Table Of ContentMU LTi USE R DETECTlON
Mulliuser Detection provides tile first comprehensive treatment of the sub-
ject of multiuser digital communications- Muitiuser detection deals with
demodulation of the mutualiy interfering digital streams of information
that occur in areas such as wireiess COInmunications,high-speed data trans-
mission, satellite communication, digital mievision, and magnetic record-
ing.The development of multiuser detection techniques is one of the mosI
important recent advances in communications technology, and this self-
contained book gives a comprehensive coverage of the design and anaiysis
of receivers for multiaccess channels,while focusing on fundamental mod-
els and algorithms.
The author begins with a review of multiaccess communications-dealing
in paIticular with code-division multipie-access(CDMA) channels-Back-
ground material on hypothesis testing and the eHect of multiuser interfer-
ence on single-user receivers are discussed next. This is followed by the
design and analysis of optimum and linear mUtiliser detectors. Also COV-
ered in detail are topics such as decision-driven muitiuser deteCHon and
noncoherent multiuser detection.
The d ements of multiuser detection are clearly and systematically pre-
sented along with more advanced recent results,some ofwhich are published
here for the k st time.The extensive set of references and bibliographical
notes oHer a comprehensive account of the state of the art in the subject.
The only prerequisites assumed are undergraduate-k vei probabiiity,lin-
ear aigebra, and introductory digital communications. The book contains
over 30Oexercises and is a suitable textbook for electrical engineering stu-
dents.It is also an ideal self-study guide for practicing engineers,aswell as
a valuabie reference volume for researchers in communications and signal
processmg.
É ) ò'
Sergio Verdd is Professor of Electrical Engineering at Princeton University-
His contributions to the technology of multiuser detection span his pioneer-
ing work in themriy 1980s to recent results included in this text-Professor
verdd is also well known for his work on information theory, in which
he explores the fundamental limits of data transmission and compression
systems-Recipient of a number of awards, he is a Fenow of the IEEE and
sewed as President of the IEEE Information Theory Society in 1997.
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PUB LlS HED B Y TH E PRESS SYNDICATE OF TH E UN l VERS ITY OF CA M B RI DGE
The Pitt Building,Trumpington Street,Cambridge,CB2 1R P United kingdom
C A M B R I DG E U N I V E R S I T Y P R ES S
The Edinburgh Building.Cambridge CB22RU,UK http://www.CUIMam-ac.uk
4OWest 20111Street,New York,NY lÞ 1l 4 2l l,USA http://www.CLIP-org
lOStamford Road,Oakleigh,Melbourne 3166,Australia
@Sergio Verdt11998
This book is in copyright.Subject to statutory exception
and to the provisions of relevant collective licensing agreements.
no reproduction of any pan may take place without
the written permission of Cambridge University Press.
First published 1998
Printed in the United States of America
Typeset in Times Roman l03 14pt.and Futura inmbX2Å[TBl
A catalog recordjbr this book is availablep om
tlze British LibraFV
LibraÇ'qf Congress Catalogiptg-iF1¤publication Data
Verdfl,Sergi0,l958-
Multiuser detection / Sergio Verdt1.
P- cm.
Includes bibliographical references.
ISBN 0¤521¤59373¤5(hardbound) ¢a
l Code division multiple access- 2. Dem?dulation (Electronics)
3. Spread spectmmcommunications, I. Titù
TK510345.V47 l998 98.16453
6213845--dd l f IP
ISBN052l 593735hardback
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c o N¡ ENTS
List qf Figures
PrÕ ce
MtJLTlACCESS COMMUNlCANONS
L l The Multiaccess Channel
l .2 FDMA and TDMA 2
l .3 Random h4tiltiaccess 4
L4 CDhfA 4
l 5 Problems lO
2 CODE-DIVlSlON MULTiPLE-ACCESS CHANNEL l9
2.l Basic Synchronous CDMA Model 19
22 Basic Asynchronous CDMA Model 21
23 Signature Waveforms 26
231 Direct-Sequence Spread Spectmm 26
232 Spreading Factor 28
233 Signature Sequences 29
23.4 Long Sequences 30
235 Random Sequences 32
23.6 Other Spread-Spectrum Formats 35
2.4 Data Streams 37
2.5 Modulation 38
25.l Carrier Modulation 38
252 NOIlantipodal Modulation 40
2.6 Fading 42
2.6.l Frequency-Flat Fading 42
2.62 Frequency-Selective Fading 45
263 Homogeneous Fading 50
V l l
CONTEN TS
2.7 Antenna ArTays 5l
2.8 Background Noise 55
29 Discrete-Time Synchronous Models 56
2.9.l Matched Filter Outputs 56
2.92 Orthonormal Projections 60
2.lO Discrete-Time Asynchronous Models 62
2.l l Bibliographical Notes 64
2.l 2 Problems 66
3 SINGLE-USER MATCHED FllTER 85
3.l Hypothesis Testing 85
3.l l Optimal Decisions 85
31.2 Continuous-Time Signals in White
Gaussian Noise 88
313 Composite Hypothesis Testing 91
32 Optimal Receiver for the Single-User Channel 93
33 The Q-Function 97
3.4 The Matched Filter in the CDMA Channel 104
3.4.l Probability of Error for Synchronous
Users 105
3.42 Probability of Error for Asynchronous
Users 118
35 Asymptotic Multiuser Efaciency and Related
Measures 119
3.6 Coherent Single-User Matched Filter in Rayleigh
Fading l24
16.l Scalar Reception 125
3.62 Diversity Reception l28
3.7 Difrerentidly-Coherent Demodulation 130
3.8 NOIlcoherent Demodulation 133
3.9 Bibliographical Notes 137
3.lO Problems 139
0 PTlMUM MULTiUSER DETECTlON 154
4.l Optimum Detector for Synchronous Channels 154
41.l Two-User Synchronous Channel 155
41.2 K-User Channel l61
42 Optimum Detector for AsynchronousChannels 166
V l l l
~~
CONTENTS
43 Minimum Error Probability inthe Synchronous
Channel l76
43 .l Two-User Channel 176
43 2 K-User Synchronous Channel 186
4.4 K-User Optimum Asymptotic Emdency and
Near-Far Resistance l95
45 Minimum Error Probability in the Asynchronous
Chan nel 202
4.6 Performance Analysis in Rayleigh Fading 206
4.7 Optimum NOIlcoherent Multiuser Detection 209
4.8 Bibliographical Notes 2l0
4 9 Problems 213
5 DECORRELAn NG DETECTOR 234
51 The DecorTd ating Detector in the Synchronous
Channel 234
52 The Decorrelating Detector in the Asynchronous
Channel 243
5.3 Truncated-Window Decoryd ating Detector 246
5.4 Approximate Decorrelator 248
5.5 Performance Analysis:Synchronous Case 249
5.6 PeIformaflee Analysis: Asynchronous Case 256
5.7 Coherent Decorrelator in the Presence of Fading 258
5.7.l Frequency-Fiat Fading 259
57 2 Homogeneous Fading 260
5.73 Diversity Reception 261
5.8 Differentially-Coherent DecorTelation 263
5.9 Decorrelation for Nonlinear Modulation 265
5.10 Bibliographical Notes 269
5.l l Probierns 272
6 NONDECORRELATING LlNEAR MULTlUSER
DETECTlON 288
6.i Optimum Linear Multiuser Detection 288
62 Minimum Mean-Square EITor (MMSE) Linear
Multiuser DeÇction 29l
6.3 Performance of MMSE Linear Multiuser Detection 299
64 Adaptive MMSE Linear Multiuser Detection 306
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6.5 Canonical Representation of Linear Multiuser
Detectors 314
6.6 Blind MMSE Multiuser Detection 318
6.6.l Gradient Descent Algorithm 3i8
6.62 Signature Waveform Mismatch 321
6.7 Bibliographical Notes 325
6.8 Problems 329
7 DECISION-DRlVEN MULTiUSER DETECTORS 344
7.l Successive Cancellation 344
72 Performance Analysis of Successive Cancel!ati011 351
7.3 Multistage Detection 361
73 .l Conventional First Stage 361
73 2 DecorTd ating First Stage 363
7.4 Continuous-Time Tentative Decisions 369
75 Decision-Feedback Multiuser Detection 370
7.5.l Synchronous DecorTelating Decision-Feedback 371
7.52 Synchronous hfh4SE Decision-Feedback 377
75 3 Asynchronous Decision-Feedback 382
7.6 Bibliographical Notes 384
387
4
Bibliography
: Author IFIdex 431
suäject Index 437
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Li ST O F Fi G U RES
l.l Multiaccess communication 2
Frequency-Division Multiple Access 3
l 2
Time-Division Multiple Access showing guard times
13
between slots 3 ¢J
1.4 Orthogonal signals asSIgned to two users 5
1.5 Fourier transforms (magnitude,f µ O) of waveforms in
Figure 1.4 5
l .6 Synchronous antipodal modulation of orthogonal signals 6
1.7 Signature waveforms in TDMA 7
1.8 Successive decoding 10
1.9 Two-user asynchronous CDMA 1 1
l l0 Wald functions of length 16 12
1.11 On-oHsignature waveform 13
1.12 Raised cosine pulse with Á = 05 i6
2.1 Offsets modeling asynchronism 21
Ü»/
2.2 Bit epochs for k = 3,M = 1 22
2.3 Intersymbol interference as an asynchronous CDMA
channel 24
2.4 Denmuon of asynchronous crosscorrelations(k < l) 25
2.5 Direct-sequence spread-spectmm signature waveform
with N = 63in the time and frequency domains
(rectangular chip waveform) 27
XI
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ilST OF FlGURES (
2.6 Direct-sequence spread-spectrum signature waveform
with N = 63 in the time and frequency domains (sine
chip waveform) 27
2.7 Noiseless sum of six modulated direct-sequence
waveforms with N = 63
2.8 Generation of pseudonoise sequence with a feedback
shift register
2.9 Direct-sequence spread-spectrum system with No= 63
and N = 7
21 0 Locus of crosscorrelations(ÑÚ,Ñ21) for N = 128 (let-l)
and N = 512 (right) with rectangular chips
2.l l Frequency-hopping spread-spectrum signature
waveform,N = 7
2.12 Probability density functions: (a) Rayleigh; (b) Rice
(d = 2);(c) Nakagarni (d = 3);(d) log- normal (Òp = 10)
2.l3 TWo-element array
2.14 TWo-clement Mray radiation pattems with equal gains
and phase oEsets of v = Ð (left) and v = yr/2 (right)
215 Discrete-time K-dimensional vector of matched alter
outputs
2.16 K ,dimensionai channel of matched alter outputs for
asynchronous CDMA channel
2.i7 Direct-sequence signature waveforms with N = 3
2.l8 TDMA signals subject to multipath- K = 2,Á1= - 05 ,
Á2= 2/3, y = 3/8
219 Six-element antenna aÐay
3.l Cauchy vs.Gaussian binary hypothesis test
32 Conditional distributions of Y given b = » l and b = + 1
33 Linear plot of Q(x) for x µ O
3.4 Log»linear plot of Q(x) and its bounds: (a) (33 4),(b)
(335),(c) (337),and (33 8) 103
35 Bank of single-user matched niters 104
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