaussian random process, the estimate of the fading can be assumed a Gaussian process since it is produced by a linear operation on a Gaussian process. Therefore, the estimation error is a complex Gaussian process. If the estimator is unbiased, the mean of the estimation error is zero. The real and imaginary parts of the estimation error have a zero mean Gaussian distribution and the amplitude has a Rayleigh distribution while the phase has a uniform distribution from â€”tv to tv. Figure 5.11 shows the distributions of the real and imaginary parts, X and Y, of the estimation error. Figure 5.12 shows the distributions of the amplitude and the phase of the estimation error. The figures are in agreement with our observation that the estimation error represents a zero mean complex random process. The figures are obtained from a simulation of a 3 users, 16-QAM system with fdTs = 0.0028 at Eb/N0 = 20 dB It is interesting to see how the system performs if the estimation error is modeled as a complex Gaussian process which its real and imaginary parts modeled as a zero mean Gaussian process 72 x Figure 5.11: The distributions of the real and imaginary parts of the estimation error for a 16-QAM system; PSAM rate = 0.2, 3 users, pg= 124, fdTs = 0.0028, Eb/N0 = 20 dB 20 =3.151- E 03 o 10h <1> â– 5 5 h =6 Q. O'â€” -0.2 mean = 4.5014e-002 variance = 1.1283e-003 nl hrii-i 0.2 0.4 Figure 5.12: The distributions of the amplitude and the phase of the estimation error for a 16-QAM system; PSAM rate = 0.2, 3 users, pg= 124, fdTs = 0.0028, Eb/N0 = 20 dB 73 with variance cr2. The estimation error can be represented as e = X + jY where X = N(0, cr2) and Y = N(0, a2). Where N stands for normal (Gaussian) distribution. Figures 5.13 and 5.14 show the performance of a 16-QAM system, when the estimation was modeled as a zero mean complex Gaussian process. The variance, cr2, varies from 0 to 0.1. The loading for the results in Figures 5.13 and 5.14 are 3 and 30 respectively. For comparison, the cases where the desired userâ€™s fading process is known or estimated with a normalized Doppler rate of 0.0028 and 0.0355, respectively, are also shown in the figures. As can be seen from these figures, if cr2 of X and Y are 1 x 10-6 the performance of the system will be the same as if the process is known. If the a2 is increased to 1 x 10~4 the performance is very close to the case when the fading process is known for ^ less than 30 dB, then it degrades. If a2 is increased further to 1 x 10-3, the performance in terms of BER is very close to the known fading case for less than 20 dB and then the BER becomes constant and the performance does not improve at higher for the 3 users case. For the 30 users case, the performance degrades substantially for ^ greater than 25 dB for cr2 = 1 x 10-3 . Increasing a2 to 1 x 10-1 will introduce an error floor at BER 0.3 which makes the system ineffective. An interesting result to see from Figures 5.13 and 5.14 is to compare the perÂ¬ formance of the 16-QAM system when the fading is estimated to the cases when X and Y are modeled as zero mean Gaussian with different variances. For example, for the estimated fading system with fdTs â€” 0.0028 the BER curves cross over the BER curve of a2 = 1 x 10~3 at ^ = 27 dB for 3 users and 33 dB for 30 users. This cross over can be attributed to the fact that the estimation of the fading improves by increasing These figures can serve as figures of merit for a system designer. By checking the variances of the real and imaginary parts of the estimation error, one can have a good idea what the system BER would be. 74 Figure 5.13: BER of 16-QAM with different estimation error variances for 3 users. For the estimated case PSAM rate =.2, L= 3 , pg= 124, Figure 5.14: BER of 16-QAM with different estimation error variances for 30 users. For the estimated case PSAM rate =.2, L= 3 , pg= 124, 75 Figure 5.15: BER of QPSK with different estimation error variances for 3 users. For the estimated case PSAM rate =.2, L= 3 , pg= 62, respectively, Figures 5.15 and 5.16 show the performance of 3 and 30 user QPSK systems when the estimation error is modeled as a zero mean complex Gaussian. These figures are to be compared to the 16-QAM Figures 5.13 and 5.14. From these figures, one can compare the sensitivity of the BER performances of the 16-QAM and the QPSK systems to the estimation error. This can be demonstrated clearly by comparing the 16-QAM and QPSK systems when the system load is 30 users. For the QPSK case, with a2 as high as 1 x 10-3, the system performance in terms of BER is the same as for the known fading case. On the other hand, for the 16-QAM case, for cr2 = 1 x 1CT3 the system performance in terms of BER degrades substantially when compared to the known fading case. This result is expected since the 16- QAM modulation constellation is more crowded than than the QPSK constellation. By comparing Figure 5.14 and 5.16 for the 16-QAM and QPSK systems, one can conclude that if the estimation error is high, for example here a2 = 1 x 10-3, there is no justification for using 16-QAM modulation. 76 Figure 5.16: BER of QPSK with different estimation error variances for 30 users. For the estimated case PSAM rate =.2, L= 3 , pg= 62, Another observation to be made from these figures is that the performance of the system in terms of BER becomes less sensitive to the increase of the real and imaginary parts of the estimation error variances at high load. This becomes clear by comparing the 3 and 30 user systems for 16-QAM or QPSK systems. For example, when o2 â€” lx 10-4, the 30 user 16-QAM based system performs very close to the system with known desired user fading while the 3 user system degrades substanÂ¬ tially. This is more clear in the QPSK system, where in the 30 user case the system performance is almost the same as that of a known fading case while for 3 users there is a loss of about 5 dB for BER more than 1 x 10-4. One can expect these results because when the system load is low, the multiple access interference is not a major factor on the BER, while the estimation error is. At high loads, the multiple access interference is a major factor in the BER performance of the system and its effects are more dominant than the effect of the estimation error. This suggests that for Table 5.1: The estimation error statistics for 16-QAM system with L = 3, PSAM = .2, 3 users and fdTs = 0.0028 f( dB) al 0 9.984 x 10~2 9.865 x 10â€œ2 5 4.763 x 10-2 4.890 x 10-2 10 1.673 x 10-2 1.672 x 10-2 15 5.129 x 10-3 4.989 x 10-3 20 1.560 x 10â€œ3 1.594 x 10-3 25 6.238 x 10-4 6.273 x 10-4 30 3.082 x 10â€œ4 3.123 x 10-4 35 1.690 x 10-4 1.675 x 10-4 40 1.036 x 10-4 1.068 x 10-4 high load systems, the estimation of the error does not have to be as accurate as for the low load systems. Table 5.1 shows the values of the variances of the real and imaginary parts of the estimation error based on simulating a 3 user 16-QAM system. The PSAM rate is 0.2, the predictor length L â€” 3 and the normalized Doppler rate, fdTs is 0.0028. This table is to be compared to Figure 5.13. In Figure 5.13 a cross over between the BERâ€™s curve corresponding to the system where the fading has been estimated and the BERâ€™s curve corresponding to cr2 = 1 x 10~3 at about ^ = 27 dB. This can be seen from 5.1 that at = 25 dB, cr2 = 1.56 x 10~3 and a2 = 1.5944 x 10~3 while at jf- = 30 dB, L=3 and fdTs of 0.0028 operating between the curves corresponding to a2 = 1 x 10~3 and a2 = lx 10~4 for = 27 dB. lv0 5.4 The Effect of Pilot Symbol Rates on the Performance of the System The effect of a pilot symbol assisted modulation (PSAM) rate on the BER perforÂ¬ mance of the system is compared for different Doppler rates and system loadings in 78 Figures 5.17 to 5.20. PSAM rates of 0.2, 0.1, 0.05, and 0.02 were used. As expected, the higher the PSAM rate the better the performance. This is more evident at high Doppler rates. The performance improvement due to the high PSAM rate in terms of BER came at the expense of the bandwidth efficiency of the system. For example, in the case of a PSAM rate of 0.2, 20% of the available bandwidth is used for sending pilot symbols where at a PSAM rate of 0.05, only 5% of the available bandwidth is used for pilot symbols. The system designer needs to balance the tradeoff between the bandwidth efficiency and the performance of the system in terms of BER. Based on these figures, we see that at low Doppler rate, independent of the loading of the system, a small penalty in ^ is paid if a PSAM rate of 0.1 is used instead of 0.2. For example; in the case of a system employing a 16-QAM modulation with a load of 30 users and the mobile speed of 5 mph which corresponds to a normalized Doppler frequency of 0.0028, the difference in performance when a PSAM rate of 0.2 and 0.1 is about 2 dB and the use of the lower PSAM rate is attractive in this situation. The use of lower than 0.1 PSAM rate even at low Doppler rates will degrade the perforÂ¬ mance substantially as shown in Figure 5.17, 5.18, and 5.21. On the other hand, At a higher Doppler rate as shown in Figures 5.22 the penalty in is about 5 dB when a PSAM rate of 0.1 is used instead of 0.2 and this penalty widens substantially when a lower PSAM rate is used. For 16-QAM system with normalized Doppler frequency, /dTs, 0.0335 which is shown in figure 5.22 there is a substantial improvement due to the use of higher rate PSAM but the system is still not attractive since an error floor develops at high BER. The improvement in the performance of the system due to the use of higher PSAM rate is due to the fact that sending PSAM frequently will improve the estimation of the fading process which translate to an improvement to the system BER performance. This can be seen from Table (5.1) and Table (5.2). By comparing the variances of the real and imaginary parts of the error process for the system with PSAM rate 79 Figure 5.17: BER of 16-QAM with different PSAM rates; L= 3 , 3 users, pg= 124, fdTs = 0.0028. Figure 5.18: BER of 16-QAM with different PSAM rates; L= 3 , 30 users, pg= 124, fdTs = 0.0028. 80 Figure 5.19: BER of 16-QAM with different PSAM rates; L= 3 , 30 users, pg= 124, fdTs = 0.017. Figure 5.20: BER of 16-QAM with different PSAM rates; L= 3 , 30 users, pg= 124, fdTs = 0.0335. 81 Figure 5.21: BER of QPSK with different PSAM rates; L= 3 , 30 users, pg= 62, speed= 5 mph fÂ¿rs = 0.0014. Figure 5.22: BER of QPSK with different PSAM rates; L= 3 , 30 users, pg= 62, speed= 60 mph /Â¿Ts = 0.017. 82 Table 5.2: The estimation error statistics for 16-QAM system with L = 3, PSAM = 0.02, 3 users and fdTs = 0.0028 0 5.1563 x 10~1 5.196 x 10-1 5 5.207 x 10-1 5.389 x 10-1 10 3.498 x 10-1 3.708 x 10â€œ1 15 2.541 x 10-1 2.388 x 10â€œ1 20 2.041 x 10-1 2.413 x 10"1 25 1.457 x 10â€œ2 1.306 x 10â€œ2 30 4.205 x 10-3 3.534 x 10-3 35 2.333 x 10-3 1.930 x 10-3 40 1.439 x 10â€œ3 2.2858 x 10-3 of 0.2 and the system with PSAM rate of 0.02, we notice that the variances for the former system are lower than that of the later system. These improvements in the estimation due to use of higher PSAM rates translate to a better BER performances. 5.5 The Effect of the Linear Predictor Length on the Performance of the System Figures 5.23 to 5.24 show the BER performance of the 16-QAM system for a cerÂ¬ tain normalized Doppler rate and number of users while the linear estimator length, L, has different values, namely; 1, 2, 3, 10, and 50. The BERs are the same indepenÂ¬ dent of these values of L at high This is due to the fact that the length of the linear estimator has a small effect on the value of the estimation error. Tables (5.1) and (5.3) show that values of a\ and a2y for different values of ^ for a simulation environment of a mobile speed of 5 mph, which corresponds to fdTs = 0.0028 in a system with 3 users employing 16-QAM and PSAM rate of 0.2. The information in these tables need to be compared to the results in Figure (5.23) for > 30, the values of crji and ay for L â€” 3, and 50 are very close. For these values of |k, we see no change in the BER as shown in Figure (5.23). For < 30, the values of al and al for L = 3, and 50 are not as close as before and this is translated x y 83 Table 5.3: The estimation error statistics for 16-QAM system with L = 50, PSAM = 0.02, 3 users and fÂ¿Ts = 0.0028 Â°x ai 0 5.1563 x 10-2 5.196 x 10"2 5 5.207 x 10â€œ2 5.389 x 10"2 10 3.498 x 10~3 3.708 x 10â€œ3 15 2.541 x 10-3 2.388 x 10â€œ3 20 2.041 x 10-4 2.413 x 10"4 25 1.457 x 10â€œ4 1.306 x 10-4 30 4.205 x 10â€œ4 3.534 x 10-4 35 2.333 x 10"4 1.930 x 10"4 40 1.439 x 10-4 2.2858 x 10-4 to a small difference in BER performance in Figure (5.23). The performances of the QPSK with different values of L are shown in Figures (5.25) to (5.26). As in the case for 16-QAM, there is no improvements in terms of BER for high values of |k. We notice from these figures that the BERs for system with L = 3 and L = 50 are very close, therefore; going to higher than L = 3 is not justified. 5.6 Summary In this chapter, we have investigated the performance of an adaptive MMSE reÂ¬ ceiver based CDMA system in a fading channel with QPSK, and 16-QAM modulation formats when the fading of the desired user is estimated. By using the estimator preÂ¬ sented in Section 5.2, the capacity is improved when a 16-QAM system is used as shown in Figures 5.9 and 5.10 at a low Doppler rate but not at high Doppler rate. A system designer can make a decision about what modulation format should be used based on the quality of the estimate of the desired userâ€™s fading process and employing Figures 5.13 to 5.16 to help in deciding whether a 16-QAM or a QPSK is to be used. If the fading process is known or the fading estimation error is very low, 16-QAM modulation should be employed to improve the system capacity . On the 84 Figure 5.23: BER of 16-QAM with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg = 124, and fÂ¿Ts = 0.0028 Figure 5.24: BER of 16-QAM with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg= 124, and fdTs = 0.0335. 85 Figure 5.25: BER of QPSK with different predictor lengths (L); PSAM rate = 0.2, 3 users, pg= 62, and fdTs = 0.0014. Figure 5.26: BER of QPSK with different predictor lengths (L); PSAM rate = 0.2, 30 users, pg= 62, and /Â¿Ts = 0.017. 86 other hand, if the fading error estimation is high, QPSK modulation should be used since it is more robust for high estimation errors. CHAPTER 6 POWER CONTROL In this chapter, a fully distributed power control algorithm is presented that is based on the MSE. We study the capacity improvements that can be gained by an MMSE receiver-based CDMA system implementing this power control algorithm. We investigate the performance of this power control algorithm when the MMSE receiver filter coefficients are obtained through the Weiner solution or adaptive algorithms like the LMS and the RLS. We also look at the convergence of the SINR and the total transmitted power in the in AWGN and fading channels. In this chapter, we propose a power control algorithm that can be used to adjust the mobile station transmitted power in a closed loop power control fashion. The power control presented here does not update the transmitter power in constant steps of Â±1 dB like the IS-95 but with variable steps that are dependent on the channel condition and the MMSE receiver filter coefficients. 6.1 Fully Distributed Power Control Algorithm Power control algorithms are based on the fact that the SINR at the receiver is diÂ¬ rectly proportional to the desired userâ€™s transmitted power and inversely proportional to the sum of the interfering signalsâ€™ transmitted powers. The goal of power control algorithms is to equalize the SINR to reduce the total transmitted power in the sysÂ¬ tem. This reduces the interference level in the CDMA system and hence increases the capacity. In general, power control algorithms are classified as centralized or disÂ¬ tributed power control algorithms. In a centralized algorithm, there is a controller that has complete knowledge of all active radio links and their terminal powers [43] and is responsible for adjusting the transmitted powers at the transmitting terminals. 87 88 On the other hand, in a distributed power control algorithm, each radio link adjusts its own transmitted power based on its own measurements [44]. For the *th user, SINRj at the output of the MMSE filter is given in [19] as 7 I H I2 Pihu af cd SINRi (6.1) l(af I)|2 + 2cr2(afaÂ¿) where the variables, is the transmitted power, cÂ¿ is the spreading of user i with a period N, hij is the channel gain of user j to the assigned base station of user i, ai is the filter coefficient vector that correspond to the ith user, I is the multiple access interference presents in the received signal, and a2 is the noise variance. For the ith user, define the desired MMSE ( MMSE, ) as the value of the MMSE which corresponds to the desired SINR (SINRj). The relation between SINRÂ¿ and MMSE* is given in [19] as 1 SINRÂ¿ = MMSE,- - 1 (6.2) The MMSEÂ¿ is obtained by the Wiener solution for the tap weights as described in [39], [20], [18], [19]. For the ith user, the MMSEÂ¿ is given by MMSE* = 1 - y/pÂ¡y/hÃ¼^f Ci (6.3) From Eqn. 6.3, we can write the transmitted power in terms of MMSE, the tap wieghts, and the spreading sequence as follows (1 - MMSE)2 Pi (6.4) ha |(af Cj)|2 We propose to update the transmitted power at the (n + 1) iteration according to the following algorithm (1 - MMSE)2 ha l(aÂ¿*(n)c/)|2 Pi(n + 1) (6.5) 89 It is clear that the transmitter needs to know (a(n)fcÂ¿) and ha to update its power. The value of these terms can be calculated by the receiver and then sent to the transmitter. The denominator of eqn.(6.5) estimation can be approached as follows. The transmitter sends a pilot symbol at the beginning of each transmission period. The receiver uses the output of the MMSE receiver that corresponds to these pilot symbols to get a noisy estimate of the the denominator of Eqn.(6.5) as follows Zi = diy/pÂ¡\/%iaf Ci + Ã± (6.6) where fi consists of the output of the filter due to the noise and the multiuser interÂ¬ ference and di is the data symbol. A noisy estimate the denominator of eqn.(6.5) is obtained from ha |(af (n)Cj)| := tj(n) Â« (6.7) The value of ^ is sent from the receiver to the transmitter which divides it by the last transmitted power value to find r](n). The transmitter then uses this value of rÂ¡(n) to update its transmitted power according to eqn. (6.5). Furthermore, when constant envelope modulation is used, no pilot symbols need to be sent since the value of \di\ is constant. 6.2 Numerical Results To show the improvements that can be realized for the system, in this section, we present some simulation results for an MMSE receiver-based DS-CDMA system using the MMSE-based PCA proposed in the previous section. In all the results in this section, a BPSK modulation format is used. To evaluate the advantage of implementing the proposed PCA, our results are compared to an MMSE receiver based system with perfect power control as well as the theoretic bounds using optimal spreading sequences [38] or asymptotic analysis (using 90 large number of users and large processing gain) [37]. To facilitate comparison for the system with perfect power control, we assume that each user transmits with a constant power of A the average total transmitted power obtain from the proposed PCA. The proposed PCA based system was found to yield on average a capacity improvement of more than 20% over the system with perfect power control. The simulated capacity results, shown in Figure 6.1, were obtained by varying the number of the CDMA system users to find the maximum number of users that can be supported by the system using a blocking probability criterion of 0.01 . Blocking is defined as a scenario in which the converged value of the SINR of any user, was less than 98% of the desired SINR; so that the capacity of the system is given by the maximum number of users that could be present in the system while satisfying the following performance criterion Pr(SINR < 0.98SINR) < 0.01 (6.8) The simulation results shown in Figure 6.1 are found to be in agreement with the theoretical capacity upper bound given in [38] and [37] by K < N(l + SINR; (6.9) despite the fact that, for the results shown in this section, short random sequences are used rather than optimal sequences as used in [38] or as asymptotic analysis using large number of users and large processing gain as in [37]. Figure 6.1 shows that for a practical system as considered in the simulation study (with finite number of users and reasonable length of processing gain) , it is possible to attain the same capacity as the MMSE system with optimal signature sequence [38] or that with large spreading gain [37] for a wide range of SINR but at the expense of transmitting more power. This is further illustrated in Table 6.1 which shows the average total transmitted power, Pt, required to attain the capacities obtained by 91 Figure 6.1: The capacity improvement due to the use of the proposed power control algorithm as compared to the capacity of a system with perfect power control and theoretical bound the proposed algorithm (6.8) for different values SINR. It is clear that while the capacities attained by the proposed algorithm are close to the theoretical capacity bounds, the associated total transmitted powers required by the proposed algorithm are somewhat higher than that for the total power given in [37] by Pt = WSINRa2 ' K \ SINR (6.10) 1 - (Â¡L). V W / l+SINR For the capacity simulation results, we use a normalized channel gain of 1, a processing gain of 31, a noise variance of 0.1, the power is updated every symbol, and we set the initial transmitted power of all users to 0.1. Figures 6.2 and 6.3 show the total transmitted power and the SINR convergence for the system using the PCA proposed in the previous sections. There are 33 users in the system and SINR of 10 dB. The SINRs of the users would converge to a value less than SINR if the number of users were more than 33. While we assume in previous results that all users have the same target SINR, the proposed PCA can 92 Table 6.1: Simulation capacity and average total transmitted powers corresponding to different SINR requirements Capacity eqn. 6.8 Pt (simulation) Pt eqn. 6.10 SINR (dB) 1 55 637.4 617 3 46 850.7 796 6 38 1037.1 746 8 35 1453.3 869 10 33 2219.7 1023 12 31 1631.4 827 14 29 800.9 726 Figure 6.2: A typical total transmitted power for MMSE receiver based CDMA system with for 33 users and SINR = 10 dB. 93 Figure 6.3: A typical SINR convergence SINR = 10 dB for 33 users. support different target SINRs without any modification. In Figure 6.4, W show the convergence of the SINR and the total transmitted power of a system with 6 users if there are two different target SINR values. Three of these users have a target SINR of 6 dB while the other 3 users have a target SINR of 10 dB. We see from the figure that each user converges to its desired target SINR. The SINR of the user with the low target SINR (6 dB) converges faster than the SINR of the users with higher target SINR. The power control algorithm performance with adaptive implemintation of the MMSE receiver in which the LMS and RLS algorithm are used to update the filter weights was studied and the results are shown in Figure 6.5, 6.6, 6.7, and 6.8. In these figures, the power has been updated every 100 iterations of the adaptive algorithm and the transmitted powers of all users where initilize to 1. As expected, the convergence of the SINR and the convergence of the total transmitted power in the adaptive cases are slower than when the receiver filter tap weights are obtained by the Weiner solution. The SINR converges to a value close to, but not exactly equal to, the target SINR due to the fact that the proposed power control algorithm has Total TX. power 94 Figure 6.4: A typical SINR and total transmitted power convergence for MMSE receiver based CDMA system with for 6 users and SINR =10 and 6 dB. 95 Figure 6.5: A typical SINR convergence SINR = 9.5 dB for 15 users using LMS algorithm Figure 6.6: A typical total transmitted power for 15 users using the LMS algorithm 96 -5 -10 -15 â€˜ * * 0 50 100 150 200 Iteration Figure 6.7: A typical SINR convergence SINR = 9.5 dB for 15 users using RLS algorithm Figure 6.8: A typical total transmitted power for 15 users using the RLS algorithm 97 been developed assuming the tap weights of the filter were obtained by the Weiner solution. Simulations show that the LMS algorithm has a better tracking capability than that of the RLS algorithm for such nonstationary environment where the signal power is changing, as shown in Figures 6.5 through 6.8. This tracking superiority of the LMS may be attributed to the fact there is an inherent dependence of the step size (/r) of the LMS algorithm on the total input power of the adaptive filter. An adaptive step size, /i = TW based on the total input has been used to obtain Figure 6.5 and 6.6. Figures 6.7 and 6.8 show the performance of the proposed power control algorithm when the RLS is used to update the tap weights. The performance of the RLS scheme is much worse if the power is updated more frequently. The forgetting factor for the RLS algorithm was 0.99. Haykin in [39] presented a detailed study of the tracking performance of these algorithms. Figures 6.9, 6.10, and 6.11 show the performance of the power control proposed in this chapter to those proposed in [36] and [35]. For these results, the number of users is 10 and the SINR is 10. As shown in the figures, these algorithms converge asymptotically to the same SINR and total transmitted values. It seems the converÂ¬ gence of the PCA proposed in this chapter is smoother but slower than the algorithms presented in [36] and [35]. As has been pointed out earlier, the PCA proposed in [35] uses measurements of the MSE which require knowledge of the actual transmitted bits in addition to knowledge of the channel gain. To implement the algorithm preÂ¬ sented in [36], sample averages of the input and the output of the MMSE receiver are required to provide an estimates for some parameters to update the power. In addition, the channel gain of the desired user needs to be estimated using pilot symÂ¬ bols. There is no knowledge of the other users information required to implement the power control algorithm proposed in this chapter. Only one parameter, given in eqn. 6.7, which includes the channel gain of the desired user need to be estimated. In fact, when constant envelope modulation is used, no pilot symbols need to be sent 98 Figure 6.9: Total transmitted power and SINR convergence of the proposed algrithm eqn. (6.5) for 10 users and SINR = 10 dB. since the value of |dÂ¿| is constant and it is known for the transmitter. In this case, only the value of the output of the MMSE filter need to be sent to the transmitter to update its power. In the previous figures, the channel gain and the parameter (afcj) are assumed to be known exactly by the transmitter. Figure 6.12 shows the convergence of the SINR and the total transmitted power when 77 is estimated using eqn. (6.7). In this case the estimates of are updated every 10th symbol. The results 2 here show that the PCA can be implemented practically and only the value of needs to be di needs to be sent to the transmitter. Practically, the the parameter quantized and then sent to the transmitter. The accuracy of these values depends on the overhead that can be tolerated by the system. To examine the performance of the proposed PCA in a slowly fading channel, an MMSE receiver based CDMA system using the proposed PCA was simulated in a fading channel. To generate Figure 6.13, the following simulation environment was chosen. The mobile speed was 3 mph, the mobile operate at the 900 MHZ band, the bit rate was 9600 bps. This corresponds to a normalized Doppler frequency (fdTs) of 0.00042. The shadowing was modeled as 99 Figure 6.10: Total transmitted power and SINR convergence of the PCA proposed in [36] for 10 users and SINR = 10 dB. Figure 6.11: Total transmitted power and SINR convergence of the PCA proposed in [35] for 10 users and SINR = 10 dB. 100 102 CD 03 10Â°[ 1 1 1 1 1 0 5 10 15 20 25 30 Iteration Figure 6.12: A typical SINR and total TX power convergence for a practical impleÂ¬ mentation of the PCA for 5 users a lognormal distribution with 8 db standard deviation. The initial tansmitted power was .1 for all users. As can be seen from the figure, the SINR converges to the desired value of 10 dB. On the other hand, unlike the previous results, the total transmitted power does not converge to a single value due to the presnce of the fading. To investigate the effect of the rate of updating the power on the convergence behavior of the SINR and the total transmitted power, a system operating in a slow fading channel with the same fading parameter as the one described in the previous paragraph and with 5 users has been simulated for different power updates rates. Figures 6.14, 6.15, and 6.16, show the performance when the transmitted power is updated every 1, 10, and 20 symbols, respectively. It can been seen that if the power is updated every symbol, the convergence of the SINR is smooth but when the power control update rate is decreased, although SINR converges to the desired value, the time varying nature of the channel effects the convergence behavior of the SINR as shown in Figure 6.15, and 6.16 . For example, it can be seen that a specific user, at a given time, may deviate from the desired SINR value and the converges back. 101 Figure 6.13: Total transmitted power and SINR convergence of the PCA proposed in a slowly fading channel for 10 users and SINR = 10 dB. Figure 6.14: SINR and Total transmitted power of the PCA proposed in a slowly fading channel for 5 users, SINR = 10 dB, and power update every 1 symbol. 102 Figure 6.15: SINR and Total transmitted power of the PCA proposed in a slowly fading channel for 5 users, SINR = 10 dB, and power update every 10 symbols. Figure 6.16: SINR and Total transmitted power of the PCA proposed in a slowly fading channel for 5 users, SINR = 10 dB, and power update every 20 symbols. 103 6.3 Summary In this chapter, a fully distributed power control algorithm based on the minimum mean-squared error (MMSE) receiver is proposed. It has been shown that using the proposed PCA, will force the SINR at the output of the MMSE receiver to converge to the target SINR. In addition, it has been shown that despite the fact that the MMSE receiver is near-far resistant, its performance in terms of capacity can be improved by usÂ¬ ing power control. The proposed PCA was shown to yield on average a capacity improvement of more than 20% over an MMSE based CDMA system with perfect power control where all users are received at the same power. Furthermore, the sysÂ¬ tem capacity obtained by using the power control algorithm proposed in this chapter is comparable to the theoretical capacity bounds of an MMSE system using optimal sequences or asymptotic assumptions. CHAPTER 7 CONCLUSION AND FUTURE WORK 7.1 Conclusion In this dissertation, the possibility of using the MMSE receiver as the underlying receiver structure for future CDMA systems has been investigated. Two areas of improvements of a MMSE receiver based CDMA system were examined; namely, the areas of multilevel modulation and power control. The performance of the MMSE receiver based CDMA with BPSK, QPSK, and 16-QAM modulation formats was examined in AWGN channel in Chapter 3. It has been shown that if the bandwidth and information rate the same for BPSK, QPSK, and 16-QAM, were kept the same, the 16QAM-based system outperforms the other modulation formats based system when the loading of the system is high. This perÂ¬ formance improvement is made possible by increasing the processing gain and hence increasing the ability of the MMSE receiver to suppress the multiple access interferÂ¬ ence. Since the MMSE receiver will be operating in a near-far resistant region, the SINR can be increased to get acceptable performance of the 16-QAM-based system. As we have seen, for highly loaded system, the system has an error floor in the case of BPSK and QPSK that is invariant to the increase of SINR. This performance limitation can be overcome by choosing a higher order modulation. The performance of the system in a fading channel with the previous modulation formats was investigated in chapter 4 and 5. The inability of the present MMSE receiver structure to operate in a fading channel for one- and two-dimension was demonstrated. A general structure of the MMSE receiver, which can perform effecÂ¬ tively for a wide range of modulation formats in a fading channel, was proposed. For successful detection of the desired userâ€™s signal, the phase and amplitude of the fading 104 105 process of the desired user fading need to be estimated. A tracking technique based on periodic pilot symbols and linear prediction was proposed to estimate the fading process of the desired user. The main reason for introducing pilot symbols here is to prevent the MMSE filter from feeding back the wrong decisions when the desired sigÂ¬ nal goes through a deep fade while the MMSE filter operating in the decision directed mode. In AWGN channel, 16-QAM modulation system was suggested to be the best choice out of the 3 modulation formats because of its ability to support more users. However, in a fading channel, if the fading process is known or the fading estimation error is very low, 16-QAM modulation should be employed. On the other hand, if the fading error estimation is high, QPSK modulation should be used since it is more robust for high estimation errors. The performance of the system in a fading channel with the previous modulation formats was investigated in Chapters 4 and 5. The inability of the present MMSE receiver structure to operate in a fading channel for one- and two-dimension was demonstrated. A general structure of the MMSE receiver which can perform effecÂ¬ tively for a wide range of modulation formats in a fading channel was proposed. For successful detection of the desired userâ€™s signal, the phase and amplitude of the fading process of the desired user fading need to be estimated. A tracking technique based on periodic pilot symbols and linear prediction was proposed to estimate the fading process of the desired user. Theoretical BER performance bound for AWGN and fading channels for these modulation formats were presented. These bounds for a single user CDMA system found to be in agreement with the well know single user BER bounds in these enÂ¬ vironments. In addition BER bounds for the case when there is a phase offset in the desired user signal were derived and found to be in a greement with the previous results. 106 The other area of the system design improvement that was investigated was the use of power control in a MMSE based CDMA system. It has been shown that despite the fact that the MMSE receiver near-far resistant, its performance can be improved by using power control. A fully distributed power control algorithm based on the desired MMSE value, which correspond to a desired SINR value, for a MMSE receiver based CDMA system was proposed. By using the proposed PCA, the capacity of the system was improved by more than 20%. The convergence speed of the power algorithm varies depending on the way the tap weights are updated. The convergence and tracking performance of the LMS algorithm are superior to those of the RLS algorithm. This may be due to the fact that the step size of the LMS algorithm is updated for each power update while the RLS parameter is kept constant. An adaptive step size for the LMS is essential to improve the tracking capability of these adaptive algorithms. The tracking of the RLS is very sensitive to the frequency of updating the power. Compared to the LMS, the RLS can not keep up with very frequent updates of the power. One may resort to an adaptive memory RLS or Kalman filtering theory to improve the performance of the RLS algorithm. Haykin in [39] presents a detailed study of the tracking performance of these algorithms. The results in this dissertation clearly indicate that using higher order modulation and power control can increase the capacity and enhance the performance of a MMSE based CDMA system. Furthermore, the results here suggests that the MMSE receiver could be a good candidate to be implemented in future CDMA systems. In the next section, some future research issues are addressed. 7.2 Future Work In this section, some areas of future research will be suggested, the results preÂ¬ sented in chapter 3,4, and 5 have clearly suggested the potential use of higher order 107 modulation formats. In chapter 5, we have proposed a tracking scheme of the deÂ¬ sired userâ€™s fading process. From the results presented there, we found that 16-QAM system performance was not acceptable at high doppler rate mainly due to the estiÂ¬ mation error. If the fading of the desired user is known to the receiver the 16-QAM system will outperform the QPSK system. One can argue that if the estimation of the fading process can be improved, the performance of the system in terms of BER and capacity will improve as well. This motivate the search for better tracking and estimation techniques. The tracking technique and the general MMSE receiver structure proposed in chapter 5 can be used as a tool to investigate the MMSE receiver performance when channel coding, like trellis-coded modulation (TCM), is used. As indicated before, adopting a higher order modulation to improve the BER performance of the system will be paid for by increasing the transmitted power. If increasing the transmitted power is not desirable, one can resort to combined modulation and coding in the form of trellis-coded modulation (TCM). TCM was introduced by Ungerboeck [45] as means of channel coding that can be used without increasing the bandwidth and transmitted power. The price for the performance improvement comes in the form of decoder complexity at the receiver. Now suppose we apply a TCM coding scheme to a higher order modulation formats (such as QPSK or 16QAM). The bandwidth and the information rate are all the same, while for a given error probability performance, the required SINR of the coded system will be less than in the uncoded system. Therefore, the interference level will be less and one would expect the capacity of the system to increase as a result of coding. TCM has major potential to be used in these systems and more research needs to be done regarding this topic as explained below. Boudreau et.al. [46] have shown that low-rate convolutional codes perform better than the corresponding trellis codes for a given complexity and throughput. This 108 result was attributed to the distance properties of the low-rate convolutional code despite the increase in cross-correlation between the spreading sequences due to the use of shorter sequences. The results presented in [46] are for a conventional receiver- based CDMA system in an AWGN channel. Oppermann et.al. [47] have shown different results for an MMSE receiver-based CDMA system operating in AWGN to that for the conventional receiver based CDMA system in [46]. Oppermann et.al. found that an MMSE based CDMA system perÂ¬ forms better with trellis coding. The apparent difference of the results of [48] and [46] on one side and [47] on the other side needs to be addressed. When the power control algorithm performance was investigated for a fading channel in chapter 6, the channel gains are assumed to be constant during the power control updates. This assumption may hold true for the shadowing effect but is not realistic for multipath fading. To get better performance one may resort to channel prediction, as described in [49] and [50], to predict the future gain of the channel and update the transmitted power accordingly. The study of power control of more sophisticated systems with different data rates and QoS requirements is appealing. Preliminary study is presented in [51]. It is interesting to extend the work presented in that dissertation to study whether the proposed power control function converges and how this convergence is affected by the traffic type probabilities. Another future research avenue of this work and built upon treatment of the power control area by Tse and Hanly in [37]. The effective bandwidth concept which has been developed by Tse and Hanly for the MMSE receiver is only valid in the perfectly power-controlled single cell case. Due to the important role this concept plays in characterizing the capacity of the system, it will be very useful and interesting to expand this concept to multicell systems. REFERENCES [1] R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, â€œTheory of spread-spectrum communicationsâ€”a tutorial,â€ IEEE Transactions on Communications, vol. 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Teh, â€œReception of PSK signals over fading channel via quadrature amplitude estimation,â€ IEEE Trans. On Commun., vol. COM-31, no. 8, pp. 1024-1027, August 83. [34] A. F. Almutairi, S. L. Miller, H. A. Latchman, and T. F. Wong, â€œMMSE based fully distributed power control algorithm,â€ IEEE Military Communications ConÂ¬ ference Proceedings, p. xxxx, 1999. [35] P. S. Kumar and J. Holtzman, â€œPower control for a spread spectrum system with multiuser receivers,â€ in IEEE PIMRCâ€™95, 1995, pp. 955-958. [36] S. Ulukus and R. Yates, â€œAdaptive power control with MMSE multiuser detecÂ¬ tors,â€ in IEEE International Conference on Communications, 1997, pp. 361-365. 112 [37] D. Tse and S. Hanly, â€œLinear multiuser receivers: Effective interference, effective bandwidth and user capacity,â€ IEEE Transactions on Information Theory, vol. 45, no. 2, pp. 641-657, March 1999. [38] P. Viswanath, V. Anantharam, and D. N. Tse, â€œOptimal sequence, power control and user capacity of synchronous CDMA system with linear MMSE multiuser receivers,â€ IEEE Transactions on Information Theory, vol. 45, no. 6, pp. 1968â€” 1983, September 1999. [39] Haykin.S, Adaptive Filter Theory, Prentice Hall, 1996. [40] I. Korn, Digital Communications, Van Nostrand Rienhold Company Inc, 1985. [41] H. V. Poor and S. VerdÃº, â€œProbability of error in MMSE multiuser detection,â€ IEEE Transactions on Information Theory, vol. 43, no. 3, pp. 858-871, May 1997. [42] M. G. Shayesteh and A. Aghamohammadi, â€œOn the error probability of linÂ¬ early modulated signals on frequency-flat ricean, rayleigh, and AWGN channels,â€ IEEE Trans. On Commun., vol. 43, no. 2/3/4, pp. 1454-1466, 1995. [43] S. A. Grandhi, R. Vijayan, D. Goodman, and J. Zander, â€œCentralized power control in cellular radio systems,â€ IEEE Transactions on Vehichular Technology, vol. 42, no. 4, pp. 466-468, November 1993. [44] T. Lee and J. Lin, â€œA fully distributed pc algorithm for cellular mobile system,â€ Ieee Journal on Selected Areas in Communications, vol. 14, no. 4, pp. 692-697, May 1996. [45] G. Ungerboeck, â€œChannel coding with Multilevel/Phase signals,â€ IEEE TransÂ¬ actions in Information Theory, vol. IT-28, pp. 55.67, Jan. 1982. [46] G. Boudreau, D. Falconer, and S. Mohamoud, â€œA comparision of trellis coded versus convolutionally coded spread spectrum multiple-access system,â€ IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 628-640, May 1990. [47] I. Oppermann, P. Rapajic, and B. Vucetic, â€œCapacity of a band-limited CDMA MMSE receiver based system when combined trellis or convolutional coding,â€ Submitted to IEEE Transactions on Communications, 1998. [48] A. J. Viterbi, â€œVery low rate convolutional codes for maximum theoretical perforÂ¬ mance of spread spectrum multible-access channels,â€ IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 641-649, may 1990. [49] C. Trabelsi, â€œLinear adaptive prediction using LMS algorithm over rician fading channel,â€ Telecommunication Systems, vol. 7, no. 2, pp. 193-199, 1996. 113 [50] K. L. Baum, D. E. Borth, and B. D. Mueller, â€œA comparison of nonlinear equalization methods for the u.s, digital cellular system,â€ IEEE International Conference on Communications (ICC), pp. 291-295, 92. [51] T. H. Hu and M. M. K. Liu, â€œA new power control function for multi-rate DS- CDMA systems,â€ submitted to IEEE Transactions on communications, 1998. BIOGRAPHICAL SKETCH Ali Faisal Almutairi was born in Kuwait City, Kuwait, in 1970. He received his B.S. degree in electrical engineering, in May 1993 from the University of South Florida, Tampa, FL. In June 1993, he joined Kuwait University as a laboratory engineer. In December 1993, he has been awarded a full scholarship from Kuwait University to pursue his graduate studies. He received his masterâ€™s degree in electrical engineering in December 1995. In the summer of 1997, he joined Motorola Land Mobile Products Sector, Plantation, FL, as an intern. He received his Ph.D. degree in electrical engineering in May 2000. 114 I certify that I have read this study and that in my opinion it conforms to acceptÂ¬ able standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Haniph A. Latchman, Chairman Associate Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptÂ¬ able standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Tan F. Wong Assistant Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptÂ¬ able standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. William W. Edmonson Assistant Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptÂ¬ able standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ulrich H. Kurzweg Professor of Aerospace Engineering, Mechanics, and Engineering Science This dissertation was submitted to the Graduate Faculty of the College of EnÂ¬ gineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. May 2000 M. J. Ohanian Dean, College of Engineering Winfred M. Phillips Dean, Graduate School 50 22 = Pf Ri :Pi [dQ1cos(A9hm) + dnsin(A9hm)\ + 2 (4.35) cos(A0liTny Making use of the matrix-inversion lemma; Rf1 can be shown to be equal Rr1 = Rr1 + 'Piicos^d^) + pf Rj-'Pij^pf Rr1 cos2(A^iim)Rj)1 cos2(A^1,m) + 2PfRr1P1 The variances of \ and 2 are equal and are given as follows: (4.36) (4.37) cl = E[ if] = Pf TL^E [yiyf ] Rf'Pi = PfR_llR1R]'1P1 (4.38) (4.39) (4.40) Substituting the value of R: 1 from Equation (4.37) into Equation (4.40) results in n siven by cos2(A01,m)PfR71P1 = (cos2(A0lim) + 2Pf R^Pr) The output of MMSE filters, Zi and z2, can be written in terms of Rr1 as zi = Kcos{A9^m)dn Ksin(A6hm)dQi + (4.41) (4.42) z2 = Kcos(A9liTn)dQi + K sin(A91,rn)dI1 + 2 (4.43) where fi\ and 2 are assumed to be N(0, an2) and K is given by K= WAfl^PfR.-P, (444) cos2(A01) + 2PfR-'P Since Zi and z2 represent the statistics of dn and 9q\, z\ and z2 can be written as z\ Kcos(A9i^m)dn + rhi (4.45) This dissertation was submitted to the Graduate Faculty of the College of En gineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. May 2000 M. J. Ohanian Dean, College of Engineering Winfred M. Phillips Dean, Graduate School 76 Figure 5.16: BER of QPSK with different estimation error variances for 30 users. For the estimated case PSAM rate =.2, L= 3 pg= 62, Another observation to be made from these figures is that the performance of the system in terms of BER becomes less sensitive to the increase of the real and imaginary parts of the estimation error variances at high load. This becomes clear by comparing the 3 and 30 user systems for 16-QAM or QPSK systems. For example, when (j2 lx 10-4, the 30 user 16-QAM based system performs very close to the system with known desired user fading while the 3 user system degrades substan tially. This is more clear in the QPSK system, where in the 30 user case the system performance is almost the same as that of a known fading case while for 3 users there is a loss of about 5 dB for BER more than 1 x 10-4. One can expect these results because when the system load is low, the multiple access interference is not a major factor on the BER, while the estimation error is. At high loads, the multiple access interference is a major factor in the BER performance of the system and its effects are more dominant than the effect of the estimation error. This suggests that for 35 Figure 3.1: Theoretical performance of BPSK, QPSK, and 16-QAM in a Gaussian channel with one user. where M is the number of points in the constellation. For BPSK, QPSK, and 16- QAM, M equals 2, 4, and 16, respectively. The justification for the Gaussian approximation is based on the central limit theorem by noting that the output of the filter is a sum of random variables with different probability density functions (pdfs). Therefore, the sum of these random variables at the output of the filter can be considered a Gaussian random variable. This approximation is widely used in evaluating conventional receivers [9]. This ap proximation is more accurate with the MMSE receiver since we have less interference at the output of the filter and more Gaussian noise [20]. Poor and Verdu in [41] have studied the behavior of the output of the MMSE receiver and found that the output is approximately Gaussian in many cases. 3.2 Results Figures 3.1, 3.2, and 3.3 show the performance of the MMSE receiver with BPSK, 80 Figure 5.19: BER of 16-QAM with different PSAM rates; L= 3 30 users, pg= 124, fdTs = 0.017. Figure 5.20: BER of 16-QAM with different PSAM rates; L= 3 30 users, pg= 124, fdTs = 0.0335. 42 Rl = + R = 2PP = R2 H R (4.5) ai = a2 = Ri Pi a where Ri = E [yiyi^]. The output of the filter can be written as zi = aHyi = 2Re[d1]P1iiRr1P1+P1HRr1yi = 2 Re [dijPi^Ri-1?! + i (4.6) (4.7) (4.8) (4.9) Now we need to find the value of Pi^Ri xPi and the variance of \. Using the matrix-inversion lemma, we can find the inverse of R as follows Rr1 Ri -i 1 + 2P1hR1 P, It can be shown that the variance of the term i is p^Rr'Pi - -i. (4.10) ^[if] = [n-2P1HR1-1Pi]i Then the output of the modified MMSE , 2PiiR_1P , z = d\\ = L1 + 2P/iR-1PJ pi/^-rp (4.11) + Njl 0, + Nq(o, [l + 2PfrR"1P] PhR-1P [l + 2PffR-1P]: (4.12) 110 [14] R. Lupas and S. Verdu, Linear multiuser detectors for synchronous code division multiple-access channels, IEEE Transactions on Information Theory, pp. 123-136, 1989. [15] R. Lupas and S. Verd, Near-far resistance of multiuser detectors in asyn chronous channels, IEEE Transactions on Communications, vol. 38, no. 4, pp. 496-508, Apr. 1990. [16] M. Varanasi and B. Aazhang, Multistage detection in asynchronous code division multiple-access communications, IEEE Transactions on Communi cations, vol. 38, pp. 509-519, 1990. [17] M. Abdulrahan, A. U. H. Sheikh, and D. D. Falconer, Decision feedback equal ization for CDMA in indoor wireless communications, IEEE Journal on Selected Areas in Communications, vol. 12, no. 4, pp. 698-706, May 1994. [18] P. B. .and Rapajic B. and S. Vucetic, Adaptive receiver structures for asyn chronous CDMA systems, IEEE Journal on Selected Areas in Communications, vol. 12, no. 4, pp. 685-697, May 1994. [19] U. Madhow and M. L. Honig, MMSE interference suppression for direct- sequence spread-spectrum CDMA, IEEE Transactions on Communications, vol. 42, no. 12, pp. 3178-3188, Dec. 1994. [20] S. L. Miller, An adaptive direct-sequence code-division multiple-access receiver for multiuser interference rejection, IEEE Transactions on Communications, vol. 43, no. 2/3/4, pp. 1746-1755, Feb./Mar./Apr. 1995. [21] C. N. Pateros and G. J. Saulnier, Interference suppression and multipath mit igation using an adaptive correlator direct sequence spread spectrum receiver, in Proceedings IEEE International Conference on Communications, 1992, pp. 662-666. [22] A. N. Barbosa and S. L. Miller, Adaptive detection of DS/CDMA signals in fading channels, IEEE Transactions on Communications, vol. 46, no. 1, pp. 115-124, Jan. 1998. [23] A. F. Almutairi, S. L. Miller, and H. A. Latchman, Performance of multi level modulation in MMSE receiver based CDMA systems, IEEE Military Communications Conference Proceedings, p. xxxx, 1999. [24] A. F. Almutairi, S. L. Miller, and H. L. Latchman, Tracking of multilevel modulation formats for DS/CDMA system in a slowly fading channel, DIM ACS Series in Discrete Mathimatics and Theoretical Computer Science, p. xxxx, 1999. TABLE OF CONTENTS gage ACKNOWLEDGMENTS iii ABSTRACT vi CHAPTERS 1 INTRODUCTION 1 1.1 Direct Sequence Code-Division Multiple-Access Systems ... 1 1.2 IS-95 CDMA Standard 7 1.2.1 Channel Structure 7 1.2.2 Modulation and Coding 8 1.2.3 Power Control 12 1.3 The MMSE Receiver 14 1.4 Motivation and An Overview of the Dissertation and Litera ture Review 16 2 SYSTEM MODEL 24 2.1 The Transmitter 24 2.2 The Receiver 25 3 MULTILEVEL MODULATION IN AWGN CHANNEL 30 3.1 Performance in A Gaussian Channel 30 3.2 Results 35 3.3 Summary 38 4 MULTILEVEL MODULATION IN A FADING CHANNEL .... 40 4.1 Performance Analysis 40 4.2 The Effect of Phase Offsets on the Performance of the System 46 4.3 Summary 57 5 FADING PROCESS ESTIMATION 58 5.1 The MMSE Receiver Behavior in A Fading Channel 58 5.2 Tracking Techniques in A Fading Channel 63 5.3 The Effect of the Fading Estimation Error on the Performance of the System 69 IV The use of higher order modulation formats, like 16 Quadrature amplitude mod ulation (16-QAM) and quadrature phase shift keying (QPSK), is investigated and compared to a binary phase shift keying (BPSK) based system in both additive white Gaussian noise (AWGN) and fading channels. One drawback was the inability of the MMSE receiver to perform properly in a more realistic wireless environment where fading is considered. This problem was investigated and a general MMSE receiver structure, which is capable of demodulating a wide range of digital modulation for mats, is proposed. It is shown that, in an MMSE based CDMA system, modulation format choice has a significant effect on the capacity of the system. The performance of such a system with the three different modulation formats mentioned previously was investigated. It is found that the 16-QAM outperforms BPSK and QPSK in AWGN and fading channels when the fading estimation error is very low for a highly loaded system. On the other hand, if the fading estimation error is high, QPSK modulation should be used since it is more robust for high estimation errors. The other area for improvement of the proposed system that has been investigated is the use of power control. It was found that the use of power control improves the performance of the MMSE receiver based CDMA system despite the fact the MMSE is known to resist interference by other users. A power control algorithm (PCA) which is based on the desired MMSE value of the user and which is capable of equalizing the output signal to interference and noise ratio (SINR) is proposed. The convergence of the algorithm in terms of SINR and total power is investigated. The implementation of the proposed PCA was found to improve the capacity of the system substantially. For example, The proposed PCA was shown to yield on average a capacity improvement of more than 20% over an MMSE based CDMA system with perfect power control where all users are received at the same power. Vll 36 Figure 3.2: Theoretical and simulation performances of BPSK, QPSK, and 16-QAM in a Gaussian channel with 20 users. QPSK, and 16-QAM in a Gaussian channel for 1-, 20-, and 50- user CDMA systems. The theoretical results are based on the BER equations obtained in the previous section. The processing gains are 31, 62, 124 for BPSK, QPSK, and 16-QAM re spectively. These processing gains were chosen to ensure the full use of the available bandwidth by these systems. We will use these values of processing gains for the modulation formats for the rest of the dissertation. For the single user case the results are the same as the results found in the digital communication literature, for example [11]. For a single user system, the bit error rate is the same for BPSK and QPSK and lower than that of 16-QAM for a given ^. When the load of the system increases to 20, the QPSK-based CDMA systems outperforms the BPSK and the 16-QAM systems. The rate of improvement is faster for QPSK than for BPSK as the increases. On the other hand, the 16-QAM sys tem starts about 1 dB worse than BPSK but at about ^ = 12 dB the 16-QAM BER becomes lower than that of BPSK for a given With the load further increased to 103 6.3 Summary In this chapter, a fully distributed power control algorithm based on the minimum mean-squared error (MMSE) receiver is proposed. It has been shown that using the proposed PCA, will force the SINR at the output of the MMSE receiver to converge to the target SINR. In addition, it has been shown that despite the fact that the MMSE receiver is near-far resistant, its performance in terms of capacity can be improved by us ing power control. The proposed PCA was shown to yield on average a capacity improvement of more than 20% over an MMSE based CDMA system with perfect power control where all users are received at the same power. Furthermore, the sys tem capacity obtained by using the power control algorithm proposed in this chapter is comparable to the theoretical capacity bounds of an MMSE system using optimal sequences or asymptotic assumptions. CHAPTER 4 MULTILEVEL MODULATION IN A FADING CHANNEL In this chapter, we will extend the work of the previous chapter by investigating the performance of the 3 modulation formats, namely, BPSK, QPSK, and 16-QAM, in a fading channel. These different modulation formats are compared based on their BER performance at different loadings of the MMSE based CDMA system. The results presented in this chapter are based on the assumption the the optimum implementation of the MMSE filter has been used. 4.1 Performance Analysis In this section, we will provide a performance analysis, both analytically and through simulation when a multilevel modulation schemes, like QPSK and 16-QAM, are used in a fading channel. In this section, the optimum MMSE filter is used and hence all the users fading processes are assumed to be known to the receiver. In the next chapter, the perfor mance of the system, where an adaptive MMSE filter implementation is used, will be investigated in detail. We modify the model presented in Chapter 2 to study the performance of the CDMA system using different modulation formats in a fading channel. This can be done by setting = 1 and assuming that user 1 is the desired user and the integrator in front of the MMSE receiver has a scale factor of \/2piTc associated with it. Based 40 25 Figure 2.1: System Model Cj(t) -yÂ¡2pÂ¡sin(wj) Figure 2.2: Transmitter of the jth user Ts/Tc. Throughout this dissertation, user 1 is considered the desired user unless spec ified otherwise. We are interested in demodulating its signal and the other users are treated as multiple access interefernce. 2.2 The Receiver After going through the communication channel, the bandpass received signal at the receiver corresponding to the jth user is given by K r(t) = Re{J2 s/hijOijity6^ gÂ¡(t Tj)eWot} + n{t) j=i (2,2) 78 Figures 5.17 to 5.20. PSAM rates of 0.2, 0.1, 0.05, and 0.02 were used. As expected, the higher the PSAM rate the better the performance. This is more evident at high Doppler rates. The performance improvement due to the high PSAM rate in terms of BER came at the expense of the bandwidth efficiency of the system. For example, in the case of a PSAM rate of 0.2, 20% of the available bandwidth is used for sending pilot symbols where at a PSAM rate of 0.05, only 5% of the available bandwidth is used for pilot symbols. The system designer needs to balance the tradeoff between the bandwidth efficiency and the performance of the system in terms of BER. Based on these figures, we see that at low Doppler rate, independent of the loading of the system, a small penalty in ^ is paid if a PSAM rate of 0.1 is used instead of 0.2. For example; in the case of a system employing a 16-QAM modulation with a load of 30 users and the mobile speed of 5 mph which corresponds to a normalized Doppler frequency of 0.0028, the difference in performance when a PSAM rate of 0.2 and 0.1 is about 2 dB and the use of the lower PSAM rate is attractive in this situation. The use of lower than 0.1 PSAM rate even at low Doppler rates will degrade the perfor mance substantially as shown in Figure 5.17, 5.18, and 5.21. On the other hand, At a higher Doppler rate as shown in Figures 5.22 the penalty in is about 5 dB when a PSAM rate of 0.1 is used instead of 0.2 and this penalty widens substantially when a lower PSAM rate is used. For 16-QAM system with normalized Doppler frequency, /dTs, 0.0335 which is shown in figure 5.22 there is a substantial improvement due to the use of higher rate PSAM but the system is still not attractive since an error floor develops at high BER. The improvement in the performance of the system due to the use of higher PSAM rate is due to the fact that sending PSAM frequently will improve the estimation of the fading process which translate to an improvement to the system BER performance. This can be seen from Table (5.1) and Table (5.2). By comparing the variances of the real and imaginary parts of the error process for the system with PSAM rate 29 the Wiener Hopf equation and the optimum vector of the filter coefficients is given by w = R_1P (2.9) The value of Jmim can be obtained by substituting the optimum vector of the filter coefficients given by Eqn. 2.9 in Eqn. 2.8. This will result in Jmin = where a2~ is the variance of the data symbols. Although the optimum tap weights force the MMSE receiver to operate at Jmin, these weights are hard to obtain in practice due to the unavailability of the autoc- corelation matrix. Adaptive algorithms like the Least- Mean-Square (LMS) and the Recursive Least-Square (RLS) are used to drive the filter coefficients close to the optimum tap weights. In this dissertation, the LMS will be used as the adaptive algorithm in the MMSE receiver unless specified otherwise. 64 system. It has been shown by [22] that phase compensation is an effective method of improving the MMSE receiver performance in a fading channel. In [22] a phase estimate is obtained by using a linear predictor. In our case, since we are dealing with multilevel modulation, 16-QAM, amplitude and phase compensation are needed to improve the performance of the MMSE receiver. We studied the capabilities of three techniques in tracking the fading amplitude and phase. These techniques are based on pilot symbols and/or linear prediction. The first tracking technique uses the decision out of the MMSE to form an es timate of the desired users fading parameters using linear prediction. The channel estimation based on this technique is shown in Figure 5.5. This technique is presented in some detail in [22] for a CDMA system with BPSK modulation. It worked fairly well for BPSK modulation but not in the case here, where 16-QAM modulation is CHAPTER 2 SYSTEM MODEL In this chapter, a general CDMA system model, shown in Figure 2.1, based on the MMSE receiver is described. The model here will be flexible and easy to modify to accommodate the study of different issues concerning the MMSE receiver based CDMA system design. For example, when we study the performance of the system in AWGN channel, we can simplify the model by setting the fading amplitude to 1 and the fading phase to zero. The system consists of K users transmitting asynchronously over an AWGN channel or Rayleigh fading channel. The received signal, which consists of the desired user signal, interference from other user signals, and AWGN, is demodulated using the MMSE reciever. In the following sections, the transmitter and the receiver, shown in Figures 2.1 and 2.2, will be described. 2.1 The Transmitter There are K transmitters, one for each user, in this system. In this dissertation, the transmitter, shown in Figure 2.2, uses either a BPSK, QPSK, or 16-QAM. Each user is assigned a unique random spreading waveform c(). The modulated signal of the jth user can be written as Sj(t) = Re (2.1) = R z{gtywot} where w0 is the carrier frequency which is the same for all users, (t) is the com plex envelope of Sj(t), Pj is the transmitted power, and dj(t) is a complex baseband signalling format with symbol interval Ts. The waveform Cj(t) is assumed to be in the polar form with chip interval Tc. Therefore, the processing gain N is equal to 24 86 other hand, if the fading error estimation is high, QPSK modulation should be used since it is more robust for high estimation errors. 96 -5 -10 -15 1 0 50 100 150 200 Iteration Figure 6.7: A typical SINR convergence SINR = 9.5 dB for 15 users using RLS algorithm Figure 6.8: A typical total transmitted power for 15 users using the RLS algorithm 53 + 2 [ V 7T Ja=o Jui = roo r Ja=0 Ju -U a exp (a2) exp dui da Ul=ai,my/\L%h 2 -U a exp (a2) exp - du2 da (4.61) ' U2=ai,m\/\Llh 2 By setting V\ = and t>2 = ^ Equation (4.61)can be written as 2 roo roo Â¡= / / aexp((a2 -f vf))dvi, da V7r Ja=0 Jvi ' Vi=ai^my/\L\h r>00 roo roo roo J a=0 JD2=o 1 V2 &l,m 4 Using the polar coordinates, we have aexp((a2 + vl))dv2, da (4-62) 2 2,2 r1 = a +v{ (4.63) . . 0 = tan 1 v (4.64) Ps - + + r\ exp(r\)dridOi r% exp(rl)dr2d02 I L\cos2{A6>iim)ciHRx \ 2 \V 4 + L?cos2(A01>m)ciirRf1c1 J If I L22cos2(Ag1;m)ciifR^1Ci \ 2 V y 4 + L\cos2{A6iim)ciHRf xcx / (4.65) If there is no phase offset, A0i)m = 0, Equation (4.65) reduces to Equation (4.23). For the 16-QAM system the probability of symbol error conditioned on ax, Ps/ai, can be approximated by the following equation after ignoring the terms that have 48 error rate (SER) bounds for QPSK and 16-QAM systems are derived when there is an imperfect phase reference. The SER for a QPSK and the 16-QAM systems can be derived as follows. We try to eliminate the phase variation in the desired signal by multiplying the received vector by the estimated phase as follows: y(m) = e-jÂ§imT(m) (4.25) where 61 is the estimated value of the desired users fading phase, the vector y(m) can be written as K y (m) = d1(m)altTnc1e + dj(m l)gj(l,S) = di(m)alimeJ01-mCi + y(m) jifil ,m $1 ,m) + E @1 ,m) 3=2 + n(m)e~^l,n dj{m)fj(l,6) (4.26) where A6fii7n = 0lim A0li?n is assumed to be \AÂ§i^m < || for QPSK and \AditTn < f | for 16-QAM because otherwise there are errors even without MAI and noise. Taking the real and imaginary parts of the vector y (m) results in yi = yt[y{m)] = [dncos{A6itm) ~ dQlsin(Ae^m)\a^mcx + yx(m) (4.27) y2 = 9f[y(m)] = \dnsin{Aehrn) dQicos(A6>i,m)]a:l!mCi + y2(m) (4.28) To find the optimum weights of the MMSE filter, ai and a2 the autocorrelation matrices Ri and R2 and the correlation vectors Pi and P2 corresponding to the received vectors yi and y2, respectively, need to be found. It can be shown that R: = R2 and Pi = P2. The optimum filter weights can be found as follows. Pi = E[[dI]y] = icos(A0lirn)alifnCi = P2 (4.29) 32 If we multiply both sides of eqn. (3.10) from the left by and the left by P and simplify the result we will get PhR-1P pffR-ip l + ptfRip (3.11) Now, we need to find the variance of the term = PHR_1f (3.12) E[H] = PHP~1E [rr^] R_1P (3.13) = PhR-1RR_1P (3.14) We can find P^R 1 by multiplying both sides of eqn. (3.10) by PH. This results in P^R1 P^R'1 = 1 + PifR1P (3.15) in a similar manner, we can find R *P by multiplying both sides of Eqn. (3.10) by P. This result in R-1P = R-*P 1 + PHR-1P Substituting Eqns. (3.15) and (3.16) into (3.14), P^R^P E [H] [1 TP^R-ip]' Then Eqn. 3.8 can be written as r PgR ~'P n 2 1L i nffp-ipJ + iV/(^0, + Nq 0, 1 + PHR_1P 1 P^R^P 2 [1 + P^R-ip]2 1 P^R^P 2 [l + ptfR~ip]: (3.16) (3.17) (3.18) 33 Having the output of the filter z in this form, it is straightforward to show that the probability of symbol error is given by [40] Pel&QAM where p ~ Q pffR-ip where the Q-function is defined as OO X (3.19) (3.20) (3.21) Equation (3.19) implicitly depends on the interfering users codes, delays, and trans mitted powers, through the matrix R. To obtain an average value for SER, one would average Eqn. (3.19) over these quantities. The symbol error rate (SER) can be related to Jmin by recalling (2.10) and recognizing that cr2- = 1. di Jmin = 1 P^R XP (3.22) substituting (3.11) into (3.22) Jmin 1 P//R~1P l + P^R-T 1 1 + P^R *P Eqn. 3.23 can be written as piip^lp Jmin Jmin then P can be written as P (i/Vr^) V V 5 Jnir, / 5 Jmin (3.23) (3.24) (3.25) 7 As it has been pointed out before, power control can greatly reduce interference and improve the system capacity by adjusting the transmitted power of the mobile users. In IS-95, power control is used so that the received signal strengths are about the same for all mobiles at the base stations. In this dissertation, we have introduced a power control algorithm that is capable of equalizing the output SINR and reducing the transmitted power for all the CDMA system users. The proposed power control algorithm is discussed in Chapter 6. Another avenue we have explored for reducing the interference is the idea of in creasing the CDMA system dimension, by choosing a higher level modulation format without increasing the bandwidth. This was accomplished by increasing the process ing gain (# of chips per symbol). This subject is treated in Chapters 3, 4, and 5 of this dissertation. 1.2 IS-95 CDMA Standard A CDMA cellular system was developed by QUALCOMM and adopted by the Telecommunications Industry Association (TIA) as a standard for digital cellular systems in 1992 under the name IS-95. We will study some aspects of IS-95 that are relevant to the work presented in this dissertation. Namely, we will discuss the channel structure, power control, and modulation and coding issues that are adopted in the IS-95. 1.2.1 Channel Structure The IS-95 CDMA system operates on the same frequency band as the Advanced Mobile Phone Systems (AMPS) with a 25 MHz channel bandwidth for the uplink (mobile to base station) and downlink (base station to mobile). The uplink uses the frequencies from 869 to 894 MHz, while the downlink uses the frequencies from 824 to 849 MHz. Sixty-four Walsh codes are used to identify the downlink channels. Long PN code sequences are used to identify the uplink channels. DESIGN ISSUES FOR MINIMUM MEAN SQUARE ERROR (MMSE) RECEIVER-BASED CDMA SYSTEMS By ALI FAISAL ALMUTAIRI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2000 27 K r 'i{m) = ^2 yjPj(m) \fhijOLj(m)e,ii'(m)dj(ra)fÂ¡(/, 6) j=i (2.3) + yjpj{m 1) i() eJ0j(m)dj(m l)g}(Z,<5) + n(m) In the above equation, t,- = ljTc + where lj is an integer and 0 < 6j < Tc. The vectors f) and g) are defined as follows f,M) yW -1 -1) + W-i) i)(1,S) = Y%j(N i -1) + (i y) %(n 0 where m = (<=?+^)/2 gj = (cf-f)/2 (Z) / \'j Cj \Cj,Nli Cj,Nl+1) Cj,N1) Cj, 1) > Cj,Nl\) Cj ( Cj,Nh Cj,JVZ+l) Cj,N1) Cj,0> Cjji, ii) Equation 2.3 can be written in a compact form as r(m) = \/pi{m) \[h~llOLÂ¡ (m)e0j (m) d(m)c + MAI + n(m) (2.4) and MAI = '22aj(m)ejej('m) yjpj(n)\ffhjdj(n)Â§ (,5) + ypj(n l)v//z^dJ(n l)g}(Z,) L In eqn. (2.4), n(m) is a vector of independent complex Gaussian random variables with zero mean and the variances of the in-phase and the quadrature components are 51 z2 = Kcos{A9^m)dQ1 + m2 (4.46) where mi = N(Ksin(A9itm)dQi, an2) (4.47) m2 = N(Ksin(A9hm)dn, an2) (4.48) Having the statistics in the form of z\ and z2, one can easily calculate the probability of symbol error conditioned on oti,Ps/ai, for QPSK an 16-QAM system. After ignoring the double Q-function terms, the Ps/ai of the QPSK system can be approximated by P, s/a i Q( K (cos(69ijjn) sin(S0ijTn)) % K (cos(59iyTn) + sin(59i ,m)) x/2 -) + Q( V2 ) (4-49) The value of can be simplified to <7m ^ K K2 4coa2( 4PfR^Pi (4.50) Let L, = cos(A6hm) sm(A(?l m) (4.51) = cos(A6im) + sin(A6hm) (4.52) Then P4/Ql can be written as -Ps/ai ~ Qi^LfPfR^Pi) + Qi^LlPfRr'Pi) (4.53) 113 [50] K. L. Baum, D. E. Borth, and B. D. Mueller, A comparison of nonlinear equalization methods for the u.s, digital cellular system, IEEE International Conference on Communications (ICC), pp. 291-295, 92. [51] T. H. Hu and M. M. K. Liu, A new power control function for multi-rate DS- CDMA systems, submitted to IEEE Transactions on communications, 1998. 14 power updates, the mobile station transmitted power is given by Preverse {dBm) Pj + The sum of the closed loop updates (1.5) The maximum value of the sum of the closed-loop updates is 24dB. A typical set of ranges and values for the parameters in the previous equations are -8 < Pnom < 7dB (1.6) A typical value of Pn0m is 0 dB. -16 < Pcorr < 15dB (1.7) A typical value of PCOrr is 0 dB. The values of these parameters for each base station are transmitted on the for ward channel in a message called the access parameters message. In Chapter 6, we introduce a power control algorithm that can be used to adjust the mobile station transmitted power in a closed loop power control fashion. The power control presented in Chapter 6 does not update the transmitter power in con stant steps of 1 dB like the IS-95 but with variable steps that are dependent on the channel condition and the MMSE receiver filter coefficients. Chapter 6 of this dissertation has been devoted to the power control issue in MMSE receiver based CDMA. 1.3 The MMSE Receiver To improve the performance of the CDMA system in the presence of MAI, and to mitigate the near-far problem, several receivers with different degrees of complexity and performance have been developed. For example, an optimum multi-user receiver is presented in [13]. The complexity of this receiver increases exponentially with the number of users. A suboptimal class of detectors with linear complexity are 67 Figure 5.7: Channel tracking using pilot symbols and linear prediction obtained by this estimate are used in demodulating the desired users signal until the next pilot symbol is received and a new estimate is made. We propose the use of pilot symbols for two reasons. First, pilot symbols can be used to periodically train the MMSE and prevent the MMSE filter from feeding back wrong decisions. The second reason for using pilot symbols is to aid the receiver in estimating the channel fading condition. The fading parameters obtained by this estimate are used in demodulating the desired users signal until the next pilot symbol is received and a new estimate is made. Obviously, this technique is suitable for a slowly fading channel and may not work well for a rapidly fading channel. We propose a third approach which consists of a combination of the first and second techniques. The tracking of the fading channel using this technique is shown in Figure 5.7. In this case, channel estimates are made by feeding back a linear prediction of the previous channel estimates. 55 Assuming that the system is using Gray coding, the bit error rate (BER) is given by BER SER log2M (4.73) Where M is the number of points in the constellation. For BPSK, QPSK, and 16- QAM, M equals 2, 4, and 16, respectively. These equations implicitly depend on the interfering user codes, delays, transmit ted powers, and fading amplitudes through the matrix R. To obtain an average value for SER or BER, one would average over these quantities. Figures 4.4 and 4.5 show the performance in terms of BER by using the theoretical error bounds presented in this section for different values of phase offsets (A9). In these figures, the A9 values are 0, 5, and 15 for the 16-QAM case and 0, 5, 15, and 30 for the QPSK case. We did not include the case where A9 30 for the 16-QAM because with such phase offset the 16-QAM system will not be operational even in the absence of MAI and noise effects. The curves, with the phase offsets, are obtained by using Eqn. (4.72) for the 16-QAM systems and Eqn. (4.65) for the QPSK systems. When the phase offset is 0, the theoretical results presented in this chapter in the form of Eqn. (4.72) and Eqn. (4.65) are in agreement with the results of the previous chapter given by Eqn. (4.21) and Eqn. (4.23). Comparing Figures 4.4 and 4.5, one notices that the 3 and 30-users 16-QAM systems have a very close BER performance while this is not true for the QPSK systems. This means that the 16- QAM is more resistant to the multiple access interference caused by the other users. From Figure 4.4, for the 3 users case, we see that the performance of the 16-QAM system with phase offset of 15 is worst than the QPSK system with phase offset of 30 by 5 dB for BER less than 1 x 10-2. For this load, the QPSK system has a better performance than that of 16-QAM. On the other hand, for the 30 users system, the 16-QAM system performs better when the phase offsets are 0 and 5. 2 either direct sequence (DS) or frequency-hopping (FH). In this work, we have chosen the first method as a means of spreading. The literature is rich in many outstanding papers about CDMA systems like ( [1], [2], [3],and [4]), to mention just a few. In DS CDMA, the data symbols of duration Ts of each user are multiplied by unique narrow chips of duration Tc. The chip rate is N times the symbol rate where N is the spreading gain. Figure 1.1 illustrates the DS-SS concept. In this figure, an unspread binary phase- shift keying (BPSK) signal of square pulses of duration Tb is shown. The signal has been spread by a spreading sequence of length N = 7. The result of the spreading is a signal with pulses of duration Tc = Tb/N rather than Tb. The power spectral densities (PSD) of the unspread and spread signal are shown here to illustrate the effect of the spreading on the signal bandwidth. The first null bandwidth of the unspread signal has expanded by a factor N as a result of the spreading process. It is desirable for the spreading sequences of all users to be approximately orthogo nal to minimize the multiple access interference (MAI) and hence enhance the receiver performance. This orthogonality is unachievable in practice for asynchronous commu nication systems. Due to their important role in the performance of CDMA systems, spreading sequences and their correlation properties are studied heavily in the liter ature. M-sequences [5] are known for their autocorrelation properties. Gold [6] and Kasami [5] sequences represent a tradeoff of the desirable autocorrelation properties of M-sequences for improved cross-correlation properties. Kasami sequences are su perior to Gold sequences in cross-correlation performance but are fewer in number for a given sequence length. The cellular concept introduces the idea of replacing high-power large single cell systems with low-power small multiple cell systems that have the same coverage area and can support a much larger user population compared to the single cell systems with the same system bandwidth. Based on this concept, each base station is assigned 74 Figure 5.13: BER of 16-QAM with different estimation error variances for 3 users. For the estimated case PSAM rate =.2, L= 3 pg= 124, Figure 5.14: BER of 16-QAM with different estimation error variances for 30 users. For the estimated case PSAM rate =.2, L= 3 pg= 124, 99 Figure 6.10: Total transmitted power and SINR convergence of the PCA proposed in [36] for 10 users and SINR = 10 dB. Figure 6.11: Total transmitted power and SINR convergence of the PCA proposed in [35] for 10 users and SINR = 10 dB. 17 receiver could be a good candidate to be implemented in the next generation of CDMA systems. This research will be targeting two areas of improvements. The first is multilevel-modulation and the second is power control . The first area to be investigated in this research is multilevel modulation. Tradi tionally, higher level modulation has been used to achieve higher bandwidth efficiency (# of information bits transmitted in a given bandwidth). The price for the higher bandwidth efficiency is paid in terms of the required SINR to achieve the same error probability. In cellular systems, the main objective of the system designers is to in crease the system capacity for a given quality of service and limited resources such as bandwidth. In the literature, BPSK and sometimes QPSK are used as modulation formats for the MMSE receiver. As noted in [18], if BPSK is used, the MMSE receiver becomes interference limited when the loading of the system becomes high enough and close to the processing gain. This threshold is reached because of the imperfect cancellation of the Multiple Access Interference (MAI) due to the lack of dimensions in the system. One way to improve the performance of the system is to introduce more dimensions while keeping the bandwidth the same to help in suppressing the MAI. To achieve that, one can choose a higher order modulation format like MPSK or 16-QAM to increase the processing gain (# of chips per symbols). The justification for increasing the processing gain for the system employing higher order modulation is presented in the following example. In an unspread system, for the same bit rate, using QPSK will result in using half the bandwidth required of a BPSK system, while using a 16-QAM will result in using one fourth of the bandwidth required by a BPSK system. In a CDMA system, to utilize the total available bandwidth when higher order mosulation formats are used, the spreading gain of the QPSK system should be twice that of the BPSK system and the spreading gain of the 16-QAM system should be 4 times that spreading gain of the BPSK system. 82 Table 5.2: The estimation error statistics for 16-QAM system with L = 3, PSAM = 0.02, 3 users and fdTs = 0.0028 ft(^) 0 5.1563 x 10-1 5.196 x 10-1 5 5.207 x 10"1 5.389 x 10-1 10 3.498 x 10-1 3.708 x 101 15 2.541 x 10-1 2.388 x 10-1 20 2.041 x 10-1 2.413 x 10"1 25 1.457 x 102 1.306 x 102 30 4.205 x 10-3 3.534 x 10-3 35 2.333 x 10-3 1.930 x 10-3 40 1.439 x 103 2.2858 x 10-3 of 0.2 and the system with PSAM rate of 0.02, we notice that the variances for the former system are lower than that of the later system. These improvements in the estimation due to use of higher PSAM rates translate to a better BER performances. 5.5 The Effect of the Linear Predictor Length on the Performance of the System Figures 5.23 to 5.24 show the BER performance of the 16-QAM system for a cer tain normalized Doppler rate and number of users while the linear estimator length, L, has different values, namely; 1, 2, 3, 10, and 50. The BERs are the same indepen dent of these values of L at high jjfc. This is due to the fact that the length of the linear estimator has a small effect on the value of the estimation error. Tables (5.1) and (5.3) show that values of a\ and a2y for different values of jf- for a simulation environment of a mobile speed of 5 mph, which corresponds to fdTs = 0.0028 in a system with 3 users employing 16-QAM and PSAM rate of 0.2. The information in these tables need to be compared to the results in Figure (5.23) for > 30, the values of a\ and ay for L 3, and 50 are very close. For these values of |k, we see no change in the BER as shown in Figure (5.23). For < 30, the values of al and al for L = 3, and 50 are not as close as before and this is translated x y 68 By comparing Figures 5.5, 5.6, and 5.7, one can conclude that the third technique has better tracking capabilities than those of the other techniques. The good per formance of the third technique can be attributed to three reasons. First, the use of pilot symbols provides the MMSE receiver with a reference that helps the receiver not to lose lock on the desired user. Second, using the linear predictor, estimates are made for every received symbol. This gives the linear predictor recent past channel estimates to predict the channel conditions. Third, pilot symbols can help the linear predictor not to lose track of the fading process by interrupting the propagation of decision errors. Figure 5.6 demonstrates that the MMSE receiver can be updated based on pilot symbols only. This is interesting since the poor performance of the MMSE receiver in a fading channel is often due to the feeding back of unreliable decisions to the adaptive algorithm during deep fades. To show the improvements of the systems, which are based in different modulation formats, Figures 5.8, 5.9, and 5.10 illustrate the BER performance of an MMSE receiver base systems with BPSK, QPSK, or 16-QAM modulation formats in a slowly fading channel for a 3 and 30-user CDMA systems. To generate these figures, the following simulation environment was chosen. The mobile speed was 5 mph, the mobile operates at the 900 MHZ band, the bit rate was 9600 bps, a pilot symbol was sent every 10th symbol. This corresponds to fsTs of 0.0028, 0.0014, 0.007 for 16-QAM, QPSK, and BPSK, respectively. The received powers were modeled as a lognormal distribution with zero mean and 1.5 dB standard deviation. The receiver structure shown in Figure 5.4 has been used. The BER performance of the 3-user system as a function of Eb/N0 is shown in Figure 5.8 for the different modulation formats. As expected, the CDMA system which based in a BPSK modulation outperforms the other systems. In this case there is no advantage of using higher order modulation since using higher order modulation will require more transmitted power to achieve the same BER. 100 102 CD 03 10[ 1 1 1 1 1 0 5 10 15 20 25 30 Iteration Figure 6.12: A typical SINR and total TX power convergence for a practical imple mentation of the PCA for 5 users a lognormal distribution with 8 db standard deviation. The initial tansmitted power was .1 for all users. As can be seen from the figure, the SINR converges to the desired value of 10 dB. On the other hand, unlike the previous results, the total transmitted power does not converge to a single value due to the presnce of the fading. To investigate the effect of the rate of updating the power on the convergence behavior of the SINR and the total transmitted power, a system operating in a slow fading channel with the same fading parameter as the one described in the previous paragraph and with 5 users has been simulated for different power updates rates. Figures 6.14, 6.15, and 6.16, show the performance when the transmitted power is updated every 1, 10, and 20 symbols, respectively. It can been seen that if the power is updated every symbol, the convergence of the SINR is smooth but when the power control update rate is decreased, although SINR converges to the desired value, the time varying nature of the channel effects the convergence behavior of the SINR as shown in Figure 6.15, and 6.16 For example, it can be seen that a specific user, at a given time, may deviate from the desired SINR value and the converges back. 59 Figure 5.1: The MMSE behavior in a fading channel in decision directed mode. like 16-QAM, we will study the ability of the present structure of the MMSE receiver to track these fading parameters. In [22], the performance of the MMSE receiver in a frequency nonselective fading channel has been evaluated when a BPSK modulation format is used. It has been shown that the MMSE has a difficult time tracking the channel variation due to the fact that during deep fades, unreliable decisions are fed back to the LMS algorithm. This will cause the MMSE receiver to lose lock on the desired signal or it may lock onto another interfering signal. In this section, we assume a slow fading environment with a processing gain of 124 chips/symbol, a 16-QAM modulation format, a mobile speed of 5 mph, a frequency band of 900 MHz, and a data rate of 9600 bps. This will result in a normalized Doppler rate, fTs of 0.0028. Figure 5.1 demonstrates the behavior of the present MMSE structure in a slowly varying Rayleigh fading channel for a single user using 16-QAM modulation. As expected, the figure shows the inability of the receiver to 83 Table 5.3: The estimation error statistics for 16-QAM system with L = 50, PSAM = 0.02, 3 users and fTs = 0.0028 Ttm al 0 5.1563 x 10-2 5.196 x 10"2 5 5.207 x 102 5.389 x 10"2 10 3.498 x 10~3 3.708 x 103 15 2.541 x 10-3 2.388 x 103 20 2.041 x 10-4 2.413 x 10"4 25 1.457 x 104 1.306 x 10-4 30 4.205 x 104 3.534 x 10-4 35 2.333 x 10"4 1.930 x 10"4 40 1.439 x 10-4 2.2858 x 10-4 to a small difference in BER performance in Figure (5.23). The performances of the QPSK with different values of L are shown in Figures (5.25) to (5.26). As in the case for 16-QAM, there is no improvements in terms of BER for high values of |k. We notice from these figures that the BERs for system with L = 3 and L = 50 are very close, therefore; going to higher than L = 3 is not justified. 5.6 Summary In this chapter, we have investigated the performance of an adaptive MMSE re ceiver based CDMA system in a fading channel with QPSK, and 16-QAM modulation formats when the fading of the desired user is estimated. By using the estimator pre sented in Section 5.2, the capacity is improved when a 16-QAM system is used as shown in Figures 5.9 and 5.10 at a low Doppler rate but not at high Doppler rate. A system designer can make a decision about what modulation format should be used based on the quality of the estimate of the desired users fading process and employing Figures 5.13 to 5.16 to help in deciding whether a 16-QAM or a QPSK is to be used. If the fading process is known or the fading estimation error is very low, 16-QAM modulation should be employed to improve the system capacity On the 26 2cos (wj) -2sin (wat) Figure 2.3: The receiver where is the channel gain of user j to the assigned base station of user i. The variables r;-, aq, 9j are the propagation delay, and the amplitude and phase of the fading process for the jth user respectively. The process n(t) is a real AWGN process with a spectral density of Na/2. The fading amplitude is Rayleigh distributed while the fading phase is uniformly distributed. The desired user propagation delay is assumed to be 0. In addition, it is assumed that the fading process of each user varies at a slow rate so that the amplitude and the phase of the fading process can be assumed constant over the duration of a symbol. The front-end part of the receiver, which is shown in Figure 2.3, consists of an in-phase (I) and a quadrature (Q) components. First, the bandpass received signal is shifted to baseband. Then, each component goes through a chip-matched filter with a scale factor of V2TC. The output of the chip-matched filter is sampled every Tc seconds. At the nth chip time, the output of the receiver front end consists of the received complex signal sample of r(n) = rÂ¡(n) + rg(n). These samples are fed at the chip rate to the MMSE receiver (the receiver is shown in Figure 1.5) until the N-tap delay line becomes full after one symbol time. The contents of the equalizer are given by 46 Figure 4.1: The performance of BPSK, QPSK, and 16-QAM in a fading channel with 3 users with optimum MMSE receiver implementation. suppress the interfering signals. The 16-QAM system outperforms the QPSK system for ^ greater than 18 dB. When the system loading was further increased to 60 users as shown in Figure 4.3, the QPSK based system would lose its ability to to suppress the new level of inter ference and would introduce an error floor while the 16-QAM system still operating effectively. 4.2 The Effect of Phase Offsets on the Performance of the System As it will be pointed in Section (5.1), the phase variations are more severe on degrading the system performance because the errors that are caused by phase varia tion often are not localized to the deep fade periods but rather propagate due to the loss of lock on the desired signal phase by the receiver. In this section, we will study the effect of the phase offsets, due to imperfect estimation of the desired users fading on the performance of the system. Symbol Total TX. power 94 Figure 6.4: A typical SINR and total transmitted power convergence for MMSE receiver based CDMA system with for 6 users and SINR =10 and 6 dB. 13 in the forward traffic channel. When a mobile user receives a power control bit it increases or decreases its power by 1 dB according to the value of the power control bit (0=increase, l=decrease). For the mobile user to access the reverse channel, it must do so with the following initial power in the access channel: Paccess (dBlTl) Pmean T Pnom, T Pcorr 73 (13) where Paccess = The initial access power in the access channel, Pmean = The mean input power of the mobile transmitter (dBm), Pnom = The nominal correction factor for the base station (dB), Pcorr = The correction factor for the base station from partial path loss (dB). Power in dB = 10log10(actual power in watts). Power in dBm = 10 log10 (actual power in watts) = 3q + power jn dB If the mobile user attempting to access the reverse channel is unsuccessful, the mobile will increase its transmitted power by a defined increment called the Power Step (Pstep) and try again. This process continues until the access attempt is success ful or the mobile reaches the maximum allowed number of attempts. When granted access to the reverse traffic channel, the mobile station transmits with initial power Pj(dBm) = Paccess + Sum of all access corrections (1.4) When the communication with the base station is established, the base station sends a power control bit to adjust the power of the mobile station transmitted signal. These adjustments are in increments of ldB. When the power control bit is 0, the mobile station transmitted power increases by 1 dB. When the power control bit is 1, the mobile station transmitted power decreases by 1 dB. After these closed-loop 97 been developed assuming the tap weights of the filter were obtained by the Weiner solution. Simulations show that the LMS algorithm has a better tracking capability than that of the RLS algorithm for such nonstationary environment where the signal power is changing, as shown in Figures 6.5 through 6.8. This tracking superiority of the LMS may be attributed to the fact there is an inherent dependence of the step size (/r) of the LMS algorithm on the total input power of the adaptive filter. An adaptive step size, /i = TW based on the total input has been used to obtain Figure 6.5 and 6.6. Figures 6.7 and 6.8 show the performance of the proposed power control algorithm when the RLS is used to update the tap weights. The performance of the RLS scheme is much worse if the power is updated more frequently. The forgetting factor for the RLS algorithm was 0.99. Haykin in [39] presented a detailed study of the tracking performance of these algorithms. Figures 6.9, 6.10, and 6.11 show the performance of the power control proposed in this chapter to those proposed in [36] and [35]. For these results, the number of users is 10 and the SINR is 10. As shown in the figures, these algorithms converge asymptotically to the same SINR and total transmitted values. It seems the conver gence of the PCA proposed in this chapter is smoother but slower than the algorithms presented in [36] and [35]. As has been pointed out earlier, the PCA proposed in [35] uses measurements of the MSE which require knowledge of the actual transmitted bits in addition to knowledge of the channel gain. To implement the algorithm pre sented in [36], sample averages of the input and the output of the MMSE receiver are required to provide an estimates for some parameters to update the power. In addition, the channel gain of the desired user needs to be estimated using pilot sym bols. There is no knowledge of the other users information required to implement the power control algorithm proposed in this chapter. Only one parameter, given in eqn. 6.7, which includes the channel gain of the desired user need to be estimated. In fact, when constant envelope modulation is used, no pilot symbols need to be sent 19 have investigated the case when the desired users fading is unknown to the receiver or it has been estimated inaccurately. The details of our results in this area are presented in [24], [23], and Chapter 3, 4, and 5 of this dissertation. In Chapter 3, the performance, in terms of BER and system loading, of an MMSE receiver based CDMA system with different modulation formats, namely, BPSK, QPSK, and 16-QAM, was investigated in AWGN channels. Based on BER perfor mance, it has been found that for a lightly loaded system BPSK outperforms QPSK and 16-QAM. For a moderately loaded system QPSK outperforms BPSK and 16- QAM. For a highly loaded system, 16-QAM outperforms BPSK and QPSK. These results are shown in [23]. The use of multi-level modulation formats, like 16-QAM, leads to some interest ing research problems. As with unspread systems, any time a multilevel modulation format is used in a fading channel, it becomes necessary to carefully track the phase and amplitude of the desired users fading process in order for the receiver to demod ulate the desired users signal successfully. Channel tracking through the use of pilot symbol assisted modulation (PSAM) has been proposed, in single user system, as a mean to estimate the fading process and mitigate its effects at the receiver by several authors [28], [29], [30], and [31]. In PSAM, pilot symbols are inserted periodically into the data stream. Channel estimates are obtained using Gaussian interpolation [30], Wiener filtering interpolation [28] or sine interpolation [31]. One needs to notice that there is always a delay associated with the use of PSAM since the demodulator has to receive a certain number of pilot symbols to estimate the fading process. This estimation technique can not apply directly to the MMSE receiver since this receiver updates its tap weights every symbol based on the demodulation of the previous symbol. Furthermore, linear prediction has been used to obtain estimates of a fading pro cess for a single user system in [32] and for multiuser systems in [22] and [24]. As REFERENCES [1] R. L. Pickholtz, D. L. Schilling, and L. B. Milstein, Theory of spread-spectrum communicationsa tutorial, IEEE Transactions on Communications, vol. COM-30, no. 5, pp. 855-884, May 1982. [2] R. A. Scholtz, The spread spectrum concept, IEEE Transactions on Commu nications, vol. 8, no. COM-25, pp. 748-755, Aug. 1977. [3] W. F. Utlant, Principles and possible application to spectrum utilization and allocation, IEEE Communication Society Magazine, pp. 21-31, 1978. [4] C. Cook and H. Marsh, An introduction to spread spectrum, IEEE Commu nication Magazine, pp. 8-16, 1983. [5] D. V. Sarwate and M. B. Pursley, Crosscorrelation properties of psuedorandom and related sequences, Proceedings of the IEEE, vol. 68, no. 5, pp. 593-619, May 1980. [6] R. Gold, Obtimal binary sequences for spread spectrum multiplexing, IEEE Transactions on Information Theory, vol. IT-13, no. 10, pp. 619-621, 1967. [7] V. MacDonald, The cellular concept, The Bell Systems Technical Journal, vol. 58, no. 1, pp. 15-43, 1979. [8] T. Rappaport, Wireless Communications Principles and Practice, Prentice Hall, 1996. [9] M. B. Pursley, Performance evaluation for phase-coded spread-spectrum multiple-access communication Part I: System analysis, IEEE Transactions on Communications, vol. 25, no. 8, pp. 795-799, Aug. 1977. [10] K. Yao, Error probability of asynchronous spread spectrum multiple access communication systems, IEEE Transactions on Communications, vol. COM- 25, pp. 803-809, 1977. [11] J. G. Proakis, Digital Communications, McGraw-Hill, 1995. [12] S. B. Wicker, Error Control Systems for Digital Communication and Storage, Prentice Hall, 1995. [13] S. Verd, Minimum probability of error for asynchronous Gaussian multiple- access channels, IEEE Transactions on Information Theory, vol. 32, no. 1, pp. 85-96, Jan. 1986. 109 18 Throughout this dissertation, we have used random sequences with spreading gains of 31 for the BPSK system, 62 for the QPSK system, and 124 for the 16-QAM system to utilize the whole available bandwidth. If m- Gold, or Kasami sequences were used, we would not be able to choose a processing gains of 62 and 124 since the processing gain of these sequences is given by 2 1 where n is the number of stages of the shift register used to generate such sequences. By adopting a higher order modulation and increasing the processing gain the MMSE receiver has been moved out of the interference limited region and can restore its ability to suppress more interference than the original system. Since the receiver now is operating in the interference resistant region, one can increase the transmitted power to obtain a higher SINR for acceptable performance. Increasing the transmitted power will increase the interference level and hence will degrade the performance of a conventional receiver-based CDMA system. On the other hand, the MMSE receiver, with the increased processing gain, will perform as a near-far resistant receiver and the increased interference level will be alleviated. Furthermore, if increasing the transmitted power is not desirable, one can resort to combined modulation and coding in the form of trellis-coded modulation (TCM). Milstein and Shamain studied the performance of QPSK and 16-QAM modulation formats in a multipath and narrowband Gaussian interference (NGI) environment, in [25] and [26] for single or two user systems. They show that when the multipaths cause significant interstmbol interference (ISI), with or without NGI, the 16-QAM system outperforms the QPSK system. In both papers, the desired users fading is assumed to be known and an optimum MMSE receiver is used. In our research, we have shown the improvement of the system performance in terms of BER and capacity when higher order modulation is used. In addition, we have investigated the performance of the system in a fading environment with optimum or adaptive implementation of the MMSE receiver for different system loadings. Furthermore, we 20 described in [22], Linear prediction of the desired users fading is performed by using the outputs of the MMSE filter from past symbol intervals. This technique can lose track of the fading process due to the aburst of decision errors as pointed out in [33] and [24]. In [24], we have shown that a combination of PSAM and linear prediction can effectively track the fading process of the desired user. The use of pilot symbols has been proven to be beneficial in preventing the MMSE receiver from feeding back unreliable decisions when it is operating in its decision directed mode while the desired user signal is going into a deep fade. Traditionally, pilot symbols are used in a single user environment to obtain an estimate of the fading process, but there is a delay associated with their use since the detector needs to detect many pilot symbols to form an estimate of the fading process. In this research, the main reason for using pilot symbols is to prevent the MMSE receiver from feeding back the unreliable decisions. In Chapters 4 and 5, the study of the performance of the system in Chapter 3, for which an AWGN channel model was used, is extended to a fading channel to represent a more realistic model for wireless communication systems. The use of mul tilevel modulation, like 16-QAM, in a fading environment introduced an interesting problem, namely, tracking the channel variation to be able to demodulate the de sired user signal. The behavior of the MMSE receiver structure, shown in Figure 1.5, in a fading channel with 16-QAM modulation was studied. It was found that the MMSE receivers present structure performs poorly in a fading channel. A general MMSE receiver structure which can be used in a fading environment to demodulate the desired users signal effectively was proposed. The performance of the different modulation formats in terms of BER was analyzed and theoretical BER bounds for, BPSK, QPSK, and 16-QAM in multiuser systems operating in a fading environment were derived. The performance in terms of BER under different loads of the three modulation formats were compared in a fading environment. xml version '1.0' encoding 'UTF-8' METS:mets xmlns:METS http:www.loc.govMETS xmlns:xlink http:www.w3.org1999xlink xmlns:xsi http:www.w3.org2001XMLSchema-instance xmlns:mods http:www.loc.govmodsv3 xmlns:sobekcm http:sobekrepository.orgschemassobekcm xmlns:lom http:sobekrepository.orgschemassobekcm_lom OBJID AA00024502_00001 xsi:schemaLocation http:www.loc.govstandardsmetsmets.xsd http:www.loc.govmodsv3mods-3-4.xsd http:sobekrepository.orgschemassobekcm.xsd METS:metsHdr CREATEDATE 2014-07-09T10:32:52Z ID LASTMODDATE 2014-07-09T12:49:05Z RECORDSTATUS PARTIAL METS:agent ROLE CREATOR TYPE ORGANIZATION METS:name UF,University of Florida OTHERTYPE SOFTWARE OTHER Spreadsheet Importer INDIVIDUAL Kendrac3 METS:note Online edit by Kendra Carter Carter ( 7/9/2014 ) METS:dmdSec DMD1 METS:mdWrap MDTYPE MODS MIMETYPE textxml LABEL Metadata METS:xmlData mods:mods mods:accessCondition The University of Florida George A. 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The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact the RDS coordinator (ufdissertations@uflib.ufl.edu) with any additional information they can provide. mods:genre authority marcgt bibliography theses non-fiction mods:identifier type OCLC 45068139 ocm45068139 mods:language mods:languageTerm text English code iso639-2b eng mods:location mods:url access object in context http://ufdc.ufl.edu/AA00024502/00001 mods:name personal mods:namePart Almutairi, Ali Faisal given Ali Faisal family Almutairi date 1970- mods:role mods:roleTerm Main Entity mods:note thesis Thesis (Ph. D.)--University of Florida, 2000. bibliography Includes bibliographical references (leaves 109-113). Printout. Vita. statement of responsibility by Ali Faisal Almutairi. mods:originInfo mods:place mods:placeTerm marccountry xx mods:dateIssued 2000 marc 2000 point start 2000 mods:recordInfo mods:recordIdentifier source sobekcm AA00024502_00001 mods:recordCreationDate 000925 mods:recordOrigin Imported from (OCLC)45068139 mods:recordContentSource University of Florida marcorg FUG OCLCF OCLCO mods:languageOfCataloging English eng mods:relatedItem original mods:physicalDescription mods:extent vii, 114 leaves : ill. ; 29 cm. mods:titleInfo mods:title Design issures for minimum mean square error (MMSE) receiver-based CDMA systems mods:typeOfResource text mods:subject jstor SUBJ650_#0_1 mods:topic Bandwidth SUBJ650_#0_2 Binary phase shift keying SUBJ650_#0_3 Code division multiple access SUBJ650_#0_4 Communication systems SUBJ650_#0_5 Multiple access SUBJ650_#0_6 Receivers SUBJ650_#0_7 Signal fading SUBJ650_#0_8 Signals SUBJ650_#0_9 Simulations SUBJ650_#0_10 Transmitters SUBJ650_2 fast Code division 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Introduction 6 PAGE8 PAGE9 PAGE10 PAGE11 PAGE12 PAGE13 PAGE14 7 PAGE15 8 PAGE16 9 PAGE17 10 PAGE18 11 PAGE19 12 PAGE20 13 PAGE21 14 PAGE22 15 PAGE23 16 PAGE24 17 PAGE25 18 PAGE26 19 PAGE27 20 PAGE28 21 PAGE29 22 PAGE30 23 PDIV7 2. System model PAGE31 24 PAGE32 25 PAGE33 26 PAGE34 27 PAGE35 28 PAGE36 29 PDIV8 3. Multilevel modulation AWGN channel PAGE37 30 PAGE38 31 PAGE39 32 PAGE40 33 PAGE41 34 PAGE42 35 PAGE43 36 PAGE44 37 PAGE45 38 PAGE46 39 PDIV9 4. a fading PAGE47 40 PAGE48 41 PAGE49 42 PAGE50 43 PAGE51 44 PAGE52 45 PAGE53 46 PAGE54 47 PAGE55 48 PAGE56 49 PAGE57 50 PAGE58 51 PAGE59 52 PAGE60 53 PAGE61 54 PAGE62 55 PAGE63 56 PAGE64 57 PDIV10 5. Fading process estimation PAGE65 58 PAGE66 59 PAGE67 60 PAGE68 61 PAGE69 62 PAGE70 63 PAGE71 64 PAGE72 65 PAGE73 66 PAGE74 67 PAGE75 68 PAGE76 69 PAGE77 70 PAGE78 71 PAGE79 72 PAGE80 73 PAGE81 74 PAGE82 75 PAGE83 76 PAGE84 77 PAGE85 78 PAGE86 79 PAGE87 80 PAGE88 81 PAGE89 82 PAGE90 83 PAGE91 84 PAGE92 85 PAGE93 86 PDIV11 6. Power control PAGE94 87 PAGE95 88 PAGE96 89 PAGE97 90 PAGE98 91 PAGE99 92 PAGE100 93 PAGE101 94 PAGE102 95 PAGE103 96 PAGE104 97 PAGE105 98 PAGE106 99 PAGE107 100 PAGE108 101 PAGE109 102 PAGE110 103 PDIV12 7. Conclusion and future work PAGE111 104 PAGE112 105 PAGE113 106 PAGE114 107 PAGE115 108 PDIV13 References PAGE116 109 PAGE117 110 PAGE118 111 PAGE119 112 PAGE120 113 PDIV14 Biographical sketch PAGE121 114 PAGE122 115 PAGE123 116 PAGE 1 '(6,*1 ,668(6 )25 0,1,080 0($1 648$5( (5525 006(f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n YLVHU 3URIHVVRU +DQLSK $ /DWFKPDQ QRW RQO\ IRU KLV WLPH EXW DOVR IRU KLV JXLGDQFH WKURXJKRXW P\ VWXGLHV ZLWK UHVSHFW WR ERWK WR UHVHDUFK LVVXHV DQG WR SURIHVVLRQDO LVn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n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f 5(&(,9(5%$6(' &'0$ 6<67(06 %\ $OL )DLVDO $OPXWDLUL 0D\ &KDLUPDQ 'U +DQLSK $ /DWFKPDQ 0DMRU 'HSDUWPHQW (OHFWULFDO DQG &RPSXWHU (QJLQHHULQJ &RGHGLYLVLRQ PXOWLSOHDFFHVV &'0$f WHFKQRORJ\ KDV EHHQ WKH VXEMHFW RI D JUHDW GHDO RI SUDFWLFDO DQG WKHRUHWLFDO UHVHDUFK RYHU WKH ODVW GHFDGH 7KH DGRSWLRQ RI WKH ,6 VWDQGDUG ZKLFK LV EDVHG RQ &'0$ WHFKQRORJ\ KDV ERRVWHG UHVHDUFK LQWHUHVW LQ WKLV DUHD 7KH PLQLPXP PHDQ VTXDUHG HUURU 006(f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f DQG FDSDFLW\ 7KLV UHVHDUFK ZLOO EH WDUJHWLQJ WZR DUHDV RI LPSURYHPHQWV QDPHO\ PXOWLOHYHO PRGXODWLRQ DQG SRZHU FRQWURO YL PAGE 7 7KH XVH RI KLJKHU RUGHU PRGXODWLRQ IRUPDWV OLNH 4XDGUDWXUH DPSOLWXGH PRGn XODWLRQ 4$0f DQG TXDGUDWXUH SKDVH VKLIW NH\LQJ 436.f LV LQYHVWLJDWHG DQG FRPSDUHG WR D ELQDU\ SKDVH VKLIW NH\LQJ %36.f EDVHG V\VWHP LQ ERWK DGGLWLYH ZKLWH *DXVVLDQ QRLVH $:*1f DQG IDGLQJ FKDQQHOV 2QH GUDZEDFN ZDV WKH LQDELOLW\ RI WKH 006( UHFHLYHU WR SHUIRUP SURSHUO\ LQ D PRUH UHDOLVWLF ZLUHOHVV HQYLURQPHQW ZKHUH IDGLQJ LV FRQVLGHUHG 7KLV SUREOHP ZDV LQYHVWLJDWHG DQG D JHQHUDO 006( UHFHLYHU VWUXFWXUH ZKLFK LV FDSDEOH RI GHPRGXODWLQJ D ZLGH UDQJH RI GLJLWDO PRGXODWLRQ IRUn PDWV LV SURSRVHG ,W LV VKRZQ WKDW LQ DQ 006( EDVHG &'0$ V\VWHP PRGXODWLRQ IRUPDW FKRLFH KDV D VLJQLILFDQW HIIHFW RQ WKH FDSDFLW\ RI WKH V\VWHP 7KH SHUIRUPDQFH RI VXFK D V\VWHP ZLWK WKH WKUHH GLIIHUHQW PRGXODWLRQ IRUPDWV PHQWLRQHG SUHYLRXVO\ ZDV LQYHVWLJDWHG ,W LV IRXQG WKDW WKH 4$0 RXWSHUIRUPV %36. 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LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ :LOOLDP : (GPRQVRQ $VVLVWDQW 3URIHVVRU RI (OHFWULFDO DQG &RPSXWHU (QJLQHHULQJ FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWn DEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 8OULFK + .XU]ZHJ 3URIHVVRU RI $HURVSDFH (QJLQHHULQJ 0HFKDQLFV DQG (QJLQHHULQJ 6FLHQFH PAGE 123 7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ RI WKH &ROOHJH RI (Qn JLQHHULQJ DQG WR WKH *UDGXDWH 6FKRRO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 0D\ 0 2KDQLDQ 'HDQ &ROOHJH RI (QJLQHHULQJ :LQIUHG 0 3KLOOLSV 'HDQ *UDGXDWH 6FKRRO 9 Wo Pilot Channel: All 0s 1.2288 Mops quadrature spreading W32 spreading Wp Wt Mops (a) MODULATION cos(2ifct ) Sequence sin(2;z/c/) (b) QUADRATURE SPREADING Figure 1.3: Forward CDMA channel structure. 16 to make a decision about which symbol was sent. These tap weights are updated every symbol interval to minimize the mean square error between the output of the filter and the desired output. In practice, the filter is trained for a reasonable period of time by a known training sequence to reach a tap weight vector that is close to the optimum weights. After the training period, the receiver switches to decision feedback mode. It has been shown in [22] that the decision directed mode proves to be troublesome in a fading channel. In deep fades, with the MMSE structure shown in Figure 1.5, incorrect decisions being fed back to the receiver cause the MMSE receiver to lose track of the desired signal. A modified MMSE receiver structure to overcome this problem was described in [22] for a BPSK modulation format and it has been generalized in [24], It should be noted that the IS-95 standard uses a conventional matched filter based receiver where the coefficients of the filter are matched to the desired users spreading sequence. The matched filter structure is optimum for a single user environment. When this structure is employed in a multiuser system, it degrades rapidly due to the presents of MAI. 1.4 Motivation and An Overview of the Dissertation and Literature Review This section presents a review of the design issues that we are researching and a layout of motivations for our research in this dissertation. As has been stated before, this research project revolves around the following question: If the MMSE receiver is used as the underlying receiver for the next generation CDMA system, how can we redesign some aspects of the system and modify the current MMSE structure to improve the performance of the CDMA system in terms of the system capacity, SINR, and BER? The motivation behind this research is that given the advantages of the MMSE receiver presented in the previous section, one would expect superior performance of a CDMA system based on the MMSE in comparison to that of a CDMA system based on the current conventional receiver, and hence, the MMSE Ill [25] P. Shamain and L. B. Milstein, Using higher order constellations with minimum mean square error (MMSE) receiver for severe multipath CDMA channel, Per sonal, Indoor, and Mobile Radio Communications, pp. 1035-1038, September 1998. [26] P. Shamain and L. B. Milstein, Minimum mean squre error (MMSE) receiver employing 16-QAM in CDMA channel with narrowband gaussian interference, Proceeding of 1999 IEEE Military Communications Conference, 1999. [27] C. N. Pateros and G. J. Saulnier, Adaptive correlator receiver performance in fading multipath channels, in Proceedings f3rd IEEE Vehicular Technology Conference, Secaucus, NJ, 1993, pp. 746-749. [28] J. K. Caves, An analysis of pilot symbol assisted modulation for rayleigh fading channels, IEEE Trans. On Veh. Technol, vol. 40, no. 4, pp. 686-693, November 1991. [29] J. K.Caves, Pilot symbol assisted modulation and differential detection in fading and delay spread, IEEE Transactions on Communications, vol. 43, no. 7, pp. 2206-2212, 1995. [30] S. Sampei and T. Sunaga, Rayleigh fading compensation for QAM in land mobile radio communications, IEEE Trans. On Veh. Technol, vol. 42, no. 2, pp. 137-147, May 1993. [31] Y. S. Kim, C. J. KIM, G. Y. Jeong, Y. J. Bang, H. K. Park, and S. S. Choi, New rayleigh fading channel estimator based on PSAM channel sounding technigue, Proc. of IEEE Intn. Conf. on Commun. ICC97, Montreal, Canada, pp. 1518 1520, June 1997. [32] P. Y. Kam and C. H. Teh, Reception of PSK signals over fading channels via quadrature amplitude estimation, IEEE Transactions on Communications, vol. COM-31, no. 8, pp. 1024-1027, Aug. 1983. [33] P. Y. Kam and C. H. Teh, Reception of PSK signals over fading channel via quadrature amplitude estimation, IEEE Trans. On Commun., vol. COM-31, no. 8, pp. 1024-1027, August 83. [34] A. F. Almutairi, S. L. Miller, H. A. Latchman, and T. F. Wong, MMSE based fully distributed power control algorithm, IEEE Military Communications Con ference Proceedings, p. xxxx, 1999. [35] P. S. Kumar and J. Holtzman, Power control for a spread spectrum system with multiuser receivers, in IEEE PIMRC95, 1995, pp. 955-958. [36] S. Ulukus and R. Yates, Adaptive power control with MMSE multiuser detec tors, in IEEE International Conference on Communications, 1997, pp. 361-365. 45 output of the MMSE receiver and found that the output is approximately Gaussian in many cases. To show the improvements of the systems employing higher order modulation formats, Figures 4.1, 4.2, and 4.3 illustrate the performance, in terms of BER, of MMSE receiver based systems with BPSK, QPSK, or 16-QAM modulation formats in a fading channel. These figures are based on the theoretical results obtained in the previous section. The received powers were modeled as a lognormal distribution with zero mean and 1.5 dB standard deviation. The BER performance of the 3-user system as a function of is shown in Fig ure 4.1 for the different modulation formats. The theoretical and simulation based performances are in agreement. The simulation results are based on modeling the fading as a complex Gaussian process. The performance of the 16-QAM worse by few dBs than that of the QPSK or the BPSK performance, on the other hand, the BPSK and QPSK have the same performance for such load. In this case there is no advantage of using 16-QAM since using this higher modulation format will require more transmitted power to achieve the same BER. When the load of the the system increases to 30 users, as shown in Figure 4.2, The performance of the system that is based on a BPSK modulation degrades rapidly. In this case, an error floor is introduced and the performance of the system cannot be improved by increasing This behavior can be explained as follows. The MMSE receiver is overwhelmed by this load and the system does not have enough dimension to overcome the interference introduced by such a high load. In addition, the QPSK and 16-QAM based systems do not develop an error floor and they outperform the BPSK based system. This basically means that we can increase the capacity of the system by increasing the processing gain, without increasing the bandwidth or the information rate by simply adapting a higher order modulation format. Using higher order modulation formats provided the MMSE receiver with enough dimensions to 92 Table 6.1: Simulation capacity and average total transmitted powers corresponding to different SINR requirements Capacity eqn. 6.8 Pt (simulation) Pt eqn. 6.10 SINR (dB) 1 55 637.4 617 3 46 850.7 796 6 38 1037.1 746 8 35 1453.3 869 10 33 2219.7 1023 12 31 1631.4 827 14 29 800.9 726 Figure 6.2: A typical total transmitted power for MMSE receiver based CDMA system with for 33 users and SINR = 10 dB. CHAPTER 6 POWER CONTROL In this chapter, a fully distributed power control algorithm is presented that is based on the MSE. We study the capacity improvements that can be gained by an MMSE receiver-based CDMA system implementing this power control algorithm. We investigate the performance of this power control algorithm when the MMSE receiver filter coefficients are obtained through the Weiner solution or adaptive algorithms like the LMS and the RLS. We also look at the convergence of the SINR and the total transmitted power in the in AWGN and fading channels. In this chapter, we propose a power control algorithm that can be used to adjust the mobile station transmitted power in a closed loop power control fashion. The power control presented here does not update the transmitter power in constant steps of 1 dB like the IS-95 but with variable steps that are dependent on the channel condition and the MMSE receiver filter coefficients. 6.1 Fully Distributed Power Control Algorithm Power control algorithms are based on the fact that the SINR at the receiver is di rectly proportional to the desired users transmitted power and inversely proportional to the sum of the interfering signals transmitted powers. The goal of power control algorithms is to equalize the SINR to reduce the total transmitted power in the sys tem. This reduces the interference level in the CDMA system and hence increases the capacity. In general, power control algorithms are classified as centralized or dis tributed power control algorithms. In a centralized algorithm, there is a controller that has complete knowledge of all active radio links and their terminal powers [43] and is responsible for adjusting the transmitted powers at the transmitting terminals. 87 98 Figure 6.9: Total transmitted power and SINR convergence of the proposed algrithm eqn. (6.5) for 10 users and SINR = 10 dB. since the value of |d| is constant and it is known for the transmitter. In this case, only the value of the output of the MMSE filter need to be sent to the transmitter to update its power. In the previous figures, the channel gain and the parameter (afcj) are assumed to be known exactly by the transmitter. Figure 6.12 shows the convergence of the SINR and the total transmitted power when 77 is estimated using eqn. (6.7). In this case the estimates of are updated every 10th symbol. The results 2 here show that the PCA can be implemented practically and only the value of 4*- needs to be di needs to be sent to the transmitter. Practically, the the parameter quantized and then sent to the transmitter. The accuracy of these values depends on the overhead that can be tolerated by the system. To examine the performance of the proposed PCA in a slowly fading channel, an MMSE receiver based CDMA system using the proposed PCA was simulated in a fading channel. To generate Figure 6.13, the following simulation environment was chosen. The mobile speed was 3 mph, the mobile operate at the 900 MHZ band, the bit rate was 9600 bps. This corresponds to a normalized Doppler frequency (fdTs) of 0.00042. The shadowing was modeled as 37 Figure 3.3: Theoretical performance of BPSK, QPSK, and 16-QAM in a Gaussian channel with 50 users. 50 users, both BPSK and QPSK will reach a point at which the bit error rate will become invariant to the increase in That basically means we can increase the load of the system by increasing the length of the processing gain but not increasing the bandwidth or information rate by simply going to a higher order modulation. Therefore, there is a tradeoff between the information rate and higher load for mul tilevel modulation. We can explain the behavior of the MMSE in these figures as follows: When the CDMA system is using BPSK, at some loading point, the MMSE will not have enough dimension, provided by the processing gain, to suppress all the interfering users. At this point, the MMSE receiver becomes interference limited, like the conventional matched filter receiver, and the performance cannot be increased by simply increasing the transmitted power. One way to overcome this is to increase the processing gain. To do so while keeping the bandwidth and information rate the same, one should choose a higher order modulation. In our case, QPSK would be CHAPTER 7 CONCLUSION AND FUTURE WORK 7.1 Conclusion In this dissertation, the possibility of using the MMSE receiver as the underlying receiver structure for future CDMA systems has been investigated. Two areas of improvements of a MMSE receiver based CDMA system were examined; namely, the areas of multilevel modulation and power control. The performance of the MMSE receiver based CDMA with BPSK, QPSK, and 16-QAM modulation formats was examined in AWGN channel in Chapter 3. It has been shown that if the bandwidth and information rate the same for BPSK, QPSK, and 16-QAM, were kept the same, the 16QAM-based system outperforms the other modulation formats based system when the loading of the system is high. This per formance improvement is made possible by increasing the processing gain and hence increasing the ability of the MMSE receiver to suppress the multiple access interfer ence. Since the MMSE receiver will be operating in a near-far resistant region, the SINR can be increased to get acceptable performance of the 16-QAM-based system. As we have seen, for highly loaded system, the system has an error floor in the case of BPSK and QPSK that is invariant to the increase of SINR. This performance limitation can be overcome by choosing a higher order modulation. The performance of the system in a fading channel with the previous modulation formats was investigated in chapter 4 and 5. The inability of the present MMSE receiver structure to operate in a fading channel for one- and two-dimension was demonstrated. A general structure of the MMSE receiver, which can perform effec tively for a wide range of modulation formats in a fading channel, was proposed. For successful detection of the desired users signal, the phase and amplitude of the fading 104 49 The correlation matrix is given by Ri = E [yi(m)y?(mj] 1 2 al,mClCi K Pi _,2 2^ J=2 a fiff + 8i8j + a2I = ^l,mC icf + Rl 2 P xPf + Ri R2 (4.30) cos2(A<9i,m) The MMSE filters optimum weights are given in terms Rf1 and Pi by ax = a2 = Rx xPi (4.31) The output of the MMSE filters can be written as zi = aIiy1 = [^PjV = Pf Rf1 [dncos{5el>m) dQisin(Sdltm)\aitmCi + Pf Rf xyx (4.32) -22 = aHy2 = [RrxPi]Hy2 = Pf Rf1 [dQiCos(69hm) + dnsin(59itm)] ai,mCi + Pf R^xy2 (4.33) Define x = Pf R^xyi and 2 = Pf Rf xy2 which consist of the contribution of MAI and the AWGN at the output of the MMSE filters. Substituting the value for aiimCi from Eqn. (4.29) into Eqn. (4.32) Eqn. (4.32) results in the outputs of the MMSE filters, Z\ and z2, written as z\ = 2 cos( A0lim) Pf Rx XPx [d/iCos(A0lim) dQ1sin(Ad1)m)] + fq (4.34) 75 Figure 5.15: BER of QPSK with different estimation error variances for 3 users. For the estimated case PSAM rate =.2, L= 3 pg= 62, respectively, Figures 5.15 and 5.16 show the performance of 3 and 30 user QPSK systems when the estimation error is modeled as a zero mean complex Gaussian. These figures are to be compared to the 16-QAM Figures 5.13 and 5.14. From these figures, one can compare the sensitivity of the BER performances of the 16-QAM and the QPSK systems to the estimation error. This can be demonstrated clearly by comparing the 16-QAM and QPSK systems when the system load is 30 users. For the QPSK case, with a2 as high as 1 x 10-3, the system performance in terms of BER is the same as for the known fading case. On the other hand, for the 16-QAM case, for cr2 = 1 x 1CT3 the system performance in terms of BER degrades substantially when compared to the known fading case. This result is expected since the 16- QAM modulation constellation is more crowded than than the QPSK constellation. By comparing Figure 5.14 and 5.16 for the 16-QAM and QPSK systems, one can conclude that if the estimation error is high, for example here a2 1 x 10-3, there is no justification for using 16-QAM modulation. 66 and Rc(r) is the autocorrelation function of the fading process and is approximated by Rc(t) = 1 (7TfDr)2 (5.8) The estimates of the fading process out of the linear predictor are then used to remove the phase of the desired user fading from the input of the modified MMSE receiver and to scale the decisions in the modified MMSE receiver, respectively. The second tracking technique is based on pilot symbols. The result of tracking the fading channel using this technique is shown in Figure 5.6. In this technique, pilot symbols, known by the receiver, are sent periodically (every 10th symbol for the case reported in Figure 5.6). The MMSE receiver uses these pilots to obtain an estimate for the fading process in the same manner as in Eqn. 5.2. The fading parameters 72 x Figure 5.11: The distributions of the real and imaginary parts of the estimation error for a 16-QAM system; PSAM rate = 0.2, 3 users, pg= 124, fdTs = 0.0028, Eb/N0 = 20 dB 20 =3.151- E 03 o 10h <1> 5 5 h =6 Q. O' -0.2 mean = 4.5014e-002 variance = 1.1283e-003 nl hrii-i 0.2 0.4 Figure 5.12: The distributions of the amplitude and the phase of the estimation error for a 16-QAM system; PSAM rate = 0.2, 3 users, pg= 124, fdTs = 0.0028, Eb/N0 = 20 dB 81 Figure 5.21: BER of QPSK with different PSAM rates; L= 3 30 users, pg= 62, speed= 5 mph frs = 0.0014. Figure 5.22: BER of QPSK with different PSAM rates; L= 3 30 users, pg= 62, speed= 60 mph /Ts = 0.017. 11 codes are generated based on a recursive generation of a Hadamard matrix as follows: Hi = 0 H2 = 0 0 0 1 h4 = 0 0 0 0 0 10 1 0 0 11 H2JV Hjv Hjy nN Hjv 0 110 In the forward channel we need a 64 x 64 Hadamard matrix to provide the needed 64 Walsh codes to label the channels. Each row of this matrix represents a Walsh code. Each channel has a unique Walsh code. The all-Zero Walsh code is assigned to the pilot channel. The synchronization channel is assigned Walsh code number 32 (row # 32 in the H matrix). The lowest code numbers are assigned to the paging channel and the rest of the codes are assigned to the forward traffic channels. The I and Q signals of the data stream are spread by different PN spreading sequences. This procedure is called quadrature spreading and the spreading sequences are called pilot PN sequences. The binary outputs of the quadrature spreading are mapped to QPSK modulation where 00 maps to tt/4, 10 maps to 37r/4, 11 maps to 3ir/4 and 01 maps to 7t/4. The reverse channel modulation process is shown in Figure 1.4. Many of the blocks in Figure 1.4 are the same as the ones shown in Figure 1.3 and will not be discussed again. The reverse channel uses a convolutional code at a rate 1/3 with code generators given by g0 = [101101111] gi = [110110011] g2 = [111001001] (1.2) 43 Having the output of the filter z in this form, it is straightforward to show that the probability of symbol error conditioned in a?i is given by [40] Pe/ai ~ 3pe/cci 1 ^Pe/ai (4.13) Pe/ai ~ Q ( 2 P^R^P M = Q ,cvi2CiiiR1 xCi (4.14) 5 J V V 10 Averaging pe/ai over the probability density function (pdf) of the desired users fading amplitude,i, gives the expression for P as POO P ~ / fa\,m{p^)Q Jo 'Ql2CiiiR1 1c1 10 da /oi,m(a) = 2aexp {a2) (4.15) (4.16) where /Ql,m(a;) is the probability density function (pdf) of the desired user fading amplitude. A closed form solution for this integral can be obtained by performing the integration and changing variables, and is given as follows: 2 f -u2 P~\ / a exp (a2) exp du,da (4-17) V 7T Ja=0 Jj^ajCiR,Â¡1ci 2 using the polar coordinates, we can write the previous equation as oo />tan' P 2 r r \Ar Jr=o Jg. -1 I / 20 HAT1* =1 1 C1 r2 exp (r2) sin(0), dr, dd Performing this integration will result in (4.18) e~1(i i/ 2 v V20+d^Rr'ci For a single user, the previous result reduces to . 1 (4.19) p~ II w E/N P~2V V 10 + Es/N0 (4.20) 95 Figure 6.5: A typical SINR convergence SINR = 9.5 dB for 15 users using LMS algorithm Figure 6.6: A typical total transmitted power for 15 users using the LMS algorithm 106 The other area of the system design improvement that was investigated was the use of power control in a MMSE based CDMA system. It has been shown that despite the fact that the MMSE receiver near-far resistant, its performance can be improved by using power control. A fully distributed power control algorithm based on the desired MMSE value, which correspond to a desired SINR value, for a MMSE receiver based CDMA system was proposed. By using the proposed PCA, the capacity of the system was improved by more than 20%. The convergence speed of the power algorithm varies depending on the way the tap weights are updated. The convergence and tracking performance of the LMS algorithm are superior to those of the RLS algorithm. This may be due to the fact that the step size of the LMS algorithm is updated for each power update while the RLS parameter is kept constant. An adaptive step size for the LMS is essential to improve the tracking capability of these adaptive algorithms. The tracking of the RLS is very sensitive to the frequency of updating the power. Compared to the LMS, the RLS can not keep up with very frequent updates of the power. One may resort to an adaptive memory RLS or Kalman filtering theory to improve the performance of the RLS algorithm. Haykin in [39] presents a detailed study of the tracking performance of these algorithms. The results in this dissertation clearly indicate that using higher order modulation and power control can increase the capacity and enhance the performance of a MMSE based CDMA system. Furthermore, the results here suggests that the MMSE receiver could be a good candidate to be implemented in future CDMA systems. In the next section, some future research issues are addressed. 7.2 Future Work In this section, some areas of future research will be suggested, the results pre sented in chapter 3,4, and 5 have clearly suggested the potential use of higher order 63 Figure 5.4: The modified MMSE structure. structure is shown in Figure 5.4. This structure assumes an estimate of the amplitude and phase of the fading process are available at the receiver. 5.2 Tracking Techniques in A Fading Channel In the previous chapter, the exact fading process of the desired user is assumed to be known and the MMSE filter weights are assumed to be optimum. In this section, the case where the desired user fading is estimated, rather than assumed to be known, is investigated. In addition, the adaptive LMS algorithm is used to update the MMSE filters coefficients. For the rest of this section, we assume a slow fading environment with a processing gain of 124 chips/symbol, a 16-QAM modulation format, a mobile speed of 5 mph, a frequency band of 900 MHz, and a data rate of 9600 bps. This will result in a normalized Doppler rate, fdTs of 0.0028. There are 3 users in the 91 Figure 6.1: The capacity improvement due to the use of the proposed power control algorithm as compared to the capacity of a system with perfect power control and theoretical bound the proposed algorithm (6.8) for different values SINR. It is clear that while the capacities attained by the proposed algorithm are close to the theoretical capacity bounds, the associated total transmitted powers required by the proposed algorithm are somewhat higher than that for the total power given in [37] by Pt = WSINRa2 ' K \ SINR (6.10) 1 (tL\. \N > l+SINR For the capacity simulation results, we use a normalized channel gain of 1, a processing gain of 31, a noise variance of 0.1, the power is updated every symbol, and we set the initial transmitted power of all users to 0.1. Figures 6.2 and 6.3 show the total transmitted power and the SINR convergence for the system using the PCA proposed in the previous sections. There are 33 users in the system and SINR of 10 dB. The SINRs of the users would converge to a value less than SINR if the number of users were more than 33. While we assume in previous results that all users have the same target SINR, the proposed PCA can CHAPTER 1 INTRODUCTION Code-division multiple access (CDMA) has been the subject of extensive atten tion by the research community in the last two decades. Due to the existence of multiuser interference in CDMA systems, near-far resistant receiver structures for di rect sequence (DS) spread spectrum (SS) have been investigated thoroughly by the CDMA research community. The minimum mean-square error (MMSE) receiver is a near-far resistant receiver structure known for its acceptable performance and low complexity. In this research, the MMSE receiver is chosen to be the underlying receiver structure for our study of DS CDMA systems. IS-95 has been developed by QUALCOMM and adapted by the US Telecommunications Industry Association (TIA) as a standard for cellular CDMA systems. This dissertation revolves around the following idea: If the MMSE receiver is used as the underlying receiver for the next generation CDMA system, how can we redesign some aspects of the system and modify the current MMSE receiver to improve its performance as measured by bit error rate (BER), Signal to Interference plus Noise Ratio (SINR), and capacity? 1.1 Direct Sequence Code-Division Multiple-Access Systems Unlike other multiple-access techniques such as frequency division multiple-access (FDMA) and time division multiple-access (TDMA) where the channel is divided into subchannels and each user is assigned to one of the available subchannels, CDMA is a digital communication multiple access technique in which the channel is not partitioned in frequency or time but each user is assigned a distinct spreading sequence to access the channel. In general, in CDMA systems, spreading is accomplished by 1 6 tight power control, and the design of the receiver rather than the implementation of geographical and spectral separation as in FDMA-based and TDMA-based cellular systems. In this section, we have discussed some major aspects of the cellular concept that are relevant to the work presented in this dissertation. Other aspects of the cellular concept like handoff, channel assignment, and cell splitting are not discussed here and the interested reader is referred to [7] and [8]. From the previous presentation, it is clear that Multiple Access Interference (MAI) is the major limiting factor in the capacity of a CDMA based cellular system. There fore, the capacity can be improved by reducing the interference level. We will discuss some of the improvements that can be adopted to reduce the interference level and how they are related to the work presented in this dissertation. Due to the presence of the interference caused by other users, the matched-filter type receiver (which is optimum for a single user in an additive white Gaussian noise (AWGN) channel) performance degrades substantially. The performance of the con ventional receiver was analyzed in [9] and [10]. The major problem of the conventional receiver is its inability to mitigate what is called the near-far problem. The near-far problem occurs when the received signal of the desired user is overwhelmed by the interfering signals of the other users. To minimize the effect of the near-far problem in CDMA systems, researchers introduced what are called near-far resistant receivers. Among this class of receivers, the MMSE receiver has attracted the attention of many researchers due to its low complexity and superior performance. This receiver struc ture, as discussed in Section 1.3, can greatly affect the capacity of the CDMA system. The MMSE receiver can be described to a certain degree, as a near-far-resistant re ceiver. This capability of the MMSE receiver will substantially increase the CDMA system capacity. The MMSE receiver is an essential component in this research and is discussed in Section 1.3. BIOGRAPHICAL SKETCH Ali Faisal Almutairi was born in Kuwait City, Kuwait, in 1970. He received his B.S. degree in electrical engineering, in May 1993 from the University of South Florida, Tampa, FL. In June 1993, he joined Kuwait University as a laboratory engineer. In December 1993, he has been awarded a full scholarship from Kuwait University to pursue his graduate studies. He received his masters degree in electrical engineering in December 1995. In the summer of 1997, he joined Motorola Land Mobile Products Sector, Plantation, FL, as an intern. He received his Ph.D. degree in electrical engineering in May 2000. 114 ACKNOWLEDGMENTS I would like to thank Professor William Edmonson and Professor Ulrich H. Kurzweg for serving as members of my committee. I would like to express my appreciation to Professor Tan Wong for his fruitful suggestions. I extend special thanks to my ad viser, Professor Haniph A. Latchman, not only for his time, but also for his guidance throughout my studies with respect to both to research issues and to professional is sues. I would like to express my greatest appreciation to my adviser, Professor Scott L. Miller, for introducing me to this topic and advising me in the early stages of this project. I thank my family, my wife, Aisha, my lovely daughters, Bashayer and Ohood, my mother, and the rest of my family members, for their support, patience and encouragement throughout my studies. I also wish to acknowledge all of my friends at the University of Florida and elsewhere, especially my colleagues Dr. Brad Rainbolt and Dr. Ron F. Smith. I would like to thank Dave Tingling, Yassine Cherkaoui, and Sid Hassan for proofreading my dissertation. I would like to thank my friends at the LIST lab for their cooperation. I am grateful to many of my friends in Gainesville for their support. Finally, I acknowledge with gratitude the financial support and encouragement of iii Kuwait University. 38 the choice for a moderately-loaded system and 16-QAM would be the choice for a highly-loaded system. Figure 3.2 compares an LMS based MMSE receiver system performance for 20 users with the theoretical results given in the previous section. The figure shows a very good agreement between the simulation and the analytical BER for the different modulation schemes. Figure 3.4 shows how the different modulation format systems deal with the near- far problem. The interfering signal received powers were modeled as lognormal distri bution. In this case, the standard deviation ap (dB) of the interfering signal received powers is varied while ^ is 5 dB for 30 users load. It is clear from the figure that, at this load, The MMSE receiver with the BPSK modulation format is not near-far resistant anymore. The QPSK and 16-QAM based MMSE receiver systems are act ing as near-far resistant. Clearly, at this level of loading, one should choose a higher order modulation format to restore the near-far resistance of the MMSE reviver. If the system loading is increased to a higher level, one would expect the QPSK based system to lose its near-far resistant property. 3.3 Summary This chapter examines the effect of using higher order modulation formats in the performance of MMSE receiver based CDMA systems in terms of bit error rate (BER) at different loading levels in (AWGN). The performance of BPSK, QPSK, and 16- QAM modulation formats are compared and analysed. In addition, simulation results are presented in terms of the bit error rates for these different modulation formats. A comparison of the rejection of the near-far effects for each modulation scheme is also presented. Under a very high loading level, 16-QAM outperforms QPSK and BPSK for identical bandwidth and information rate while, at a moderate loading levels, QPSK represents the best option. CHAPTER 5 FADING PROCESS ESTIMATION In Chapters 3 and 4, we have shown that the use of multilevel modulation can improve the performance of the system in terms of BER and capacity. In Chapter 3, the AWGN channel model was used while in Chapter 4, a fading channel model and an optimum MMSE receiver implementation were used. The optimum receiver is impractical and hard to construct because it assumes that the powers, the fading processes, the time delays, and the spreading sequences of all users are known. An adaptive MMSE receiver based on the LMS algorithm can be used as a practical alternative to implement the MMSE receiver. In this chapter, a practical situation is considered where an adaptive implemen tation of the MMSE receiver based on the LMS algorithm is used. In addition the desired users fading process is estimated to provide the receiver with a reference phase and amplitude to demodulate the desired user signal. The estimation of the desired users fading process is accomplished through the use of a technique based on linear prediction and pilot symbols which will be described shortly. For most of this chapter, only the performance of QPSK and 16-QAM modulation will be inves tigated since, as we have seen in the previous chapter, the BPSK system is not able to perform effectively even when an optimum implementation of the MMSE filter is used when the system has 30 users. 5.1 The MMSE Receiver Behavior in A Fading Channel In this section, we study the behavior of the MMSE receiver in a fading channel when a multilevel modulation format is used. Since tracking the phase and magnitude of the fading is essential for successful demodulation of a multilevel modulation format 58 88 On the other hand, in a distributed power control algorithm, each radio link adjusts its own transmitted power based on its own measurements [44]. For the zth user, SINRj at the output of the MMSE filter is given in [19] as 7 I H I2 Pihu af cd SINRi (6.1) |(afl)|2 + 2<72(afai) where the variables, is the transmitted power, c is the spreading of user i with a period N, hij is the channel gain of user j to the assigned base station of user i, ai is the filter coefficient vector that correspond to the ith user, I is the multiple access interference presents in the received signal, and a2 is the noise variance. For the ith user, define the desired MMSE ( MMSE, ) as the value of the MMSE which corresponds to the desired SINR (SINRj). The relation between SINR and MMSE* is given in [19] as 1 SINR = MMSE,- - 1 (6.2) The MMSE is obtained by the Wiener solution for the tap weights as described in [39], [20], [18], [19]. For the ith user, the MMSE is given by MMSE* = 1 y/pÂ¡y/hiia.f Ci (6.3) From Eqn. 6.3, we can write the transmitted power in terms of MMSE, the tap wieghts, and the spreading sequence as follows (1 MMSE)2 Pi (6.4) ha |(afc)|2 We propose to update the transmitted power at the (n + 1) iteration according to the following algorithm (1 MMSE)2 ha |(af (n)Cj)|2 Pi(n + 1) (6.5) 79 Figure 5.17: BER of 16-QAM with different PSAM rates; L= 3 3 users, pg= 124, fdTs = 0.0028. Figure 5.18: BER of 16-QAM with different PSAM rates; L= 3 30 users, pg= 124, fdTs = 0.0028. 62 Constant fading amplitude Constant fading phase Figure 5.3: The behavior of the MMSE when the the amplitude or the phase of the fading is held constant. 8 The forward CDMA channel, shown in Figure 1.3, consists of 64 channels of which, 1 is a pilot channel, 1 is a synchronization (sync) channel, up to 7 are paging channels, and the rest are forward traffic channels. The pilot channel helps the mobile in clock recovery, provides phase reference for coherent demodulation, and helps in handoff decisions. The sync channel is used to provide frame synchronization. The paging channels are used to transmit control and paging messages to the mobile stations. The forward traffic channels are used by the base to transmit voice or data traffic to the mobile. The reverse CDMA shown in Figure 1.4 consists of access channels and reverse traffic channels. The access channels are used by the mobile to initiate a call with the base station. The reverse traffic channel transmits voice and data from the mobile to the base station. The blocks in Figures 1.3 and 1.4 will be discussed in the next subsection. 1.2.2 Modulation and Coding In this subsection, we will discuss the modulation and coding processes in the forward and reverse traffic channels as represented by the blocks shown in Figures 1.3 and 1.4 respectively. In IS-95, the modulation process is performed in stages. For the forward traffic channel, the data is grouped into 20 ms frames. The data then is convolutionally encoded by a rate 1/2 code. The code generators for the convolutional codes [11] and [12] are: g0 = [111101011] gi = [101110001] If the data rate is less than 9600 bps, the encoded bits are repeated until a rate of 19.2 Ksps is achieved. After convolutional encoding and repetition, interleaving is performed on the data. The main purpose of interleaving, as in any communication Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DESIGN ISSUES FOR MINIMUM MEAN SQUARE ERROR (MMSE) RECEIVER-BASED CDMA SYSTEMS By Ali Faisal Almutairi May 2000 Chairman: Dr. Haniph A. Latchman Major Department: Electrical and Computer Engineering Code-division multiple-access (CDMA) technology has been the subject of a great deal of practical and theoretical research over the last decade. The adoption of the IS-95 standard, which is based on CDMA technology, has boosted research interest in this area. The minimum mean squared error (MMSE) receiver is a near- far resistant receiver that has attracted the interest of many researchers over the years. The popularity of the MMSE receiver is due to the fact that its performance is comparable to many complex multiuser receivers while its complexity is comparable to the conventional matched filter based receiver. This dissertation examines the benefits of using the MMSE receiver for the next generation of CDMA systems and how some aspects of the system can be redesigned or modified to improve the performance of the CDMA system in terms of bit error rate (BER) and capacity. This research will be targeting two areas of improvements, namely multilevel modulation and power control. vi 61 variations is more severe because the errors in this case are not made just in deep fades but they propagate due to the loss of lock on the desired signal phase by the receiver. Having shown the inability of the present MMSE structure to work in a fading environment described in the previous section, we now consider modification of the MMSE receiver to be capable of demodulating multilevel modulation schemes in a fading environment. In [22], a modified MMSE structure for one-dimensional (BPSK) modulation is presented. We will present a more general modified MMSE structure capable of demodulating a wide range of digital modulation formats. First, since the errors due to the phase of the fading process are dominant, we need to eliminate this phase variation from the input to the adaptive filter. In addition, to eliminate the problem of the MMSE receiver locking to other users phases, we need to take the real and imaginary part of the input to the adaptive filter. The modified 108 result was attributed to the distance properties of the low-rate convolutional code despite the increase in cross-correlation between the spreading sequences due to the use of shorter sequences. The results presented in [46] are for a conventional receiver- based CDMA system in an AWGN channel. Oppermann et.al. [47] have shown different results for an MMSE receiver-based CDMA system operating in AWGN to that for the conventional receiver based CDMA system in [46]. Oppermann et.al. found that an MMSE based CDMA system per forms better with trellis coding. The apparent difference of the results of [48] and [46] on one side and [47] on the other side needs to be addressed. When the power control algorithm performance was investigated for a fading channel in chapter 6, the channel gains are assumed to be constant during the power control updates. This assumption may hold true for the shadowing effect but is not realistic for multipath fading. To get better performance one may resort to channel prediction, as described in [49] and [50], to predict the future gain of the channel and update the transmitted power accordingly. The study of power control of more sophisticated systems with different data rates and QoS requirements is appealing. Preliminary study is presented in [51]. It is interesting to extend the work presented in that dissertation to study whether the proposed power control function converges and how this convergence is affected by the traffic type probabilities. Another future research avenue of this work and built upon treatment of the power control area by Tse and Hanly in [37]. The effective bandwidth concept which has been developed by Tse and Hanly for the MMSE receiver is only valid in the perfectly power-controlled single cell case. Due to the important role this concept plays in characterizing the capacity of the system, it will be very useful and interesting to expand this concept to multicell systems. 52 Recalling Pi from Equation (4.29) Pi = ^cos(A0i)m)o;i,mCi Then Ps/ai can be written in terms of aq,, Ci, and Ri as (4.54) Ps/oci 0?a?,mCOs2(A^l,m)cf Ri XCX) + Q{ ^2al,mCOs2(A^l,m)cf R-i XCi) (4.55) Averaging Ps/ai over the probability density function (pdf) of the desired users fading amplitude, oq, gives the expression for the symbol error rate, Ps, as POO Ps / /ai,m (a)PSiQldO! (4.56) Ja-0 fcn,m(a) = 2a exp(a2) (4.57) where fai m (a) is the pdf of the desired users fading amplitude which is assumed to be Rayleigh distributed ps = J fai,m{a)Q(^\Llalmcos2{^i,m)c?Ri1Ci)da + J fai,m (a)Q(^J\L2ai,mCos2{A6ltm)c? R^cijda (4.58) Where Q is the Q-function which is defined as OO Q(z) = y= J exp(-y)dA (4.59) Z Let h = cos2 (A0i,m)ciHR1 xci (4.60) 31 energy per symbol. The probabilities of error for 16-QAM, QPSK, and BPSK are derived below. r(m) can be written in the form r(ra) = di(m)ci + ?(ra) (3.2) Since E [did{] = 1, the correlation vector P, the autocorrelation matrix R, and the tap weights vector a can be written as follows (dropping the dependence on m for convenience): P = E [djr] = E[\d1\2]c1 (3.3) = Ci R = E [\dx\2] Clc[ + R H ~ (3-4) = pph + r and the tap weights vector, a, given in terms P and R by a = R-1P (3.5) where R E [rfH] .The output of the filter can be written as 2 = afir (3.6) = dx PhR-xP + PHR~1i (3.7) = d1PIiR~1P + (3.8) Now we need to find the value of P-^R^P and the variance of . Using the matrix- inversion lemma, we can find the inverse of R as follows: R"1 RT1 + R_1P(1 + PHR-1P)~1'PH'Rr1 - R_1PPhR_1 R1 + = (1 + PHR1P)1 (3.9) (3.10) 70 Figure 5.9: The performance of BPSK, QPSK, and 16-QAM in a slow fading channel with 30 users, fading estimated. Figure 5.10: The performance QPSK (known fading), and 16-QAM (known and estimated fading) in a slow fading channel with 60 users. 107 modulation formats. In chapter 5, we have proposed a tracking scheme of the de sired users fading process. From the results presented there, we found that 16-QAM system performance was not acceptable at high doppler rate mainly due to the esti mation error. If the fading of the desired user is known to the receiver the 16-QAM system will outperform the QPSK system. One can argue that if the estimation of the fading process can be improved, the performance of the system in terms of BER and capacity will improve as well. This motivate the search for better tracking and estimation techniques. The tracking technique and the general MMSE receiver structure proposed in chapter 5 can be used as a tool to investigate the MMSE receiver performance when channel coding, like trellis-coded modulation (TCM), is used. As indicated before, adopting a higher order modulation to improve the BER performance of the system will be paid for by increasing the transmitted power. If increasing the transmitted power is not desirable, one can resort to combined modulation and coding in the form of trellis-coded modulation (TCM). TCM was introduced by Ungerboeck [45] as means of channel coding that can be used without increasing the bandwidth and transmitted power. The price for the performance improvement comes in the form of decoder complexity at the receiver. Now suppose we apply a TCM coding scheme to a higher order modulation formats (such as QPSK or 16QAM). The bandwidth and the information rate are all the same, while for a given error probability performance, the required SINR of the coded system will be less than in the uncoded system. Therefore, the interference level will be less and one would expect the capacity of the system to increase as a result of coding. TCM has major potential to be used in these systems and more research needs to be done regarding this topic as explained below. Boudreau et.al. [46] have shown that low-rate convolutional codes perform better than the corresponding trellis codes for a given complexity and throughput. This 101 Figure 6.13: Total transmitted power and SINR convergence of the PCA proposed in a slowly fading channel for 10 users and SINR = 10 dB. Figure 6.14: SINR and Total transmitted power of the PCA proposed in a slowly fading channel for 5 users, SINR = 10 dB, and power update every 1 symbol. 28 equal to N0/2TC. The output of the MMSE receiver filter corresponding to the _?th user is Zi(m) = w(m)jfr(m) (2.5) where w is the filter coefficients that correspond to fth user received signal. These coefficients are adjusted by an adaptive algorithm, like the LMS and RLS algorithms, to minimize the mean squar error J(w) which is given by J(w) = E[\e{m)\2] (2.6) Initially, the MMSE receiver works in a training mode. In this mode of operation, a known data squence is sent by the transmitter and this sequnce is used as a reference for demodulated desired users data. When the variable J reaches an acceptable value, the MMSE receiver switches to decision directed mode. The error, e(m), in a training mode is given by e(m) = di(m) Zi(m) (2.7) In a decision directed mode d(m) is substituted by the decision di(m). The mean square error, J is shown in [39] to be a quadratic function of the filter coefficients and is given by J(w) = E[di(m)2] Pf w w^Pj + whRw (2.8) Where R is the autocorrelation matrix of the equalizer contents, R = E [r(m)r(m)Hj and P is a correlation between the desired user response and the received signal and given by Pi = E [d*(m)r(m)]. The minimum mean square error, Jmn, is achieved when the tap weights are the optimum weights. These optimum weights are obtained by differentiating equation 2.8 with respect to w and equating the result to zero. This will result in a form of 10 Access Primary, User k Long secondary CodeMask and To quadrature spreading User k Long CodeMask Figure 1.4: Reverse CDMA channel structure. system operating in a radio channel, is to eliminate the occurrence of blocks of error due to the fading effects on the transmitted signal. Because of interleaving, no adja cent bits are transmitted near each other. This will result in different effects of the radio channel fading on these bits and therefore will randomize the errors caused by fading. In the forward traffic channel, a long pseudo-noise (PN) sequence is used to scramble the data output of the interleaver. After data scrambling, a power control bit is inserted every 1.25 ms. This represent 2 modulation symbols in every 24 modu lation symbols (about 8%). If a 0 is transmitted, the mobile is instructed to increase its transmitted power by 1 dB. If a 1 is transmitted, the mobile is instructed to lower its transmitted power by 1 dB. After these stages, the data stream is spread using 1 of 64 Walsh codes. These codes are orthogonal to each other and of length 64. Walsh 39 (X LU m 10 -2 I X o X o o X * * * * * 0=BPSK *=QPSK X=16QAM 0 3 6 9 12 15 18 opm Figure 3.4: BER of QPSK, BPSK, and 16-QAM as a function of near-far ratio for 30 users. 21 To improve the poor performance of the MMSE receiver in a fading channel, we proposed a tracking scheme which is based on the use of both periodic pilot symbols (PPS) and linear prediction. The introduction of PPS helps to improve the performance of the MMSE receiver in two ways. First, and more important, the pilot symbols provide the receiver with a reliable reference when it operates in a decision directed mode. Second, the pilot symbols might be used to get channel estimates. The effect of the estimation errors, which results from inaccurate estimation of the fading process, on the performance of the 16-QAM and QPSK systems is investigated. Theoretical bounds based on the BER when there is a phase offset due to imperfect estimation of the desired signal phase were derived. The effects of the PSAM rate and the linear predictor length (L) values on the estimation error and on the performance of the system in terms of BER were investigated. In Chapter 6, The power control improvement area was investigated in AWGN and fading channels. The main reason for using power control in a conventional receiver based DS-CDMA system is to combat the near-far problem which occurs when an undesired users signal over-powers the desired users signal. The MMSE receiver is known to be near-far resistant but power control can still be used to reduce multiuser interference, increase the system capacity, compensate for channel loss, reduce the transmitted power and hence prolong the battery life. As shown in [20], the MMSE receiver can achieve many of the performance mea sures of other multi-user receivers performance without the need for side information like user sequences, clock offsets, and the received powers of all the interfering signals. This receiver offers a strong potential for capacity improvement over a conventional receiver-based CDMA system. In a conventional receiver based system, the transmit ted power of the mobile user must be tightly controlled so that the received powers of all users are very close to be equal. This type of power control which equalizes the received powers does not guarantee the equalization of the SINRs at the output Table 5.1: The estimation error statistics for 16-QAM system with L = 3, PSAM = .2, 3 users and fdTs = 0.0028 a\ al 0 9.984 x 10~2 9.865 x 102 5 4.763 x 10-2 4.890 x 10"2 10 1.673 x 10-2 1.672 x 10-2 15 5.129 x 10-3 4.989 x 10-3 20 1.560 x 103 1.594 x 10-3 25 6.238 x 10-4 6.273 x 10-4 30 3.082 x 104 3.123 x 10-4 35 1.690 x 10-4 1.675 x 10-4 40 1.036 x 10-4 1.068 x 10-4 high load systems, the estimation of the error does not have to be as accurate as for the low load systems. Table 5.1 shows the values of the variances of the real and imaginary parts of the estimation error based on simulating a 3 user 16-QAM system. The PSAM rate is 0.2, the predictor length L 3 and the normalized Doppler rate, fdTs is 0.0028. This table is to be compared to Figure 5.13. In Figure 5.13 a cross over between the BERs curve corresponding to the system where the fading has been estimated and the BERs curve corresponding to cr2 = 1 x 10~3 at about ^ = 27 dB. This can be seen from 5.1 that at = 25 dB, cr2 = 1.56 x 10~3 and a2 = 1.5944 x 10~3 while at jf- = 30 dB, L=3 and fdTs of 0.0028 operating between the curves corresponding to a2 = 1 x 10~3 and a2 = lx 10~4 for = 27 dB. lv0 5.4 The Effect of Pilot Symbol Rates on the Performance of the System The effect of a pilot symbol assisted modulation (PSAM) rate on the BER perfor mance of the system is compared for different Doppler rates and system loadings in 93 Figure 6.3: A typical SINR convergence SINR = 10 dB for 33 users. support different target SINRs without any modification. In Figure 6.4, W show the convergence of the SINR and the total transmitted power of a system with 6 users if there are two different target SINR values. Three of these users have a target SINR of 6 dB while the other 3 users have a target SINR of 10 dB. We see from the figure that each user converges to its desired target SINR. The SINR of the user with the low target SINR (6 dB) converges faster than the SINR of the users with higher target SINR. The power control algorithm performance with adaptive implemintation of the MMSE receiver in which the LMS and RLS algorithm are used to update the filter weights was studied and the results are shown in Figure 6.5, 6.6, 6.7, and 6.8. In these figures, the power has been updated every 100 iterations of the adaptive algorithm and the transmitted powers of all users where initilize to 1. As expected, the convergence of the SINR and the convergence of the total transmitted power in the adaptive cases are slower than when the receiver filter tap weights are obtained by the Weiner solution. The SINR converges to a value close to, but not exactly equal to, the target SINR due to the fact that the proposed power control algorithm has 71 in Eqn. 5.2 as (5.9) where the variables ijm and are the estimated amplitude and phase of the desired users fading process. As has been shown in [22] the Lth order linear prediction of the fading channel is given by L (5.10) Let 7(77i) be the exact desired user fading process. Then fading estimation error is defined as e(m) 7(771) /3(m) = X + jY (5.11) Since 7(7n) was modeled as a complex zero mean Gaussian random process, the estimate of the fading can be assumed a Gaussian process since it is produced by a linear operation on a Gaussian process. Therefore, the estimation error is a complex Gaussian process. If the estimator is unbiased, the mean of the estimation error is zero. The real and imaginary parts of the estimation error have a zero mean Gaussian distribution and the amplitude has a Rayleigh distribution while the phase has a uniform distribution from ir to tt. Figure 5.11 shows the distributions of the real and imaginary parts, X and Y, of the estimation error. Figure 5.12 shows the distributions of the amplitude and the phase of the estimation error. The figures are in agreement with our observation that the estimation error represents a zero mean complex random process. The figures are obtained from a simulation of a 3 users, 16-QAM system with fTs = 0.0028 at Eb/N0 = 20 dB It is interesting to see how the system performs if the estimation error is modeled as a complex Gaussian process which its real and imaginary parts modeled as a zero mean Gaussian process CHAPTER 3 MULTILEVEL MODULATION IN AWGN CHANNEL The goal of this chapter is to investigate the performance of the MMSE receiver with BPSK, QPSK, and 16-QAM modulations in an AWGN channel. These different modulation formats were compared based on their BER performance at different loadings of the MMSE based CDMA system. It should be noted that in this dissertation, we simply modulate the data stream using BPSK, QPSK, or 16-QAM modulation formats for comparison. Then the mod ulated signal is spread using a random spreading sequence. We do not use any type of channel coding. In IS-95, the data is processed (by coding and interleaving) and then modulated using a QPSK as shown in Figures 1.3 and 1.4. 3.1 Performance in A Gaussian Channel In this section, we modify the model presented in Chapter 2 to study the per formance of the CDMA system using different modulation formats in a Gaussian channel. This can be done by setting the amplitude and phase of the fading process to 1 and zero in Equation (2.3) respectively. In addition, assume hik = 1 and that user 1 is the desired user and the integrator in front of the MMSE receiver has a scale factor of y/2piTc associated with it. Based on these assumptions, we can rewrite Equation (2.3) as K r(m) = dx(m) Ci + 3=2 + dj(m l)gj(l,S) n(m) (3.1) Where n(m) consists of independent zero-mean complex Gaussian random variables whose real and imaginary parts have variances of where Es is the average 30 xml version 1.0 encoding UTF-8 REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd INGEST IEID EJVB0SWTC_1TPR6V INGEST_TIME 2015-02-05T21:48:12Z PACKAGE AA00024502_00001 AGREEMENT_INFO ACCOUNT UF PROJECT UFDC FILES 112 [37] D. Tse and S. Hanly, Linear multiuser receivers: Effective interference, effective bandwidth and user capacity, IEEE Transactions on Information Theory, vol. 45, no. 2, pp. 641-657, March 1999. [38] P. Viswanath, V. Anantharam, and D. N. Tse, Optimal sequence, power control and user capacity of synchronous CDMA system with linear MMSE multiuser receivers, IEEE Transactions on Information Theory, vol. 45, no. 6, pp. 1968 1983, September 1999. [39] Haykin.S, Adaptive Filter Theory, Prentice Hall, 1996. [40] I. Korn, Digital Communications, Van Nostrand Rienhold Company Inc, 1985. [41] H. V. Poor and S. Verd, Probability of error in MMSE multiuser detection, IEEE Transactions on Information Theory, vol. 43, no. 3, pp. 858-871, May 1997. [42] M. G. Shayesteh and A. Aghamohammadi, On the error probability of lin early modulated signals on frequency-flat ricean, rayleigh, and AWGN channels, IEEE Trans. On Commun., vol. 43, no. 2/3/4, pp. 1454-1466, 1995. [43] S. A. Grandhi, R. Vijayan, D. Goodman, and J. Zander, Centralized power control in cellular radio systems, IEEE Transactions on Vehichular Technology, vol. 42, no. 4, pp. 466-468, November 1993. [44] T. Lee and J. Lin, A fully distributed pc algorithm for cellular mobile system, Ieee Journal on Selected Areas in Communications, vol. 14, no. 4, pp. 692-697, May 1996. [45] G. Ungerboeck, Channel coding with Multilevel/Phase signals, IEEE Trans actions in Information Theory, vol. IT-28, pp. 55.67, Jan. 1982. [46] G. Boudreau, D. Falconer, and S. Mohamoud, A comparision of trellis coded versus convolutionally coded spread spectrum multiple-access system, IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 628-640, May 1990. [47] I. Oppermann, P. Rapajic, and B. Vucetic, Capacity of a band-limited CDMA MMSE receiver based system when combined trellis or convolutional coding, Submitted to IEEE Transactions on Communications, 1998. [48] A. J. Viterbi, Very low rate convolutional codes for maximum theoretical perfor mance of spread spectrum multible-access channels, IEEE Journal on Selected Areas in Communications, vol. 8, no. 4, pp. 641-649, may 1990. [49] C. Trabelsi, Linear adaptive prediction using LMS algorithm over rician fading channel, Telecommunication Systems, vol. 7, no. 2, pp. 193-199, 1996. 5.4 The Effect of Pilot Symbol Rates on the Performance of the System 77 5.5 The Effect of the Linear Predictor Length on the Performance of the System 82 5.6 Summary 83 6 POWER CONTROL 87 6.1 Fully Distributed Power Control Algorithm 87 6.2 Numerical Results 89 6.3 Summary 103 7 CONCLUSION AND FUTURE WORK 104 7.1 Conclusion 104 7.2 Future Work 106 REFERENCES 109 BIOGRAPHICAL SKETCH 114 v 60 track the magnitude and phase of the fading process when the desired user goes into deep fades. The phase estimate in Figure 5.1 represents the MMSE receiver estimate of the phase based on the receiver coefficients. In a single user case, if the MMSE is doing its job of tracking the channel variation, the phase of the MMSE filter coefficients is equal to the opposite value of the phase of the channel. The amplitude estimate is calculated from the value of the filter output. It is clear from Figure 5.1 that the MMSE receiver does a good job in tracking the amplitude variation of the fading channel except during the deep fade period. On the other hand, the receiver does a poor job in tracking the phase of the fading process. In fact, the receiver ends up locked 180 out of phase to the desired user after the deep fade period is over. Differential detection may be considered to solve this problem, but differential encoding will not solve the more practical problem, when the MMSE receiver locks on to other interfering signals. Figure 5.2 shows that in a training mode, the MMSE receiver always tracks phase and amplitude of the fading channel well. This shows that the decision-directed mode of operation of the MMSE receiver is a disadvantage to its performance in this environment. Therefore, if there is a technique by which we can feed back reliable decisions to the adaptive algorithm, the LMS in this case, then the MMSE will perform in an acceptable manner. This is part of the motivation for using periodic pilot symbols to provide a reliable feedback for the LMS and this will be discussed in the next section. In Figure 5.3, the effect of the phase variation while the amplitude is kept constant is shown in the top graphe and the effect of the amplitude variation while the phase is kept constant is shown in the bottom graph. It seems that when the phase is held constant, the amplitude variation leads to errors only in the deep fade periods. This is due to the fact that during deep fades the desired users signal to noise ratio value decreases to a low level at which the receiver can not demodulate the signal correctly. In addition, it can be concluded from the figure that the effect of phase 5 Figure 1.2: Illustration of the frequency reuse concept. concepts. These separations will guarantee the reduction of the interference level and hence improve the system capacity. From the previous presentation, we see that in a traditional narrowband system based on TDMA and FDMA multiple access techniques, capacity is limited by the number of time slots or frequency channels available in the system for a given cell. In CDMA-based cellular systems, channel access is granted through codes, not frequency channels or time slots. Therefore, the loading of the system in terms of active users is not determined by the available frequency channels or time slots but rather by the level of interference the receivers at the base station can tolerate. Each mobile contributes a certain amount to the total interference experienced at the base station receivers. The amount of interference introduced by each mobile depends on the power level at which the signal is received at the base station and the cross-correlation value of its spreading sequence with the other users spreading sequences. A fundamental difference between CDMA-based cellular systems on one hand, and FDMA-based and TDMA-based cellular systems on the other hand, is that of interference elimination strategies. In CDMA based cellular systems, interference elimination is achieved through the choice of spreading codes with low cross-correlation, the use of very 69 Figure 5.8: The performance of BPSK, QPSK, and 16-QAM in a slow fading channel with 3 users, fading estimated. When the load of the the system increases to 30 users, as shown in Figure 5.9, The performance of the system that is based on a BPSK modulation degrades rapidly. In this case, an error floor is introduced and the performance of the system can not be improved by increasing Eb/N0. When the system loading further increased to 60 users as shown in Figure 5.10, the QPSK based system would lose its ability to to suppress the new level of interference and would introduced an error floor. In the next section, we will be examining the third tracking technique that we have proposed in this section in some details. For example, we examine the effect of the predictor length and the pilot symbol rates on the performance of the QPSK and 16-QAM systems. 5.3 The Effect of the Fading Estimation Error on the Performance of the System In coherent detection of a desired signal, the fading process of the desired user need to be estimated. The estimate of the fading of the desired users fading is given 4 a set of radio channels which represents a portion of the total channels available to the entire system. Different sets of channels are assigned to the neighboring base stations. The same set of channels can be assigned to another base station provided that the co-channel interference is at a tolerable level. The use of the same frequency channels by several cells introduces interference to the signals that share this spectrum. This kind of interference is called co-channel interference. Unlike other type of channel impairments (thermal noise, fading and shadowing), the co-channel interference can not be overcome by increasing the transmitted power since this action will increase the co-channel interference for the other users. The use of the same channel set in another base station has resulted in a substantial increase in the capacity of the entire system. The concept of using the same channel sets at different cells is called frequency reuse. The design process by which channel sets are assigned to all the cells in the cellular system is called frequency planning. The frequency reuse factor represents the fraction of the total channels available in the system that may be used by an individual cell. A frequency reuse design which has 7 channel sets and a frequency reuse factor of 1/7, which is shown in Figure 1.2, is commonly used to describe these concepts. The channel sets are labeled A, B, C, D, E, F and G. The base station coverage areas are shown as hexagonal for simplicity. A cluster is a group of all channel sets and is shown in bold in the figure. The cluster in Figure 1.2 includes 7 cells. From the figure, one can see that the capacity of the system, which can be defined as the total number of active mobiles the system can support at a given time, is directly proportional to the number of times the cluster has been repeated in a coverage area. Therefore, the main objective of the designers of TDMA-based and FDMA-based cellular systems is to maximize the system capacity by providing spectral and ge ographical separations, through the use of frequency reuse and frequency planning 57 4.3 Summary In this chapter, we have investigated the performance of an MMSE receiver based CDMA system in a fading channel with BPSK, QPSK, and 16-QAM modulation formats. It has been found that for the same bandwidth and bit rate, the 16-QAM system outperforms the BPSK and QPSK system when the loading of the system is high compared to the processing gain (pg) of the BPSK or QPSK systems. This performance improvement is made possible by increasing the ability of the MMSE receiver to suppress the multiple access interference by using a higher processing gain. In this context, for MMSE receiver based CDMA systems, one should look at the higher order modulation as a means to increase the system efficiency by allowing more users to access the available bandwidth. The estimation of the desired users fading process plays an essential role in deter mining how much capacity improvement can be gained by using the different modu lation formats. In the next chapter, the performance of such systems is investigated when the desired users fading is estimated. 73 with variance cr2. The estimation error can be represented as e = X + jY where X = N(0, cr2) and Y = N(0, a2). Where N stands for normal (Gaussian) distribution. Figures 5.13 and 5.14 show the performance of a 16-QAM system, when the estimation was modeled as a zero mean complex Gaussian process. The variance, cr2, varies from 0 to 0.1. The loading for the results in Figures 5.13 and 5.14 are 3 and 30 respectively. For comparison, the cases where the desired users fading process is known or estimated with a normalized Doppler rate of 0.0028 and 0.0355, respectively, are also shown in the figures. As can be seen from these figures, if cr2 of X and Y are 1 x 10-6 the performance of the system will be the same as if the process is known. If the a2 is increased to 1 x 10~4 the performance is very close to the case when the fading process is known for ^ less than 30 dB, then it degrades. If a2 is increased further to 1 x 10-3, the performance in terms of BER is very close to the known fading case for less than 20 dB and then the BER becomes constant and the performance does not improve at higher ^ for the 3 users case. For the 30 users case, the performance degrades substantially for ^ greater than 25 dB for cr2 = 1 x 10~3 Increasing a2 to 1 x 10-1 will introduce an error floor at BER 0.3 which makes the system ineffective. An interesting result to see from Figures 5.13 and 5.14 is to compare the per formance of the 16-QAM system when the fading is estimated to the cases when X and Y are modeled as zero mean Gaussian with different variances. For example, for the estimated fading system with fdTs 0.0028 the BER curves cross over the BER curve of a2 = 1 x 10~3 at ^ = 27 dB for 3 users and 33 dB for 30 users. This cross over can be attributed to the fact that the estimation of the fading improves by increasing jf-. These figures can serve as figures of merit for a system designer. By checking the variances of the real and imaginary parts of the estimation error, one can have a good idea what the system BER would be. I certify that I have read this study and that in my opinion it conforms to accept able standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Haniph A. Latchman, Chairman Associate Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to accept able standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Tan F. Wong Assistant Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to accept able standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. William W. Edmonson Assistant Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to accept able standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ulrich H. Kurzweg Professor of Aerospace Engineering, Mechanics, and Engineering Science 41 on these assumptions, we can rewrite the received vector given in Equation (2.3) as K r(m) = di(m)ai(m)e-?e^m)c1 + ^ ^-otj(m)e:ej^ j=2 Pl dj(m)fj(l, 6) dj(m l)gj(l,S) (4.1) + n(m) Assuming the desired users phase is known exactly, the input to the MMSE receiver can be written as y(m) = e i'fll,mr(m) (4.2) where is the estimated phase of the desired users fading and here we assumed 9iiTn = Substituting Eqn. 4.1 into Eqn. 4.2, the input to the MMSE receiver, y (m), can be written as K y(m) = di(m)ai,mci + ^ i=2 dj(m)ij(l, 6) + dj (m + n(m)e ^1,m = di(m)aitmci +y (4.3) here A9j user signal, we need to calculate the optimum tap weights for the I and Q channels. It is straightforward to show that the optimum tap weights for the I and Q channel filters are the same. Let the autocorrelation matrices for the I and Q channels received vectors (yi and y2) at the input of the MMSE filters be Ri and R2 and the steering- vectors be Pi and P2, respectively. We have E [Re [dx] Re [d{]] = |. In addition, the correlation vector Px, the autocorrelation matrix Rx, and the tap weights vector ax can be written as follows (dropping the dependence on m for convenience): Pi E [Re [c?i]yi] = -aq)mc i = P 2 (4.4) 65 used. This has motivated the search for a better tracking method. We will now sum marize the procedure used to obtain channel estimates using linear prediction. The tracking of the desired users fading process can be accomplished as follows. From Figure 5.4, the output of the filter output, z(m), when r(m) is the input, is given by z(m) = di(m)iime-?6,1marci + (5.1) A noisy estimate of the fading process can be given by z(m) P(m) =
Qi.me'*1'(5.2) In a decision-directed mode, di(m) is replaced by di(m). The linear prediction can be formulated by the following. As has been shown in [22] the L th order linear prediction of the fading channel is given by L P(m) = ^2 *) (5.3) t=i The optimum coefficients of the linear predictor which minimize the mean-square error between the actual fading process and its estimates are given by = c_1v (5.4) The expressions for C and v for the single user case are given in [22] as C = B+(|)-1I (5.5) where B is a L x L matrix whose elements are given by j)Ts) (5.6) (5.7) [v]i = Rc(iT,) 22 of the matched filter receiver and hence, users may experience an unequal quality of service (QoS). On the other hand, consider the MMSE receiver based CDMA system. Since the MMSE receiver is near-far resistant, the SINR at the output of the MMSE receiver is largely independent of the variation of the received powers of the other users. Therefore, a mobile unit can adjust its transmitted power to achieve a target output SINR without affecting the other users output SINRs. For example, a re ceiver experiencing a low SINR can instruct the corresponding transmitter to increase its transmitted power without having much effect on the other users output SINRs. Likewise, a receiver enjoying a high SINR can instruct the corresponding transmitter to decrease its transmitted power to conserve battery life without having much of an effect on the other users output SINRs. Our results in Chapter 6 and in [34] show that the blockage based system capacity of an MMSE receiver based CDMA system can be improved substantially by applying such a power control algorithm. The major problem with many of the power control techniques presented in the literature is their need, with varying degree, for side information such as channel gains, spread sequences, bit error rate, received powers and the SINRs of all users. The power control algorithm (PCA) proposed in [35] uses measurements of the mean- squared error (MSE) which require knowledge of the actual transmitted symbols. This makes it hard to implement in a fading channel since in deep fades the symbol estimates out of the decision device of the receiver are unreliable [22] and [24]. Both the power algorithms proposed in this paper and the one proposed in [36], do not use the MSE measurements. To implement the algorithm presented in [36], a sample average of the the output of the MMSE receiver is required to provide an estimate of the interference to update the power. In addition, the channel gain of the desired user needs to be estimated. The PCA proposed in Chapter 6 does not require knowledge of the interference caused by other users. Indeed, only one parameter which includes the channel gain of the desired user needs to be estimated.'Additionally, in contrast |