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Design issues for minimum mean square error (MMSE) receiver-based CDMA systems

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Design issues for minimum mean square error (MMSE) receiver-based CDMA systems
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Almutairi, Ali Faisal, 1970-
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vii, 114 leaves : ill. ; 29 cm.

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Bandwidth ( jstor )
Binary phase shift keying ( jstor )
Code division multiple access ( jstor )
Communication systems ( jstor )
Multiple access ( jstor )
Receivers ( jstor )
Signal fading ( jstor )
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Code division multiple access ( fast )
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Thesis:
Thesis (Ph. D.)--University of Florida, 2000.
Bibliography:
Includes bibliographical references (leaves 109-113).
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Printout.
General Note:
Vita.
Statement of Responsibility:
by Ali Faisal Almutairi.

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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 �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 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 �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

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 � 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 �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 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




Full Text
89
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 := r¡(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^
+ ^ Averaging P4/Ql over the Rayleigh pdf of the desired users fading amplitude, the
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 + £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 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.

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

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 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

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

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

spread waveform unspread waveform
3
â–²
* t
â–º
Tb
*• 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 ge¬
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 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. 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.

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.

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 0’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 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

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 —37t/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)

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
TÓÍÍTT ÍToíÓl > (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

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) — 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 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

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

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 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. 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.

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 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 user’s fading process in order for the receiver to demod¬
ulate 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 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

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 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 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 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

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

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.

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¿(í). 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 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

25
Figure 2.1: System Model
Cj(t) -fipjñní.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 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 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) = r¡(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 '
T¿.
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,N—li Cj,N—l+1) Cj,N—1) Cj, 1) •••> Cj,N—l—1/
Cj ( Cj,N—h Cjtpj—i+i) Cj,N—l i ^j,0) Cjji, C^jv—Í—l)
Equation 2.3 can be written in a compact form as
r¿(m) = y/pi(m) \[h~aOLj (m)e8j (m) d¿(m)c¿ + MAI + n(m) (2.4)
and
MAI = y^aj(m)eJA(^) y/Pj(«)y/h^dj(n)fj(l, S) + ^(n - l)y^dj(n - l)g¿(/,¿)
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) = w¿(m)jfír¿(m) (2.5)
where w¿ 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 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 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, Jm¿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_1P¿ (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 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)ij{l,S)
+ dj(m - l)gj(¿,¿)
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) ’ 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 — 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 + ñ (3.8)
Now we need to find the value of P^R^P and the variance of ñ. 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 ñ
ñ = P^R-1? (3.12)
E[ññH] = 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 [ññH]
[1 + P*R-1P]‘
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 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
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 Jm¿n are given as
PeBPSK ~q(\——j—(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].
p’BpsK=Q{\fW)
PeQPSK =
For 16-QAM
-«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 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,

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

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

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.

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.

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

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,6)
(4.1)
+ n(m)
Assuming the desired user’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 user’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 ^1’m
= di(m)o;i,mCi + y
(4.3)
here A9j 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 (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]
- = 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?! + ñi
(4.6)
(4.7)
(4.8)
(4.9)
Now we need to find the value of Pi^Ri *Pi and the variance of ñ\. 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 ñi is
p/Rr'Pi
- -i.
(4.10)
^[ñiñf] =
[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 user’s fading
amplitude,«i, gives the expression for P as
POO
P ~ / fa\,m{p^)Q
Jo
'Ql2CiiiR1 1c1
10
da
faum(a) = 2a exp (—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:
Í2 f°° -u2
P~\ — / a exp (—a2) exp —— du,da (4-17)
V 7T Ja=0 Jj^ajCiííR,¡“1ci 2
using the polar coordinates, we can write the previous equation as
oo />tan'
P
2 r°° r
\Ar Jr=o Je.
I I / 20
â–  h R.r i c
=1 1 C1 ' r2 exp (—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~E‘!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, 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

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

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 user’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-j§imT(m) (4.25)
where 9i is the estimated value of the desired user’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 — 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[»[dI]y]
= ^cos(A9hm)ahmc1 = P2
(4.29)

49
The correlation matrix is given by
Ri = E [yi(m)y?(m)]
1
— 2 al,mClCi
K
Pi _,2
2^
J=2
a
fiff + gjgj
+ = 7^,mClCf + 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 = aHy1
=
= Pf Rf1 [dnco8{59i,m) - dQ1**n(£0lim)]alifBc1 + PfR^yi (4.32)
22 = a.Hy2
= [Rrlpi]Hy2
= Pf Rf1 [dQicos(59itm) + dnsin(59itm)] ai,mCi + Pf R“xy2 (4.33)
Define ñx = Pf R^xyi and ñ2 = 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( A01¡m)
Pf Rx XPx [d/icos(A0lim) - dQ1sin(A9ltm)\ +
(4.34)

50
z2 =
Pf Ri :Pi [dQ1cos(A9hm) + dnsin(A9hm)\ + ñ2 (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 ñr1
cos2(A^iim)Rj)1
cos2(A^1,m) + 2PfRr1Pi
The variances of ñi and ñ2 are equal and are given as follows:
(4.36)
(4.37)
ol =
E[ñ iñf]
= PfBí^IyiyflBí'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 + ñ2 (4.43)
where fi\ and ñ2 are assumed to be N(0, an2) and K is given by
K= (444)
cos2(A01„) + 2PfR-'P
Since Z\ and z2 represent the statistics of dn and dQi, z\ and z2 can be written as
z\ — Kcos(A9i^m)dn + rhi
(4.45)

51
z2 = Kcos(A9ltm)dQ1 + rh2
(4.46)
where
mi = N(—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) — sin(69ijTn)) % , K (cos(S9iiTn) + sin(59i ,m))
V2
-) + Q(
V2
) (4-49)
The value of — 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(A0i„) + 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
ó¿?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 user’s fading
amplitude, aq, gives the expression for the symbol error rate, Ps, as
POO
Ps — / /ai,m (®)Ps,a\dOi
(4.56)
Ja-0
fcn,m(a) = 2aexp(—a2)
(4.57)
where fai m (a) is the pdf of the desired user’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
+
Í2
V 7T Ja=o Jui =
roo r
J a=0 J U\
-U
a exp (—a2) exp dui da
ui-ai -u
a exp (—a2) exp —— du2 da (4.61)
' U2=a\,m\J\í\h 2
By setting V\ = and t>2 = ^ Equation (4.61)can be written as
2 roo roo
— / / aexp(—(a2 -f vf))dvi, da
V7r Ja=0 Jvi
' «i=ai,m-\/\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
r{ = a +v{
(4.63)
. .Ü
0 - tan 1 —
v
(4.64)
Ps -
+
+
r\ exp(—r\)dridOi
r% ex-p(—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(A0i¡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 — 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/^ + \q(\J ^ + ^ Averaging P4/Ql over the Rayleigh pdf of the desired user’s fading amplitude, the
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 8 V V 20 + £lcos2(A0lim)c? R^ci /
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, 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°.

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 user’s 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 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 implemen¬
tation 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 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

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, f¿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 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 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
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
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 es¬
timate 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 sum¬
marize 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)«iime-?6,1’marci + ñ (5.1)
A noisy estimate of the fading process can be given by
z(m)
P(m) =
<¿i(m)aTCi
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
$(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
á = 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
— 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 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 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.

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 user’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 áijm and 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
(5.10)
Let 7(77i) be the exact desired user fading process. Then fading estimation error is
defined as
e(m) — 7 (m) — /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 —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'—
-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 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 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 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 — 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

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 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, fdTs 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 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, Figure 5.13 in which we see that the 3 user 16-QAM system with PSAM=0.2 and
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

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

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 f¿rs = 0.0014.
Figure 5.22: BER of QPSK with different PSAM rates; L= 3 , 30 users, pg= 62,
speed= 60 mph /¿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 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 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 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 — 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 f¿Ts = 0.0028
°x
ai
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 |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 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
Figure 5.23: BER of 16-QAM with different predictor lengths (L); PSAM rate = 0.2,
3 users, pg = 124, and f¿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 /¿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 ±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 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 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

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(afa¿)
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/p¡y/hü^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(a¿*(n)c/)|2
Pi(n + 1)
(6.5)

89
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 = diy/p¡\/%iaf Ci + ñ (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)| := tj(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
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 \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 - (¡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 ‘ * *
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 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

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
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
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.

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 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 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 user’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 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 user’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 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.

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

107
modulation formats. In chapter 5, we have proposed a tracking scheme of the de¬
sired user’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 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

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.

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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 master’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 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

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



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) -y¡2p¡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^ g¡(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
¡= / / 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-j§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 \A§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)f¡(/, 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~llOL¡ (m)e0j (m) d(m)c + MAI + n(m) (2.4)
and
MAI = '22aj(m)ejej('m) yjpj(n)\ffhjdj(n)§ (,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( (cos2(M1)m) + 2Pf R^Pi) cos2(09hm)P? Rr'Pi
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) = r¡(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


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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.


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mods:genre authority marcgt bibliography
theses
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mods:identifier type OCLC 45068139
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mods:language
mods:languageTerm text English
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mods:url access object in context http://ufdc.ufl.edu/AA00024502/00001
mods:name personal
mods:namePart Almutairi, Ali Faisal
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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.
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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 multiple access
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METS:structMap STRUCT1 physical
METS:div DMDID ADMID Design issures for minimum mean square error (MMSE) receiver-based CDMA systems ORDER 0 main
PDIV1 1 Title Page
PAGE1 i
METS:fptr FILEID
PDIV2 2 Dedication
PAGE2 ii
PDIV3 Acknowledgments 3 Section
PAGE3 iii
PDIV4 4 Table Contents
PAGE4 iv
PAGE5 v
PDIV5 5 Abstract
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PDIV6 Chapter 1. Introduction 6
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PDIV7 2. System model
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PDIV8 3. Multilevel modulation AWGN channel
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PDIV9 4. a fading
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PDIV10 5. Fading process estimation
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PDIV11 6. Power control
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PDIV12 7. Conclusion and future work
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PDIV13 References
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PDIV14 Biographical sketch
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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,¡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/p¡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, Figure 5.13 in which we see that the 3 user 16-QAM system with PSAM=0.2 and
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


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112
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45, no. 2, pp. 641-657, March 1999.
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and user capacity of synchronous CDMA system with linear MMSE multiuser
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1983, September 1999.
[39] Haykin.S, Adaptive Filter Theory, Prentice Hall, 1996.
[40] I. Korn, Digital Communications, Van Nostrand Rienhold Company Inc, 1985.
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[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
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[44] T. Lee and J. Lin, A fully distributed pc algorithm for cellular mobile system,
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[45] G. Ungerboeck, Channel coding with Multilevel/Phase signals, IEEE Trans
actions in Information Theory, vol. IT-28, pp. 55.67, Jan. 1982.
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1990.
[47] I. Oppermann, P. Rapajic, and B. Vucetic, Capacity of a band-limited CDMA
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Submitted to IEEE Transactions on Communications, 1998.
[48] A. J. Viterbi, Very low rate convolutional codes for maximum theoretical perfor
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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 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 (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