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## Material Information- Title:
- Digital single sideband (DSSB) with pilot symbol assisted modulation (PSAM) in mobile radio
- Creator:
- Kim, Seungwon, 1964-
- Publication Date:
- 1999
- Language:
- English
- Physical Description:
- viii, 137 leaves : ill. ; 29 cm.
## Subjects- Subjects / Keywords:
- Bandwidth ( jstor )
Cosine function ( jstor ) Dynamic range ( jstor ) Interpolation ( jstor ) Power efficiency ( jstor ) Rayleigh fading ( jstor ) Repeaters ( jstor ) Sidebands ( jstor ) Signals ( jstor ) Transmitters ( jstor ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Thesis:
- Thesis (Ph. D.)--University of Florida, 1999.
- Bibliography:
- Includes bibliographical references (leaves 132-136).
- General Note:
- Typescript.
- General Note:
- Vita.
- Statement of Responsibility:
- by Seungwon Kim.
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- University of Florida
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- 41934932 ( OCLC )
ocm41934932
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DIGITAL SINGLE SIDEBAND (DSSB) WITH PILOT SYMBOL ASSISTED MODULATION (PSAM) IN MOBILE RADIO By SEUNGWON KIM 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 1999 To my wife, Inseon Choi, our children, Juhae, Juyoung, Juchan and my mother-in-law, Soonsub Shim ACKNOWLEDGEMENTS I would like to express my profound gratitude to Professor Leon W. Couch II, who served as a chairman of my supervisory committee. His sincere guidance, continuous encouragement, constructive criticism, invaluable technical advice made this work possible. I also extend my deepest appreciation to him for being very polite, understanding and making himself available during all working days to discuss anything I wanted to, and also for spending his precious time reviewing this manuscript. I must admit that it has been a pleasure to have been his student. I'm also indebted to Professors Haniph A. Latchman, Tan F. Wong, Ewen M. Thomson and Randy Y. C. Chow who very kindly agreed to serve on my Ph.D. committee. I would like to specially thank Professors Haniph A. Latchman and Tan F. Wong for their invaluable suggestions and advice. I would also like to acknowledge the support of this research by ETRI, Taejon Korea. Without support, this work would not have been possible. Of all who supported and provided assistance, none was as valuable as my dear wife, Inseon Choi. I would like to express my deepest gratitude and love to her, for sharing not only the moments of happiness and joy, but also being with me in difficult times of my life, when I needed her the most. I would also like to acknowledge my children, Juhae, Juyoung and Juchan, who provide me much needed relief and comfort through their activities and love. 111 Finally, I would like to express my profound respects and thanks to my both parents. Especially without sacrifices of my mother-in-law, Soonsub Shim, it would not have been possible to pursue my graduate studies. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS .................................. .. .................iii ABSTRACT ............... .................................... vii CHAPTERS 1. INTRODUCTION............................ .................. T he H istory of S SB ........................................................................................................ SSB with Pilot Symbol Assisted Modulation (PSAM) ................... .................. 2. DSSB PSAM SYSTEM M ODEL ................................................................. ....10 G eneral D escription .......................................... ....... ..................... ................... 10 Configuration of the Transmitter........................................................ 10 Filtering for Zero ISI and for Low P, ............................................................... 10 DSSB M odulation ................................. ................ ............ 15 The Problem Using Only One Symbol as a Pilot Symbol ........................................... 19 Fading C hannel E ffects ................................................................... ........ ...........26 Configuration of the Receiver ....................................... .................. .. ...............27 Demodulation .................................................. 27 Sampling and Pilot Symbol Extraction ...................................29 Fading Estimation and Compensation ............ ..........................29 C hannel Interpolation ................................................................................... 3 1 3. PERFORMANCE EVALUATION OF DSSB .............................................42 Theoretical BER Performance under Nonfading .......................................42 Theoretical BER Performance under Fading ................. ......................................44 V BER Performance obtained by Computer Simulation ................................ 47 T he E ffect of R oll-off Factor, r ......................................................... .................47 T he E ffect of T im e Span .................................................................. ......47 The Effect of Frame Length, N. ...................................................... ..... ......52 The Effect of Gaussian Interpolation Order ...................................54 The Effect of Co-Channel Interference (CCI) ..................................... 57 The Effect of Adjacent Channel Interference (ACI) ............................. ............... 61 4. COMPARISON OF DSSB-PSAM, QPSK-PSAM AND OQPSK-PSAM ................ 63 D ynam ic R ange ...............................................................................................63 Peak To Average Power Ratio ......................................................... 71 Spectral Occupancy ................ ... .... .. ........... ............ 87 Comparison of BER Performance for QPSK-PSAM and DSSB-PSAM .........................89 The Choice of Roll-off Factor, r........................... ..................92 5. CON CLU SION .......................................... ........ ....................................... 108 APPENDIX A ........................................................ 111 Derivation of Square Root Raised Cosine Roll-off Pulse .............................................. 111 A PPEN D IX B ................................................. 120 Derivation of the Hilbert Transform of the Square Root Raised Cosine Roll-off Pulse.. 120 A PPEN D IX C .................................................. 127 Description of Simulation Software........................ .............. 127 REFERENCE LIST ....................................... ................. 132 BIOGRAPHICAL SKETCH ............................................... 137 vi 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 DIGITAL SINGLE SIDEBAND (DSSB) WITH PILOT SYMBOL ASSISTED MODULATION (PSAM) IN MOBILE RADIO By SEUNGWON KIM May 1999 Chairman: Dr. Leon W. Couch Major Department: Electrical and Computer Engineering Single sideband (SSB) modulated by digital data with rectangular pulse shapes has infinite amplitude around the data transition times. This is caused by the Hilbert transformation of rectangular pulse shape. In practice, SSB with this type of modulation cannot be used. However, if we use a roll-off pulse shape, the SSB signal will have a reasonable peak value and digital data transmission can be accomodated via SSB. In this dissertation, a bandlimited square root raised cosine (SRRC) pulse is used as a roll-off pulse shape, and digital single sideband (DSSB) is defined as the SSB modulation technique using this pulse shaping filter at the transmitter and lowpass matched filter at the receiver for the digital data transmission system. DSSB is shown to have peak to average power ratios (PAPR) that are from 1.83 to 2.85 dB lower than those for offset quadrature phase shift keying (OQPSK) and quadrature phase shift keying (QPSK) for a roll-off factor of r = 0.115 and 12T, time vii span. The QPSK dynamic range is infinite and the dynamic range of OQPSK-PSAM is 27 dB whereas the dynamic range of DSSB-PSAM is 10.91 dB for a roll-off factor of r = 0.115 and +12T, time span. With DSSB, we can take advantage of the much reduced dynamic range and adopt high efficiency amplifiers even though they have poor linearity. The proposed DSSB also does not need very sharp cut-off filtering and only sloped filtering can be used. Although SSB is bandwidth efficient, its performance in fading channels is very poor unless a reference signal is included. Transmitting a low level pilot tone along with the SSB signal has been used to estimate the phase and amplitude distortion caused by fading. However, we use pilot symbol assisted modulation (PSAM) instead of pilot tone assisted modulation (PTAM) since PSAM has several advantages. Hence, we analyze DSSB with PSAM in a Rayleigh fading channel environment and show that DSSB with PSAM is suitable for mobile radio communications. viii CHAPTER 1 INTRODUCTION The History of SSB Single sideband (SSB) has been used since the early 1900's to transmit analog audio information. In 1915 H.D. Arnold implemented reduced carrier and reduced lower sideband transmission [Osw56]. During the same year, B.W. Kendall patented the product detector which enhanced the detection process. Based on these results, J.R. Carson proposed the method of the single sideband with suppressed carrier communication in 1915 and was granted in U. S. Patent 1,449,382. In 1918 SSB was first introduced in a telephone frequency multiplex system,Western Electric Company Type A, and in 1922 a transatlantic station operated at 57kHz using upper SSB at 150kW [Osw56]. In the late 1920's the Bell Telephone Laboratories constructed a special receiver which was used to investigate the characteristics of shortwave single sideband reception. SSB on shortwave frequencies (3 30 MHz) appeared in 1936 and AT&T company made a shortwave radio which had crystal filters, multiple conversion, and pilot carriers for automatic frequency control (AFC) and for automatic gain control (AGC). Until about 1936 all the shortwave systems transmitted double sideband and carrier because the art in this frequency range did not permit practical single sideband operation. Shortwave SSB proliferated in long-distance telephone links during the next 10 years. During World War II, single sideband systems provided valuable service with connections 1 2 between United States and the armed forces in various parts of the globe. In 1948 many hams pioneered the amateur usage of SSB. A long period of analytical and experimental investigation has proven the efficacy of SSB at HF frequencies. SSB has been adopted as the standard mode for point-to-point communications at HF frequencies. In 1956 Weaver discovered the third method of generation and detection of single sideband signals [Wea56]. The three methods of SSB generation are the filter method, the phase shift method and the Weaver method. This will be discussd later in Chapter 3. Today the filter method is used almost exclusively in analog circuit implementations, while the phase shift and Weaver methods are used in digital circuit implementations. Since the September 1979 World Administrative Radio Conference (WARC), there has been considerable research in the use of the radio spectrum in an efficient way. Since that time, marine, aeronautical, amateur and military services used SSB at HF. At this point in time, the U.K. land mobile radio service used 12.5 kHz bandwidth AM and FM systems at VHF (30-300 MHz) and 25kHz FM at UHF (0.3 3 GHz). In the U.S., 25kHz and 30kHz FM were used at both VHF and UHF [Bat85]. It is already reconized that the efficiency of channel usage is improved by the use of schemes such as dynamic channel allocation and cellular radio. The efficiency can also be improved with the selection of the appropriate modulation technique such as narrow band single side band. All of the above uesd analog modulating signals. In this dissertation we will develop techniques for digital data transmission via SSB. 3 SSB with Pilot Tone Assisted Modulation (PTAM) SSB as a suitable modulation for the land mobile communication has been developed [Wel78], [Lus78],[Gos78]. Though SSB have the advantage of being very bandwidth efficient, the performance in fading channel is very poor. In conventional SSB receivers, it is difficult to synchronize the local oscillator frequency. If the incoming carrier frequency is not the same as the frequency of the oscillator at the product detector in the receiver, product detection will lead to shifting the demodulated spectrum by an amout equal to the difference in frequencies. Doppler spread and Rayleigh fading can shift the signal spectrum causing amplitude and phase variations in the received signal. Reliable receiver carrier synchronization can be achieved if a low-level pilot tone is inserted into the transmitted SSB signal. Hence SSB systems often incorporate a constant amplitude sinusoidal reference tone at some frequency in the transmitted spectrum. The question of where in the spectrum to locate the pilot tone is a difficult one. The research has concentrated on three systems which differ in the spectral position of the low-level pilot tone ( -7.5 to -15 dB below the peak power of the SSB). The systems are as follows: 1) pilot carrier SSB developed by Philips Research Laboratories in U.K. [Wel78] 2) pilot tone in-band SSB developed by the University of Bath in U.K. [Gos78]. 3) pilot tone above-band SSB investigated at Stanford University in U.S. for the Federal Communications Commission (FCC) [Lus78] The emitted spectra for each of these three systems are shown in Fig. 1-1. Of these, the tone in band SSB system offers the greatest degree of adjacent channel 4 protection and a good correlation between the fades experienced by the pilot tone and the SSB signal. In this technique, a part of the SSB spectrum is removed from the central region by a notch filter for the low level pilot tone to be inserted in its place. To remove the low level pilot tone from the receiver output, it is required to remove a segment of the recovered baseband by filtering. Such a procedure has little effect on speech quality even if the filtered segment approaches 1kHz in bandwidth, but it does create problems for data transmission [McG84]. For proper operation of tone in band SSB system for data transmission, the low level pilot tone must be transparent to data and be located across the band. This technique, termed transparent tone in band (TTIB), is shown in Fig. 1-2. and used in conjunction with a procedure known as feed forward signal regeneration (FFSR) [Bat85]. The idea of this procedure is that the receiver uses this pilot tone not only to obtain a frequency reference for demodulation and as a known signal for AGC reference, but also to act as a basis for re-establishing the amplitude and phase features of the original transmitted SSB signal by compensating for the effect of Rayleigh fading. However, when TTIB is used to transmit data signals, the receiver oscillator must be phase locked to that in the transmitter, or the signal is distorted and an unacceptible bit error rate results. Phase locked TTIB (PLTTIB) was proposed as a way of achieving lock without requiring transmission of an explicit synchronization signal, such as another pilot tone [Mcg84]. However, the method has been shown to generate a high level of self noise. The random data signal itself disturbs the phase lock and results in a very long acquisition time [Cav89]. Bateman proposed a symmetric form of the PLTTIB phase detector that can eliminate the self noise [Bat90]. But there still exists a two-fold phase ambiguity, which forces the use of differential encoding, with an additional loss of 3 dB 5 (a) Depressed carrier SSB (b) Tone in band SSB (c) Tone above band SSB Fig. I-1. Three different type pilot tone SSB signal [McG81]. 6 ab pilot tonef, g SSB [ ,t "Modulator (a) Transmitter block diagram a dl e f2 fl (b) Spectra for TTIB transmit processing. Fig. 1-2. General implimentation of TTIB [adapted from [Mcg84]]. 7 in fading channels [Cav91a]. Hence, we can conclude that pilot tone assisted modulation (PTAM) such as TTIB requires complicated signal processing such as frequency shift, band split filtering and using a PLL. The PTAM technique also increases in both peak and the average powers, for data transmission addition of the tone shifts the center of the constellation away from the origin [Cav92]. SSB with Pilot Symbol Assisted Modulation (PSAM) For SSB data transmission, here I propose to use pilot symbol assisted modulation (PSAM) as an alternative. With PSAM, the transmitter modulator periodically inserts known symbols into the data stream to provide the required reference. PSAM provides the reference in the time domain, while TTIB or pilot tone assisted modulation (PTAM) provides a frequency domain reference for the receiver. Like PTAM, PSAM suppresses the error floor. It does so with no change to the transmitted pulse shape or peak to average power ratio (PAPR). However, the information data rate is somewhat lower for a given transmitted bandwidth. Processing at the transmitter and receiver is also simpler than with PTAM. Using PSAM with quadrature amplitude modulation (QAM) already has been proposed for mobile communications [Moh89][Cav91b] and a comparison of PTAM and PSAM for QAM has been presented [Cav92]. Here, we will develop a digital single sideband algorithm using PSAM and analyze the performance of this system. Some key topics and the motivation for their development are as follows: (i) Digital single sideband (DSSB) 8 No report can be found for the analysis of pulse shaped (such as raised cosine pulse) DSSB even though this scheme has approximately the same bandwidth efficiency and power efficiency as Quadrature Phase Shift Keying (QPSK) [Pro89]. (ii) Pilot symbol assisted modulation (PSAM) As mentioned above, both PSAM and PTAM mitigate the effects of multipath fading. But PSAM has more advantages than PTAM. Hence, DSSB with PSAM will be investigated under Rayleigh fading channel conditions. (iii) Peak to average power ratio (PAPR) DSSB with PSAM shows better peak to average power ratio than QPSK and offset quadrature phase shift keying (OQPSK). For square root raised cosine pulse (SRRC), DSSB is shown to have peak to average power ratios (PAPR) that are from 1.83 to 2.85 dB lower than those for offset quadrature phase shift keying (OQPSK) and quadrature phase shift keying (QPSK) for a roll-off factor of r = 0.115 and 12T, time span. DSSB is also shown to have PAPR that are from 3.2 to 4.38 dB lower than those for OQPSK and QPSK for a roll-off factor of r = 0.115 and 6T, time span. (iv) Use of efficient power amplifiers DSSB with PSAM has a much reduced dynamic range when compared to pulse shaped QPSK and OQPSK. We will show that the dynamic range is for DSSB is 10.91 dB, whereas the OQPSK dynamic range is 27 dB and the QPSK dynamic range is infinite for a roll-off factor of r = 0.115 and +12T, time span. We will also show that the dynamic range is for DSSB is 5.38 dB, whereas the OQPSK dynamic range is 22.7 dB and the QPSK dynamic range is infinite for a roll-off factor of r = 0.115 and 6T, time span. With DSSB, we can take advantage of the much reduced dynamic range and use high 9 efficiency amplifiers even though they have poor linearity. (v) No need for sharp cut-off filtering Because of the truncation of the Hilbert transform of the square root raised cosine pulse, the PSD of the proposed DSSB looks like that of vestigial sideband (VSB) as shown in Chap 5. VSB has been chosen for the high definition television (HDTV) standard since it had better performance than QAM for terrestrial HDTV broadcasting [GRA94]. When the baseband signal contains significant components at extremely low frequencies, the use of analog SSB modulation is inappropriate for the transmission of such baseband signals due to the difficulty of obtaining the very sharp cut-offfiltering needed. That is the reason why SSB can not be used with analog TV. But the proposed DSSB does not need the very sharp cut-off filtering. The gradual sloped filtering, such as raised cosine filtering, can be used for the proposed DSSB. CHAPTER 2 DSSB PSAM SYSTEM MODEL General Description The block diagram of the DSSB PSAM system studied here is shown in Fig. 2-1. Known pilot symbols are inserted periodically into the every frame of length N symbols as shown in Fig. 2-2. The reason why we use three pilot symbols instead of one pilot symbol will be explained in later. The transmit lowpass filter is assumed to be a square root raised cosine filter (SRRC) as shown later by (2-1). The modulated DSSB signal is transmitted in the usual way over a channel characterized by flat fading and additive white gaussian noise (AWGN). The demodulated signals are sampled at the symbol rate 1/T and the frame rate 1/TF =/NT,. It is assumed that this timing is regenerated perfectly. The samples at kTF correspond to the pilot values out of the receive lowpass filter. These pilot values are used to estimate the channel state. Compensation is carried out by the corresponding fade estimation. Configuration of the Transmitter Filtering for Zero ISI and for Low P, We desire to determine the composite characteristic of the transmitter and receiver filter which results in a signal stream at the decision threshold that is free of intersymbol 10 n s SRRC LPF datatput data Pilot Ts P Pilot Symbolst(t Symbol scData Symbo/2 Insertiontted frame structure. H-SRRC LPF Rayleigh fading Fading AWGN Esti mation x(t) Channel & Sain S C s,(t) Compen- Symbol sation Extraction SRRC 7c/2 osc Hilbert transform SRRC : Square Root Raised Cosine H- SRRC : Hilbert transform of Square Root Raised Cosine Output data Fig. 2-1. DSSB PSAM system. SD PI PI PD *** D P P P *** Ts P :Pilot Symbol D : Data Symbol NTs Fig. 2-2. Transmitted frame structure. 12 interference (ISI) at the sampling instants. Given this constraint on composite filtering, transmitter filtering can be specified in order to limit the transmitted signal bandwidth to the available transmission channel, and receiver filtering specified to limit adjacent channel interference and ISI and to optimize Pe versus receiver input S/N performance. The optimum requirement is that both transmitter filtering and receiver filtering have to be chosen such that the probability of making a decision error at the receiver is minimized. With the presence of AWGN in the channel, it is well known [Luc68] that a transmitter filter response Tx(f) and receiver filter response Rx(f) which gives optimum Pe is given by M(f) Tx(f)- M(f) (2-1) D(f) Rx(f) = He(f) 1/2 (2-2) where M (f) = H(f) (2-3) 1 H(f) 12 D(f) is the Fourier transform of the input data signaling pulse shape and He (f) is the raised cosine filter which is defined by [Cou97] He(f) = 1, Ifl { 1 +cos[ 2(]}, f< If
2 20, Ifl >B (2-4) 13 where B is the absolute bandwidth and the parameters f andfd are fa = B -fo (2-5) fi Afo -fa (2-6) 1 D fo (2-7) 2 T, 2 where fo is the 6-dB bandwidth of the raised cosine roll-off filter, T, is the duration of one data symbol and D is the symbol (baud) rate. The roll-off factor is defined to be r f (2-8) lo The filter characteristic is illustrated in Fig. 2-3. The corresponding impulse response is h, (t) = f'[H,(f) ] sin(2nfot) cos(2nfat) 2fo* (2-9) (2nfOt) [1- (4fAt)2] To express in terms of the roll-off factor r, from (2-6), (2-7), and (2-8) fA= rfo (2-10) 1-r f, (2-11) 2T 14 I He(f) fd fd 1.0 0.5 -B -fo -f1 0 f, fo B f--N Fig. 2-3. Raised cosine roll-offfilter characteristics [Cou97]. t A7rt sin(-) cos( ) 1 T, T, he(t) = 1 (2-12) T, at 2rt 2 T, T, He(f) = 1, f < 1-r 2T, 1-r 1+ [ 2T, 1-r 1+r { 1 +cos[ ] } < If < 2 r 2T, 2T, O, If 1 >+r 2T, (2-13) 15 Plots of the frequency and the impulse response are shown in Fig. 2-4. Hence, the required normalized transmitter filter response Tx(f) is given by Tx(f) D(O) Ifl < 1-r D(f)' 27T D(O) rT, f | 1 1-r < +r D(f) 2r 4 r 2T 2T 0, Ifl >l +r 2T (2-14) DSSB Modulation In filter SSB method, it is apparent that the filter must have very sharp cut-off characteristics, and the higher the frequency at which the signal is generated, the more difficult this becomes. The phase shift (or Hartley) method is an alternative. In this method the modulating signal is processed in two parallel paths, one of which contains a 900 phase shifter. Unfortunately, any imperfections, such as occur if the Hilbert transform does not maintain a 90' phase shift over the whole bandwidth of modulation, lead to some of the unwanted sideband being generated, and this causes interference to other radio users. The problem of maintaining the 900 phase shift over the full bandwidth of the baseband signal can be overcome by using two stages of quadrature modulation. This technique was first described by Weaver [Wea56]. It is sometimes referred to as the 16 0.9 --------------- ------------------- ----- 0 .7 ..... ................. .................... ................ 0 o 0.7 -----.6 -- -------- -- -- ------------o 0.6 --3 -2 -1 0 1 2 3 zofo 0.1 -. . = r (a) Magnitude frequency response 10. -------------------------------------0.8 ------------- ---- ------- ---- --- ---- ------ ---- ------ ----------0 4 - - - - - - - - - -- - -- - 0.6 E Mr=1 -3 -2 -1 0 1 2 3 trrs (b) Impulse response Fig. 2-4. Frequency and time response for different roll-off factors [Cou97]. 0.4 ............... -----r----Fig. 2-4. Frequency and time response for different roll-offfactors [Cou97]. 17 'Third Method', and is attractive because there is now only a requirement for 90" phase shift at single frequencies. The Weaver SSB generator is in principle realizable in VLSI. However, the Weaver method require very sharp lowpass filters and the two parallel processing channels need to have the same (matched) gain. We assume that here the phase shift method is used for the proposed DSSB system as shown in Fig. 2-1 since the sharp lowpass filters are not needed. We require only the SRRC filter and the Hilbert transform of the SRRC filter. The filtered output is shown in Fig. 2-5. The SRRC and the Hilbert transform of the SRRC will be truncated by using Gaussian window to decrease both ISI of adjacent symbol and peak power which is also shown in Fig. 2-6. The modulated signal s, (t) at the transmitter output is given by 0.8 0 .8 ------------- --- ---- -------- -------- ------------ ------------ 4 --------------0.6 ------------- -SRRC ------ ---------H-SRRC 0 .2 --------------- --------- --- ------ ----- ................ ---------0.4 -0.4 -0.6 -0.8 -- 0 .6 ------ ------------------------------ .. .. .. .. .. .. . . . ------ ----- ----- ----- ------ ---- ---- -----6 -4 -2 0 2 4 6 tiTs Fig. 2-5. The square root raised cosine pulse ('SRRC') and the Hilbert transform of the square root raised cosine pulse ('H-SRRC') with roll-off factor r = 0.35. 18 1 - -------------------------0.8G-SRRC 0.6 ----------- ----- ----- G-H-SRRC 0 ................. --- ------- ----- -- -- ---- --0 .2 --------------- I ----------- --- --- -- -- -- - ---- .... --------- ------ - -0.4 -------------- ------------ ------- ------- --------- --0.6 -0.8 --------------- ------------- ----- ------------------------------ ............... ............... -0 .8 -- - - - - - - - -6 -4 -2 0 2 4 6 tfTs Fig. 2-6. The square root raised cosine pulse with Gaussian window ('G-SRRC') and the Hilbert transform of the square root raised cosine pulse with Gaussian window ('G-H-SRRC') with roll-off factor r = 0.35. s~(t) = Am(t)cos(2 fit) Amh(t)sin(2 nft) (2-15) where A is the amplitude of input data d(t) that corresponds to binary digit 1(or A for 0), the (+) sign used for lower single sideband (LSSB), (-) sign is used for upper single sideband (USSB), m(t) is the normalized SRRC pulses and mh(t) denotes the Hilbert transform of m(t) (see Appendices A and B). m(t) = sin(2fot 2fAt) + 8f~t cos(2fot + 27nft) (2-16) 2nf ot(1 64 f 2 t2) 19 mh(t) = m(t) h(t) =1 64f, 2t2 cos(2nf0t 2nft) + 8ft sin(21fot + 2nfAt) (2-17) 2nf t( 64fA2t2) 1 where h(t) (2-18) If we assume USSB is used to transmit the modulated signal s,(t), this can also be represented as st(t) = Re[zr(t)exp(j2f4t)] (2-19) where zy(t) = A [m(t) + jmh(t)] (2-20) is commonly referred to as the complex envelope of the transmitted signal or the complex transmitted baseband signal [Cou97]. The Problem Using Only One Symbol as a Pilot Symbol The effect of phase error on BER performance where no pilot symbol is used is shown in Fig. 2-7. Without pilot reference, there is a significant bit error increase when the phase error is increased. Hence, pilot symbol must be added to provide the receiver with an explicit amplitude and phase reference for detection. The impulse response of the complete filter response is shown in Fig. 2-8. However, because of the ISI of the Hilbert transform of the raised cosine (RC) pulse which is shown in Fig. 2-9, there is an amplitude and phase ambiguity for the case of using only one symbol as a pilot symbol as shown in Fig. 2-10. To greatly reduce this ISI, we add more adjacent symbols as pilot symbols. 20 - r=0.5 , 0- r035 / 0.001 --- r=0115 .... ... i..... ..:.. ..... ... 0.0001-- ------- -0.00 0.05 0.10 0.15 0.20 0.25 Phase error(rad) Fig. 2-7. The effect of phase error on BER in AWGN where no pilot reference is used, EN = 8dB and different roll-off factors are used. Table 2-1 and Table 2-2 shows the ISI values for different roll-off factors, r for the Hilbert transform of RC pulse, such as shown in Fig. 2-9. We can calculate the average ISI from Table 2-3 and Table 2-4 when the number of pilot symbol is used. Let's define the average ISI, IA, as the absolute value of the mean of the sum of the ISI that corresponding to the pilot symbol value of G-H-RC. Matlab is used to calculate the average ISI given in Table 2-1 through Table 2-2. For example, in the case of 6T,, Table 2-1 is used to calculate the average ISI for 213 possible bit patterns. The BER performance by pilot symbol phase error is shown in Fig. 2-11 through Fig. 2-12 and it is shown that there is a large (above 2dB) BER performance degradation when we use one pilot symbol. If we use three or five pilot symbols, the performance is almost same. If we 21 use more pilot symbols, the average ISI decreases but the power loss is increased. There is a 10log[N/(N-K)] (dB) power loss by inserting K pilot symbols. There is a slight difference in average ISI between using three pilot symbols and using five pilot symbols. Hence, we will use three adjacent pilot symbols in one frame and the amplitude and the phase estimation of the fading will be made at the middle point in the middle pilot symbol. This is shown in Fig. 2-16. 0.6 ------------- 1 G-RC G-H-RC 0.4 ------------ -- -- ------- .-- -- -- ---- ---- -H-RC ---- E 0 ....... ..... ..... ... -0.2 -0.6--------------------0.8 -6 -4 -2 0 2 4 6 t/Ts Fig. 2-8. The impulse response of the complete filter response where roll-off factor r = 0.35. G-RC : Raised Cosine pulse with Gaussian window G-H-RC : Hilbert transform of Raised Cosine pulse with Gaussian window 22 0.9 --------------- ---------------- O .8 ------------------ r = 0.115 0.7 ----< 0 .4 -- -------- -- .......... .. ....... ........ L .................. .... .............. -.................. O .3 ---- ------- -- -- ------- -- -------- ----- r = 0.5 r= 1 0.1 ---- ----- ------------------- ----------0 1 2 3 4 5 6 tITs Fig. 2-9. The effect of Intersymbol Interference (ISI) with a different roll-off factor due to the Hilbert transform of the RC pulse with +6T, time span. Table 2-1. The ISI value with different roll-off factors, r with +6T, time span r= 0.115 r= 0.35 r=0.5 r= 1 0 0 0 0 0 1 T, 0.5192 0.4937 0.4663 0.3483 2T, 0.0035 0.0280 0.0481 0.0770 3 T, 0.0339 0.0231 0.0179 0.0184 4T, 0.0006 0.0032 0.0036 0.0034 5 T, 0.0008 0.0004 0.0005 0.0005 6T, 0 0 0 0 Total ISI 0.558 0.5484 0.5364 0.4476 23 Table 2-2. The ISI value with different roll-off factors, r with +12T, time span r= 0.115 r 0.35 r=0.5 r= 1 0 0 0 0 0 1 T, 0.6022 0.5726 0.5409 0.4039 2T, 0.0063 0.0506 0.0871 0.1393 3 T, 0.1287 0.0877 0.0680 0.0699 4T, 0.0066 0.0344 0.0385 0.0367 5T, 0.0319 0.0173 0.0185 0.0187 6T, 0.0034 0.0095 0.0087 0.0009 7T, 0.0061 0.0040 0.0040 0.0041 8T, 0.0010 0.0016 0.0017 0.0017 9T, 0.0008 0.0006 0.0006 0.0006 10 T, 0.0002 0.0002 0.0002 0.0002 11T, 0.0001 0.0001 0.0001 0.0001 12T, 0 0 0 0 Total ISI 0.7873 0.7786 0.7683 0.6842 2, *1HR G-H-RC I_ 1 1.5 ------------- ......... .....G R ------ -...... G 1- H.i tr........m of...... ..... ......... t Gaussian--- wind -. -- - T = 0 .5 --------------- -T ----- -----.. -- --- --......... ; ------ --- .... T ....... ---------- -- x -------- o .......... ........ 1 i ................ ..I' .......--- .-- ----. . ....... -" . --1 .5 --R- ---- - -, .... ........... . .. .... .... -2 0 2 4 6 8 10 12 t/Ts Fig. 2-10. Amplitude and phase ambiguity in case of one bit pilot symbol with roll-off factor r = 0.35 where ( 1 0 0 0 1 0 11 ) bit pattern is used( 1L: pilot symbol). G-RC : Raised Cosine pulse with Gaussian window G-H-RC : Hilbert transform of Raised Cosine pulse with Gaussian window 24 0.1 0.01 0.001 0.001 .. .. ... ...... ..... ... ... ... ...... --- Theory -U- 1 pilot symbol 3 pilot symbolsJ -r- 5 pilot symbols 0.0001 1 2 3 4 5 6 7 8 9 EbfNo(dB) Fig.2-11. BER performance under AWGN where different pilot symbols are used, roll-off factor r = 0.35, time span = 6T, and frame length N= 20. :: :: :::: :::: :::: :::: :::: 3 pilot symbols 5 pilot symbols 0.0001 .... 1 2 3 4 5 6 7 8 9 Eb/No(dB) Fig.2-12. BER performance under AWGN where different pilot symbols are used, roll-off factor r = 0.35, time span = +12T, and frame length N= 20. 25 Table 2-3. The average ISI where 6T, time span is used r = 0.115 r = 0.35 r = 0.5 r = 1 1 pilot symbol 0.2541 0.2538 0.2209 0.1408 3 pilot symbols 0.0395 0.0451 0.0583 0.0596 5 pilot symbols 0.0321 0.0407 0.0526 0.0539 Table 2-4. The average ISI where 12T, time span is used r= 0.115 r= 0.35 r = 0.5 r = 1 1 pilot symbol 0.2275 0.2290 0.2024 0.1991 3 pilot symbols 0.0942 0.0983 0.0914 0.0878 5 pilot symbols 0.0655 0.0602 0.0465 0.0399 7 pilot symbols 0.0298 0.0326 0.0271 0.0173 2 1.5 ------------------ -------------- - __ ............ --- R-C -.-.....---0 . 0.5 ...... .. ..... .. ... .. ... ........ ................. 1 /-- --------- 10.5 .... - -.... - - .. ........... ...... . ...... ..... -1.5 ------ RC -2 0 2 4 6 8 10 12 t/Ts Fig. 2-16. Explicit amplitude and phase reference in case of three pilot symbols with roll-off factor r = 0.3 5 where ( 1 0 0 0 1 0 ) bit pattern is used ( 0I : pilot symbols). 26 Fading Channel Effects In a land mobile radio channel, the received signal is a linear combination of a large number of carrier signals spread in time and frequency, each corrupted by AWGN. In relatively low symbol rate systems, e.g., f, < 50kbaud, the time delay spread among these multiple signal paths is frequently a negligible fraction of the symbol duration T, [Lee89]. We limit ourselves to such cases, i.e., nonfrequency selective fading (or flat fading). The resulting faded carrier has been shown to have a random phase and amplitude modulation imposed upon it by the channel. The random amplitude has been shown to have a Rayleigh distribution, and the random phase a uniform distribution [Jak74]. The complex envelope of the faded carrier u(t) may be represented as u(t) = c(t)z(t) (2-23) where the quantity c(t) c(t) = a(t)e'dt) (2-24) represents the fading which is a complex zero mean, stationary Gaussian random process characterized by its frequency spectrum C(f) given by [Jak74] 2 cy) c (2-25) 2;rf 2 _f2 Here fD is the maximum Doppler frequency experienced by the moving vehicle, which is related to the vehicle speed by 27 fD =fc( -) (2-26) where fc = transmitted carrier frequency v = relative velocity of source and receiver c = 3 x 108 m/sec The amplitude or the envelope process a(t) then has the Rayleigh probability density function given by [Jak74] f(a)=(-a)exp(- ), 0< a oo (2-27) 2 2 where 02 0 (2-28) 2 is the common variance of c(t). The random phase 0(t) of c(t) is independent of a(t) and is uniformly distributed over 0 < 0 < 2;. Configuration of the Receiver Demodulation The received signal s,(t) is demodulated with a locally generated carrier of frequency ft =fc -foff, whereff is the residual frequency offset of the local oscillator. As is given by (2-23), the received signal is expressed by 28 s,(t) = Re[c(t)z7(t)exp(j2nfrt)+ nc(t)] (2-29) The subsequent lowpass filter is a square root raised cosine filter. This, in cascade with the transmit filter, assures ISI free transmission and optimum BER performance in AWGN channel. The demodulated and lowpass filtered complex signal is given by, x(t) = [c(t)ZR(t) + n(t)]exp(j2nffft) (2-30) Here, ZR(t) is the signal component of the received complex baseband signal which can be expressed by ZR(t) = zz(t) m(t) (2-31) where m(t) is a SRRC filter. The noise term n(t) is SRRC lowpass filtered AWGN with power spectral density No in both real and imaginary baseband components corresponding to a bandpass PSD of No/2. The distortion caused by the fading channel is represented by the complex channel gain c(t) given by (2-24). We assume that the receiver lowpass filters pass thisfoff component undistorted, since the bandwidth of the fading process is significantly larger than the symbol rate. The minimum sampling rate, that is Nyquist frequency, for symbol extraction is given by f symbol extraction > 2(fD + fff), wheref symbol extraction = 1/NT. (2-32) Hence, the receiver works if 2(fD + fof) << DN. (2-33) where D = 1/T, 29 Sampling and Pilot Symbol Extraction The demodulated complex baseband signals x(t) are sampled for data at the symbol rate 1/Ts, and for the pilot reference at the frame rate 1/TF = 1/NTs. It is assumed that this timing is recovered perfectly. The samples at kTF give the received complex symbols corresponding to the pilot symbols. Samples at (k + m/N)TF, m = 1,2, ... (N-1) give the yet uncompensated received data symbols. Fading Estimation and Compensation Normally, the pilot symbol would be randomized to avoid transmission of a tone, and the receiver would make appropriate corrections based on its knowledge of the transmitted pilot values. However, in the following analysis of fade compensation, it is assumed for simplicity that a constant pilot sequence have value d' = A and data symbols are d(k) = -A. The distortion due to fading for kth pilot symbol is calculated as follows. For t = kTF(corresponding to the received pilot symbols) x(k) = [Ac(k) + n(k)]exp(27rffgkTF) (2-34) Where x(k) and n(k) are the complex sample values of x(t) and n(t) at t = kTF. The fading estimation 8 (k) of c(t) at t = kTF is found by dividing x(k) by the corresponding transmitted pilot symbol. Hence, 86(k) = [c(k) + n(k)/A]exp(j2foqkTF) (2-35) The fading at the other points (k + m/N)TF can be obtained by interpolating the estimates 30 at kTF. We use the Gaussian interpolation which is the interpolation method [Sam89] that discovered by and named after Carl Friedrich Gauss [Ham73]. This method achieves good compensation with significantly reduced complexity and processing delay compared to the Wiener filter to minimize the variance of the estimation error presented in [Cav9lb]. As shown by (2-37),(2-38) and (2-39), zeroth order uses only one pilot symbol, first order uses two pilot symbols and second order uses three pilot symbols for channel estimation. Using second order Gaussian interpolation, the interpolated estimates 0 (k + m/N) are formed as, (k + m/N) = Q.;(m/N) 8 (k -1) + Qo(m/N) 8 (k) + Q;(m/N) N (k + 1) m = 1,2,3,... (N-1) (2-36) where 2N N Qo(m/N)= ( )2 N Q(m/N) = [ ( )2 + ( ) ] (2-37) 2N N In case of first order and zeroth order interpolation, the coefficients Q is obtained as, Q- = 0 m Qo = 1 - : first order N m Q (2-38) N 31 Q. =0 Qo = 1 : zeroth order Q, = 0 (2-39) It is seen that estimation errors may be caused by noise, frequency offset in the receiver local oscillator and non-ideal interpolation. Compensation is carried out by dividing each received symbol by the corresponding fade estimation. The compensated complex samples (k + m/N) are given by, i (k + m/N) = x(k + m/N)/ 6 (k + m/N) m = 1,2,3, ...(N-1) (2-40) Hence, the decision input is given by the real component of 2 (k + m/N). Channel Interpolation The signal received by a moving vehicle in a land mobile channel consists of multiple reflected rays due to local scattering and the lack of a line-of-sight path between the transmitter and the receiver. Due to such multipath fading, the received signal is subjected to random amplitude and phase fluctuations. It has been shown that if the delay spread between the multiple rays is negligible in comparison to the symbol duration, then the channel is characterized by a complex gain whose amplitude has a Rayleigh distribution and the phase has a uniform distribution [Jak74]. Since the in phase and quadrature components of the channel gain are narrowband Gaussian processes, periodic 32 sampling of the channel by pilot symbols inserted into the data stream may be used to recover this process. The pilot symbols which is located N symbols apart provide a noise corrupted estimate of the channel gain at the sampling instants. The channel sampling rate is fc, f (2-41) N wheref, is the symbol rate and Nis the frame of length. For the kth frame, the channel estimate obtained from the received pilot symbol is given by (2-35) c (kN) = c(kN) + n(kN) /d (2-42) A where c(kN) is the sample of the fading process c(t), c (kN) is the corresponding channel estimate, n(kN) is the sample of the AWGN corrupting the system and d is the known pilot symbol. From the Nyquist theorem, for the reconstruction of the fading process, fc, 2 2fD (2-43) wherefD is the maximum Doppler frequency. The Nyquist frequency for channel sampling is fN = 2fD (2-44) Since N 2 2 for any information transfer over the channel and the actual pilot symbol rating is given by 33 fpilot symbol extraction (2-45) NT, Hence, the normalized fading rates of fDT for N 2 2 may be theoretically estimated by fDTs 0.25 (2-46) A At the receiver, the channel samples c (kN) are interpolated to give estimates of the fading for the data symbols. An interpolation schemes may be generally represented by c (kN + m) = (mN) c [ (k+r)N ], 1 m < N-1 (2-47) where Qr (m/N) are the interpolation coefficients. Alternatively, the interpolation may be represented by using the impulse response h(m) of the interpolator c(kN+ m)= c(kN+j)h( m -j), 1 m < N-1 (2-48) j=-0 The realtionship between the impulse response and the interpolation coefficients obtained from (2-47) and (2-48) Qr (m/N) = h(m rN) (2-49) The resulting estimates may be expressed as, c (kN + m) = c (kN + m) + e(kN + m) + n(kN + m) (2-50) 34 where e(kN + m) is due to interpolation error and n(kN + m) is due to noise. The composite error denoted by F (kN + m) so that A c(kN+m)=c(kN+ m) + (kN+ m) (2-51) where & (kN + m) = e(kN + m) + n(kN + m) The interpolator corresponding to sampling the channel at the minimum Nyquist frequency is an ideal lowpass filter whose impulse response is given by [Sha73], h(n) in(- oo < n < oo (2-52) an/ N ' The corresponding frequency response is given by, H[exp(jw/w, )]= I h(n)[exp(-jmw /w,)] = N, |w/wI<0, otherwise (2-53) This extracts a single image of the sampled Doppler spectrum without distortion or aliasing as shown in Fig. 2-18. Such an interpolator however can not be realized in practice, due to its infinitely long impulse response as can be seen by (2-52). The length of impulse response is also propotional to the complexity of the interpolator and to the processing delay. Hence, the impulse response must be truncated to meet the systems requirements and constraints. 35 A truncated interpolator may use Q channel estimates from Q frames to obtain N-1 fade estimates within a frame. The maximum processing delay Td is given by, Td= NQ / 2, if N is even N(Q-1)/ 2, otherwise (2-54) The length of the impulse response is given by [Sha73], Np= NQ, if both N and Q are odd NQ -1, otherwise (2-55) By truncating the interpolator to meet the constraints on complexity, delay etc, pass band distortion and stop band sidelobes are produced in the frequency response. This results in errors in the interpolation estimates due to distortion and aliasing as shown in Fig. 2-19. Hence, performance is compromised due to truncation of the interpolator. This degradation in performance may be overcome to a certain extent by increasing the channel sampling rate abovefN, i.e., by closer spacing of the pilot symbols. In doing this, the Doppler spectral images are moved further apart, so that the effects of aliasing are reduced. Fig. 2-20 shows this with the same truncated interpolator as shown in Fig. 2-19. Oversampling the channel can be expressed by fc, = 2ffD (2-56) where / is the oversampling factor given by, 36 1 1 (2-57) 2NfD T Although the performance degradation is reduced by oversampling the channel, there is a power loss by a factor, 1/ (N- 1). The Gaussian interpolation for the kth frame is given by [Sam89] c(kN + m) = Q(m/N) c[ (k+r)N], (2-58) where the interpolation coefficients Qr are given by, 1 m2 m Q.;(m/N) =- [ ( ) 2 N N Qo(m/N) = 1 ( )2 N 1 m QI(m/N)= [( )2+( )] (2-59) 2 N N To find the impulse response hG(n), we may use (2-49) yielding, n+N Ql[ ], -N < nO N n-N Q-l[ ], N< n < 2N (2-60) N 37 Substituting from (2-59), 1 n)2 3n -[( )2 +( ) + 2 ], -N hG(n) ()2, 0 n N N 1 n 3n 1[( )+ 2], NI n2N (2-61) 2N N Fig. 2-21 shows this impulse response for N= 20. The frequency response of this interpolator is shown in Fig. 2-22 and compared with that of an ideal interpolator, from which the pass band distortion as well as the aliasing that could be caused by the sidelobes may be observed. The pass band distortion starts around 0.2fcs. The first spectral nulls around the channel sampling frequency is narrow. Therefore, if fD > 0. If,,, the effect of aliasing will be seen in the interpolated estimation. Hence, to avoid aliasing, the channel has to be sampled at least 5 times the minimun Nyquist rate. Hence, the performance degradation as well as the required increase in overhead resulting from the use of a non ideal interpolator is evident. -fD 0 fD f Fig. 2-17. Doppler spectrum. 38 1 2 3 f/f, Fig. 2-18. Ideal lowpass filter interpolation with channel sampling at the Nyquist rate. 1 2 3 f/f Fig. 2-19. Non-ideal lowpass filter interpolation with channel sampling at the Nyquist rate. 1 ifs Fig. 2-20. Non-ideal lowpass filter interpolation with channel sampling above the Nyquist rate. 39 1T 0 .8 ----- --............. 0.6 a. 0.4 E 0.2 0.2 ---------- ---O -- ---- ----- -- ----- ------------ -- -- - --- - --- -- --- -- --0.2 0 10 20 30 40 50 60 n Fig. 2-21. The impulse response of a Gaussian interpolator with Q = 3 and N = 20. 0 -5 ~ ~ ~ ---------- ------------------- ------------------.. .. ........ .... .. ..... .................................. -5 ------1 0 ---------------- -- --------- ---- - - - -- - - - ---- ------- --15 -20 ---------------- -- -- -- -------Gaussianinterpolator -25 ---------------------------- -- --------- ----30 .. .. . .. . -. -- -- -- -- -- -- --.---.- -- ---.- ---.I..... .... .... .. .. .. .. -- -- -- -- -40 4 0 .. . . .. . . -- - - - - - - - - - - - -- - - . . . . . . . . . -45 -50 0 0.5 1 1.5 2 2.5 3 frequency Fig. 2-22. The frequency response of a Gaussian interpolator with Q = 3 and N= 20. 40 Hence, the requirements in the design of a suitable channel interpolation are as follows. 1. Good performance 2. Low complexity 3. Low processing delay 4. Low overhead A method of estimation and compensation for the amplitude and phase variation in mobile channel is based on the insertion of known pilot symbols periodically into the data stream. This method however, requires the transmission of redundant symbols. Another disadvantage is that this processing incurs some delay in the received data. The minimum overhead is achieved when pilot symbols are sampled at the Nyquist rate, which is twice the maximum Doppler frequency. However, the infinitely long interpolator corresponding to this sampling rate can not be realized due to practical constraints in processing delay and system complexity. Hence, the interpolator must be truncated to a reasonable limit at the cost of system performance. The performance with lowpass filter interpolation as a function of the noise bandwidth of the interpolator has been studied in [Moh89]. To reduce the effects of noise, the channel estimates are filtered with a filter which is approximately matched to the fading process. They choose a filter bandwidth correspond to the worst case fading rate. This non-ideal lowpass filtering results in degradation in the estimates due to aliasing and distortion as shown in Fig. 2-19. Optimum interpolation technique is studied in [Cav9 Ib] using Wiener filtering of the received pilot symbols. This technique requires adaptive updating of the tap coefficients 41 and has considerable processing delay. The performance obtained by this optimal interpolation is within 1-2 dB of the theoretical coherent performance. We use the Gaussian interpolation used in [Sam89]. This method achieves good compensation(1-3 dB) with significantly reduced complexity and processing delay compared to the optimum interpolation technique presented in [Cav9lb]. However, Gaussian interpolation require closer spacing of pilot symbols compared with that of ideal lowpass filtering. This would result in introducing more redundant bit into the data stream, increasing the overhead. CHAPTER 3 PERFORMANCE EVALUATION OF DSSB Theoretical BER Performance under Nonfading BER performance of DSSB under coherent detection with AWGN, matched filter reception and optimum threshold setting can be calculated as follows [Cou97]. Pe = Q( ) (3-1) 1 (-2 Where Q (x) = ( ~ ) exp(- ) d (3-2) 2 Here Ed is the difference signal energy at the receiver input. T Ed f[ s(t) s2(t) 2dt (3-3) 0 The normalized average difference power of the DSSB signal, Sd(t) is given by [Cou97] < (t) > = < gd(t) 12 > (3-4) 2 where gd(t) is the complex envelope for DSSB signal at the decision input. Hence, 42 43 Ed = < I gd(t) 1 2> T 2 = 1< 2[m(t) +jmh(t)] 12> Tb 2 = 2 1 = 4A2Tb (3-7) Hence, Pe= Q( ) (3-8) b No Here Eb is given by Eb = < Ig(t)2 > Tb 2 = < I [m(t) +jmh(t)] 12 > Tb 2 1 I 2 = A2Tb (3-9) 44 Therefore, Pe = Q( ) (3-10) SNo This result is used for the theoretical performance curves that is plotted in Fig. 3-1. The following items are considered causes of the performance degradations. 1) Power loss by inserting pilot symbols given by D1= 10 log( )(dB) (3-11) N-3 2) Degradation by the noise included in the pilot symbols 3) ISI of the Hilbert transformed signal of the RC pulse 4) Degradation due to inaccuracy of estimation Fig. 3-1 also shows the BER performance of DSSB with PSAM in AWGN. The performance of DSSB with PSAM is degraded by about 2 dB for N = 20 from the theoretical value due to the degradations items. Theoretical BER Performance under Fading Let us assume that the channel fading is sufficiently slow to that the phase shift 0 can be estimated from the received signal without error. The SNR y = WEb /No is a varying quantity on account of the effect of the fading and proportional to the square of the Rayleigh fading envelope, r 2, which can be obtained by letting pr(r) = 1 exp(- ) (3-12) 7 0 70 45 where y,= E[ y ] E =( b )E[a ] (3-13) NO Since a is a Rayleigh distributed, a2 has a chi-square probability distribution with 2 degrees of freedom. Consequently y also is chi-square distribution. The average error rate obtained as follows [Rap96] ( P")= o Pr(Y)Pe( Y) dy S co1 exp( ) ( ) erfc( ) dy Yo Yo 2 1 1 2 1 = ( 1- ) (3-14) This result is used for the theoretical performance curves that is plotted in Fig. 3-2 where E[ d ] = 1. 46 0 .1 .. .. .... .... 0.0001 ... .... .... ....... .... ~-4Theory 0.001 !i !- DSS -PSAM 5 10 15 2 0 25 30 35 Eb/No(dB) Fig. 3-2. BER Performance under Ravleigh fading environments where Er a 1 = 1. 0.01 0.0001 ... .. . Ebo(dB) Fig. 3-2. BER Performance under nonfading (AWGN) environments where = .5, .............. ... : : : : : :.. Fig. 3-2. BER Performance under Rayleigh fading environments where E[ 1. =i 47 BER Performance obtained by Computer Simulation We will examine BER performance curves for values of normalized Doppler frequencyfDT, using computer simulation. The Effect of Roll-off Factor, r It is seen that there is different intersymbol interference (ISI) with different rolloff factors due to the change of shape of the Hilbert transform of the raised cosine(H-RC) pulse as shown in Fig. 2-8. As the roll-off goes to 1, ISI decreases and as the roll-off goes to zero, ISI increases. Hence, the BER performance is a function of the roll-off factor. However, there is only a slight difference in the BER performance with the different rolloff factors as shown in Fig. 3-3 through Fig. 3-6. Using a roll-off factor greater than zero gives an increase over the bandwidth obtained for the r = 0 case. Hence, for the trade off between low BER and excess bandwidth, choose a roll-off factor of r = 0.115. This gives a small bandwidth increase of 11.5%. The Effect of Time Span Pulse shaping filters have to be truncated. If we have the longer time span, the bandwidth decreases but there is more ISI in adjacent symbol. Fig. 3-7 through Fig. 3-10 shows that 12T, time span is considered to be optimum. If time span is less than 12T,, there is an ISI decrease in adjacent symbols but the original RC and H-RC will be distorted more due to truncation and Gaussian windowing. If time span is more than 12T,, there is an ISI increase in adjacent symbol but the original RC and H-RC will be 48 0.1 -* theory -- r= 0.115 ...... ............ t-A- r = 0 5 0.001 0.0001 ... .... .... . 5 10 15 20 25 30 35 EblNo(dB) Fig. 3-3. Effect of roll-off factor, r, on BER for DSSB-PSAM where time span= +127T,, N= 20,fDTs = 0.001 and 1st Gaussian interpolation. 0.1 -4- theory r 0 115 ...... i i.. -r=035 .......... r= 05 0.01. 0.001 0.0001 5 10 15 20 25 30 35 Eb/No(dB) Fig. 3-4. Effect of roll-off factor, r, on BER for DSSB-PSAM where time span = +12T,, N= 20,fDT, = 0.0025 and 1st Gaussian interpolation. 49 0 .1 . . . . . . . . . . r=0.115 -- r=0.35 -- r=05 0.01 0.001 , l , 5 10 15 20 25 30 35 EbNo(dB) Fig. 3-5. Effect of roll-off factor, r, on BER for DSSB-PSAM where time span= I12T,, N= 20, fDT, = 0.00625 and 1st Gaussian interpolation. 0.1 -- theory -- r = 0a115 r = 035 -- r = 0.5 0.01 0.001 0.0001 5 10 15 20 25 30 35 Eb/No(dB) Fig. 3-6. Effect of roll-off factor, r, on BER for DSSB-PSAM where time span = +12T,, N= 20, fDT, = 0.01 and 1st Gaussian interpolation. 50 0.1 S--- theory S--a- 12T, .i .- . - 18T, 0.01 o i .. ... .. ......- -.... .... ........ ....... 0.001 .. . .. .. . .. . . .. .. . . 0.0001 5 10 15 20 25 30 35 Eb/No(dB) Fig. 3-7. Effect of time span for each symbol on BER for DSSB-PSAM where r = O. 115,fDT, = 0.001, N= 20 and 1st Gaussian interpolation. 0.1 -- -: .-- .:--- .-- .- -----:---:---.....'...S- - -theory + 6T, .. .....7 -A- 12T, i.i0 i--18T, li 0.01 0 0 "!- -i- i. - ..i. .... ....... . .... ....... ........ ... ... ...i...i. .i. . 0 .0 0 1i. ....'.I. .....I ... .... .. 0.0001 5 10 15 20 25 30 35 EbNVo(dB) Fig. 3-8. Effect of time span for each symbol on BER for DSSB-PSAM where r = 0.115,fDT, = 0.0025, N= 20 and 1It Gaussian interpolation. 51 0.1 --- theory 6--- 6T, -A 12T5 -.-- 18Ts 0.01 0.001 0.0001 5 10 15 20 25 30 35 EblVo(dB) Fig. 3-9. Effect of time span for each symbol on BER for DSSB-PSAM where r = O. 115, fDT, = 0.00625, N= 20 and 1st Gaussian interpolation. 0.1 -- 6T, 18T, 0.001 .. .. . .i 0.0001 5 10 15 20 25 30 35 EbV/No(dB) Fig. 3-10. Effect of time span for each symbol on BER for DSSB-PSAM where r = 0.115,f DT, = 0.01, N= 20 and 1st Gaussian interpolation. 52 distorted less due to truncation and Gaussian windowing. The Effect of Frame Length, N The frame length, N, needs to be optimum value, which represents a trade-off between power loss of extra pilot symbols and coarse receiver estimation of the fading process. By sampling theorem, the rate of pilot symbol insertion must be at least the Nyquist rate of fading process, so that N < 1/(2fDT). When fast fading expected for example, 400Hz Doppler in a 40 ksymbolls system givesfDT = 0.01, then N= 20 is the optimum value as shown in Fig. 3-14. Hence, N= 20 is selected as the benchmark. 0.1 -* Eb o=10dB -- EbmAo =20dB ::::i : : : :. :-A-- EbR o = 30dB 0.01 span= +12T. JnT. = 0.001 and 1st Gaussian interpolation. ..i....i.. ....i.. l.. .l............ .. .. . .. . ..i. ............................... . .. .. ... ... .. .. ... .. .. ? S. !... .. .. .. ..... .. ?.. ... .. . .. .. . . . . . ! span = 12T,, fDT, = 0.001 and Ist Gaussian interpolation. 53 0.1 -- Eb/No = 10dB .... ... ..... .... .~~.-0-- EbNo = 20dB p -A-- EbNo = 3dB -. ... ..-.... 0.001 -. . 0.0001 5 10 15 20 25 30 35 40 45 Frame length, N Fig. 3-12. Effect of frame length, N, on BER for DSSB-PSAM where r = 0.115, time span = 12T,, fDT, = 0.0025 and 1st Gaussian interpolation. 0.1 Eb/o = 10Od B ........--:::: Ebmo= 20d B i ...ii_......... -A- EbNo=3OdB 0 .... .. .... .... .... -------- -" -- -- -- ---- - -- -.... - ... 0.01 : ..... .. ....... . L :.... : ..... . . .0.001 0.0001 I I 5 10 15 20 25 30 35 40 45 Frame length, N Fig. 3-13. Effect of frame length, N, on BER for DSSB-PSAM where r = 0.115, time span = 12T,, fDT, = 0.00625 and 1st Gaussian interpolation. 54 0.1 .... .. .... .... ... .:. Eb/No = 10dB ... -,-:-: : ..: .; .u Eb/No = 2 0dB 0.01 ..................... .. 0.01 -.. ~; .. Ii". . . . . . 0.001 .... span = +12T, fDT = 0.01 and 1st Gaussian interpolation. The Effect of Gaussian Interpolation Order The estimation of the fading distortion at the other pilot symbols can be obtained by Gaussian interpolation. Fig. 3-15 through Fig. 3-18 show the BER performance with the parameter Eb/No and the order of interpolation. 1 order Gaussian interpolation is suitable for the fading compensation. However, the performance of the 1It order and the 2"nd order interpolations are almost equal. 55 0.1 i .. .. .. ., .i oI ooi iii .- 1st order. .. . .. ..............A N ........ ........ 0.00 1 7 r7............ .. 5 10 15 20 25 30 35 Eb/No(dB) Fig. 3-15. Effect of Gaussian interpolation order on BER for DSSB-PSAM where r =0.115, time span = 12T,, fDTs, = 0.001 andN= 20. 0.1 "i.......... ..........o rde -*...... -- theory -U- Oth order -A- 1st order y- 2nd order o.oo ................... ........................ 0.0001 ...... . 5 10 15 20 25 30 35 EbRo(dB) Fig. 3-16. Effect of Gaussian interpolation order on BER for DSSB-PSAM where r = 0.115, time span = +12T,, fDT, = 0.0025 and N= 20. 56 0.1 --- theory -- Oth order Sc...I- I st order -- 2nd order 0.0 1 : : : ::- : : : : Ln, 0.001 . 0.0001 5 10 15 20 25 30 35 Eb/No(dB) Fig. 3-17. Effect of Gaussian interpolation order on BER for DSSB-PSAM where r = 0.115, time span= 12T,, fDT, = 0.00625 and N= 20. 0.1 -.................. .1 -- theory -- Oth order -A- 1storder - -9- 2nd order 0.01 -. . ...i .. ... ... :::::: :::::::::: :::: 0.001 0.0001 5 10 15 20 25 30 35 EbAVo(dB) Fig. 3-18. Effect of Gaussian interpolation order on BER for DSSB-PSAM where r= 0.115, time span= +12T,, fDT, = 0.01 andN= 20. 57 The Effect of Co-Channel Interference (CCI) The frequency reuse method is useful for increasing efficiency of spectrum usage but results in CCI because the same frequency channel is used repeatedly in different cochannel cells. The BER performance of the DSSB-PSAM in a CCI controlled environment investigated by computer simulation. NONFADING ENVIRONMENT The received signal sr(t) is expressed by M s,(t) = Re[ Azy(t)exp(j2rnft) + nc(t) + I RkZk(t) exp(j2nfft + k)] (3-15) k=1 where A2/2 is the power in the signal, I (R 2 / 2) is the power in the multiple k=1 cochannel interference, f, is the carrier frequency, zT is the complex envelope of the transmitted DSSB signal, Zk(t) is the CCI-DSSB signal and n,(t) is the zero-mean complex white Gaussian noise with variance 2. We assume that the interference is statistically independent of the signal and that Ok's are uniformly distributed over the range [0,27x]. The probability of error Pe is given by [Feh87] Pe = erfc(A/o--2 ) + exp( A2 / 2c2) D 2k (A/o2 ) ur2k (3-16) 2 k=1 where D,(x) = x"R".,, H,.l(x) / n! (3-17) 58 Dn(x) = 2x 2Rmax [ D,.l(x) (n-2)R,,axDn2(x) / (n-1) ]/n (3-18) DI(x) = xRmax, D2(x) = X3R2max (3-19) Rm,ax = ma{ Rk 7,r= 77 /Rm and U,k = E[ r,k] (3-20) H,(x) represents the Hermite polynomial of order n. [j/2] IJ(x) =j! (-1)(2 x) j-2m / (m! (j-2m).!) (3-21) m=O where [b] = the largest integer contained in b H+,,(x) = 2 xH,(x) H1,.(x), n 1, Ho(x) = 1 (3-22) RAYLEIGH FADING ENVIRONMENT In the Rayleigh fading, the envelope of the desired signal has Rayleigh statistics. The PDF of the corresponding signal power x is [Pee93] 1 px(x) = exp(-x / X) (3-23) where the mean signal power is X. Each cochannel interferer is subject to Rayleigh fading also and its power is exponentially distributed. Assuming that all interferers are independent and have the same mean power Y, the PDF of the total interference power y of M interferers is obtained using an I-fold convolution of independent and identical exponential PDF. This results is a Gamma PDF of the form [Yao92]. 59 M-1 py (y) = exp( ) (3-24) YM (M 1)! Y Defining the signal-to-interference power ratio as r = x /y, the PDF ofr as follows [Yao92]. p(r) = ypx(ry)py(y)dy ( b )M+1 (3-25) b r+b where b (3-26) Y The static probability of bit error of DSSB (in a nonfading environment), P, is given by Pe(r) = () erfc ( F) (3-27) 2 where r (3-28) 20-2 When the channel is subject to fading, signal to noise power ratio, r, is a random variable and the 'dynamic' bit error probability is derived by averaging ( 3-27) over all possible values of signal to noise power ratio. This method can also be used to derive the bit error probability when the signal is subject to interfering in a fading environment [Woj86]. Following this approach, the bit error probability, assuming that all interferers 60 have the same mean power, is obtained using (3-25) and (3-27) P = Pe(r)p,(ry)dr 0 M b~ )M erfc(I)dr (3-29) 2b f r+b Assume that there are 6 mutually independent Rayleigh faded interferers, each with equal mean power. We can get a theoretical approximation result from (3-29) if we use the integration interval from 0 to 25. Fig. 3-19 shows that the BER performance in case of CCI obtained by computer simulation is in good agreement with the theoretical approximation result. 0.01 . . .. ...... -... ........ -...... ...-.... ... ... ... .... .. ....... -- Theory approx . ...... i i0025 0.001o -~- f= 000625 S.iiii f ..... 01 5 10 15 20 25 30 35 EbRNo(dB) Fig. 3-19. BER for DSSB-PSAM in case of Co-Channel Interference (CCI) where Eb/No = 60 (dB), r = 0.115, time span = +12T, N= 20 and 1st Gaussian interpolation. 61 The Effect of Adjacent Channel Interference (ACI) In the case of adjacent channel interefrence, only the tails of the adjacent channel signal enter the desired signal. The PSD of the desired signal which is centered at 27kHz and adjacent channel interferer is shown in Fig. 3-20. We locate the center of adjacent channel OkHz and 54kHz so that the adjacent channel interference is -60 dB. Fig. 3-21 shows the BER performance for DSSB-PSAM in case of ACI. The channel spacing is 27kHz, the bit rate of DSSB-PSAM is 40kbps, Eb/No = 60 dB, roll-off factor r = 0.115, time span = +12T,, frame size N= 20 and 1" Gaussian interpolation is used. -50 -- 0 1 2 3 4 5 6 7 8 -x100 -30 - ----4 0 .-------------- .....-.------------------- .----------.------------ .---------------- 5 0 --- ----- -------- ---.. .... .... . ---... .... .... ---.. .... .... ...- .. ............ .. ----- ------- -----.. --... .......... Fig. 3-21. The PSD of desired and adjacent channel signals where the desired signal is centered at 27kHz, the bit rate is 40kbps and r = 0. 115. 62 le-1 l e .. . . ... le-3 -0 -25 -20 1 'K' '. C/I(dB) Fig. 3-22. BER for DSSB-PSAM in case of Adjacent Channel Interference (ACI) where Eb No = 60 (dB), r = 0.115, time span = 12Ts, N= 20, AfT = 0.675 and 1st Gaussian interpolation. Af T, = 0.675 and 1st Gaussian interpolation. CHAPTER 4 COMPARISON OF DSSB-PSAM, QPSK-PSAM AND OQPSK-PSAM Dynamic Range Nonlinear amplification of the zero-crossings can bring back the filtered sidelobes. Hence, linear amplifiers which are less efficient should be used to prevent the spectral widening. If the signal is limited to an annular region over which the amplifier nonlinearity is moderate, it is easier to linearize these amplifiers. As a measure of difficulty of linearization, the dynamic range, defined as the ratio of maximum to minimum instantaneous powers is commonly used. Table 4-1 through 4-15 shows the dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM. QPSK signal envelope pass through zero due to phase shift of n radians. The dynamic range of QPSK is infinite and require more effort in the design of a linearizer, or more expensive and less efficient amplifiers. OQPSK signal envelope does not go to zero, since 7C phase transitions have been removed. The envelope variations are less than that of QPSK. The QPSK dynamic range is infinite and the dynamic range of OQPSK-PSAM is 22.7 dB whereas the dynamic range of DSSB-PSAM is 5.38 dB for a roll-off factor of r = 0.115 and 6T, time span which is shown in Table 4-2. We also show that the dynamic range is for DSSB is 10.91 dB, whereas the OQPSK dynamic range is 27 dB and the QPSK dynamic range is infinite for a roll-off factor of r = 0.115 and 12T, time span 63 64 which is shown in Table 4-7. The issue of amplifier efficiency is very important when designing portable communication system since the battery life is related to the amplifier efficeincy. Typical efficiencies for class A or AB amplifiers are 30-40%, meaning that 30-40% of the applied DC power to the final amplifier circuit is converted into radiated RF power. Class C amplifiers have efficiencies on the order of 70% [Rap96]. With DSSB-PSAM, therefore, we can take advantage of the much reduced dynamic range and adopt high efficiency Class C amplifiers. Table 4-1. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6T,, frame length N= 20 and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 1.24 5.12 3.69 Minumum Power 0.3586 0 0 Dynamic Range (dB) 5.38 0 00o Table 4-2. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6 T,, frame length N = 20 and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 1.295 2.23 3.395 Minumum Power 0.375 0 0.018 Dynamic Range (dB) 5.38 00 22.7 65 Table 4-3. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6T,, frame length N= 20 and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 1.415 2.465 2.29 Minumum Power 0.4 0 0.19 Dynamic Range (dB) 5.49 00 10.81 Table 4-4. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +6T,, frame length N = 20 and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 1.49 2.155 1.99 Minumum Power 0.425 0 0.3225 Dynamic Range (dB) 5.44 00 7.90 Table 4-5. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6 T, frame length N = 20 and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 1.975 2.285 1.62 Minumum Power 0.2781 0 0.525 Dynamic Range (dB) 8.51 00 4.89 66 Table 4-6. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +12T,, frame length N= 20 and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 2.04 10.98 8.87 Minumum Power 0.12265 0 0 Dynamic Range (dB) 12.21 00oo oo00 Table 4-7. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +12T,, frame length N= 20 and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 2.10 4.475 3.535 Minumum Power 0.17 0 0.007 Dynamic Range (dB) 10.91 00 27 Table 4-8. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 12T,, frame length N= 20 and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 2.24 2.51 2.315 Minumum Power 0.29 0 0.19 Dynamic Range (dB) 8.87 00oo 10.85 67 Table 4-9. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +12T, frame length N = 20 and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 2.3185 2.17415 2.00 Minumum Power 0.325 0 0.3185 Dynamic Range (dB) 8.53 00 7.97 Table 4-10. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 12T,, frame length N= 20 and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 2.995 2.29 1.62 Minumum Power 0.2758 0 0.51995 Dynamic Range (dB) 10.35 00 4.93 Table 4-11. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18T,, frame length N = 20 and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 2.56 5.66 4.365 Minumum Power 0.0344 0 0 Dynamic Range (dB) 18.71 00o oo00 68 Table 4-12. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18Ts, frame length N= 20 and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 2.62 4.48 3.52 Minumum Power 0.071 0 0.007 Dynamic Range (dB) 15.67 00 27 Table 4-13. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +18T,, frame length N= 20 and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 2.76 2.508 2.1 Minumum Power 0.154 0 0.19 Dynamic Range (dB) 12.53 00 10.84 Table 4-14. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18 T, frame length N= 20 and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 2.835 2.175 2.00 Minumum Power 0.1795 0 0.3175 Dynamic Range (dB) 11.98 00 7.99 69 Table 4-15. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18T,, frame length N = 20 and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 3.61 2.29 1.625 Minumum Power 0.2396 0 0.50 Dynamic Range (dB) 11.78 00 5.11 24 22 ::: :::::::::::::::::::::::: - DSSB PSAM -u- OQPSK PSAM 20 18 .. ... ... ... S -- ...-....-.....-.----- ... . ..... -.-... .- -.i...... .. 6 --- i ii -- -i ------ -- !-----; ;-- ..-- ..- .. i .i ........ "... ... . .i.. . .. . 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Roll off factor, r Fig. 4-1. Comparison of Dynamic Range (dB) for DSSB-PSAM and OQPSK-PSAM with varying roll-offfactor, r where Time span = +6T, and frame length N= 20. 10 J .:F :............. with varying.. roll-off fatr..wee.iespn...~adrmlnt 3 0 . . . . . 20 Fi.42.oprs o D mi ..... -e DSSB-PSAMa :::::::::: :::::::.:::::*:::::::::-::- DSSB a PSAM 25 ................... ...... .......... ... ........ 0 :1 : : : : ::: : : :: :: :: 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Roll off factor, r Fig. 4-2. Comparison of Dynamic Range (dB) for DSSB-PSAM and OQPSK-PSAM with varying roll-off factor, r where Time span= 12T, and frame length N= 20. --B- OQPSK-PSAM 2 i.. i.....l .i '.. iiii.. ;---;-----------------a .................................. .... .. . .... . . . . I ... I . . . . Fig. 4-3. Comparison of Dynamic Range (dB) for DSSB-PSAM and OQPSK-PSAM N= 20. N= 20. 71 Peak To Average Power Ratio The transmitted signal s(t) is given by s(t) = [ m(t)cos(2nft) mh(t)sin(2ft)] = Re [ z(t)exp(j2rfct)] where zr(t) = [ m(t) + jmh(t)] Hence, the Average power [Cou97] 1 2 2 where the time average operator can be expressed by T/2 <[.]>= lim [.dt (4-2) T- T /2 The peak envelope power of DSSB is [Cou97] 1 1 - max I T2t) -max [ m2(t) + mh2(t)] (4-3 ) 2 2 The instantaneous powers for ZT(t), m(t) and mh(t) are ZT(t), m2(t) and mh2(t), respectively. We try all possible bit pattern by computer simulation to find the bit pattern where the DSSB peak power occurs. Next, we analyze why peak power happens. To examine the bit pattern that causes peak power by computer simulation, we use 212, 224 and 236 total run length data for Gaussian windowed 6T, 12T, and 18T, time span pulse shape. Fig. 4-4 shows that the bit pattern that causes the peak power for 72 both DSSB and QPSK. Due to Hilbert transform of the SRRC pulse, the pulse shaped DSSB has less envelope fluctuation than that of QPSK which is shown in Fig. 4-5. However, the worst case peak power of the DSSB occurs for the case of a long stream of ones and zeros as shown in Fig. 4-4. This peak power of DSSB is due to by only the Hilbert transform of SRRC pulse, mh(t) as shown in Fig. 4-6. In this case, the peak power of m(t) which has a SRRC pulse shape is zero due to the cancellation of each other which is shown in Fig. 4-7. The peak power of DSSB is shown in Fig. 4-8. Hence, we can check the peak power by adding the value of middle point of mh(t). mid[mh (t)]1, 0 mid[mh (t)]2, Ts < mh (t) < 2T, mid[mh(t)]3, 2T, < mh(t) < 3T, mid[mh(t)]nl, 11T, Hence, the peak power of DSSB is 1 11 11 { 2 mid [mh(t)]m } = mid [mh(t)]m (4-5) 2 m=1 m=1 Table 4-19 shows the peak power with different time span and different roll-off factors. We use here Gaussian window for truncation and windowing the pulse shaped filter. The impulse response of the Gaussian window is given by 73 hG (t) exp(- -2 ) (4-6) a a where a is related to B, the 3-dB bandwidth of the baseband Gaussian shaping filter a ifln 2 0.5887 a= 2 (4-7) J2B B As a increases, the spectral occupancy of the Gaussian filter decreases and time dispersion of the applied signal increases. The impulse response of the baseband Gaussian filter for various of 3-dB bandwidth-symbol time product (BT,) is shown in Fig. 4-9. We can reduce ISI ofmh(t) by using the Gaussian window compare to the other window which is shown in Fig. 4-10. Table 4-20 through 4-34 shows peak to average power ratios for DSSB-PSAM, QPSK- PSAM and OQPSK- PSAM where different roll-off factors are used. It is shown that DSSB-PSAM peak to average power ratios are from 2.85 to 4.38 dB lower than those for QPSK-PSAM when roll-off factor r = 0.115 and time span is from 6T, to +12T,. For the case ofr = 0.35 and time span is from 6T, to 12T, DSSB- PSAM peak to average power ratios are somewhat (0.19 1.66 dB) lower than those for QPSKPSAM. Fig. 4-12 through Fig. 4-14 shows the comparison of peak to average power ratios for DSSB- PSAM, QPSK-PSAM and OQPSK-PSAM varying with roll-off factor r. For QPSK- PSAM and OQPSK-PSAM, the peak to average power ratios decreases as the roll off factor, r goes to 1. However, for DSSB-PSAM the peak to average power ratios increases as the roll-off factor, r goes to 1. As shown in Fig 4-11, the DSSB peak 74 power increases when roll-off factor, r increases. This is the reason why the peak to average power ratios increases as the roll-off factor, r goes to 1 for DSSB-PSAM. The operational efficiency of a linear amplifiers is highly dependent on the PAPR of a signal [Ant86]. Therefore, a low PAPR signal is required for improving the power amplifier efficiency of a linear power amplifier. Hence there is much improved the power amplifier operational efficiency for DSSB when we use small roll-off factor. QPSK : m(t)2 + mq(t)2 ( Both have SRRC pulse shape) Peak Power point 010101010101 1010 101010 ... DSSB : m(t)2 + mh (t)2( m is SRRC and mh is the Hilbert transform of SRRC) Peak Power point 0000000o00000ooo 1 111111111 ... Fig. 4-10. Bit pattern that causes the instantaneous peak power for both DSSB and QPSK. 75 2 .5 ---------- ------- ---------- -- -- -------- ---- I -- -- --o 2 ...........---------- --.. . ..-.......... --- -- --- -- ---.......... a. o 1.5 (D O 5 - - - - -------- --------- -------- --- --- .. ....-- -- ------ 0.5 50 100 150 200 250 300 350 400 450 time(ns) (a) DSSB 3 2 .5 --------- --. -- ---. --------- ----- --------------- -- --------- ------------- ---------- -------- -o 2 ----- ---- -- ----------------- ------- -- --- t ---- -------- --- ---- 1.5 50 100 150 200 250 300 350 400 450 time(ns) (b) QPSK Fig. 4-5. The instantenous envelope power of DSSB and QPSK 76 1 1 1 1 1 0 0 0 0 0 (a) Bit pattern 0.8 0 .6 ------------ -- -0.4 0 .2 -- -- .-... .- -..- - -- - -- --.-- 0 -0.2 -------- ---- --------------- -------------0 .4 ------------- ------------ --- ------------ -- -- ---------0 .6 ------------- ------ --- - --- --------- -----0.8 0 50 100 150 200 250 300 350 400 time(ns) (b) The amplitude of mh(t) corresponding bit pattern (a) 2.5 2 ------------------- --- ------------ ----- ---- ------ ----- ... .. .. . .. --------- ---1 .5 ---------------- -- - --------- .. .. -- -. ----------------------- 1.5 o 1 -- --- -- -- - ------------ ----- --- -- ---- ------- ------ - -- - --- -0.5 1. ------------------ -- -------- -- -- ----- - - -- ---- -- -- - -- --- - - - - - - - - - - 0 100 200 300 400 500 time (c) The instantenous power of mh(t) corresponding bit pattern (a) Fig. 4-6. The amplitude and power of mht) corresponding bit pattern (a). 77 11 1 0 0 0 0 0 ... (a) Bit pattern 1.5 1 -------- ------ -------------------- ----- -----0 .5 --------------- --------- -- -- --. ..................... -.------------ -- -- -----. -a 0 -c. E -0 .5 -------------- ---L- .......... ....---------- ------------- ------------ -------1 -1.5 0 50 100 150 200 250 300 350 400 time(ns) (b) The amplitude of m(t) corresponding bit pattern (a) 0.9 0.8 -------------- ---- ------- -------0.7 O .7 ------------- -I- - -- ------------ . . . .I .. . .---- -- - 0.6 -------------- ---0.5 o. -L O .4 --- -------- - -- -- - - - - - - - - - - - 0 .3 ---- -------- ---- - - -- - --- -- .... ... ..- - - - - ------ - -- - - O .2 - - ------ --- -- - ----- -O.1 ----------0 50 100 150 200 250 300 350 400 time(ns) (c) The instantenous power of m(t) corresponding bit pattern (a) Fig. 4-7. The amplitude and power of m(t) corresponding bit pattern (a). 78 2.5 0 2----------0 .5 ----------4------------ --- -- ----- -------- ------0 50 100 150 200 250 300 350 400 time(ns) Fig. 4-8. The DSSB instantenous peak power characteristics due to long bits of ones and long bits of zeros. Table 4-19. The DSSB peak power with different time span and different roll-off factors Roll-off factor 6T, 12T, 18T, r = 0 1.24 2.04 2.56 r = 0.115 1.295 2.10 2.62 r = 0.35 1.415 2.24 2.76 r = 0.5 1.49 2.315 2.835 r = 1 1.975 2.995 3.605 79 0.9 ............. 0.8 ----- -- I a= 1.5 0.7 =- ----------... ...... 3.0-o 0.6 --- a0.75 0 .5 ------------- ---------------E < 0.4 a=2.25 0.3 --------0.2 ---------- -- -- ----0.1 ------------0 -4 -3 -2 -1 0 1 2 3 4 t/Ts Fig. 4-9. Impulse response of a Gaussian pulse shaping filter. 1 0 .4 --------- ......------ ..............-- -.- -.--.---- H a----------- .nni 0. E 0 .2 - -------- - --- -- ---- -- - . . . . - -- - - - - o E 0 -0 .2 -- ------ - ------ -- - - - -- - - - - -- - - - - - - - - -0.4 --------- -- -- -0.4 -0 .6 .... ..... ...... I ---------------- ---- -------- --------------- ---------------- ----------- ----0.8 -15 -10 -5 0 5 10 15 t/Fig. 4-10. Different type of window to use Ts Fig. 4-10. Different type of window to use the reduction of ISI of wh(t). 80 5 ...............6 ....................... ...................... ....................... -gg- 12Ts . 4 --- 18Ts 3 --ll -- ....................... ................ ... I ....................... o .... . .. .. ...... .................. ..... ............. 2 ...................................... ......................... ....................... 0 0 1 Roll off factor, r Fig. 4-11. The DSSB peak power with different time span and different roll-off factors. Table 4-20. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6T, and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 1.24 5.12 3.695 Average Power 0.76 0.975 0.975 Peak to Average Power ratio (dB) 2.12 7.20 5.78 81 Table 4-21. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6T, and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 1.295 4.46 3.395 Average Power 0.795 1 1 Peak to Average Power ratio (dB) 2.11 6.49 5.31 Table 4-22. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6T, and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 1.415 2.465 2.29 Average Power 0.84 1 1 Peak to Average Power ratio (dB) 2.26 3.92 3.60 Table 4-23. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6T, and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 1.49 2.155 1.99 Average Power 0.850 1.00 1.00 Peak to Average Power ratio (dB) 2.43 3.33 2.98 82 Table 4-24. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6T, and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 1.975 2.285 1.62 Average Power 0.88 1 1 Peak to Average Power ratio (dB) 3.51 3.58 2.09 Table 4-25. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 12T, and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 2.04 5.49 4.435 Average Power 0.88 0.985 0.985 Peak to Average Power ratio (dB) 3.65 7.46 6.53 Table 4-26. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +12T, and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 2.10 4.475 3.535 Average Power 0.905 1 1 Peak to Average Power ratio (dB) 3.65 6.50 5.48 83 Table 4-27. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 12T, and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 2.24 2.51 2.315 Average Power 0.93 1 1 Peak to Average Power ratio (dB) 3.81 4.00 3.65 Table 4-28. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +12T, and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 2.315 2.17 2.00 Average Power 0.93 1 1 Peak to Average Power ratio (dB) 3.96 3.36 3.00 Table 4-29. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +12T, and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 2.995 2.29 1.62 Average Power 0.945 1 1 Peak to Average Power ratio (dB) 5.00 3.59 2.09 84 Table 4-30. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18T, and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 2.56 5.66 4.365 Average Power 0.92 0.98 0.98 Peak to Average Power ratio (dB) 4.44 7.61 6.48 Table 4-31. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18T, and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 2.62 4.48 3.52 Average Power 0.945 1 1 Peak to Average Power ratio (dB) 4.42 6.51 5.46 Table 4-32. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18T, and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 2.76 2.53 2.305 Average Power 0.955 1 1 Peak to Average Power ratio (dB) 4.60 4.03 3.63 85 Table 4-33. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18T, and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 2.835 2.175 2.00 Average Power 0.955 1 1 Peak to Average Power ratio (dB) 4.72 3.37 3.00 Table 4-34. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18T, and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 3.605 2.29 1.625 Average Power 0.965 1 1 Peak to Average Power ratio (dB) 5.72 3.59 2.10 7 S--- OQPSK-PSAM S........ ..... ... ... ........ 6 -4 .. ,.i. .i ... ... ... ... i.i............ .... ....... ......... .... .... 3! 2 ....I I I 0.0 0.2 0.4 0.6 0.8 1.0 Roll off factor, r Fig. 4-12. Comparison of Peak to Average Power Ratio (dB) for DSSB-PSAM, QPSKPSAM and OQPSK-PSAM with varying roll-off factor, r where time span = 6T,. 86 ... i ........ I S -'.i : ..- QPSK-PSAM.:: ::- I5 2 1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2 .. . . I . . . . I 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Roll off factor, r Fig. 4-13. Comparison of Peak to Average Power Ratio (dB) for DSSB-PSAM, QPSKPSAM and OQPSK-PSAM with varying roll-off factor, r where time span = 12T, .... .. ... QPSK-PSAM ........ 6 --- OOPSK-PSAM Ii i i I :::.::::.::.::.::.::::::... .... ........ .-: .. . -- - . . . ---v ..: .. ... .... :. . . .. . . . . 0.0 0.2 0.4 0.6 0.8 1.0 Roll off factor, r Fig. 4-14. Comparison of Peak to Average Power Ratio (dB) for DSSB-PSAM, QPSKPSAM and OQPSK-PSAM with varying roll-offfactor, r where time span +18T,. 87 Spectral Occupancy The proposed DSSB requires windowing to reduce ISI and peak power. This causes the increase of spectral occupancy of DSSB. The PSD of DSSB with Gaussian windowing is shown in Fig. 4-15. Table 4-38 shows the increase percentage of spectral occupancy of DSSB with Gaussian windowing. The definition of Bounded spectrum bandwidth, say 50dB, below the maximum value of the PSD [Cou97] is applied. As shown in Fig. 4-15, the PSD of the proposed DSSB looks like that of vestigial side band (VSB) shown in Fig. 4-16. VSB has been chosen for the High Definition Television (HDTV) standard, since it had better performance than QAM for terrestrial HDTV broadcasting [GRA94]. When the baseband signal contains significant components at extremely low frequencies, the use of SSB modulation is inappropriate for the transmission of such baseband signals due to the difficulty of obtaining the very sharp cut-off filtering needed. That is the reason why SSB can not be used with analog TV. But the proposed DSSB does not need the very sharp cut-offfiltering. The gradual sloped filtering, such as raised cosine filtering, can be used for the proposed DSSB. Table 4-38. The percentage of PSD increase of DSSB for Gaussian window with different time span factor Time Span +6T, +12T, +18T, Percentage of PSD Increase 38% 28% 18% 88 -10 -20 + 18 T, -30 -------------- -.--- --- -- .---------- -----. 6 T -40- ---- ---------- -- 12 T, -50 --------------60 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 frequency x 105 Fig. 4-15. PSD of DSSB with Gaussian window where symbol rate D = 40000, roll-off factor r = 0.115 and carrier frequencyfc = 200Khz. 0 .7 0 Suppressed Carrier 0.31 5.38 MHz 0.31 6.0 MHz Fig. 4-16. PSD ofVSB [GRA94]. 89 Comparison of BER Performance for QPSK-PSAM and DSSB-PSAM The bit error probability of coherent QPSK [Cou97] and coherent DSSB in AWGN are given by Pc, QPSK in AWGN = Pe, DSSB in AWGN = Q(2E ) (4-8) N0 It can be also shown that the average error probability of coherent QPSK [Rap96] and coherent DSSB in a slow, flat, Rayleigh fading channel are given by Pc, QPSK in fading = Pe, DSSB in fading = [ 1- ] (4-9) where To = (Eb )E[d] (4-10) No Fig. 4-17 shows the BER performance obtained by computer simulation in AWGN channel. Fig. 4-18 shows the BER performance obtained by computer simulation in Rayleigh fading channel, when frame length N=20, the order of Gaussian interpolation is 1, the normalized Doppler frequencyfDT = 0.001, the time span is +12T,, the transmitter and the receiver filters are SRRC filters with roll-off factor r = 0.115. The performance of the proposed DSSB is almost same result with the QPSK as shown in Fig. 4-17 and Fig. 4-18. The difference (0.3 dB) comes from the power loss by inserting different pilot symbols. QPSK needs only one pilot symbol in one frame but DSSB needs three pilot symbols in one frame. From (4-8) we can see that both QPSK and DSSB have the same power efficiency. Power efficiency is defined as the ratio of the signal energy per bit to 90 noise power spectral density (Eb / No) require at the receiver input for a certain probability of error. Bandwidth efficiency is defined as the ratio of the data rate per Herz in a given bandwidth. If we assume that the roll-off factor r = 1 is used, then the QPSK data rate RQ that can pass through a baseband RC filter is given by 2 T, where T, is the duration of one data symbol The QPSK bandwidth BQ is given by 1 BQ T, Then the bandwidth efficiency of QPSK is RQ I1QPSK- 2 B, The DSSB data rate RD that can pass through a baseband RC filter is given by RD The DSSB bandwidth BD is given by 1 BD = 2T, Then the bandwidth efficiency ofDSSB is T1DSSB RD 2 BD Hence, Both QPSK and DSSB have the same bandwidth efficiency theoretically. 91 0.1 -:: :::::- Theory a. -u- QPSK-PSAM -A- DSSB-PSAM 0.01 . 0.001 .. . 1 2 3 4 5 6 7 8 9 Eb/No(dB) Fig. 4-17. The Comparison of BER performance in AWGN channel for QPSK- PSAM and DSSB-PSAM where roll-off factor r = 0.115, time span = +12Ts, frame length N = 20 and 1st Gaussian interpolation. 0.1 I .... .. . .. . .. ... . . 1 -2-- Theory Fig. 4-17. The Comparison ofBER performance in AWGN channel for QPSK- PSAM and DSSB-PSAM where roll-off factor r = 0. 115, time span 12Ts, frame 0 :..... ... .. .. . .. .... . :;. : : z v --_---0.001 -4.... ..... .. .. .......... .... .! ........ . 0.0001 5 10 15 20 25 30 35 Eb/No(dB) Fig 4.18. The Comparison of BER performance in Rayleigh fading channel for QPSKPSAM and DSSB-PSAM where roll off factor r = 0.115, time span = +12Ts, fDT = 0.001, frame length N= 20 and 1st Gaussian interpolation. fD = 0. 00 1, frame length N = 20 and I st Gaussian interpolation. 92 The Choice of Roll-off Factor, r The parameters that influence the choice of roll-off factor, r is as follows. 1. BER performance 2. Bandwidth 3. Peak to Average power ratio 4. Filter design 1. As the roll-off factor, r increases to 1, ISI due to the Hilbert transform of raised cosine pulse which is shown in Fig. 2-8 decreases and there is an improvement of the BER performance. As the roll-off factor, r decreases to 0, ISI due to the Hilbert transform of raised cosine pulse increases and there is a degradation of the BER performance. However, there is only a slight difference of 1 dB in the BER performance with different roll-off factors as is shown in Fig. 3-3. Hence we can consider there is a little contribution from the BER performance for the choice of roll-off factor, r. 2. Roll-off factor, r is sometimes called the excess bandwidth factor because it indicates the amount of occupied bandwidth that is required in excess of the ideal occupied bandwidth. For example, if we choose a roll-off factor of r = 0.35, this gives a moderate bandwidth increase of 35%. However if we choose a roll-off factor of r = 1, this gives a large bandwidth increase of 100%. Also a roll-off factor, r of zero is impossible to implement. In practice, the United States Digital Cellular (USDC) IS-54 standard specifies square root raised cosine filtering with roll-off factor of r = 0.35 while |

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Table 4-3. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 67^, frame length N = 20 and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 1.415 2.465 2.29 Minumum Power 0.4 0 0.19 Dynamic Range (dB) 5.49 00 10.81 Table 4-4. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6Ts, frame length N= 20 and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 1.49 2.155 1.99 Minumum Power 0.425 0 0.3225 Dynamic Range (dB) 5.44 00 7.90 Table 4-5. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6TS, frame length N = 20 and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 1.975 2.285 1.62 Minumum Power 0.2781 0 0.525 Dynamic Range (dB) 8.51 00 4.89 APPENDIX A Derivation of Square Root Raised Cosine Roll-off Pulse From (2-3) and (2-4), M(f) 1, ^ o. I/I (A-l) oo m(t)= J M(f)exp(j2ntf)df -oo = J J"[l + cos(7r<~ ^ j/f'^)] exp(j2rtf)df+ j exp{j2rtf)df + f .HI + cos^)] exp(j27rtf) <# /, V2 2/a (A-2) Since co/(x) = -^ [ 1 + cos (2x) ], 111 48 Fig. 3-3. Effect of roll-off factor, r, on BER for DSSB-PSAM where time span 127;, N= 20,f dTs = 0.001 and 1st Gaussian interpolation. Fig. 3-4. Effect of roll-off factor, r, on BER for DSSB-PSAM where time span 127;, N= 20,/dTs = 0.0025 and 1st Gaussian interpolation. f B= In 36 _1 2 NfDTs (2-57) Although the performance degradation is reduced by oversampling the channel, there is a power loss by a factor, 1/ (N- 1). The Gaussian interpolation for the kth frame is given by [Sam89] c (kN+ m) = Qr (m/N) c [ (k+r)N ], (2-58) r--\ where the interpolation coefficients Qr are given by, J QdmM)= l-(-^)2 , Q,(m/N) = [(-^-)2+(-^)] (2-59) IN N To find the impulse response ha{n), we may use (2-49) yielding, n + N ( Q,[-tt1], -N ho{n)= { Oo[~], 0 ^ Q.,[ N (2-60) 15 Plots of the frequency and the impulse response are shown in Fig. 2-4. Hence, the required normalized transmitter filter response Tx(f) is given by Tx(f) D( 0) D(f) Â£>(/) 2 r 4Vr I/I < 1 -r 2 7 < I/I < 27 27 I/I >- 1 + r_ 27 (2-14) DSSB Modulation In filter SSB method, it is apparent that the filter must have very sharp cut-off characteristics, and the higher the frequency at which the signal is generated, the more difficult this becomes. The phase shift (or Hartley) method is an alternative. In this method the modulating signal is processed in two parallel paths, one of which contains a 90 phase shifter. Unfortunately, any imperfections, such as occur if the Hilbert transform does not maintain a 90 phase shift over the whole bandwidth of modulation, lead to some of the unwanted sideband being generated, and this causes interference to other radio users. The problem of maintaining the 90 phase shift over the full bandwidth of the baseband signal can be overcome by using two stages of quadrature modulation. This technique was first described by Weaver [Wea56], It is sometimes referred to as the 25 Table 2-3. The average ISI where 67^ time span is used r = 0.115 r = 0.35 r = 0.5 r = 1 1 pilot symbol 0.2541 0.2538 0.2209 0.1408 3 pilot symbols 0.0395 0.0451 0.0583 0.0596 5 pilot symbols 0.0321 0.0407 0.0526 0.0539 Table 2-4. The average ISI where 127^ time span is used r = 0.115 r = 0.35 in O II r = 1 1 pilot symbol 0.2275 0.2290 0.2024 0.1991 3 pilot symbols 0.0942 0.0983 0.0914 0.0878 5 pilot symbols 0.0655 0.0602 0.0465 0.0399 7 pilot symbols 0.0298 0.0326 0.0271 0.0173 Fig. 2-16. Explicit amplitude and phase reference in case of three pilot symbols with roll-off factor r = 0.35 where (01000 1 010) bit pattern is used (010: pilot symbols). APPENDIX C Description of Simulation Software Overview This appendix describes the software written in MATLAB for the simulation of DSSB-PSAM, QPSK-PSAM and 16QAM-PSAM. Transmit data is created from randint command in MATLAB. Randint(n) generates an n-by-n uniformly distributed random binary matrix. The data is then sent through the system, which may include baseband signal shaping, filtering and the channel. The channel may be modeled as either static or fading, corrupted by AWGN, Rayleigh fading, CCI and ACI. AWGN is created from randn command in MATLAB. Randn generates random numbers and matrices whose elements are normally distributed with mean 0 and variance 1 [For77], Fig. C-l shows the Gaussian distribution with mean = 0 and variance = 1. The simulations are carried out in baseband, i.e., modulation is not performed. The equivalency of lowpass and bandpass systems have been verified in [ Pro89] among others. Simulation of Rayleigh Fading The widely used multi-tone technique [Jak74] is used for the simulation of Rayleigh fading. A number of sinusoids with uniformly distributed phases are scaled and 127 14 f~* Fig. 2-3. Raised cosine roll-off filter characteristics [Cou97], K(t) = ^ sin() cos() 1 T. T. i (2rty (2-12) He(f) = ( 1, 1 *(l/l { 1 + cos [ 2 T J ]}, v o. I/! < 1 -r IT, 1 -r 2 T, <1/1 < l+r 2T. I/I > l+r IT, (2-13) 83 Table 4-27. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 127^ and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 2.24 2.51 2.315 Average Power 0.93 1 1 Peak to Average Power ratio (dB) 3.81 4.00 3.65 Table 4-28. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 127^ and roll-off factor r 0.5 DSSB QPSK OQPSK Peak Power 2.315 2.17 2.00 Average Power 0.93 1 1 Peak to Average Power ratio (dB) 3.96 3.36 3.00 Table 4-29. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 127^ and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 2.995 2.29 1.62 Average Power 0.945 1 1 Peak to Average Power ratio (dB) 5.00 3.59 2.09 11 Input data SRRC LPF H-SRRC LPF Fading Esti mation Fading Compen sation Sampling & Pilot Symbol Extraction Hilbert transform SRRC : Square Root Raised Cosine H- SRRC : Hilbert transform of Square Root Raised Cosine ^z(k) Output data Fig. 2-1. DSSB PSAM system. D P P P D D P P P ! ^ Ts P : Pilot Symbol D : Data Symbol k S NTs Fig. 2-2. Transmitted frame structure. 6 (a) Transmitter block diagram (b) Spectra for TTIB transmit processing. Fig. 1-2. 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Non-ideal lowpass filter interpolation with channel sampling at the Nyquist rate. Fig. 2-20. Non-ideal lowpass filter interpolation with channel sampling above the Nyquist rate. CHAPTER 4 COMPARISON OF DSSB-PSAM, QPSK-PSAM AND OQPSK-PSAM Dynamic Range Nonlinear amplification of the zero-crossings can bring back the filtered sidelobes. Hence, linear amplifiers which are less efficient should be used to prevent the spectral widening. If the signal is limited to an annular region over which the amplifier non linearity is moderate, it is easier to linearize these amplifiers. As a measure of difficulty of linearization, the dynamic range, defined as the ratio of maximum to minimum instantaneous powers is commonly used. Table 4-1 through 4-15 shows the dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM. QPSK signal envelope pass through zero due to phase shift of n radians. The dynamic range of QPSK is infinite and require more effort in the design of a linearizer, or more expensive and less efficient amplifiers. OQPSK signal envelope does not go to zero, since n phase transitions have been removed. The envelope variations are less than that of QPSK. The QPSK dynamic range is infinite and the dynamic range of OQPSK-PSAM is 22.7 dB whereas the dynamic range of DSSB-PSAM is 5.38 dB for a roll-off factor of r - 0.115 and 6TS time span which is shown in Table 4-2. We also show that the dynamic range is for DSSB is 10.91 dB, whereas the OQPSK dynamic range is 27 dB and the QPSK dynamic range is infinite for a roll-off factor of r = 0.115 and 127, time span 63 30 at kTp. We use the Gaussian interpolation which is the interpolation method [Sam89] that discovered by and named after Carl Friedrich Gauss [Ham73], This method achieves good compensation with significantly reduced complexity and processing delay compared to the Wiener filter to minimize the variance of the estimation error presented in [Cav91b], As shown by (2-37),(2-38) and (2-39), zeroth order uses only one pilot symbol, first order uses two pilot symbols and second order uses three pilot symbols for channel estimation. Using second order Gaussian interpolation, the interpolated estimates c(k + m/N) are formed as, c(k + m/N) = Q-i(m/N)c(k-l) + Q0{m/N) c (k) + Qi(m/N)c(k + 1) m = 1,2,3, ...(N-l) (2-36) where \ r m 2 r M \ -i { Qm/N)= Â¡-(^f N 1 r)] (2-37) In case of first order and zeroth order interpolation, the coefficients QÂ¡ is obtained as, r Q-, = 0 < Qo = 1 : first order (2-38) 51 Fig. 3-9. Effect of time span for each symbol on BER for DSSB-PSAM where r = 0.115,f dTs = 0.00625, N=20 and 1st Gaussian interpolation. Fig. 3-10. Effect of time span for each symbol on BER for DSSB-PSAM where r = 0.1 \5,fDTs = 0.01, N= 20 and 1st Gaussian interpolation. 88 O -10 -20 -30 -40 -50 -60 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 frequency x 1Q5 Fig. 4-15. PSD of DSSB with Gaussian window where symbol rate D = 40000, roll-off factor r 0.115 and carrier frequency fc = 200Khz. Fig. 4-16. PSD of VSB [GRA94], 90 noise power spectral density (Eb / No) require at the receiver input for a certain probability of error. Bandwidth efficiency is defined as the ratio of the data rate per Herz in a given bandwidth. If we assume that the roll-off factor r = 1 is used, then the QPSK data rate Rq that can pass through a baseband RC filter is given by where Ts is the duration of one data symbol The QPSK bandwidth Bq is given by Then the bandwidth efficiency of QPSK is Rg _ fiQPSK 2 Bq The DSSB data rate RD that can pass through a baseband RC filter is given by The DSSB bandwidth BD is given by Then the bandwidth efficiency of DSSB is Bdssb _ - Rd = 2 Br Hence, Both QPSK and DSSB have the same bandwidth efficiency theoretically. amp litud e 77 1 1 1 1 1 0 0 0 0 0 (a) Bit pattern (b) The amplitude of m(t) corresponding bit pattern (a) (c) The instantenous power of m(t) corresponding bit pattern (a) Fig. 4-7. The amplitude and power of m(t) corresponding bit pattern (a). BER i>j BER 53 Eb/No = 10dB Eb/No = 20dB A Eb/No = 30dB -12. Effect of frame length, N, on BER for DSSB-PSAM where r = 0.115, time span = 127;, foTs = 0.0025 and 1st Gaussian interpolation. Eb/No = 10dB Eb/No = 20dB -A- Eb/No = 30dB Frame length, N Fig. 3-13. Effect of frame length, N, on BER for DSSB-PSAM where r = 0.115, time span = 127;, foTs = 0.00625 and 1st Gaussian interpolation. 68 Table 4-12. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18 Ts, frame length N= 20 and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 2.62 4.48 3.52 Minumum Power 0.071 0 0.007 Dynamic Range (dB) 15.67 00 27 Table 4-13. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 187^, frame length N = 20 and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 2.76 2.508 2.1 Minumum Power 0.154 0 0.19 Dynamic Range (dB) 12.53 00 10.84 Table 4-14. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 18 7^, frame length N = 20 and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 2.835 2.175 2.00 Minumum Power 0.1795 0 0.3175 Dynamic Range (dB) 11.98 00 7.99 69 Table 4-15. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 187^, frame length N= 20 and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 3.61 2.29 1.625 Minumum Power 0.2396 0 0.50 Dynamic Range (dB) 11.78 00 5.11 Roll off factor, r Fig. 4-1. Comparison of Dynamic Range (dB) for DSSB-PSAM and OQPSK-PSAM with varying roll-off factor, r where Time span = 67!s and frame length N 20. 64 which is shown in Table 4-7. The issue of amplifier efficiency is very important when designing portable communication system since the battery life is related to the amplifier efficeincy. Typical efficiencies for class A or AB amplifiers are 30-40%, meaning that 30-40% of the applied DC power to the final amplifier circuit is converted into radiated RF power. Class C amplifiers have efficiencies on the order of 70% [Rap96], With DSSB-PSAM, therefore, we can take advantage of the much reduced dynamic range and adopt high efficiency Class C amplifiers. Table 4-1. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 67^, frame length N = 20 and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 1.24 5.12 3.69 Minumum Power 0.3586 0 0 Dynamic Range (dB) 5.38 00 00 Table 4-2. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 67^, frame length N = 20 and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 1.295 2.23 3.395 Minumum Power 0.375 0 0.018 Dynamic Range (dB) 5.38 00 22.7 116 1 expl/ta/j -nB- Sf^ntB) 1 exp(-jjnf, -nB- 8f^ntB) 2 4/a 2 4A y(^ + 8/^) 4/a (A-9) m)= Sin(2"/l> 7rf + sin( Irtfi) sin( 2^/,) n-Zf^rt n + Kf^ni 4/a 4/a . .7if, -ttB + 8f.7itB' rnf,-nB-%f.7tiB. sin( ~ /A ) sin( ) 4/a 4/a ^ ~ 8/a^ 4/a 7Z- + 8/a^/ 4/a From (2-5) and (2-6), (A-10) = sin(2^/0 -2^/a) n{2ntf0-2ntfh) U ^ 4/a 4/a K-%f^7tt 7T + 8 fÂ¡Jit sin, ^(/o ~ A ) ^(/o + A ) + 8/A^(/q + /a ) s 4/a ^ 8/a^ 4/a 27 fo=M~) (2-26) c where fc = transmitted carrier frequency v = relative velocity of source and receiver c = 3 x 108 m/sec The amplitude or the envelope process eft) then has the Rayleigh probability density function given by [Jak74] f(oc) = (-^)exp(--^--), 0 < a 2 where a2 = (2-28) is the common variance of c(t). The random phase 6 (/) of c(t) is independent of a(t) and is uniformly distributed over 0 < 6 < 2n. Configuration of the Receiver Demodulation The received signal sr(t) is demodulated with a locally generated carrier of frequency f = fc faff, where faff is the residual frequency offset of the local oscillator. As is given by (2-23), the received signal is expressed by 124 = cos(2rtf,) cos(27rt/,) ' n-%f,nt tt + 8f,nt 4/a 4/a - ttB + 8f.TCtB 7Â¡f, -7tB- 8 f.rttB^ cos( : ) cos( ) 4/a 4/a ^ ~ 8/a^ 4/a k + 8/a^ 4/a + 1 cos(2;z/J) From (2-5) and (2-6) (B-9) mh(t) = cos(2/rf/0 2ntfh ) -4/a +. 4/a n-Zf^nt n + 8/A7rf CQ^(/o A) ^(/o + /a ) + 8/a^(/o + /a )) n-KftJti 4/a f ^(/o /a ) ^(/o + /a ) 8/a^(/o + /a / 4A TT+Sf^Tlt 4/a 74 power increases when roll-off factor, r increases. This is the reason why the peak to average power ratios increases as the roll-off factor, r goes to 1 for DSSB-PSAM. The operational efficiency of a linear amplifiers is highly dependent on the PAPR of a signal [Ant86], Therefore, a low PAPR signal is required for improving the power amplifier efficiency of a linear power amplifier. Hence there is much improved the power amplifier operational efficiency for DSSB when we use small roll-off factor. QPSK : mÂ¡(t)2 + mq (t)2 ( Both have SRRC pulse shape) Peak Power point ... 0 1 0 1 0 1 0 1 0 1 0 it 1 0 1 0 1 0 1 0 1 0 1 0 ... DSSB : m(t)2 + mh (tf{ m is SRRC and mh is the Hilbert transform of SRRC) Peak Power point ... oooooooooooot 1 1 1 1 1 1 1 1 1 1 1 1 ... Fig. 4-10. Bit pattern that causes the instantaneous peak power for both DSSB and QPSK. Finally, I would like to express my profound respects and thanks to my both parents. Especially without sacrifices of my mother-in-law, Soonsub Shim, it would not have been possible to pursue my graduate studies. IV 121 From (A-8), ^-/-^exP^fW -B 4/a fl exp(-y \t)~~ 1 exp(J(rÂ¥i ~xB + 8f^ntB) 4/a 7(-^ + 8/a^) 4/a 1 exp(- j2nfti) -1 expQW, fl Sfctffi) 2 2 4/A -j(-7T-8fA7lt) 4/a (B-5) j e_os(7r(/ /,) exp^j2j^ dj A 4/a 1 exP(i(~M + xB + 8fA7itB) = 2 4/, X^ + 8/a^) 4/a 2 expO^^O 1 exp(-y(-V, +8-8/aaB) _lexpa2M<) /4/A 2 4/a (B-6) amplitude 39 Fig. 2-21. The impulse response of a Gaussian interpolator with Q = 3 and N= 20. Fig. 2-22. The frequency response of a Gaussian interpolator with Q = 3 and N= 20. 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 DIGITAL SINGLE SIDEBAND (DSSB) WITH PILOT SYMBOL ASSISTED MODULATION (PSAM) IN MOBILE RADIO By SEUNGWON KIM May 1999 Chairman: Dr. Leon W. Couch Major Department: Electrical and Computer Engineering Single sideband (SSB) modulated by digital data with rectangular pulse shapes has infinite amplitude around the data transition times. This is caused by the Hilbert transformation of rectangular pulse shape. In practice, SSB with this type of modulation cannot be used. However, if we use a roll-off pulse shape, the SSB signal will have a reasonable peak value and digital data transmission can be accomodated via SSB. In this dissertation, a bandlimited square root raised cosine (SRRC) pulse is used as a roll-off pulse shape, and digital single sideband (DSSB) is defined as the SSB modulation technique using this pulse shaping filter at the transmitter and lowpass matched filter at the receiver for the digital data transmission system. DSSB is shown to have peak to average power ratios (PAPR) that are from 1.83 to 2.85 dB lower than those for offset quadrature phase shift keying (OQPSK) and quadrature phase shift keying (QPSK) for a roll-off factor of r = 0.115 and 127^ time vii CHAPTER 1 INTRODUCTION The History of SSB Single sideband (SSB) has been used since the early 1900s to transmit analog audio information. In 1915 H.D. Arnold implemented reduced carrier and reduced lower sideband transmission [Osw56], During the same year, B.W. Kendall patented the product detector which enhanced the detection process. Based on these results, J.R. Carson proposed the method of the single sideband with suppressed carrier communi cation in 1915 and was granted in U. S. Patent 1,449,382. In 1918 SSB was first introduced in a telephone frequency multiplex system,Western Electric Company Type A, and in 1922 a transatlantic station operated at 57kHz using upper SSB at 150kW [Osw56], In the late 1920s the Bell Telephone Laboratories constructed a special receiver which was used to investigate the characteristics of shortwave single sideband reception. SSB on shortwave frequencies (3 30 MHz) appeared in 1936 and AT&T company made a shortwave radio which had crystal filters, multiple conversion, and pilot carriers for automatic frequency control (AFC) and for automatic gain control (AGC). Until about 1936 all the shortwave systems transmitted double sideband and carrier because the art in this frequency range did not permit practical single sideband operation. Shortwave SSB proliferated in long-distance telephone links during the next 10 years. During World War II, single sideband systems provided valuable service with connections 1 DIGITAL SINGLE SIDEBAND (DSSB) WITH PILOT SYMBOL ASSISTED MODULATION (PSAM) IN MOBILE RADIO By SEUNGWON KIM 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 1999 TABLE OF CONTENTS ACKNOWLEDGEMENTS iii ABSTRACT vii CHAPTERS 1. INTRODUCTION 1 The History of SSB 1 SSB with Pilot Symbol Assisted Modulation (PSAM) 7 2. DSSB PSAM SYSTEM MODEL 10 General Description 10 Configuration of the Transmitter 10 Filtering for Zero ISI and for Low Pe 10 DSSB Modulation 15 The Problem Using Only One Symbol as a Pilot Symbol 19 Fading Channel Effects 26 Configuration of the Receiver 27 Demodulation 27 Sampling and Pilot Symbol Extraction 29 Fading Estimation and Compensation 29 Channel Interpolation 31 3. PERFORMANCE EVALUATION OF DSSB 42 Theoretical BER Performance under Nonfading 42 Theoretical BER Performance under Fading 44 v 60 have the same mean power, is obtained using (3-25) and (3-27) co P = J Pe(r) pr{ry) dr 0 J (3-25) 2b r + b Assume that there are 6 mutually independent Rayleigh faded interferes, each with equal mean power. We can get a theoretical approximation result from (3-29) if we use the integration interval from 0 to 25. Fig. 3-19 shows that the BER performance in case of CCI obtained by computer simulation is in good agreement with the theoretical approximation result. Eb/N 0(dB) Fig. 3-19. BER for DSSB-PSAM in case of Co-Channel Interference (CCI) where Eb /Na = 60 (dB), r = 0.115, time span = +127^, N= 20 and 1 st Gaussian interpolation. CHAPTER 3 PERFORMANCE EVALUATION OF DSSB Theoretical BER Performance under Nonfading BER performance of DSSB under coherent detection with AWGN, matched filter reception and optimum threshold setting can be calculated as follows [Cou97], Pe = Q{ (3-1) exp(-^) dC (3-2) Here Ed is the difference signal energy at the receiver input. T Ed = \ [s,(t)-s2(t)]2dt (3-3) o Where Q (x) = ( V2n ou )J The normalized average difference power of the DSSB signal, s^t) is given by [Cou97] where gJJ) is the complex envelope for DSSB signal at the decision input. Hence, 42 To my wife, Inseon Choi, our children, Juhae, Juyoung, Juchan and my mother-in-law, Soonsub Shim This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fullfillment of the requirements for the degree of Doctor of Philosophy. May, 1999 Winfred M. Phillips Dean, College of Engineering M. J. Ohanian Dean, Graduate School 75 (a) DSSB (b) QPSK Fig. 4-5. The instantenous envelope power of DSSB and QPSK 118 + cos(2 fAnt + 2 f07it) + cos(2 fArt + 2/0?rf) ^ ~ 8/a^ n + %fAT 4/a 4/a (A-14) = sin(2^/0 -2^/a) + sin(2^/0 -2^/a) Trt 64/a2^? ;r2-64/AVi2 + cos(2/a^ + 2fQ7tt) 8/a^~ 7T2-64fA27T2t2 (A-15) = sin(27rf/0 -2^/a) cos(2/a^ + 2/0^) U 1 | 64/aV 8/a^ Trf 7T2 -64/A27T2t2 TV2 -64fAn2t2 (A-16) = sin(2^/0 -2^/a) + cos(2/a^ + 2/0^) Â£ 8/a^ /(tt2 64fA7v2t2) n2 64fAn2t2 (A-17) w(0 = n sin(27rf/0 2rtfA) + 8/A^cos(2^/A + 2^/0) /(^2 -64fA 7T2t2) (A-18) 105 The cost function C is maximized when the roll-off factor, r = 0.1 which is shown in Fig. 4-39. ( 5 ) If we emphasize the filter design, for example, w4 = 0.4 and wl = w2 = w3 = 0.2 The cost function C is maximized when the roll-off factor, r = 0.18 which is shown in Fig. 4-40. Hence from ( 1 ) to ( 5 ), the cost function, C is maximized when the small roll-off factor, r is used. In practice, it is possible to implement roll-off factor, r below 0.2. For example, HDTV has been chosen for the roll-off factor, r = 0.115. we can select such a small roll-off factor of r = 0.1 or r = 0.18 based on the cost function. But we choose here the roll-off factor of r = 0.115 as one of the small roll-off factors. Fig. 4-36. Cost, C versus different roll-off factors, r where wl= w2 = w3 =w4 = 0.25. power 76 1 1 1 1 1 0 0 0 0 0 (a) Bit pattern (c) The instantenous power of mh(t) corresponding bit pattern (a) Fig. 4-6. The amplitude and power of mh(t) corresponding bit pattern (a). BER 24 Fig.2-11. BER performance under AWGN where different pilot symbols are used, roll-off factor r = 0.35, time span = 67^ and frame length N = 20. Fig.2-12. BER performance under AWGN where different pilot symbols are used, roll-off factor r = 0.35, time span = 127^ and frame length N= 20. 103 Fig. 4-35. Filter length, Nf where different roll-off factors with different time span is used (r = 0.1 with 127^, r = 0.35 with 1TS ,r = 0.5 with 57^ r = 0.75 with 4Fj ,r=l with 3 Ts). Hence, the cost function, C is given by C = wlxl + w2x2 + w3x3 + w4x4 (4-11) where, wl,w2,w3 and w4 are weighting coefficients and r xl BER performance x2 : Bandwidth x3 : Peak to Average power ratio x4 : Filter design Using polynomial curve fitting, we can obtain the equation from the previous result. CHAPTER 5 CONCLUSION We have shown that the feasibility of DSSB with PSAM for mobile communication. The BER performance under Rayleigh fading environments was investigated by computer simulation. It is concluded that: 1)As the roll-off factor, r, goes to 1, ISI decreases and shows better BER performance. However, there is only a slight difference in the BER performance with the different roll-off factor. Using any roll-off factor larger than zero, there is an excess bandwidth of r x 100%. Hence, for the baseband pulse shaping of DSSB, aroll-off factor, r-0.115 gives an increased bandwidth of 11.5% compared to the bandwidth for the r 0 case. 2) It is shown that 127^, time span gives the minimum BER. But 6TS and 187^ also can be used with slight BER performance degradation. 3) We select a frame length N = 20 symbols as the benchmark. It represents a 0.79 dB power loss but it does accommodate fade rates up 1% of the symbol rate. 4) 1st order Gaussian interpolation is suitable for the fading compensation. However, the performance of the 1st order and the 2nd order interpolations are almost equal. 5) The BER performance in case of CCI obtained by computer simulation is in 108 12 interference (ISI) at the sampling instants. Given this constraint on composite filtering, transmitter filtering can be specified in order to limit the transmitted signal bandwidth to the available transmission channel, and receiver filtering specified to limit adjacent channel interference and ISI and to optimize Pe versus receiver input S/N performance. The optimum requirement is that both transmitter filtering and receiver filtering have to be chosen such that the probability of making a decision error at the receiver is minimized. With the presence of AWGN in the channel, it is well known [Luc68] that a transmitter filter response Tx(f) and receiver filter response Rx(f) which gives optimum Pe is given by Tx(f) = M{f) D{f) Rx(f)~ \H.(f) (2-1) (2-2) where M(f) = He{f) I (2-3) D(f) is the Fourier transform of the input data signaling pulse shape and He(f) is the raised cosine filter which is defined by [Cou97] He(f) = r 1. l{l+cos[^lItM 2 2/a ]}, I/I
I/I >B(2-4) 41 and has considerable processing delay. The performance obtained by this optimal interpolation is within 1-2 dB of the theoretical coherent performance. We use the Gaussian interpolation used in [Sam89], This method achieves good compensation 1-3 dB) with significantly reduced complexity and processing delay compared to the optimum interpolation technique presented in [Cav91b], However, Gaussian interpolation require closer spacing of pilot symbols compared with that of ideal lowpass filtering. This would result in introducing more redundant bit into the data stream, increasing the overhead. 57 The Effect of Co-Channel Interference (CCI) The frequency reuse method is useful for increasing efficiency of spectrum usage but results in CCI because the same frequency channel is used repeatedly in different co channel cells. The BER performance of the DSSB-PSAM in a CCI controlled environment investigated by computer simulation. NONFADING ENVIRONMENT The received signal sr(t) is expressed by M sr(t) = Re[ Azj{t)exp(J2jrfcf) + nc(t) + ^Rkz^t) exp{j2nfct + &)] (3-15) =i M where A2/2 is the power in the signal, ^ {R2 / 2) is the power in the multiple k=1 cochannel interference, fc is the carrier frequency, zt is the complex envelope of the transmitted DSSB signal, zk(t) is the CCI-DSSB signal and nc(t) is the zero-mean complex white Gaussian noise with variance a2. We assume that the interference is statistically independent of the signal and that 6k s are uniformly distributed over the range [0,2tc], The probability of error Pe is given by [Feh87] Pe- erfc(A/ where D(x) = xnRnmaxH.I(x) /n! (3-17) BIOGRAPHICAL SKETCH Seungwon Kim was born in Korea on June 9, 1964. He received his BSEE and MSEE from Sungkyunkwan University, Korea, in Febuary 1986 and 1988 respectively. After graduation, he served in the Korea Army as a Reserved Officer from August 1988 to Febuary 1989. Since June 1989 he has been employed at ETRI(Electronics and Telecommunications Research Institute), Korea. 137 98 Fig. 4-25. The Power spectral density of the SRRC filter where 5 Ts time span with the roll-off factor of 0.5 is used. Fig. 4-26. The impulse response of the SRRC filter where 5TS time span with the roll off factor of 0.5 is used. s cn p' to A to ft + I On 4^ to On 4^ cn 5 to ft i to ft 00 > 4^ 5> cn Â¡3 T to I ^ + to a + to a p" T to I i} to :s to H On 4^ > t "i. to to ON IS > I t* U> (Y^Z Y^Z )u!s (vfaz faz )u!s 3 -t- > S + 00 N. a + s S a 4^ S + 00 S 4*. S to ? I 00 S 00 s S cn 45- S + 00 s cn 5 4^ S > I fo > ^(/o /a ) *(Jo + /a ) 8/a^(/o + /a ) I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. f u Leon W. Couch II, Chairman Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor-ofLEhilosophy, Haniph A. Latchman Associate Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Assistant Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. fM Ewen M. Thomson Associate Professor of Electrical and Computer Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philos; Randy Y. CCChd^wj Professor of Computer and Information Science and Engineering 71 Peak To Average Power Ratio The transmitted signal s(t) is given by s(t) = [ m(t)cos(2nfct) mh(i)sin(2 jrfj)] = Re [ Zj{t)exp(j27tfct)\ where zj{t) = [ m(t) + Hence, the Average power [Cou97] < /(,) > = I < | zT\t) |>=I[< m\t) > + < W(0> ] ( 4-1 ) where the time average operator can be expressed by <[]>= Jim y j [.]dt (4-2) * -TI2 The peak envelope power of DSSB is [Cou97] max [ | zr2(t) | ] = max [ m\t) + mh2(t) ] ( 4-3 ) 2 2 The instantaneous powers for zT(t), m(t) and mh(t) are zT2{t), m2{t) and mh2(t), respectively. We try all possible bit pattern by computer simulation to find the bit pattern where the DSSB peak power occurs. Next, we analyze why peak power happens. To examine the bit pattern that causes peak power by computer simulation, we use 212, 224and 236 total run length data for Gaussian windowed +67^, 127^ and 187^ time span pulse shape. Fig. 4-4 shows that the bit pattern that causes the peak power for 113 m(t)= I exP(~-/Vi) ~J expQ'(-^ + 8/A^)/ dj 2 4/A _b 4/a 1 expQV,) 'r1 exp(-y(-^-8/A^)/ 2 4/a j, 4/a sm(2rtfx) 7 1 expC-yV,) | exp(jQ + 8/A7rf)/ 2 4/a J 4/a 1 expQVi) r exp(-j(7r 8fA7rt)f 2 4/a j 4/a J (A-6) w(0 = 2 exp (-//,) 4/a exp(-y(~^ + 8/a^)/i exp(-X-^r + 8fA7rt)B 4/a 4/a j(-7T+8fA7lt) 4/a exp(i(-^ 8/a^)/ exp(y(-;r 8/A;rf)ff 1 expOV,) 4/a 4/a 2 4/a -j{-7t-8fArt) 4/a 13 where B is the absolute bandwidth and the parameters// and f are a =B-f0 fi A/o ~Ia (2-5) (2-6) (2-7) where fo is the 6-dB bandwidth of the raised cosine roll-off filter, Ts is the duration of one data symbol and D is the symbol (baud) rate. The roll-off factor is defined to be r (2-8) The filter characteristic is illustrated in Fig. 2-3. The corresponding impulse response is he(t) =fl[He(f)] = 2, sin(2^/~0Q cos(2^Q J0% (2nf0t) *[1-(4/a/)2] To express in terms of the roll-off factor r, from (2-6), (2-7), and (2-8) Ia= rfo (2-10) (2-11) 81 Table 4-21. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 67) and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 1.295 4.46 3.395 Average Power 0.795 1 1 Peak to Average Power ratio (dB) 2.11 6.49 5.31 Table 4-22. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 67) and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 1.415 2.465 2.29 Average Power 0.84 1 1 Peak to Average Power ratio (dB) 2.26 3.92 3.60 Table 4-23. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 67) and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 1.49 2.155 1.99 Average Power 0.850 1.00 1.00 Peak to Average Power ratio (dB) 2.43 3.33 2.98 86 Fig. 4-13. Comparison of Peak to Average Power Ratio (dB) for DSSB-PSAM, QPSK- PSAM and OQPSK-PSAM with varying roll-off factor, r where time span = 1271 Roll off factor, r Fig. 4-14. Comparison of Peak to Average Power Ratio (dB) for DSSB-PSAM, QPSK- PSAM and OQPSK-PSAM with varying roll-off factor, r where time span = 187;. 93 Japanese Digital Cellular (JDC) standard specifies the roll-off factor of r = 0.5 [EIA90], Bandwidth efficiency is the ability of a modulation scheme to accommodate data within a limited bandwidth and defined as the ratio of the transmitted data rate per Herz in a given bandwidth. If R is the data rate in bits per second, and B is the bandwidth occupied by the modulated RF signal, then the bandwidth efficiency, rÂ¡ is given by V = ~ ( bps/Hz ) (4-8) The data rate R that can pass through a baseband square root raised cosine roll-off filter is also expressed R 2 B 1 + r (4-9) Substituting (4-9) into (4-8), we obtain the bandwidth efficiency as the roll-off factor is included V = 1 + r (4-10) Therefore, to improve the bandwidth efficiency, a small roll-off factor, r has to be used. 3. Peak to average power ratio is directly related to the power amplifier efficiency. Power amplifier efficiency is defined as the percentage of the applied DC power to the final amplifier circuit which is converted into radiated RF power. Power amplifier efficiency is very important when we design a portable wireless communication system. Battery life of the portable size is tied to the power amplifier efficiency. Class A, AB and 122 f / i 1 exp(-y'27#/Â¡) jf exp{j2ntf)df= v ZTfl eXpU2n,f)df= ret Hence, mh{t) = iexp(-j2nftt)-1 expQ(-^-^ + 8/^g) 2 4/a (-* + 8/a^) 4/a 1 exp(-,'2#,0 -1 exp(y(^ -S-SfcaB) 2 2 4/a -(-tt-8/a7#) 4/a l-exp(-y2^/;) + 1 exp(j2ntf]) 2;# 27# 1 expQW, + + 8/.^g) II 2 4/a 2 - (7T + 8/a7#) 4/a 119 m{t) = sin(2ntfQ lntfA) + 8fAnt cos(2ntfA + 2ntf0) t{n -64/aV t2) (A-19) Hence, normalized by 2/0) /?;(/) = sin(2jtif0 2?rf/A ) + 8 fj cos(2^/a + 2ntf0) 2/0^(l -64/AV) (A-20) span. The QPSK dynamic range is infinite and the dynamic range of OQPSK-PSAM is 27 dB whereas the dynamic range of DSSB-PSAM is 10.91 dB for a roll-off factor of r = 0.115 and 12TS time span. With DSSB, we can take advantage of the much reduced dynamic range and adopt high efficiency amplifiers even though they have poor linearity. The proposed DSSB also does not need very sharp cut-off filtering and only sloped filtering can be used. Although SSB is bandwidth efficient, its performance in fading channels is very poor unless a reference signal is included. Transmitting a low level pilot tone along with the SSB signal has been used to estimate the phase and amplitude distortion caused by fading. However, we use pilot symbol assisted modulation (PSAM) instead of pilot tone assisted modulation (PTAM) since PSAM has several advantages. Hence, we analyze DSSB with PSAM in a Rayleigh fading channel environment and show that DSSB with PSAM is suitable for mobile radio communications. viii APPENDIX B Derivation of the Hilbert Transform of the Square Root Raised Cosine Roll-off Pulse From (2-17) and (2-18), H(f) =f [ h[t) ] corresponds to a -90 phase shift network: m = f -j, /> o 1 j. /< o (B-l) mh(t) = m(t) *h(t) <->Mh(f) = M(f)H(f) (B-2) mh(t)=f-l[Mh(f)] (B-3) m(t)= ] ( co^7r(- f &) exp( j27ttf)df +j f exp{j27Vtf) df -B 4/a J, + (-j)j exp(]2ntf) df +(-j) J cos (n(J-fx) 4/a exp(j2jvtf) df (B-4) 120 17 'Third Method', and is attractive because there is now only a requirement for 90 phase shift at single frequencies. The Weaver SSB generator is in principle realizable in VLSI. However, the Weaver method require very sharp lowpass filters and the two parallel processing channels need to have the same (matched) gain. We assume that here the phase shift method is used for the proposed DSSB system as shown in Fig. 2-1 since the sharp lowpass filters are not needed. We require only the SRRC filter and the Hilbert transform of the SRRC filter. The filtered output is shown in Fig. 2-5. The SRRC and the Hilbert transform of the SRRC will be truncated by using Gaussian window to decrease both ISI of adjacent symbol and peak power which is also shown in Fig. 2-6. The modulated signal st(t) at the transmitter output is given by Fig. 2-5. The square root raised cosine pulse (SRRC) and the Hilbert transform of the square root raised cosine pulse (H-SRRC) with roll-off factor r = 0.35. 96 CQ -O -100 200 300 frequency 500 Fig. 4-21. The Power spectral density of the SRRC filter where 127i time span with the roll-off factor of 0.1 is used. Fig. 4-22. The impulse response of the SRRC filter where 12 Ts time span with the roll off factor of 0.1 is used. 92 The Choice of Roll-off Factor, r The parameters that influence the choice of roll-off factor, r is as follows. f 1. BER performance 2. Bandwidth 3. Peak to Average power ratio v. 4. Filter design 1. As the roll-off factor, r increases to 1, ISI due to the Hilbert transform of raised cosine pulse which is shown in Fig. 2-8 decreases and there is an improvement of the BER performance. As the roll-off factor, r decreases to 0, ISI due to the Hilbert transform of raised cosine pulse increases and there is a degradation of the BER performance. However, there is only a slight difference of 1 dB in the BER performance with different roll-off factors as is shown in Fig. 3-3. Hence we can consider there is a little contribution from the BER performance for the choice of roll-off factor, r. 2. Roll-off factor, r is sometimes called the excess bandwidth factor because it indicates the amount of occupied bandwidth that is required in excess of the ideal occupied bandwidth. For example, if we choose a roll-off factor of r = 0.35, this gives a moderate bandwidth increase of 35%. However if we choose a roll-off factor of r = 1, this gives a large bandwidth increase of 100%. Also a roll-off factor, r of zero is impossible to implement. In practice, the United States Digital Cellular (USDC) IS-54 standard specifies square root raised cosine filtering with roll-off factor of r = 0.35 while 84 Table 4-30. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 187^ and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 2.56 5.66 4.365 Average Power 0.92 0.98 0.98 Peak to Average Power ratio (dB) 4.44 7.61 6.48 Table 4-31. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 187* and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 2.62 4.48 3.52 Average Power 0.945 1 1 Peak to Average Power ratio (dB) 4.42 6.51 5.46 Table 4-32. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 187^ and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 2.76 2.53 2.305 Average Power 0.955 1 1 Peak to Average Power ratio (dB) 4.60 4.03 3.63 104 rxJ = 1 -(0.01 87a-2- 0.0261/' + 0.0404 )/ 0.0404 x2= 1 -( 70.96r + 16.87)/ 16.87 x3 = 1 ( 2.577r2 4.8854/* + 4.031) / 4.031 x4-\-{ 272.185/-2- 490.55/* + 283.02) /283.02 then C = w7(-0.463/^ + 0.643r ) + w2(-4.2r) + wi(-0.639/^ + 1.21/-) + w4(-0.96/-2 + 1.733) (4-12) ( 1 ) If we have the same weighting factor, wl = w2 = w3= w4 0.25 The cost function C is maximized around the roll-off factor, r = 0 which is shown in Fig. 4-36. ( 2 ) If we emphasize the BER performance, for example, wl = 0.4 and w2 = w3 = w4 0.2 The cost function C is also maximized around the roll-off factor, r = 0 which is shown in Fig. 4-37. ( 3 ) If we emphasize the bandwidth increase, for example, w2 = 0.4 and wl = w3 -w4 = 0.2 The cost function C is also maximized when the roll-off factor, r = 0 which is shown in Fig. 4-38. ( 4 ) If we emphasize the peak to average power ratio, for example, w3 = 0.4 and wl =w2 = w4 = 0.2 110 3) Spectral occupancy If we use 127^ time span combined with Gaussian window, there is a 28% bandwidth increase. However, if we use 18 7^, time span combined with Gaussian window, there is a 18% bandwidth increase and slight degradation of BER performance. In all cases, no sharp cut-off filtering is needed for DSSB compared to analog SSB. The gradual sloped filtering, such as raised cosine filtering can be used. 101 Fig. 4-31. The BER performance where different ISI is used ( +11 Ts with the maximum ISI of 0.1, 127^ with the maximum ISI of 0.048, and 137], with the maximum ISI of 0.02). Fig. 4-32. BER performance where different roll-off factors with different time span is used ( r = 0.1 with 12rs, r = 0.35 with 1TS, r = 0.5 with +57^, r = 0.75 with 4Ts, r = 1 with 3TS) where frame length N= 20, fdTs = 0.001 and Ef/N0= 10 dB. ACKNOWLEDGEMENTS I would like to express my profound gratitude to Professor Leon W. Couch II, who served as a chairman of my supervisory committee. His sincere guidance, continuous encouragement, constructive criticism, invaluable technical advice made this work possible. I also extend my deepest appreciation to him for being very polite, understanding and making himself available during all working days to discuss anything I wanted to, and also for spending his precious time reviewing this manuscript. I must admit that it has been a pleasure to have been his student. Im also indebted to Professors Haniph A. Latchman, Tan F. Wong, Ewen M. Thomson and Randy Y. C. Chow who very kindly agreed to serve on my Ph.D. committee. I would like to specially thank Professors Haniph A. Latchman and Tan F. Wong for their invaluable suggestions and advice. I would also like to acknowledge the support of this research by ETRI, Taejon Korea. Without support, this work would not have been possible. Of all who supported and provided assistance, none was as valuable as my dear wife, Inseon Choi. I would like to express my deepest gratitude and love to her, for sharing not only the moments of happiness and joy, but also being with me in difficult times of my life, when I needed her the most. I would also like to acknowledge my children, Juhae, Juyoung and Juchan, who provide me much needed relief and comfort through their activities and love. 37 Substituting from (2-59), N 0 < n < N ^ -[( )2-( ) + 2], N (2-61) Fig. 2-21 shows this impulse response for N= 20. The frequency response of this interpolator is shown in Fig. 2-22 and compared with that of an ideal interpolator, from which the pass band distortion as well as the aliasing that could be caused by the sidelobes may be observed. The pass band distortion starts around 0.2The first spectral nulls around the channel sampling frequency is narrow. Therefore, if fD> 0.1/, the effect of aliasing will be seen in the interpolated estimation. Hence, to avoid aliasing, the channel has to be sampled at least 5 times the minimun Nyquist rate. Hence, the performance degradation as well as the required increase in overhead resulting from the use of a non - ideal interpolator is evident. -fo 0 fD f Fig. 2-17. Doppler spectrum. 31 r Q-i = o < Qo = l : zeroth order Q, =0 (2-39) It is seen that estimation errors may be caused by noise, frequency offset in the receiver local oscillator and non-ideal interpolation. Compensation is carried out by dividing each received symbol by the corresponding fade estimation. The compensated complex samples z (k + m/N) are given by, z(k + m/N) = x(k + m/N) / c(k + m/N) m = 1,2,3,...(N-1) (2-40) Hence, the decision input is given by the real component of z(k + m/N). Channel Interpolation The signal received by a moving vehicle in a land mobile channel consists of multiple reflected rays due to local scattering and the lack of a line-of-sight path between the transmitter and the receiver. Due to such multipath fading, the received signal is subjected to random amplitude and phase fluctuations. It has been shown that if the delay spread between the multiple rays is negligible in comparison to the symbol duration, then the channel is characterized by a complex gain whose amplitude has a Rayleigh distribution and the phase has a uniform distribution [Jak74], Since the in phase and quadrature components of the channel gain are narrowband Gaussian processes, periodic 4 protection and a good correlation between the fades experienced by the pilot tone and the SSB signal. In this technique, a part of the SSB spectrum is removed from the central region by a notch filter for the low level pilot tone to be inserted in its place. To remove the low level pilot tone from the receiver output, it is required to remove a segment of the recovered baseband by filtering. Such a procedure has little effect on speech quality even if the filtered segment approaches 1kHz in bandwidth, but it does create problems for data transmission [McG84], For proper operation of tone in band SSB system for data transmission, the low level pilot tone must be transparent to data and be located across the band. This technique, termed transparent tone in band (TTIB), is shown in Fig. 1-2. and used in conjunction with a procedure known as feed forward signal regeneration (FFSR) [Bat85], The idea of this procedure is that the receiver uses this pilot tone not only to obtain a frequency reference for demodulation and as a known signal for AGC reference, but also to act as a basis for re-establishing the amplitude and phase features of the original transmitted SSB signal by compensating for the effect of Rayleigh fading. However, when TTIB is used to transmit data signals, the receiver oscillator must be phase locked to that in the transmitter, or the signal is distorted and an unacceptible bit error rate results. Phase locked TTIB (PLTTEB) was proposed as a way of achieving lock without requiring transmission of an explicit synchronization signal, such as another pilot tone [Mcg84], However, the method has been shown to generate a high level of self noise. The random data signal itself disturbs the phase lock and results in a very long acquisition time [Cav89], Bateman proposed a symmetric form of the PLTTIB phase detector that can eliminate the self noise [Bat90], But there still exists a two-fold phase ambiguity, which forces the use of differential encoding, with an additional loss of 3 dB 32 sampling of the channel by pilot symbols inserted into the data stream may be used to recover this process. The pilot symbols which is located N symbols apart provide a noise corrupted estimate of the channel gain at the sampling instants. The channel sampling rate is fcs (2-41) where f is the symbol rate and N is the frame of length. For the kth frame, the channel estimate obtained from the received pilot symbol is given by (2-35) c (kN) = c(kN) + n(kN) / d (2-42) where c(kN) is the sample of the fading process c(t), c (kN) is the corresponding channel estimate, n(kN) is the sample of the AWGN corrupting the system and d is the known pilot symbol. From the Nyquist theorem, for the reconstruction of the fading process, fcs > 2fD (2-43) where fo is the maximum Doppler frequency. The Nyquist frequency for channel sampling is fN = 2fo (2-44) Since N > 2 for any information transfer over the channel and the actual pilot symbol rating is given by 59 Py(y) = y M-\ YM{M-1)! exp(- y) (3-24) Defining the signal-to-interference power ratio as r = x /y, the PDF of r as follows [Yao92], Pr(r) = J ypx (ry) Pyiy) dy 0 _ ^ b b v r + b (3-25) where b= Y (3-26) The static probability of bit error of DSSB (in a nonfading environment), Pe is given by Pe(r) = (~)erfc(4r) (3-27) where r = - 2cr2 (3-28) When the channel is subject to fading, signal to noise power ratio, r, is a random variable and the dynamic bit error probability is derived by averaging ( 3-27) over all possible values of signal to noise power ratio. This method can also be used to derive the bit error probability when the signal is subject to interfering in a fading environment [Woj86], Following this approach, the bit error probability, assuming that all interferes 26 Fading Channel Effects In a land mobile radio channel, the received signal is a linear combination of a large number of carrier signals spread in time and frequency, each corrupted by AWGN. In relatively low symbol rate systems, e.g., fs < 50kbaud, the time delay spread among these multiple signal paths is frequently a negligible fraction of the symbol duration Ts [Lee89], We limit ourselves to such cases, i.e., nonfrequency selective fading (or flat fading). The resulting faded carrier has been shown to have a random phase and amplitude modulation imposed upon it by the channel. The random amplitude has been shown to have a Rayleigh distribution, and the random phase a uniform distribution [Jak74], The complex envelope of the faded carrier u(t) may be represented as u(t) = c(t)z7(t) (2-23) where the quantity c(t) c(t) = citym (2-24) represents the fading which is a complex zero mean, stationary Gaussian random process characterized by its frequency spectrum C(/) given by [Jak74] 2 C Here fa is the maximum Doppler frequency experienced by the moving vehicle, which is related to the vehicle speed by 22 t/Ts Fig. 2-9. The effect of Intersymbol Interference (ISI) with a different roll-off factor due to the Hilbert transform of the RC pulse with 67^ time span. Table 2-1. The ISI value with different roll-off factors, r with +6TS time span II o >* r = 0.35 II o r= 1 0 0 0 0 0 ir. 0.5192 0.4937 0.4663 0.3483 2TS 0.0035 0.0280 0.0481 0.0770 3 T, 0.0339 0.0231 0.0179 0.0184 4TS 0.0006 0.0032 0.0036 0.0034 5TS 0.0008 0.0004 0.0005 0.0005 6TS 0 0 0 0 Total ISI 0.558 0.5484 0.5364 0.4476 50 Fig. 3-7. Effect of time span for each symbol on BER for DSSB-PSAM where r = 0.M5, fDTs = 0.001, N= 20 and 1st Gaussian interpolation. Fig. 3-8. Effect of time span for each symbol on BER for DSSB-PSAM where r = 0.115,foTs = 0.0025, N- 20 and 1st Gaussian interpolation. 34 where e(kN + m) is due to interpolation error and n(kN + m) is due to noise. The composite error denoted by c (kN + m) so that c (kN + m)-c (kN + m) + c (kN + m) (2-51) where c (kN + m) = e(kN + m) + n(kN + m) The interpolator corresponding to sampling the channel at the minimum Nyquist frequency is an ideal lowpass filter whose impulse response is given by [Sha73], h(ri) = n(rml N) m/N - oo < n < oo (2-52) The corresponding frequency response is given by, oo H[exp(jw /ws)] = ^ h(ri)[exp( -jmw /ws) ] m=-co = r*f, \w/w,\< i { v 0, otherwise (2-53) This extracts a single image of the sampled Doppler spectrum without distortion or aliasing as shown in Fig. 2-18. Such an interpolator however can not be realized in practice, due to its infinitely long impulse response as can be seen by (2-52). The length of impulse response is also propotional to the complexity of the interpolator and to the processing delay. Hence, the impulse response must be truncated to meet the systems requirements and constraints. 94 class B which are linear amplifiers have less efficiency than a nonlinear Class C amplifier. Fig. 4-13 is shown that the proposed DSSB peak to average power ratio are much lower than those for QPSK when small roll-off factor such as below 0.35 is used. For QPSK and OQPSK, the peak to average power ratio decreases as the roll-off factor increases [Yas89], However, for DSSB, the peak to average power ratio increases as the roll-off factor increases. For QPSK and OQPSK, there is a trade-off between bandwidth efficiency and power amplifier efficiency when small roll-off factor is used. But the proposed DSSB has bandwidth efficiency and power amplifier efficiency when small roll off factor is used. This is a great advantage for DSSB system compared to QPSK and OQPSK. 4. Various filter design methods can be considered when we decide how many filter length that represent the complexity is used. It was suggested by Presti that simple design tables for square root raised cosine digital filters can be obtained when we consider two criterion [Pre89], One is the intersymbol interference (ISI), which can be ideally eliminated when the both transmitter and receiver filter transfer function is satisfies the Nyquist filter response. But the truncation of time span negatively affects the ISI performance, especially for small values of the roll-off factor, r [Pre89], We define here the maximum ISI as the absolute value of the sum of the difference at each symbol period, Ts between the original(not truncated) RC pulse and truncated RC pulse with time span, T. The other design constraint is the sidelobe amplitude, which has to be minimized to reduce the interchannel interference (ICI). The stop band is defined as the frequency range starting at the first null sample of the filter transfer function and with a 52 distorted less due to truncation and Gaussian windowing. The Effect of Frame Length, N The frame length, N, needs to be optimum value, which represents a trade-off between power loss of extra pilot symbols and coarse receiver estimation of the fading process. By sampling theorem, the rate of pilot symbol insertion must be at least the Nyquist rate of fading process, so that N < M(2fDTs). When fast fading expected for example, 400Hz Doppler in a 40 ksymbol/s system gives ft>Ts = 0.01, then N= 20 is the optimum value as shown in Fig. 3-14. Hence, N = 20 is selected as the benchmark. - Eb/No = 10dB - Eb/No = 20dB -A- Eb/No = 30dB Fig. 3-11. Effect of frame length, N, on BER for DSSB-PSAM where r = 0.115, time span = 127^, foTs = 0.001 and 1st Gaussian interpolation. 70 Fig. 4-2. Comparison of Dynamic Range (dB) for DSSB-PSAM and OQPSK-PSAM with varying roll-off factor, r where Time span = 127^ and frame length N=20. Roll off factor, r Fig. 4-3. Comparison of Dynamic Range (dB) for DSSB-PSAM and OQPSK-PSAM with varying roll-off factor, r where Time span = +187^ and frame length N = 20. Amplitude ^ Amplitude 79 t/Ts -9. Impulse response of a Gaussian pulse shaping filter. Fig. 4-10. Different type of window to use the reduction of ISI of trih(t). 49 Fig. 3-5. Effect of roll-off factor, r, on BER for DSSB-PSAM where time span = 12Ts, N= 20,f dTs = 0.00625 and 1st Gaussian interpolation. Fig. 3-6. Effect of roll-off factor, r, on BER for DSSB-PSAM where time span 127^, N=20, f dTs = 0.01 and 1st Gaussian interpolation. 129 Simulation of 16QAM-PSAM The BER performance of 16QAM-PSAM obtained from simulation program is compared with corresponding theoretical curves and reference paper [Sam89], Fig. C-5 shows this result. random number Fig. C-l. The Gaussian distribution with mean = 0 and variance = 1. 82 Table 4-24. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6TS and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 1.975 2.285 1.62 Average Power 0.88 1 1 Peak to Average Power ratio (dB) 3.51 3.58 2.09 Table 4-25. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 127) and roll-off factor r- 0 DSSB QPSK OQPSK Peak Power 2.04 5.49 4.435 Average Power 0.88 0.985 0.985 Peak to Average Power ratio (dB) 3.65 7.46 6.53 Table 4-26. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = +127) and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 2.10 4.475 3.535 Average Power 0.905 1 1 Peak to Average Power ratio (dB) 3.65 6.50 5.48 136 Woj86 Yan89 Yao90 Yao92 Yas89 Wojnar, A.H., Unknown Bounds on Performance in Nakagami Channels, IEEE Tram., Com-34, pp. 22-24, 1986. Yang, J., Simulation Software for Rayleigh Fading with Doppler Spread, Digital Communications Laboratory Report, University of California, Davis, June, 1989. Yao, Y.D. and Sheikh, A.U.H., Outtage Probability Analysis for Microcell Mobile Radio Systems with Cochannel Interferes in Rician/Rayleigh Fading Environment, Electron. Letter, pp. 864- 866, 1990. Yao, Y.D. and Sheikh, A.U.H., Bit Error Probability of NCFSK and DPSK Signals in Microcellular Mobile Systems, Electron. Letter, pp. 363-364, 1992. Yasushi, Y., Shigeki, S., Hiroshi, S. and Toshio, N., Performance of 7I/4-QPSK Transmission for Digital Mobile Radio Applications, IEEE Globecom, pp. 443-447, 1989. 21 use more pilot symbols, the average ISI decreases but the power loss is increased. There is a 101og[A7(.A/-Ar)] (dB) power loss by inserting K pilot symbols. There is a slight difference in average ISI between using three pilot symbols and using five pilot symbols. Hence, we will use three adjacent pilot symbols in one frame and the amplitude and the phase estimation of the fading will be made at the middle point in the middle pilot symbol. This is shown in Fig. 2-16. Fig. 2-8. The impulse response of the complete filter response where roll-ofF factor r = 0.35. G-RC : Raised Cosine pulse with Gaussian window G-H-RC : Hilbert transform of Raised Cosine pulse with Gaussian window 85 Table 4-33. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 187^ and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 2.835 2.175 2.00 Average Power 0.955 1 1 Peak to Average Power ratio (dB) 4.72 3.37 3.00 Table 4-34. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 187^ and roll-off factor r = 1 DSSB QPSK OQPSK Peak Power 3.605 2.29 1.625 Average Power 0.965 1 1 Peak to Average Power ratio (dB) 5.72 3.59 2.10 Fig. 4-12. Comparison of Peak to Average Power Ratio (dB) for DSSB-PSAM, QPSK- PSAM and OQPSK-PSAM with varying roll-off factor, r where time span = 6 Ts. 8 No report can be found for the analysis of pulse shaped (such as raised cosine pulse) DSSB even though this scheme has approximately the same bandwidth efficiency and power efficiency as Quadrature Phase Shift Keying (QPSK) [Pro89], (ii) Pilot symbol assisted modulation (PSAM) As mentioned above, both PSAM and PTAM mitigate the effects of multipath fading. But PSAM has more advantages than PTAM. Hence, DSSB with PSAM will be investigated under Rayleigh fading channel conditions. (iii) Peak to average power ratio (PAPR) DSSB with PSAM shows better peak to average power ratio than QPSK and offset quadrature phase shift keying (OQPSK). For square root raised cosine pulse (SRRC), DSSB is shown to have peak to average power ratios (PAPR) that are from 1.83 to 2.85 dB lower than those for offset quadrature phase shift keying (OQPSK) and quadrature phase shift keying (QPSK) for a roll-off factor of r = 0.115 and 1271 time span. DSSB is also shown to have PAPR that are from 3.2 to 4.38 dB lower than those for OQPSK and QPSK for a roll-off factor of r = 0.115 and 671 time span. (iv) Use of efficient power amplifiers DSSB with PSAM has a much reduced dynamic range when compared to pulse shaped QPSK and OQPSK. We will show that the dynamic range is for DSSB is 10.91 dB, whereas the OQPSK dynamic range is 27 dB and the QPSK dynamic range is infinite for a roll-off factor of r = 0.115 and 1271 time span. We will also show that the dynamic range is for DSSB is 5.38 dB, whereas the OQPSK dynamic range is 22.7 dB and the QPSK dynamic range is infinite for a roll-off factor of r = 0.115 and 671 time span. With DSSB, we can take advantage of the much reduced dynamic range and use high 115 m(t) = 1 exp +xB + 8 /A xtB) 1 + 4/a --Qxp(j2nfxt) j(7T+8f^7Tt) 4/a + 1 exp(-y(-^l + kB ~%fAntB) 2 4/a 4/a -^exp(y27z/;0 (A-8) 2 exP(./2^/,0 -1 exp(-/2^0 j(-x + %f^xt) 4/a sin(2^/;) TCl - expQ'2^0 i exp(-72^,0 /O + 8/a^) 4/a 1 exp(/(^/j xB + 8fAntB) 1 exp(-/(a/; + 8fAxtB) 2 4^ 2 4^ j(x-SfAxt) 4/a 16 f/fo (a) Magnitude frequency response t/Ts (b) Impulse response Fig. 2-4. Frequency and time response for different roll-off factors [Cou97], 126 mh(t) = 1 64/AV cos(27df0 2) + sin(2^/0 +2ntfA) 7rt(\ 64fA2t2) 8/a n n2-64 /AV/2 (B-14) mh(t) = 1 ~ 64/AV cos(27rtf0 2^/a ) + 8fj sin(2^/0 + 2tz//a ) /rf(l-64/AV) (B-15) Hence, normalized by 2/0, *(0 = 1 ~ 64/a2*2 ~ cos(2trf/0 2^/a) + 8/Afsin(2^/0 + 27rtfA) 2;z//(1-64/aV) (B-16) 78 Fig. 4-8. The DSSB instantenous peak power characteristics due to long bits of ones and long bits of zeros. Table 4-19. The DSSB peak power with different time span and different roll-off factors Roll-off factor 6TS 127; 187; r = 0 1.24 2.04 2.56 r = 0.115 1.295 2.10 2.62 r = 0.35 1.415 2.24 2.76 r = 0.5 1.49 2.315 2.835 r= 1 1.975 2.995 3.605 72 both DSSB and QPSK. Due to Hilbert transform of the SRRC pulse, the pulse shaped DSSB has less envelope fluctuation than that of QPSK which is shown in Fig. 4-5. However, the worst case peak power of the DSSB occurs for the case of a long stream of ones and zeros as shown in Fig. 4-4. This peak power of DSSB is due to by only the Hilbert transform of SRRC pulse, mh(t) as shown in Fig. 4-6. In this case, the peak power of m{t) which has a SRRC pulse shape is zero due to the cancellation of each other which is shown in Fig. 4-7. The peak power of DSSB is shown in Fig. 4-8. Hence, we can check the peak power by adding the value of middle point of nth(t). ( mid[w*(0]i, 0 { mid[m(Ok 2Ts Hence, the peak power of DSSB is li ii { 2 2 mid [mh (Ok } = 2 11x1(11mh (Ok " m=1 m=1 (4-5) Table 4-19 shows the peak power with different time span and different roll-off factors. We use here Gaussian window for truncation and windowing the pulse shaped filter. The impulse response of the Gaussian window is given by 133 Cav91b Cav92 Cou97 Del32 EIA90 Feh87 For77 Gin91 GRA94 Goo91 Gos78 Ham73 IMS90 Cavers, J.K., An Analysis of Pilot Symbol Assisted Modulation for Rayleigh Fading Channels, IEEE Tram., Veh., Technol., Vol., 40, pp. 686-693, Nov., 1991. Cavers, J.K. and Maria Liao, A Comparison of Pilot Tone and Pilot Symbol Techniques for Digital Mobile Communication, IEEE Global Telecomm., Conf, pp. 915-921, Dec., 1992. Couch, L.W., Digital and Analog Communication systems, Fifth edition, Prentice Hall, Upper Saddle River, NJ, 1997. Deloraine, E. M., Single Sideband Short Wave Telephone, Society Francaise Electicity, Bull. 2, pp. 940-1009, Sept., 1932. EIA/TIA Interim Standard, Cellular System Dual Mode Mobile Station - Land Station Compatibility Specifications, IS-54, Electronic Industries Association, May, 1990. Feher, K., Advanced Digital Communications, Prentice Hall, Upper Saddle River, NJ, 1987. Forsythe, G.E., M.A.Malcom and C.B. Moler, Computer Methods for Mathematical Computations, Prentice-Hall, Upper Saddle River, NJ, 1977 Ginn, S., Personal Communications Services : Expanding the Freedom to Communicate, IEEE Communications Magazine, Vol. 29, No. 2, pp. 30-39, Feb, 1991. Grand Alliance, VSB Transmission System, Technical Details, February, 1994. Goodman, D.J., Trends in Cellular and Cordless Communications, IEEE Communications Magazine, Vol. 29, No. 6, pp. 31-40, June, 1991. Gosling, W., J.P. McGreehan, and P.G. Holland, Receivers for The Wolfson Single Sideband VHF Land Mobile Radio System, Proc. IERE conf, Radio Receivers and Associated Systems, South Hampton, England, pp. 169-178, July, 1978. Hamming R.W., Numerical Methods for Scientists and Engineers, McGraw-Hill, New York, 1973. Implementation of Current Mobile Satellite Systems, Proceedings of the Second International Mobile Satellite Conf, EMSC 90, Ottawa, Ontario, Canada, June, 1990. 43 Ed=\< I 8t)\2>Tb = ~ < 12[m(t) + jmh(t)] 12 > Tb = 2 | Since Ed = 4 = 4A2Tb (3-7) Hence, ft = Q( ) (3-8) Here is given by \g(t)\2>Tb = I [w(0 + J7Wa(0] I 2 > 7ft = | I = A2Tb (3-9) 40 Hence, the requirements in the design of a suitable channel interpolation are as follows. 1. Good performance 2. Low complexity 3. Low processing delay 4. Low overhead A method of estimation and compensation for the amplitude and phase variation in mobile channel is based on the insertion of known pilot symbols periodically into the data stream. This method however, requires the transmission of redundant symbols. Another disadvantage is that this processing incurs some delay in the received data. The minimum overhead is achieved when pilot symbols are sampled at the Nyquist rate, which is twice the maximum Doppler frequency. However, the infinitely long interpolator corresponding to this sampling rate can not be realized due to practical constraints in processing delay and system complexity. Hence, the interpolator must be truncated to a reasonable limit at the cost of system performance. The performance with lowpass filter interpolation as a function of the noise bandwidth of the interpolator has been studied in [Moh89], To reduce the effects of noise, the channel estimates are filtered with a filter which is approximately matched to the fading process. They choose a filter bandwidth correspond to the worst case fading rate. This non-ideal lowpass filtering results in degradation in the estimates due to aliasing and distortion as shown in Fig. 2-19. Optimum interpolation technique is studied in [Cav91b] using Wiener filtering of the received pilot symbols. This technique requires adaptive updating of the tap coefficients 80 Fig. 4-11. The DSSB peak power with different time span and different roll-off factors. Table 4-20. The Peak to Average Power Ratio for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 6 Ts and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 1.24 5.12 3.695 Average Power 0.76 0.975 0.975 Peak to Average Power ratio (dB) 2.12 7.20 5.78 130 Fig. C-2. Rayleigh fading generated by Jakes fading simulation. Fig. C-3. Doppler power spectrum with 100 Hz and Carrier frequency fc = 5000 Hz. 3 SSB with Pilot Tone Assisted Modulation (PTAM) SSB as a suitable modulation for the land mobile communication has been developed [Wel78], [Lus78],[Gos78], Though SSB have the advantage of being very bandwidth efficient, the performance in fading channel is very poor. In conventional SSB receivers, it is difficult to synchronize the local oscillator frequency. If the incoming carrier frequency is not the same as the frequency of the oscillator at the product detector in the receiver, product detection will lead to shifting the demodulated spectrum by an amout equal to the difference in frequencies. Doppler spread and Rayleigh fading can shift the signal spectrum causing amplitude and phase variations in the received signal. Reliable receiver carrier synchronization can be achieved if a low-level pilot tone is inserted into the transmitted SSB signal. Hence SSB systems often incorporate a constant amplitude sinusoidal reference tone at some frequency in the transmitted spectrum. The question of where in the spectrum to locate the pilot tone is a difficult one. The research has concentrated on three systems which differ in the spectral position of the low-level pilot tone ( -7.5 to -15 dB below the peak power of the SSB). The systems are as follows: 1) pilot carrier SSB developed by Philips Research Laboratories in U.K. [Wel78] 2) pilot tone in-band SSB developed by the University of Bath in U.K. [Gos78], 3) pilot tone above-band SSB investigated at Stanford University in U S. for the Federal Communications Commission (FCC) [Lus78] The emitted spectra for each of these three systems are shown in Fig. 1-1. Of these, the tone in band SSB system offers the greatest degree of adjacent channel 35 A truncated interpolator may use Q channel estimates from O frames to obtain N-1 fade estimates within a frame. The maximum processing delay Td is given by, Td = r NQ / 2, if N is even ^ N(Q-1 )t 2, otherwise (2-54) The length of the impulse response is given by [Sha73], Np = f NQ, if both N and Q are odd L NQ -1, otherwise (2-55) By truncating the interpolator to meet the constraints on complexity, delay etc, pass band distortion and stop band sidelobes are produced in the frequency response. This results in errors in the interpolation estimates due to distortion and aliasing as shown in Fig. 2-19. Hence, performance is compromised due to truncation of the interpolator. This degradation in performance may be overcome to a certain extent by increasing the channel sampling rate above f v, i.e., by closer spacing of the pilot symbols. In doing this, the Doppler spectral images are moved further apart, so that the effects of aliasing are reduced. Fig. 2-20 shows this with the same truncated interpolator as shown in Fig. 2-19. Oversampling the channel can be expressed by fas = 2 PfD (2-56) where /? is the oversampling factor given by, 23 Table 2-2. The ISI value with different roll-off factors, r with 127; time span >! II O r = 0.35 O II Ss. r= 1 0 0 0 0 0 1 Ts 0.6022 0.5726 0.5409 0.4039 2TS 0.0063 0.0506 0.0871 0.1393 3TS 0.1287 0.0877 0.0680 0.0699 47; 0.0066 0.0344 0.0385 0.0367 5 T, 0.0319 0.0173 0.0185 0.0187 6TS 0.0034 0.0095 0.0087 0.0009 1TS 0.0061 0.0040 0.0040 0.0041 87; 0.0010 0.0016 0.0017 0.0017 97; 0.0008 0.0006 0.0006 0.0006 107; 0.0002 0.0002 0.0002 0.0002 117; 0.0001 0.0001 0.0001 0.0001 127; 0 0 0 0 Total ISI 0.7873 0.7786 0.7683 0.6842 Fig. 2-10. Amplitude and phase ambiguity in case of one bit pilot symbol with roll-off factor r 0.35 where (1_100010.11) bit pattern is used ( 1_: pilot symbol). G-RC : Raised Cosine pulse with Gaussian window G-H-RC : Hilbert transform of Raised Cosine pulse with Gaussian window 123 1 exp {-jirTrf, +7zB-%f^7tB) + 2 4A (tz:-8/aO 4/a 1 2 exp(7'2^/;0 (B-7) wA(0 = ^ exp(j2nf) + i exp(-y2^0 O 8/A7rf) 4/a + | expO'^O +1 exp(-j2nf) O + 8/atQ 4/a 1 expQP/i -nB + 8fAntB) | 1 exp(-j(7/, -nB + &f70B) 2 4/a + 2 4/a 1 expOX^/i O 8/A?rf) 4/a 8/a^5) i 1 exp(-y'(7z/j -7tB- 8fA7vtB) 2 4/a ' 2 4/a (n + 8fA?rt) 4/a 2- 2cos(2^/j0 2 7lt (B-8) 54 Eb/No = 10dB Eb/No = 20dB A Eb/No = 30dB Fig. 3-14. Effect of frame length, N, on BER for DSSB-PSAM where r = 0.115, time span = \2TS, fDTs = 0.01 and 1st Gaussian interpolation. The Effect of Gaussian Interpolation Order The estimation of the fading distortion at the other pilot symbols can be obtained by Gaussian interpolation. Fig. 3-15 through Fig. 3-18 show the BER performance with the parameter Eb /N0 and the order of interpolation. 1st order Gaussian interpolation is suitable for the fading compensation. However, the performance of the 1st order and the 2nd order interpolations are almost equal. 44 Therefore, Pe = 0( (3-10) This result is used for the theoretical performance curves that is plotted in Fig. 3-1. The following items are considered causes of the performance degradations. 1)Power loss by inserting pilot symbols given by Dj = 10 log ( p-- ) (dB) (3-11) N-3 2) Degradation by the noise included in the pilot symbols 3) ISI of the Hilbert transformed signal of the RC pulse 4) Degradation due to inaccuracy of estimation Fig. 3-1 also shows the BER performance of DSSB with PSAM in AWGN. The performance of DSSB with PSAM is degraded by about 2 dB for N= 20 from the theoretical value due to the degradations items. Theoretical BER Performance under Fading Let us assume that the channel fading is sufficiently slow to that the phase shift 9 can be estimated from the received signal without error. The SNR y = o? Eb / No is a varying quantity on account of the effect of the fading and proportional to the square of the Rayleigh fading envelope, r2, which can be obtained by letting 1 y PA/) = exp( ) Yo Y0 (3-12) 135 Nob62 Och89 Opp75 Osw56 Par89 Pee93 Pro89 Rap96 Sam89 Sha73 TIA93 Wal90 Wea56 Wel78 Noble D., The History of Land Mobile Radio Communications, IEEE Vehicular Technology Transactions, pp. 1406-1416, May, 1962. Ochsner, H., DECT Digital European Cordless Telecommunications, IEEE Vehicular Technology 39th Con/., pp. 718-721, 1989. Oppenheim, A. V. and R.W. Shafer, Digital Signal Processing, Prentice Hall, Upper Saddle River, NJ, 1975. Oswald, A. A., Early History of Single Sideband Transmission, Proceedings of the IRE, pp. 1676-1679, Dec., 1956. Parson, J.D. and Gardiner, J.G., Mobile Communication Systems, Blackie & Son New York,1989. Peebles, P.Z., Jr., Probability Random Variables and Random Signal Principles, Third Edition, McGraw-Hill, New York, 1993. Proakis, J.G., Digital Communications, McGraw-Hill, New York, 1989. Rappaport, T.S., Wireless Communications, Prentice Hall, Upper Saddle River, NJ, 1996. Sampei, S and T. Sunaga, Rayleigh Fading Compensation Method for 16 QAM in Digital Land Mobile Radio Channels, Proc., IEEE Veh., Technol, Conf., San Francisco, CA, pp. 640-646, May, 1989. Shaper, R.W. and Rabiner, L.R., A Digital Signal Processing Approach to interpolation, Proceedings of the IEEE, Vol. 61, No. 6, pp. 692-702, June, 1973. TIA/EIA Interim Standard 95, Mobile Station Base Station Compatibility Standard for Dual-Mode Wideband Spread Spectrum Cellular System, July, 1993. Walker, J., Mobile Information Systems, Artech House, Inc., 685 Canton Street, Norwood, MA 02062, 1990. Weaver, D. K., Jr., A Third Method of Generation and Detection of Single-Sideband Signals, Proceedings of IRE, pp. 1703-1705, 1956. Wells, R SSB for VHF Mobile Radio at 5Khz Channel Spacing, IERE Conf, Proc. Radio Receivers and Associated Syst., South Hampton, England, pp. 29-36, July, 1978. 128 summed to form the narrowband complex Gaussian noise which constitute the components of Rayleigh fading. To perform the actual fading in baseband, a complex multiplication of the data and this noise is carried out, which is equivalent to the modulation of the data carried by the random noise. Fig. C-2 shows a Rayleigh distributed signal envelope as a function of time used in simulation. Fig. C-3 shows its Doppler power spectrum with fD= 100 Hz. A complete verification is found in [Yan89], Estimation of the probability of error The Monte Carlo method of error counting is used to estimate the probability of error. The number of errors encountered in the simulation or the total number of bits processed through the system is a key factor in the confidence level of the estimate. It has been shown in that 99% confidence interval of a factor of two at a BER of lx 10'k is obtained for a total run length of 10k+1 10k+2 bits, when independent errors are observed. However, in the simulation of Rayleigh fading channels, the errors are not independent, and hence the above rule does not apply. In our simulations, the run length was set at 200 cycles of the Doppler frequency, so that a sufficient number of fades is simulated. For example, at foTs of 0.001, one Doppler cycle spans the duration of 1000 symbols. Hence, the total run length was selected as 200000 symbols. Fig. C-4 shows the comparison of theoretical and simulated BER performance of DSSB-PSAM in AWGN and Rayleigh fading (f'DTS = 0.001) channels. 125 + \-cos(2nf0t-27if) nt (B-10) mh(t) = cos(2ntf0 2ntf^) -64/aV n2-64f2n2t2 cos( + - 2t/a + 8fA2nt + 8fJ0nt) 4/a n 8/A?rf 4/a ) cos(- 2Va -8/a2^-8/a/o^) 4/a ) ?r+ 8 /A;rf 4/a J_ cos(2^/0 -2^/a) 7# 7Z (B-l 1) ^a(0 = J_+ cos(27rf/0 2ntfh) nt ~64fA2nt 1 n1 -64f2n2t2 nt COS(-^ + 2/A7rf + 2f07Tt) cos(- ^ 2/a^ 2f07rt) n-&fAnt n + 8/A7rf 4/a 4/a (B-l 2) W/,(0 = J_ cos(2ntf0 -2ntfJ nt 1 *(l-64/AV) sin(2/A7rf + 2/07rf) n~&f&nt | n + 8fA7vt 4/a 4/a (B-13) 97 Fig. 4-23. The Power spectral density of the SRRC filter where 1TS time span with the roll-off factor of 0.35 is used. Fig. 4-24. The impulse response of the SRRC filter where 7TS time span with the roll-off factor of 0.35 is used. 47 BER Performance obtained by Computer Simulation We will examine BER performance curves for values of normalized Doppler frequency fDTs using computer simulation. The Effect of Roll-off Factor, r It is seen that there is different intersymbol interference (ISI) with different roll off factors due to the change of shape of the Hilbert transform of the raised cosine(H-RC) pulse as shown in Fig. 2-8. As the roll-off goes to 1, ISI decreases and as the roll-off goes to zero, ISI increases. Hence, the BER performance is a function of the roll-off factor. However, there is only a slight difference in the BER performance with the different roll off factors as shown in Fig. 3-3 through Fig. 3-6. Using a roll-off factor greater than zero gives an increase over the bandwidth obtained for the r = 0 case. Hence, for the trade off between low BER and excess bandwidth, choose a roll-off factor of r = 0.115. This gives a small bandwidth increase of 11.5%. The Effect of Time Span Pulse shaping filters have to be truncated. If we have the longer time span, the bandwidth decreases but there is more ISI in adjacent symbol. Fig. 3-7 through Fig. 3-10 shows that 1271 time span is considered to be optimum. If time span is less than 127^, there is an ISI decrease in adjacent symbols but the original RC and H-RC will be distorted more due to truncation and Gaussian windowing. If time span is more than 127^, there is an ISI increase in adjacent symbol but the original RC and H-RC will be 67 Table 4-9. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 127^, frame length ,/V = 20 and roll-off factor r = 0.5 DSSB QPSK OQPSK Peak Power 2.3185 2.17415 2.00 Minumum Power 0.325 0 0.3185 Dynamic Range (dB) 8.53 00 7.97 Table 4-10. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 127^, frame length N= 20 and roll-off factor r= 1 DSSB QPSK OQPSK Peak Power 2.995 2.29 1.62 Minumum Power 0.2758 0 0.51995 Dynamic Range (dB) 10.35 00 4.93 Table 4-11. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 187j, frame length N = 20 and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 2.56 5.66 4.365 Minumum Power 0.0344 0 0 Dynamic Range (dB) 18.71 00 00 33 f pilot symbol extraction NT (2-45) Hence, the normalized fading rates of foTs for TV > 2 may be theoretically estimated by foTs < 0.25 (2-46) At the receiver, the channel samples c (kN) are interpolated to give estimates of the fading for the data symbols. An interpolation schemes may be generally represented by c(kN+m) = Qrim/N) c[(Â£+r)A], 1 < m < N-l (2-47) r=oo where Qr (m/N) are the interpolation coefficients. Alternatively, the interpolation may be represented by using the impulse response h(m) of the interpolator c (kN + m) c (kN + j) h(m-j), 1 < m < N-l (2-48) J=-CO The realtionship between the impulse response and the interpolation coefficients obtained from (2-47) and (2-48) Qr (m/N) = h(m rN) (2-49) The resulting estimates may be expressed as, c (kN + m) = c (kN + m) + e(kN + m) + n(kN + m) (2-50) 62 C/7(dB) Fig. 3-22. BER for DSSB-PSAM in case of Adjacent Channel Interference (ACI) where Eb/N0 = 60 (dB), r = 0.115, time span = 12TS,N= 20, AfTs = 0.675 and 1st Gaussian interpolation. 87 Spectral Occupancy The proposed DSSB requires windowing to reduce ISI and peak power. This causes the increase of spectral occupancy of DSSB. The PSD of DSSB with Gaussian windowing is shown in Fig. 4-15. Table 4-38 shows the increase percentage of spectral occupancy of DSSB with Gaussian windowing. The definition of Bounded spectrum bandwidth, say 50dB, below the maximum value of the PSD [Cou97] is applied. As shown in Fig. 4-15, the PSD of the proposed DSSB looks like that of vestigial side band (VSB) shown in Fig. 4-16. VSB has been chosen for the High Definition Television (HDTV) standard, since it had better performance than QAM for terrestrial HDTV broadcasting [GRA94], When the baseband signal contains significant components at extremely low frequencies, the use of SSB modulation is inappropriate for the transmission of such baseband signals due to the difficulty of obtaining the very sharp cut-off filtering needed. That is the reason why SSB can not be used with analog TV. But the proposed DSSB does not need the very sharp cut-off filtering. The gradual sloped filtering, such as raised cosine filtering, can be used for the proposed DSSB. Table 4-38. The percentage of PSD increase of DSSB for Gaussian window with different time span factor Time Span 6TS 127; 187; Percentage of PSD Increase 38% 28% 18% 5 / (a) Depressed carrier SSB (b) Tone in band SSB (c) Tone above band SSB Fig. 1-1. Three different type pilot tone SSB signal [McG81], 7 in fading channels [Cav91a]. Hence, we can conclude that pilot tone assisted modulation (PTAM) such as TTIB requires complicated signal processing such as frequency shift, band split filtering and using a PLL. The PTAM technique also increases in both peak and the average powers, for data transmission addition of the tone shifts the center of the constellation away from the origin [Cav92], SSB with Pilot Symbol Assisted Modulation (PSAM) For SSB data transmission, here I propose to use pilot symbol assisted modulation (PSAM) as an alternative. With PSAM, the transmitter modulator periodically inserts known symbols into the data stream to provide the required reference. PSAM provides the reference in the time domain, while TTIB or pilot tone assisted modulation (PTAM) provides a frequency domain reference for the receiver. Like PTAM, PSAM suppresses the error floor. It does so with no change to the transmitted pulse shape or peak to average power ratio (PAPR). However, the information data rate is somewhat lower for a given transmitted bandwidth. Processing at the transmitter and receiver is also simpler than with PTAM. Using PSAM with quadrature amplitude modulation (QAM) already has been proposed for mobile communications [Moh89]- [Cav91b] and a comparison of PTAM and PSAM for QAM has been presented [Cav92], Here, we will develop a digital single sideband algorithm using PSAM and analyze the performance of this system. Some key topics and the motivation for their development are as follows: (i) Digital single sideband (DSSB) 66 Table 4-6. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 1271, frame length N = 20 and roll-off factor r = 0 DSSB QPSK OQPSK Peak Power 2.04 10.98 8.87 Minumum Power 0.12265 0 0 Dynamic Range (dB) 12.21 00 oo Table 4-7. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 1271, frame length 77= 20 and roll-off factor r = 0.115 DSSB QPSK OQPSK Peak Power 2.10 4.475 3.535 Minumum Power 0.17 0 0.007 Dynamic Range (dB) 10.91 00 27 Table 4-8. The Dynamic range for DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM where time span = 1271, frame length N = 20 and roll-off factor r = 0.35 DSSB QPSK OQPSK Peak Power 2.24 2.51 2.315 Minumum Power 0.29 0 0.19 Dynamic Range (dB) 8.87 OO 10.85 28 sr(t) = Re [c(()zI{)exp(J2 7vfct) + nc(t)] (2-29) The subsequent lowpass filter is a square root raised cosine filter. This, in cascade with the transmit filter, assures ISI free transmission and optimum BER performance in AWGN channel. The demodulated and lowpass filtered complex signal is given by, x(t) = \c(i)zR(i) + n{t)\exp(j2nf0fft) (2-30) Here, zR(t) is the signal component of the received complex baseband signal which can be expressed by zR(t) = zi(t) m(t) (2-31) where m(t) is a SRRC filter. The noise term n(t) is SRRC lowpass filtered AWGN with power spectral density No in both real and imaginary baseband components corresponding to a bandpass PSD of No/2. The distortion caused by the fading channel is represented by the complex channel gain c(t) given by (2-24). We assume that the receiver lowpass filters pass this foff component undistorted, since the bandwidth of the fading process is significantly larger than the symbol rate. The minimum sampling rate, that is Nyquist frequency, for symbol extraction is given by f symbol extraction ^ 2{fD + foff), where/symboi extraction 1 /NTS. (2-32) Hence, the receiver works if 2(/0 + f0jf) D/N. (2-33) where D 1/TS 89 Comparison of BER Performance for QPSK-PSAM and DSSB-PSAM The bit error probability of coherent QPSK [Cou97] and coherent DSSB in AWGN are given by Pe, QPSK in AWGN Pe, DSSB in AWGN ~ Q( (4-8) It can be also shown that the average error probability of coherent QPSK [Rap96] and coherent DSSB in a slow, flat, Rayleigh fading channel are given by Pe, QPSK in fading Pe, DSSB in fading [ 1 " (4-9) 17 where /o~( )E[o? ] (4-10) N0 Fig. 4-17 shows the BER performance obtained by computer simulation in AWGN channel. Fig. 4-18 shows the BER performance obtained by computer simulation in Rayleigh fading channel, when frame length N=20, the order of Gaussian interpolation is 1, the normalized Doppler frequency foTs = 0.001, the time span is 127*, the transmitter and the receiver filters are SRRC filters with roll-off factor r = 0.115. The performance of the proposed DSSB is almost same result with the QPSK as shown in Fig. 4-17 and Fig. 4-18. The difference (0.3 dB) comes from the power loss by inserting different pilot symbols. QPSK needs only one pilot symbol in one frame but DSSB needs three pilot symbols in one frame. From (4-8) we can see that both QPSK and DSSB have the same power efficiency. Power efficiency is defined as the ratio of the signal energy per bit to 114 + sin(2^/,) 7t exp Q'Qr + 8 fAnt)B exp (jpr + 8 fATtt)fx J_ exp( -jjtfJ 4/a 4 /A 2 4/a j{7T + 8fA7Tt) 4/a exp(-,/P -&fA7tt)B exp(-/Qr 8/A^)/, 1 exp CM) f 4/, 4A 2 4/a j(7C-%fAKt) 4/a (A-7) (0 = 1 exp(-y'2^;0 1 exp(;(-p1 ;c8 + %fA7itB) 2 4A y(~^ + 8/A^f) 4/a lexP(-;2^,r) -1 ~ ~ 8/>*> 2 FV 7 ^ 2 4/a 4/a sm(2rtfx) Ttt 102 Fig. 4-33. Bandwidth increase(%) where different roll-off factors with different time span is used (r = 0.1 with 127^, r = 0.35 with 7TS ,r = 0.5 with 57^, r = 0.75 with 47^ r = 1 with 37^). Fig. 4-34. Peak to average power ratio (dB) where different roll-off factors with different time span is used (r = 0.1 with 127^, r = 0.35 with 7TS, r = 0.5 with 57^, r = 0.75 with +4Ts ,r= 1 with 37^). 100 Fig. 4-29. The Power spectral density of the SRRC filter where 3TS time span with the roll-off factor of 1 is used. Fig. 4-30. The impulse response of the SRRC filter where 37^ time span with the roll off factor of 1 is used. 20 Fig. 2-7. The effect of phase error on BER in AWGN where no pilot reference is used, EtfNo = 8dB and different roll-off factors are used. Table 2-1 and Table 2-2 shows the ISI values for different roll-off factors, r for the Hilbert transform of RC pulse, such as shown in Fig. 2-9. We can calculate the average ISI from Table 2-3 and Table 2-4 when the number of pilot symbol is used. Lets define the average ISI, IA, as the absolute value of the mean of the sum of the ISI that corresponding to the pilot symbol value of G-H-RC. Matlab is used to calculate the average ISI given in Table 2-1 through Table 2-2. For example, in the case of 675, Table 2-1 is used to calculate the average ISI for 213 possible bit patterns. The BER performance by pilot symbol phase error is shown in Fig. 2-11 through Fig. 2-12 and it is shown that there is a large (above 2dB) BER performance degradation when we use one pilot symbol. If we use three or five pilot symbols, the performance is almost same. If we 58 Dn(x) = 2x2Rmax [ Dn,(x) (n-2)RmaxD.2(x) /(-/) ] M (3-18) D,(x) = xRmax, D2(x) = X 3R2max (3-19) Rmax = max{ Rk}, Tjr = ?j /Rmax and urk = E[ Tjrk ] (3-20) H(x) represents the Hermite polynomial of order n. 1//2] /*) =/' Z ( -W /(' (/-M)0 (3-21) m= 0 where [A] = the largest integer contained in b Hn+I(x) = 2 xH(x) Hn.](x), n > 1, H0(x) = 1 (3-22) RAYLEIGH FADING ENVIRONMENT In the Rayleigh fading, the envelope of the desired signal has Rayleigh statistics. The PDF of the corresponding signal power x is [Pee93] px(x) = ~exp( -x/X) (3-23) where the mean signal power is X. Each cochannel interferer is subject to Rayleigh fading also and its power is exponentially distributed. Assuming that all interferers are independent and have the same mean power Y, the PDF of the total interference power y of M interferers is obtained using an /-fold convolution of independent and identical exponential PDF. This results is a Gamma PDF of the form [Yao92], 56 Fig. 3-17. Effect of Gaussian interpolation order on BER for DSSB-PSAM where r = 0.115, time span = 127^, foTs 0.00625 and N= 20. Fig. 3-18. Effect of Gaussian interpolation order on BER for DSSB-PSAM where r = 0.115, time span = 127*, fDTs = 0.01 and N = 20. 107 Fig. 4-39. Cost, C versus different roll-off factors, r where w3 = 0.4, wl = w2 = w4 = 0.2. Fig. 4-40. Cost, C versus different roll-off factors, r where w4 = 0.4, wl = w2 = w3 = 0.2. 73 a hG{t)= exp(-4t2) a (4-6) where is related to B, the 3-dB bandwidth of the baseband Gaussian shaping filter Vh2 V2B 0.5887 B (4-7) As a increases, the spectral occupancy of the Gaussian filter decreases and time dispersion of the applied signal increases. The impulse response of the baseband Gaussian filter for various of 3-dB bandwidth-symbol time product (BTS) is shown in Fig. 4-9. We can reduce ISI of mh(t) by using the Gaussian window compare to the other window which is shown in Fig. 4-10. Table 4-20 through 4-34 shows peak to average power ratios for DSSB-PSAM, QPSK- PSAM and OQPSK- PSAM where different roll-off factors are used. It is shown that DSSB-PSAM peak to average power ratios are from 2.85 to 4.38 dB lower than those for QPSK-PSAM when roll-off factor r = 0.115 and time span is from 67^ to 127^. For the case of r = 0.35 and time span is from 6TS to 127^, DSSB- PSAM peak to average power ratios are somewhat (0.19 1.66 dB) lower than those for QPSK- PSAM. Fig. 4-12 through Fig. 4-14 shows the comparison of peak to average power ratios for DSSB- PSAM, QPSK-PSAM and OQPSK-PSAM varying with roll-off factor r. For QPSK- PSAM and OQPSK-PSAM, the peak to average power ratios decreases as the roll off factor, r goes to 1. However, for DSSB-PSAM the peak to average power ratios increases as the roll-off factor, r goes to 1. As shown in Fig 4-11, the DSSB peak 19 mh(t) = m(i) *h(t) = l-64/V -cos(27rf0t -2nfAl) + 8fJsm(2nf0t + 2?rfJ) 2t^(1-64/aV) (2-17) where h(t) = (2-18) If we assume USSB is used to transmit the modulated signal 5,(t), this can also be represented as st(t) = Re[zj where zj{t) = A[m{t) + jmh{t)\ (2-20) is commonly referred to as the complex envelope of the transmitted signal or the complex transmitted baseband signal [Cou97], The Problem Using Only One Symbol as a Pilot Symbol The effect of phase error on BER performance where no pilot symbol is used is shown in Fig. 2-7. Without pilot reference, there is a significant bit error increase when the phase error is increased. Hence, pilot symbol must be added to provide the receiver with an explicit amplitude and phase reference for detection. The impulse response of the complete filter response is shown in Fig. 2-8. However, because of the ISI of the Hilbert transform of the raised cosine (RC) pulse which is shown in Fig. 2-9, there is an amplitude and phase ambiguity for the case of using only one symbol as a pilot symbol as shown in Fig. 2-10. To greatly reduce this ISI, we add more adjacent symbols as pilot symbols. BER Performance obtained by Computer Simulation 47 The Effect of Roll-off Factor, r 47 The Effect of Time Span 47 The Effect of Frame Length, N. 52 The Effect of Gaussian Interpolation Order 54 The Effect of Co-Channel Interference (CCI) 57 The Effect of Adjacent Channel Interference (ACI) 61 4. COMPARISON OF DSSB-PSAM, QPSK-PSAM AND OQPSK-PSAM 63 Dynamic Range 63 Peak To Average Power Ratio 71 Spectral Occupancy 87 Comparison of BER Performance for QPSK-PSAM and DSSB-PSAM 89 The Choice of Roll-off Factor, r 92 5. CONCLUSION 108 APPENDIX A Ill Derivation of Square Root Raised Cosine Roll-off Pulse 111 APPENDIX B 120 Derivation of the Hilbert Transform of the Square Root Raised Cosine Roll-off Pulse.. 120 APPENDIX C 127 Description of Simulation Software 127 REFERENCE LIST 132 BIOGRAPHICAL SKETCH 137 vi CHAPTER 2 DSSB PSAM SYSTEM MODEL General Description The block diagram of the DSSB PSAM system studied here is shown in Fig. 2-1. Known pilot symbols are inserted periodically into the every frame of length N symbols as shown in Fig. 2-2. The reason why we use three pilot symbols instead of one pilot symbol will be explained in later. The transmit lowpass filter is assumed to be a square root raised cosine filter (SRRC) as shown later by (2-1). The modulated DSSB signal is transmitted in the usual way over a channel characterized by flat fading and additive white gaussian noise (AWGN). The demodulated signals are sampled at the symbol rate 1/TS and the frame rate 1/TF=1/NTS. It is assumed that this timing is regenerated perfectly. The samples at kTF correspond to the pilot values out of the receive lowpass filter. These pilot values are used to estimate the channel state. Compensation is carried out by the corresponding fade estimation. Configuration of the Transmitter Filtering for Zero ISI and for Low Pe We desire to determine the composite characteristic of the transmitter and receiver filter which results in a signal stream at the decision threshold that is free of intersymbol 10 99 Fig. 4-27. The Power spectral density of the SRRC filter where 4TS time span with the roll-off factor of 0.75 is used. Fig. 4-28. The impulse response of the SRRC filter where 47^ time span with the roll off factor of 0.75 is used. 131 Fig. C-4. Comparison of theoretical and simulated BER performance of DSSB-PSAM in Rayleigh fading (f'DTS = 0.001) channels where r = 0.115, \2TS time span, 1st Gaussian interpolation and N= 20. Fig. C-5. The BER performance of 16QAM-PSAM obtained from simulation program is compared with corresponding theoretical curves and reference paper. 2 between United States and the armed forces in various parts of the globe. In 1948 many hams pioneered the amateur usage of SSB. A long period of analytical and experimental investigation has proven the efficacy of SSB at HF frequencies. SSB has been adopted as the standard mode for point-to-point communications at HF frequencies. In 1956 Weaver discovered the third method of generation and detection of single sideband signals [Wea56], The three methods of SSB generation are the filter method, the phase shift method and the Weaver method. This will be discussd later in Chapter 3. Today the filter method is used almost exclusively in analog circuit implementations, while the phase shift and Weaver methods are used in digital circuit implementations. Since the September 1979 World Administrative Radio Conference (WARC), there has been considerable research in the use of the radio spectrum in an efficient way. Since that time, marine, aeronautical, amateur and military services used SSB at HF. At this point in time, the U.K. land mobile radio service used 12.5 kHz bandwidth AM and FM systems at VHF (30-300 MHz) and 25kHz FM at UHF (0.3 3 GHz). In the U.S., 25kHz and 30kHz FM were used at both VHF and UHF [Bat85], It is already reconized that the efficiency of channel usage is improved by the use of schemes such as dynamic channel allocation and cellular radio. The efficiency can also be improved with the selection of the appropriate modulation technique such as narrow band single side band. All of the above uesd analog modulating signals. In this dissertation we will develop techniques for digital data transmission via SSB. 45 where y = E[ y ] = (^)E[a>] (3-13) Since a is a Rayleigh distributed, cC has a chi-square probability distribution with 2 degrees of freedom. Consequently y also is chi-square distribution. The average error rate obtained as follows [Rap96] (pe)= Py)pe(y)dy = f exp( ) (-^) erfc(Jy ) dy Jo 7o Yo 2 1 ) (3-14) This result is used for the theoretical performance curves that is plotted in Fig. 3-2 where E[ ( ] = 1. 112 m{) = m{t) = m(t) = J -B eosQr(-/ f) 4/a exp{j2if) df+ exp(/2^/,) exp(-/2^/|) jlrt J C0S(^-/-) exp(j2jtf)df /l (A-3) l| exp(^(-/ f ) + exp(-M-/ /) + sin(27rt/j) 7lt exp CM/ /,) + exp (~M/ ~ /i) 4/a exp( j2jrtf ) df (A-4) 1 "f exPOH/ ~^i + OMO ^ +I "f exp(-j(~Â¥ MH) w- 2 i 4/a 7 2 4/a J n(27ttfx) 7tt expQ'Q/ -ft/j + 8/MQ + I f exP(~./W rf\ ~ 8/MO df 4/a 2 J 4/a (A-5) 91 Fig. 4-17. The Comparison of BER performance in AWGN channel for QPSK- PSAM and DSSB-PSAM where roll-off factor r = 0.115, time span = 127^, frame length N = 20 and 1st Gaussian interpolation. Eb/No(dB) Fig 4.18. The Comparison of BER performance in Rayleigh fading channel for QPSK- PSAM and DSSB-PSAM where roll off factor r = 0.115, time span = +127^, fdTs = 0.001, frame length N = 20 and 1st Gaussian interpolation. 61 The Effect of Adjacent Channel Interference (ACI) In the case of adjacent channel interefrence, only the tails of the adjacent channel signal enter the desired signal. The PSD of the desired signal which is centered at 21kHz and adjacent channel interferer is shown in Fig. 3-20. We locate the center of adjacent channel 0kHz and 54kHz so that the adjacent channel interference is -60 dB. Fig. 3-21 shows the BER performance for DSSB-PSAM in case of ACI. The channel spacing is 21kHz, the bit rate of DSSB-PSAM is 40 kbps, Eb/No = 60 dB, roll-off factor r = 0.115, time span = 127^, frame size N = 20 and 1st Gaussian interpolation is used. x 104 Fig. 3-21. The PSD of desired and adjacent channel signals where the desired signal is centered at 21kHz, the bit rate is 40kbps and r = 0.115. 106 Fig. 4-37. Cost, C versus different roll-off factors, r where wl = 0.4, w2 = w3 = w4 = 0.2. Fig. 4-38. Cost, C versus different roll-off factors, r where w2 = 0.4, wJ = w3 = w4 = 0.2. 134 Jak74 Lee89 Leo90 Luc68 Lus78 Mac90 Mai 8 9 Mar88 McG81 McG84 Moh89 Mor89 Mul91 Jakes, W.C. Jr., Microwave Mobile Communications, Wiley, New York, 1974. Lee, W. C., Mobile Communications Engineering, McGraw-Hill, New York, 1989. Leopold, R.J., Low-Earth Orbit Global Cellular Communications Network, Proceedings of the Mobile Satellite Communications Conf, Adelaide, Australia, August, 1990. Lucky, R.W., J. Salz and E.J. Weldon, Principles of Data Communication, McGraw-Hill, New York, pp. 54, 1968. Lusignan, B.B., Single-Sideband Transmissions for Land Mobile Radio, IEEE Spectrum, pp. 33-37, July, 1978. Macario, R.C.V., Personal and Mobile Radio Systems, Peter Peregrinus Ltd., London, UK, 1990. Maloberti, A., Radio Transmission Interface of the Digital Pan Europe Mobile System, IEEE Veh., Technology Conf, Orlando, FL, pp. 712- 717, May, 1989. Martin, P.M., The Implementation of a 16-QAM Mobile Data System using TTIB-based Fading Correction Techniques, Proc., IEEE Veh., Technol., Conf, Philadelphia, PA, pp. 71-76, 1988. McGeehan, J.P., Lymer, A., Problem of Speech Pulling and its Implemen tation for the Design of Phase-locked SSB radio systems, IEE Proc., Vol. 128, Pt. F, No. 6, November, 1981. McGeehan, J.P. and A.J. Bateman, Phase Locked Transparent Tone-in- Band(TTIB): A new Spectrum Configuration particularly suited to the Transmission of Data over SSB Mobile Radio Networks, IEEE Trans. Comm., Vol. com-32, pp. 81-87, Jan., 1984. Moher, M.L. and J.H. Lodge, TCMP- A Modulation and Coding Strategy for Rician Fading Channels, IEEEJ. Select. Areas Comm., Vol. 7, pp. 1347-1355, Dec., 1989. Moralee, D., CT-2 a New Generation of Cordless Phones, IEE Review, pp. 177- 180, May, 1989. Mulder, R.J., DECT A Universal Cordless Access System, Philips Telecommunications Review, Vol. 49, No.3, pp. 68 73, September, 1991. 95 width equal to the filter bandwidth. ICI is propotional to the amplitude of the median lobe in the stopband [Pre89], As mentioned before, ISI increase greatly for the small roll-off factors such as below 0.1 when we use small time span. If we want to use a small roll-off factor to decrease the maximum of ISI, we have to increase time span. Using frequency sampling method for FIR filter design, we found 127; time span with the roll-off factor of 0.1 has the maximum of ISI is 0.048 and the the minimum of ICI is -50 dB. Hence for the optimal filter design, we set up the maximum of ISI is 0.05 and the minimum of ICI is less than -50 dB. Hence, to setup the cost function, we choose 127; time span for the roll-off factor of r = 0.1, 1TS time span for the roll-off factor of r = 0.35, 57; time span for the roll-off factor of r = 0.5, 47; time span for the roll-off factor of r = 0.75 and 3 Ts time span for the roll-off factor of r = 1. The impulse response and PSD for these time span and roll-off factors is shown in Fig. 4-20 through Fig. 4-30. Fig. 4-31 shows the BER performance where different ISI is used. The result shows that there is BER performance degradation greater than 3 dB when we use the maximum of ISI above 0.5. Then, the filter length Nf is given by 2NSEP, where Ns is the number of samples for symbol period and Ep is the number of time span. Based on three different roll-off factors with different time span, Fig. 4-32 shows the BER performance. Bandwidth increase (%) and peak to average power ratio (dB) is shown in Fig. 4-33 through Fig 4-34. We use =10 and the filter length Nf is given by 240 for 127;, 140 for 77;, 100 for 57;, 80 for 47; and 60 for 37; which is shown in Fig. 4-35. 18 Fig. 2-6. The square root raised cosine pulse with Gaussian window (G-SRRC) and the Hilbert transform of the square root raised cosine pulse with Gaussian window (G-H-SRRC) with roll-off factor r = 0.35. st(t) = Am{t)cos{27rfct) Amh(\)n(27rfci) (2-15) where A is the amplitude of input data d(t) that corresponds to binary digit 1 (or A for 0), the (+) sign used for lower single sideband (LSSB), (-) sign is used for upper single sideband (USSB), m(t) is the normalized SRRC pulses and mh(t) denotes the Hilbert transform of m{t) (see Appendices A and B). sin(27rf0t 2nfj) + 8 fj cos(2rf0t + 2nfAt) 2nf0t(\-64f,2t2) (2-16) 109 good agreement with the theoretical approximation result. The comparison of DSSB-PSAM, QPSK-PSAM and OQPSK-PSAM can be summarized as follows. 1) Dynamic Range The QPSK dynamic range is infinite and the dynamic range of OQPSK-PSAM is 22.7 dB whereas the dynamic range of DSSB-PSAM is 5.38 dB for a roll-off factor of r = 0.115 and 6TS time span. For a roll-off factor of r = 0.115 and 12Ts time span, we also show that the dynamic range is for DSSB is 10.91 dB, whereas the OQPSK dynamic range is 27 dB and the QPSK dynamic range is infinite. With DSSB-PSAM, therefore, we can take advantage of the much reduced dynamic range and adopt high efficiency Class C amplifiers which has small dynamic range. 2) Peak to Average Power Ratio DSSB is shown to have peak to average power ratios (PAPR) that are from 3.2 to 4.38 dB lower than those for OQPSK and QPSK for a roll-off factor of r = 0.115 and 6Ts time span. DSSB is also shown to have PAPR that are from 1.83 to 2.85 dB lower than those for OQPSK and QPSK for a roll-off factor of r = 0.115 and 127^ time span. For QPSK-PSAM and OQPSK-PSAM, the peak to average power ratios decreases as the roll-off factor, r goes to 1. However, for DSSB-PSAM the peak to average power ratios increases as the roll-off factor, r goes to 1. Hence, there is much improved the power amplifier efficiency for the DSSB when we use small roll-off factor. 9 efficiency amplifiers even though they have poor linearity. (v) No need for sharp cut-off filtering Because of the truncation of the Hilbert transform of the square root raised cosine pulse, the PSD of the proposed DSSB looks like that of vestigial sideband (VSB) as shown in Chap 5. VSB has been chosen for the high definition television (HDTV) standard since it had better performance than QAM for terrestrial HDTV broadcasting [GRA94], When the baseband signal contains significant components at extremely low frequencies, the use of analog SSB modulation is inappropriate for the transmission of such baseband signals due to the difficulty of obtaining the very sharp cut-off filtering needed. That is the reason why SSB can not be used with analog TV. But the proposed DSSB does not need the very sharp cut-off filtering. The gradual sloped filtering, such as raised cosine filtering, can be used for the proposed DSSB. 29 Sampling and Pilot Symbol Extraction The demodulated complex baseband signals x(t) are sampled for data at the symbol rate 1/Ts, and for the pilot reference at the frame rate 1/TF = 1/NTs. It is assumed that this timing is recovered perfectly. The samples at kTF give the received complex symbols corresponding to the pilot symbols. Samples at (k + m/N)TF, m = 1,2, ...(N-l) give the yet uncompensated received data symbols. Fading Estimation and Compensation Normally, the pilot symbol would be randomized to avoid transmission of a tone, and the receiver would make appropriate corrections based on its knowledge of the transmitted pilot values. However, in the following analysis of fade compensation, it is assumed for simplicity that a constant pilot sequence have value d' = A and data symbols are d(k) = A. The distortion due to fading for Ath pilot symbol is calculated as follows. For t = kTF (corresponding to the received pilot symbols) (2-34) x(k) = [.Ac(k) + n(k)\exp(j2jrf0j]kTF) Where x(A) and n(k) are the complex sample values of x(t) and n(t) at t = kTF. The fading estimation c (k) of c(t) at t = kTF is found by dividing x(k) by the corresponding transmitted pilot symbol. Hence, c (k) = [c(k) + n(k)/A]exp(j27rf0flkTF) (2-35) The fading at the other points (k + m/N)TF can be obtained by interpolating the estimates REFERENCE LIST Aka87 Ant86 Bat85 Bat90 Bel92 Ben65 Bou81 Cal88 Cav89 Cav91a Akaiwa, Y. and Nagata, Y., Highly Efficient Digital Mobile Communications with Linear Modulation Method, IEEE Journal on Selected Areas in Communications, Vol. SAC-5, No.5, pp. 890-895, June, 1987. Antognetti, P., Power Integrated Circuits : Physics, Design and Applications, McGraw-Hill, New York, 1986. Bateman, A.J., Lightfoot, G., Lymer, A., and McG. J.P., Speech and Data Communication over 942 Mhz TAB and TTIB Single Sideband Mobile Radio Systems Incorporating Feed Forward Signal Regeneration, IEEE Trans., Veh., Technol., Vol. VT-34, pp 13-21, Feb., 1985. Bateman, A. J., Feedforward Transparent Tone-In-Band: Its Imple mentations and Applications, IEEE Trans., Veh., Technol., Vol. 39, No. 3, pp. 235-243, August, 1990. Bell, T.E., Technology 1992 : Telecommunications Intelligent Networks, IEEE Spectrum, Vol. 29, No.l, pp. 36-38, January, 1992. Bennett, W. and J. Davey, Data Transmission, McGraw-Hill, New York, 1965. Boutin, N.,and S. Morissette, Useful Signaling Waveforms and Related Transmit Filter Function in Bandwidth Limited Channels, Correspondence IEEE Tran, on Comm., Vol. Com-29, No.2, pp. 177-180, Feb., 1981. Calhoun, G., Digital Cellular Radio, Artech House, Inc., Norwood, MA, 1988. Cavers, J. K., Phase Locked Transparent Tone in Band, IEEE Veh., Technology, Conf., San Francisco, CA, pp. 73-76, 1989. Cavers, J.K., The Performance of Phase Locked Transparent Tone-in -Band with Symmetric Phase Detection, IEEE Trans., Comm., Vol. 39, pp.1389-1399, Sept., 1991. 132 BER 46 Fig. 3-1. BER Performance under nonfading (AWGN) environments where r 0.35, time span = 127^, N= 20 and 1st Gaussian interpolation. Fig. 3-2. BER Performance under Rayleigh fading environments where E[ a2] = 1. 55 HvWo(dB) Fig. 3-15. Effect of Gaussian interpolation order on BER for DSSB-PSAM where r = 0.115, time span = 127^, fDTs = 0.001 and N= 20. Fig. 3-16. Effect of Gaussian interpolation order on BER for DSSB-PSAM where r = 0.115, time span = 127^, foTs = 0.0025 and N- 20. |