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Digital single sideband (DSSB) with pilot symbol assisted modulation (PSAM) in mobile radio

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Title:
Digital single sideband (DSSB) with pilot symbol assisted modulation (PSAM) in mobile radio
Creator:
Kim, Seungwon, 1964-
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Language:
English
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viii, 137 leaves : ill. ; 29 cm.

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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 )
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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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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 r(I f I-f)
{ 1 +cos[ 2(]}, f< If 2 2

0, 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 2N 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 + I Tb (3-5) Since = (3-6) Ed = 4 Tb


= 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 + I Tb
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 < s -(t) > = < | z(t) I > [ < m2(t) >+ ] (4-1 )
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




Full Text
65
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 I/I >B
(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 N
ho{n)= { Oo[~], 0 N
^ Q.,[ N 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)
£>(/) 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. General implimentation of TTEB [adapted from [Mcg84]].


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38
Fig. 2-19. 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)= ¡-(^f
N
1 r)] (2-37)
In case of first order and zeroth order interpolation, the coefficients Q¡ 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 f¡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 O" 2o"
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 7¡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 : m¡(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(r¥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]
= \gd(t)\2> (3-4)
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^)
£ 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 f,< 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/ 2 k=i
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.


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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, r¡ 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#/¡)
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 N 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 2W/o -/
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 [mh (Ok Ts < mh (t) <2 Ts
{ mid[m(Ok 2Ts ^ mid[/wA(0]n, UTs (4-4)
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 | + | Tb (3-5)
Since = (3-6)
Ed = 4 Tb
= 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 + | Tb
= 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[(£+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 (2-19)
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
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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.,
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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.