-.

_.-

SEQUENCE BASED RECEIVERS

FOR

BANI:lLIMITED NONLINEAR CHANNELS

by

'i1:\IAL KISHORE DUBEY. B.Sc. (Hans.). B.E.. ~l.E.

A Thesis

Submitted to the School of Graduate Studies

in Partial Fulfilment of the Requirements

for the Degree

Doctor of Philosophy

:"1c~1:.lste!"Cniversity

.June.1986

•

·..

~EQt:E:-;CE BASED RECEIVERS

: .... .

DOCTOR OF PHILOSOPHY (19861(Electrical Engineering) Hamilton, Ontario, Canada

:\lcMASTER C:-;IVERSITY

TITLE:

ACTHOR:

Sequence Based Receivers for Bandlimited ='onlinear Channels

vnlAL h.1SHORE DtiBEYB.Sc. tHons.) (t:niversity ofRajasthan, India)B.E. (Indian Institute of Science, Bangalorel~I.E. (Indian Institute ofScience, Bangalorel

.-St:PERVISOR, Professor D.P. Taylor

:-;t:~lBEROF PAGES, :w,145

,

ABSTRACT

This thesis examines receh'er stI'Uctures based on ma:umum likelihood sequence

estimation C\ILSEl for receiving quaternary phase-shift-keyed (QPSKl signals over

bandlimited. non· linear satellite channels. in the presence of additive down link gaussian

noise. Two satellite channel models are considered. In the first channel model. the effects of

intersymbol interference caused by filtenng followed by A_\l/A~l and A_\lIP~l.conversions are

taken into account while the second channel model includes a post-nonlinearity filter.

An e:<plicit e:<~ion for t.he output of the bandpass nonlinearity (BP);"U for a

QPSK signal is obtained .in terms of an ;nphase (1)-quadrature (Q) path mem?ry parameter

Pk. The computation of the output of the BP);"L requires a knowledge of its transfer-_/

characteristic. The transfer characteristics may be specified either analytically or through

experimental measurements.

An optimum MLSE ~eceiver structure for bandlimited. non-linear satellite channel

is derived and its performance e\'aluated usin.g computer simulation. Simulatirog the ~ILSE

receiver in optimum form is too time consumL"1g. so we estimated the I-Q 'Path history

parameter Pk'S by using a simple procedure analogous to decision feedback processing.

Although this method is not thecretically equivalent to an optimum computation. our results

show that it performs essentially as well as an optimum computation. For :noderate to high

S);"R. an upperbound on.the prob~bilityof symbol error is obtained. using the concept of error

events. A si::lplified expression for an upperbounci on probability of symbol error, for the case

when single-error error. e\'ents are dominant. is also obtained. A sub-opti~um reee:\'er

structure is then derived using average matched filter responses. The sub-opti~u:::1 receiver

which turns out to be a complex' filter followed by a decision device. is a relatively sim?le

'.

(..

structure.. The performllnce of the suh-optimum receiver wns estimated for two different

uplink filters. The effect of var~..ing the BPKL input drive level was also studied. Our

simulation results indicate that the performllnce of both the :'1LSE and the sub,optimum

receivers approach nsymptotically the same optimum performance band.

Finally, we extend our results .on an optimum receiver structure for receiving

QPSK signals over a digital satellite communications channel. to include the effec~s of

filtering' following the non,line,,, satellite transponder. It is 'shown that the complexity of the

:'ILSE receiver is primarily determined by the uplink chllnnel mem"ory The error perfor­...mance of the reeeivcr at low sign111~to·noise ratios is evaluated by computer simulation. An

upperbound on the probability of symbol error at modera;.e to high S:\R is also obtained. .\'.

sub-optimu;" re<:eiver similar to the uplink channel filtering case is developed and its

performance evaluated using computer simulation. The deg-radation in performance of the

sub--uptimum receiver compared to the optimum :-eceiver is found to be small.

/

--,

I

ACKNOWLEDGEME~~S

>

I would like to e:q>ress my sincere gratitude to my supervisor. Pro(essor D.P. Taylor

for his llSsistnnc~and guidance during the course of my studies and preparation of this thesis.

I would also like to thank Professors C.R. C~ter and W.F.S. Poehlman for'serving

on the Supervisor:; Committee. Thanks are alSQ due to the E:ngirreering Word Processing

Centre for their excellent work in typing this thesis.

-l am also grateful to the Canadian Commonwealth Scholarship and Fellowship

Administration for. the support provided during the course of this research.

Last but not least. I would like to e:q>ress my·deepest thanks and appreciation to

my.wife Archana. for the innumerable sacrifices she made during the course of this

investigation. and to my son, Abhinav and my daughter. Richa. for the sacrifices they made~

unk:,owingly.

v

DEDICATED

TO

MY PAREl'iTS

VI

\

.-

-

,

2.7 Conclusions

ABSTRACT

ACKl"OWLEDGEMEKTS

LIST OF ILLUSTRATIOKS

-Page

iii

v

x

1

2

5

779

1113

15

17

17

19

20

~-_I

29

3030323~

~1

-I ,/

TABLE OF CONTENTS

"-The 1-laximum Likelihood Sequence Recei'·er (~ILSR)2.6.1 The Complex Envelope of Received Signal2.6.2 Finite State ~1achine ~Iodel (FS~I)

2.6.3 The ~u.sRStructure

Determination ofF(Z)

The BP:"L Output for Channel ~Iemoryv = 3

•Introduction

MAXI~IUM LIKELIHOOD SEQUE:"CE RECEIVER FOR:"ON-LINEAR BANDLI~lITEDQPSK CHANNELS

The System Model,The BP:"L Output

Digital Modulation Techniques

INTRODUCTION

Scope of the Thesis

BriefReview ofMultiple Access Techniques forSatellite Communication Systems

Sources oflmpairments in Digital Satellite Communication Systems1.3.1 The Satellite Channel1.3.2 Transmitting Earth Station1.3.3 Satelli_te Repeater1.3.4 ReceiVing Earth Station

1A

1.1

1.3

2.1

2.2

2.3

2.4.. .

~ 2.5,

2.6

CHAPTER 2

CHAPTER 1

V11-

•

-----

,

, ,\./ .

TABLE OF CONTENTS

4.5 Conclusions,

Page

42

42

..,~-

46

50

51

55

56

56

5656589191

Q-..104104 ..~104104

107

109

109

109

112

119

F'

RECEI\'ERS FOR THE :SO:S·U:SEAR CHA:S:SEL I:SCLL'DI:SCPRE· A:SO POST·:SO:SLI)."EARITY FILTERI)."C

l:1troouctio:1.

St"'.l~ure :\laximum Likelihood Receiver

The System :\Iociel

Introduction

Sub-<Jptir.1Um Receiver Structures

snlt:LATIO:S OF :\lLSR A); 0 OEVELOP:\1E:ST OFSt:B-OPTI:\1U:\l RECEIVER

Receiver Performance4.2.1 The Satellite Channel :\IOOel Assumed for Simulation4.~.2 :'wtemory Requirements4.2.3 The Computations of Branch ~lctric

4.2,4 Simulation Resul~-- .

5.3

SA

5.1

4.4 Sub-optimu:n Receiver: Simulation":'04.1 Example 14.4.2 Example ~

4.4.3 Sensitivity to T\VTA input back oiT

.".~.~

, .,~.-

4,.1

CHAPTER 4

CHAPTER 3 MLSR ERROR PERFOR.\lA:SCE

3.1 Introduction

.;. 3.2 Error Events

3.3 Probability ofan Error Event

3.4 Probability ofSymbol Error

3.5 Single Error Events

3.6 Conclusions ,

----

- .

TABLE OF CONTENTS -. ..Page

CHAPTER 5 (continued)

5.5 Receiver Performance.'

5.6 Simplified Receiver

5.7 Conclusions••

CHAPTER 6 COKCLL"SIO~S ~'m SL"GGESTIO~S FOR FL"TL"RE WORK

• 6.1 Conclusions'-~

6.2 Suggestions for Future Work

APPE"DIX A DERIVATIOK OF EQL"ATIO:- (3.9)

APPE"DIX B PROCEDL"RES FOR OBTAl~IKGTHE COMPLEX FILTERRESPOKSES OF THE StiB-OPTnlt:-:-'l RECEIVERS,DEVELOPED r" CHAPTERS 2 ......:..0 5

REFERE~CES 142

,.

,

•

•

r/

(

LIIWl' OF ILLUSTRATIONS

Fig. 1.1 Comparison ofdigital modulation systems based onaverage power [41.

Fig. 1.2 Typical satellite communications system.

Fi&. 1.3 Basic stages ofa earth station.

Fig. 104 Transfer characteristics of Hughes 261-H TWT.

Fig. 1.5 .. The satellite channel model..

Fig. 2.1 Coherent demodu~tion.

,Computation of minimum branch metric for optimum :'lLSEreceiver. \' ::: 3.

Structure of the :'lLSE for a channel memorv of... = 3.") .Fig. 2.3

Fig. 2.2

Fig. 3.1 Correct path and incorrect path chosen by VA.

Fig. 3.2 An error evellt at time k1..

Fig.·U The pulse response ofa fourth-order Chebyshev filter [39J .. for2BT = 1.

Fig.4.2(a) The generic waveform FHa) for TWTA input back-off of a dB.

Fig.4.2(bl--- The generic waveform FH1) forT\VTA input back-offof a dB.

Fig.4.2(c) The generic waveform FH2) for T\VTA input back-offof a dB.

Fig.4.2(d) The generic waveform FH3) for TWTA input back-offof a dB.

Fig.4.2(e) The generic waveform FH4) for TWTA input back-offof a dB.

Fig. 4.2(:) The generic waveforr:! FH5) for TWTA input back-offof a dB.

Fig.4.2lg)

Fig. 4.2(h)

The generic. waveform n(6) for TWTA input back-offof a dB.

The generic wave~ormFH7) for T\\iTA i..,put back-offof a dB.

Fig.4.2(i) The genenc waveforr:! FHS) for TWTA input back-o::cfO dB.

LIST OF ILLUSTRATIONS (continued) ...../

Page

Fig. 4-.2(j)

Fig.4.2(k1

. Fig. 4.2(1)

Fig.4.2(m)

Fig.4.2(n)

Fig. 4.2(0)

Fig.4.2(p)

Fig. 4.3(a1

Fig.4.3<bl

Fig. 7.3(c)

Fig.4.3(d1

Fig.4.3(e)

Fig.4.3(f)

Fig.4.3(gl

Fig.4.3(h1

Fig. ~.3(i)

Fig. 4.3(j)

Fig. 4.3(k)

Fig. 4.3(1)

Fig. ·i.3{m)

Fig.4.3(nl

Fig. -*.3(0)

Fig.4.3(p)

The generic waveform Fl(9) for TWTA input back-offof 0 dB.

The generic waveform FIOO) for TWTA input back-offof 0 dB.

The generic waveform Fl(ll) forTWTA input back-offofO dB.

The generic waveform Fl(12) forTWTA input back-offofO dB.

~he generic waveform Fl(13) for TWTA input back-offofO dB.

The generic waveform Fl(14) for TWTA input b'ack-offofO dB.

The generic waveform FlOS) for TWTA input back-offof0 dB.

The generic waveform F3lCO) forTWTA input back-offof0 dB.

The generic waveform F3H11 forT'.VTA input back-offof 0 dB.

The generic waveform F3H21 for TWTA input back-offof 0 dB.

The generic waveform F3l(3) for T\\TTA input back-offof 0 dB.

The generic waveform F3H4) for TWTA input back-offof 0 dB.

The generic waveform F3l(S) for TVv"TA input back-offof 0 dB.

The generic waveform F31(6) for T\\TTA input back-off of 0 dB.

The generic wavejorm F3l(71 for TWTA input back-off of 0 dB.

The~nericwa\'eform F31l81 for TWTA input back-offof 0 dB.

The generic waveform F3H91 for T\\TTA input back-offof 0 dB.

The generic waveform F3l0Q) for T\\TTA input back-offofO dB.

The generic waveform F31(11) forT\'i'TA input back-offof 0 dB.

The generic waveform F31l 12) for T\VTA input back-oITof 0 dB.

The generic waveform F31l131 for TWTA inpu:; back-oITofO dB.;

The generic waveform F31l 14) for T\\T'TA innut back-oITof 0 dB...

The generic w::lVeform F3l11S1 for TWTA input back-offof 0 dB.

68

69"

70

71

73

74

7S

76

77

78

79

80

81

82

83

85

86

87

88

89

90

--LIST OF ILLUSTRATIONS (continued)

Fig. 4.4

Fig. 4.5

Fig. 4.6

'.

Fig. 4.7

Fig. 4.8

Fig. 4.9

Fig. 4.10

Fig. 4.11

Fig.4.12

Fig. 4.13

The ma:amum likelihood sequence receiver as simulatedfor channel memory ofv = 3.

Performance comparison ofMLSE and sub-optimum receiverfor a fourth-order Chebyshev filter with 2BT = 1.

The average generic waveform F1{(t).A} for 3 dBinput back-ofToftheTWTA.

The average generic waveform F1{(t),A} for 6 dB inputback-ofTof the T\VTA.

The average generic waveform F1{(t),A} for input bac~-ofTofOdB.

Sub-optimum receiver. defined by eqn. (4.4)

Baseband realization of the sub-optimum receiverstructure as defmed by eqn. (4.6), .

Frequency response of baseband "average" matched filterg~IFR{(t),A}.

Frequency response of baseband "average" matched filterg~IFR{(t), A}.

Performance of the sub-optimum receiver when the bandlimitingfilter consists of the cascade ofa 30% roll-ofT ;';yquistfilter and the fourth order Chebyshev filter.

Page

92~

9;

95

96

98

100 .101

10:.!

103 _

105

Fig.4.14· Performance of the sub-optimum receiver when the TWTAis operated at the input ~ack-offof6 dB.

Fig. 5.1 The satellite channel model including pre- and post­nonlinearity{lltering.

Fig. 5.2 Structure of the approximate :\lLSR as simulated for an uplinkchannel memory of v = 3, and downlink memory v' = 3.

Fig. 5.3 Estimation OfPk'S using simplified procedure.

Fig. 5.4 Per:ormance comparison of the :\lLSE and the simplifiedreceiver structure for the clown-link filtering channel.

Fig. 5.5 Sub-optimum recei"er, defined by eqn. 15.221.

106

110

ll8

121

123

--LIST OF ILLUSTRATIONS (continued),

Page

Fig. 5.6

Fig. 5.7

Fig. 5.8

Baseband realization of the sub-optimum receiver structuredefined by eqn. (5.23).

Frequency res\i1lnse of the imaginary component of the basebandaverage matched filter.

Frequency response of the real component ofthe basebandaverage matched filter.

:'<111

128

129

po

I.\

SYmbol

AM-AM

AM-PM

BW

BPNL

BPSK

CDMA

DS!

E(·)

EIRP

FD~I

FDMA

F(Z)

fq(ll {(t-kTl, p0

fq .,05.'3) ({t- kT), p0

f1ll, f13ll. f1321, f133>

FSM

G(v)

a(v)

-

.'

LIST OF PRINCIPAL SYMBOLS·

Representation

Amplitude modulation to amplitude modulation

Amplitude modulation to phase modulation

Bandwidth

Bandpass nonlinearity

Binary phase shift keying

. Code-division multiple acess'

Digital speech interpolation

Error function

Bit energ:.' to noise density ratio

EfTective isotropic radiated power

Frequency Modulation

Frequency division multiplex

Frequency division.multiple access

defined on page 21

interpulse product defined on page 24

defined on page 25

defined on page 26

•defined on page 28

Finite state machine

A~1JAM characteristic ofBP:-;L

A~I!PM characteristic of BP:-;L

XIV

LIST OF PRINCIPAL SYMBOLS (continued)

Svmbol

IF

MLSE

MSK

MLSR

Ns

n(t)

Pk

Q

QPSK

RF

OQPSK

SPADE

SNR.'TDMA

TWTA

UIC

VA

Representation

Hankel transform of order 1

Intersymbol Interference

Intermediate frequency

Bessel function oforder one

Metric in MLSE

Maximum likelihood sequence estimation·

Minimum shift. keying

Maximum likelihood sequence receiver

Number of possible states of FS1>l

Noise

I-Q phase history

Inphase component -

Quadrature Component

Quarternary phase-shift-keyed signals

Radio frequency

Offset QPSK

Single channel per carrier, pulse code modulation, multiple access,demand assignment equipment

Signal-to-noise ratio

Time division multiple aCCess

Travelling wave tube amplifier

lJp-converter

Viterbi Algorithm

xv

LIST OF PRINCIPAL SYMBOLS (continued)

Svmbol

v

HPA

FFSK

h(t)

T

·Yil,Yi2,Yi3.Yi4.

,\

E

c

II n

Re [ I

, ,I I

Bi

vI

Representation

Channel memory

High power amplifier

Fast frequency shift keying

trnit pulse response of the bandlimiting filter

State of the channel at t = KT

Defmed on page 36

. Data pulse durati<>n

defined on page 136

Error event

Length oferror event

Set of allowable state sequence segments

State transition

Likelihood ratio

Element of

Super set of

Subset of

,,"orm

Real part of

:Vlagnitude

Phase of the ith transmitted pulse

One-sided white spectral density

,'lnput back-offofTWTA

,Down-link cnannel memory

XVl

.~

•

CHAPTER 1

INTRODUCTION

~lodern satelliq, communications systems suffer from both power and bandwidth, . .limitations. Becaus~ of the power limitation, digital satellite cO(ll!nunication systems are

normally operated with a non-linear amplifier, usually a travelling wave tube amplifier

(TWTA), in the satellite transponder. In the non-linear region of qperation, a TWTA e"hibits

both a non-linear input amplitude to output amplitude (A.\1-AM conversion) charact~ristic

and a non-linl!ar input amplitude to output phase (A.\1-PM conversion) characteristic. In

addition, because of the limited availability of satellite bandwidth, the transmitted signals

must be tightly band-limited, and this introduces intersymbol interference (lSI). The lSI

combined with non-linear amplification causes significant degradation of system

performance.

In this thesis we are concerned with the problem of developing an optimum receiver

structure and"'estlmating its performance for quarternary phase-shift keyed (QPSK)

signalling over bandlimited, nonlinear satellite channels. In deriving the receiver, the

ma;timum likelihood sequence estimation (MLSE) approach will be used, so that the receiver

. is optimum in the sense of minimizing sequence error probability on the bandlimited non-

linear channel.

A satellite must share its capacity among a large number of earth terminals. This

sharing is achieved by some form of multiple-access technique. The multiple-access problem

is fundamental to satellite communications, because it is by this means that the wide,

geographic coverage capability of the satellite channel is e:<ploited. The satellite channel

model in this thesis assumes in particular Time Di"ision :I1ultiple Accessing (TD~1AL In

1

2

oreler for us to-bring out the point that current trends are toware! using TDMA, we briefly

---describe severnl \asic multiple access techniques.

1.1 A Brief Review of Multiple Access Techniques for Satellite

Communication Systems

Commer~ialCommunicationsby satellite began officially in April 1965, when the

world's fll"st Communication Satellite INTELSAT I (known as "Early Bird"), was launched...

The fully mature phase of satellite communications probably began with the installation of

the L.'ITELSAT IV into the global system starting in 1971. The INTELSAT system serves

most of the countries of the world and has satellites over the Atlantic, Pacific and Indian

Oceans.

Frequency-Division Multiple Access (FDMAl, is one widely used multiple access

techniqu·e. In FDMA, different carrier frequencies are used for each transmitting station.,

This allows use of the same transponder amplifier until finally the overall noise level limits

the capacity of the amplifier. The presence of multiple carriers in any non-linear amplifier

produce intermodulation products which raise the apparent noise level. To reduce

intermodulation noise, the TWT drive level should be "backed-off" to avoid non-linear

operation. The carrier received power level now is less and thus the effect of thei-mal noise

generated in the earth station receiver is increased. This reduction in input drive level must

thus be optimized. Even after optimization, the effect is not trivial and the reduction in

capability ofa transponder over what it would have ifall the available information was multi-

plexed on a single carrier frequency can be as much as 6 dB. :-;evertheless, FD~IA remains a

very popular technique for high capacity transmission commercial communication satellites.

It is efficient if one is not power limited, and it is the natural expansion of terrestrial

communications methods.

)3

FDMA can be implemented in two ways. One is to multiplex, in the conventional

terrestrial manner, many channels on each carrier that is~mittedthrough the satellite.

Another is to use a separate carrier frequency for each telephone'or baseband channel within

the satellite. If many carriers are used, the intermodulation problem is still more serious. On

the other hand, it does approach, .asymptotically a li~ting level that is usually acceptable.

This sin:;le-channel per-earner approach has particular advantages in systems where there

are many links to be made, each one having only a few circuits to be handled at anyone time.. .:-<"ormal multiplexing is very convenient terrestrially but may be economical only if each

carrier has traffic, for example, in a group ofl2 channels or more.

Both systems are in extensive use today. INTELSAT uses both systems, the

SPADE (Single Channel per tarrier, Pulse Code modulation, multiple Access, Demand

assignment Equipment) being a single channel per carrier modulation-access system.

Ca'nada, Indonesia and A!geria, to mention a few, countries who use single-channel-per-

carrier sy~tems.

Time-Division :>1ultiple Access (TDMAl is the next basic technique of multiple

access. Here each earth station is assigned a periodic time slot for its transmission, and all

the earth stations use the'same carrier frequency within a periodic particular transponder. In

terms of the total satellite performance, this is the superior method because the

intermodulation noise is eliminated and. there is an increase in capacity. The required

transponder back-off is much less, just that required to achieve acceptable spectrum

spreading. T'he price paid is an increase in complexity of the g;ound equipment.. It does seem. ..

as if the long term trend will be towarcl...~ more TD1-1A since it fits natUI:ally with the

digital communications systems tJ:at are rapidly proliferating terrestrially, not only for data

transmision but more and more fo~ digitlzed voice.

r