John G. Proakis
Masoud
Salehi
WksM
Fifth Edition
Digital
Communications
Digital
Communications
Fifth Edition
John G. Proakis
Professor Emeritus Northeastern University
,
Department of Electrical and Computer Engineering,
University of California,
San Diego
Masoud
Salehi
Department of Electrical and Computer Engineering,
Northeastern University
H
Boston
Bangkok
Milan
Burr Ridge, IL
Bogota
Montreal
Caracas
New
Delhi
McGrawHill
Higher Education
Dubuque,
IA
New York
Kuala Lumpur
Santiago
Seoul
San Francisco St. Louis
London Madrid Mexico City
Singapore Sydney Taipei Toronto
Lisbon
The
McGrawHill Companies
McGrawHill
Higher Education
DIGITAL COMMUNICATIONS, FIFTH EDITION
Published by McGrawHill, a business unit of The McGrawHill Companies,
Americas,
New York, NY
10020. Copyright
reserved. Previous editions
in
© 2001
and 1995.
any form or by any means, or stored
of The McGrawHill Companies,
Inc.,
1221 Avenue of the
© 2008 by The McGrawHill Companies, Inc.
No part of this
publication
All rights
may be reproduced
or distributed
in a database or retrieval system, without the prior written consent
Inc., including,
but not limited
to, in
any network or other electronic
storage or transmission, or broadcast for distance learning.
Some
ancillaries, including electronic
and print components,
may
not be available to customers outside
the United States.
This book
is
printed on acidfree paper.
1234567890
DOC/DOC
0 9 8 7
ISBN 9780072957167
MHID 0072957166
Global Publisher: Raghothaman Srinivasan
Executive Editor: Michael Hackett
Director of Development: Kristine Tibbetts
Developmental Editor: Lorraine K. Buczek
Executive Marketing Manager: Michael Weitz
Senior Project Manager: Kay J. Brimeyer
Lead Production Supervisor: Sandy Ludovissy
Associate Design Coordinator: Brenda A Rolwes
Cover Designer: Studio Montage, St. Louis, Missouri
.
Compositor:
ICC Macmillan
Roman
Typeface: 10.5/12 Times
Printer: R. R.
Donnelley Crawfordsville, IN
(USE) Cover Image: Chart located at top left (Figure 8.96): ten Brink, S. (2001 ). “ Convergence behavior
of iteratively decoded parallel concatenated codes,” IEEE Transactions on Communications, vol. 49,
pp. 17271737.
Library of Congress CataloginginPublication Data
Proakis, John G.
Digital communications
p.
/
John G. Proakis, Masoud Salehi.
—
5th ed.
cm.
Includes index.
ISBN 9780072957167
Masoud. II.
TK5103.7.P76 2008
621.382— dc22
I.
Salehi,
—ISBN 0072957166
Title.
2007036509
www.mhhe.com
(hbk.
:
alk.
paper)
1.
Digital communications.
DEDICATION
To
Felia, George,
and Elena
John G. Proakis
To
Fariba, Omid, Sina,
and My Parents
Masoud Salehi
in
BRIEF CONTENTS
Preface
xvi
Chapter 1
Introduction
Chapter 2
Deterministic and
Chapter 3
Digital Modulation
Chapter 4
Optimum Receivers
Chapter 5
Carrier and
Chapter 6
An Introduction to Information
Chapter 7
Linear Block Codes
Chapter 8
Trellis
Chapter 9
Digital
1
Random
Signal Analysis
17
Schemes
for
95
AWGN Channels
160
Symbol Synchronization
290
Theory
330
400
and Graph Based Codes
491
Communication Through BandLimited
Channels
597
Chapter 10
Adaptive Equalization
689
Chapter 11
Multichannel and Multicarrier Systems
737
Chapter 12
Spread Spectrum Signals for Digital Communications
762
Chapter 13
Fading Channels
I:
Chapter 14
Fading Channels
II:
Chapter 15
Multiple Antenna Systems
966
Chapter 16
Multiuser Communications
1028
Appendix A
Matrices
1085
B
Appendix C
Error Probability for Multichannel Binary Signals
1090
Characterization and Signaling
830
Capacity and Coding
899
Appendices
Appendix
Appendix D
Error Probabilities for Adaptive Reception of
M Phase
Signals
1096
Square Root Factorization
1
107
References and Bibliography
1109
Index
1142
V
CONTENTS
Preface
Chapter
xvi
1
Introduction
Elements of a Digital Communication System
1
1.2
Communication Channels and Their
Characteristics
3
1.3
Mathematical Models for Communication Channels
10
1.4
A 7Historical Perspective in the Development of
Digital
Chapter 2
1
1.1
Communications
12
1.5
Overview of the Book
15
1.6
Bibliographical Notes and References
15
Deterministic and
Random Signal Analysis
17
2.2—
2.1
Bandpass and Lowpass Signal Representation
18
2.22.77 Bandpass and Lowpass Signals / 2.12 Lowpass
Equivalent of Bandpass Signals /
2.
13 Energy
Considerations / 2.14 Lowpass Equivalent of a
Bandpass System
2.2
2.6Signal Space Representation of Waveforms
1
28
Vector Space Concepts / 2.2—2 Signal Space
Concepts / 2.23 Orthogonal Expansions of Signals /
2.3
2.4
4 Gram Schmidt Procedure
Some Useful Random Variables
2.8
Bounds on
Sums
56
Random
2.5
Limit Theorems for
2.6
Complex Random Variables
1 Complex Random Vectors
2.7
Random
2.
1
40
Tail Probabilities
of
Variables
63
63
Processes
WideSense Stationary
66
Random Processes /
2.
72
Random Processes / 2. 73 Proper and
Random Processes / 2. 74 Markov Chains
Series Expansion of Random Processes
1 Sampling Theorem for BandLimited Random
Cyclostationary
Circular
2.8
74
Processes / 2.8—2 The KarhunenLoeve Expansion
2.9
vi
Bandpass and Lowpass Random Processes
78
Contents
vii
2.10
Chapter 3
Bibliographical Notes and References
82
Problems
82
Digital
Modulation Schemes
95
3.1
3.2Representation of Digitally Modulated Signals
95
3.2
Memoryless Modulation Methods
97
1
Pulse Amplitude Modulation (PAM) / 3.22 Phase
3.3Modulation
/ 3.23 Quadrature Amplitude
Modulation / 3.24 Multidimensional Signaling
3.3
3.4
Signaling Schemes with Memory
3.41 Continuous Phase FrequencyShift Keying
114
(CPFSK) / 3.32 ContinuousPhase Modulation (CPM)
Power Spectrum of Digitally Modulated Signals
1 Power Spectral Density of a Digitally Modulated Signal
with
Memory
/ 3.42
131
Power Spectral Density of Linearly
Modulated Signals / 3.43 Power Spectral Density of
Digitally Modulated Signals with Finite Memory / 3.44
Power Spectral Density of Modulation Schemes with a Markov
Structure / 3.45 Power Spectral Densities of CPFSK and
CPM Signals
4.13.5
Chapter 4
Bibliographical Notes and References
148
4.2Problems
148
Optimum Receivers for AWGN Channels
4.1
160
Waveform and Vector Channel Models
160
4.31 Optimal Detection for a General Vector Channel
4.2
Waveform and Vector AWGN Channels
1
167
Optimal Detection for the Vector AWGN
Channel / 4.22 Implementation of the Optimal Receiver for
/ 4.23 A Union Bound on the Probability of
AWGN Channels
4.3
Error of Maximum Likelihood Detection
4.4Optimal Detection and Error Probability for B andLimited
188
Signaling
1
Optimal Detection and Error Probability for ASK or
PAM Signaling
Probability for
/ 4.32 Optimal Detection and Error
PSK Signaling
Error Probability for
/ 4.33 Optimal Detection
QAM Signaling
and
/ 4.34 Demodulation
and Detection
4.4
Optimal Detection and Error Probability for PowerLimited
Signaling
1
Optimal Detection and Error Probability for Orthogonal
Signaling / 4.42 Optimal Detection and Error Probability
for Biortho gonal Signaling / 4.43 Optimal Detection and
Error Probability for Simplex Signaling
203
Contents
4.5
Optimal Detection in Presence of Uncertainty:
N oncoherent Detection
210
4.51 Noncoherent Detection of Carrier Modulated
7
Signals / 4.52 Optimal Noncoherent Detection of FSK
Modulated Signals / 4.53 Error Probability of Orthogonal
Signaling with Noncoherent Detection / 4.54 Probability of
Error for Envelope Detection of Correlated Binary
4.6
PSK (DPSK)
A Comparison of Digital Signaling Methods
Signals / 4.55 Differential
4.6
1
4.7
Lattices and Constellations Based on Lattices
4.84.
4.8
4.10
4.9
226
Bandwidth and Dimensionality
1
An Introduction
to Lattices / 4.
230
72 Signal
4.9Constellations from Lattices
4.9Detection of Signaling Schemes with
1
The
Memory
Maximum Likelihood Sequence Detector
Optimum Receiver for CPM Signals
1 Optimum Demodulation and Detection of CPM
242
246
/
2 Performance of CPM Signals / 4.93 Suboptimum
Demodulation and Detection of CPM Signals
Performance Analysis for Wireline and Radio
Communication Systems
259
4.101 Regenerative Repeaters / 4.102 Link Budget
Analysis in Radio Communication Systems
4.11
Chapter 5
Bibliographical Notes and References
265
5.2Problems
5.2
266
Carrier and Symbol Synchronization
290
5.1
Signal Parameter Estimation
5.35.11 The Likelihood Function / 5.12 Carrier Recovery and
5.3Symbol Synchronization in Signal Demodulation
290
5.2
Carrier Phase Estimation
295
1
MaximumLikelihood Carrier Phase Estimation /
2 The PhaseLocked Loop / 5.23 Effect of Additive
Noise on the Phase Estimate / 5.24 DecisionDirected
Loops / 5.25 NonDecisionDirected Loops
5.3
Symbol Timing Estimation
1
315
MaximumLikelihood Timing Estimation /
2 NonDecisionDirected Timing Estimation
Chapter 6
Symbol Timing
5.4
Joint Estimation of Carrier Phase and
5.5
Performance Characteristics of
5.6
Bibliographical Notes and References
326
Problems
327
ML Estimators
An Introduction to Information Theory
6.1
Mathematical Models for Information Sources
321
323
330
331
1
Contents
IX
6.2
6.3
A Logarithmic Measure of Information
332
6.3Lossless Coding of Information Sources
1
335
The Lossless Source Coding Theorem / 6.32 Lossless
6.4Coding Algorithms
6.4
Lossy Data Compression
6.5
1
Random
6.5
348
Entropy and Mutual Information for Continuous
Variables / 6.42 The Rate Distortion Function
Channel Models and Channel Capacity
1
354
Channel Models / 6.52 Channel Capacity
6.6
Achieving Channel Capacity with Orthogonal Signals
367
6.7
The Channel
369
6.8
The Channel Cutoff Rate
Reliability Function
37
6.81 Bhattacharyya and Chernov Bounds / 6.82
Random
Coding
6.9
Bibliographical Notes and References
380
7.1Problems
381
7.2
Chapter 7
7
Linear Block Codes
7.1
400
401
Basic Definitions
The Structure of Finite Fields / 7.12 Vector Spaces
7.3General Properties of Linear Block Codes
7.31
7.2
1
411
Generator and Parity Check Matrices / 7.22 Weight
and Distance for Linear Block Codes / 7.23 The Weight
Distribution
Polynomial / 7.24 Error Probability of Linear
7
Block Codes
7.5
7.3
Some
Specific Linear
1 Repetition
420
Block Codes
Codes / 7.32 Hamming Codes /
3 MaximumLength Codes / 7.34 ReedMuller
Codes / 7.35 Hadamard Codes / 7.36 Golay Codes
7.4
7.5
Optimum
Soft Decision Decoding of Linear
Block Codes
424
Hard Decision Decoding of Linear Block Codes
428
7.71
Error Detection and Error Correction Capability of
Block
7.8 Codes / 7.52 Block and Bit Error Probability for Hard
Decision Decoding
7.6
Comparison of Performance between Hard Decision and
7.7
Bounds on Minimum Distance of Linear Block Codes
436
Soft Decision Decoding
Bound
Bound /
Singleton
7.
1
7.
3 Plotkin
/
7.
7.
72
74 Elias Bound /
McElieceRodemichRumseyWelch
7.8
440
Hamming Bound /
7.
75
(MRRW) Bound
/
6 Varshamov Gilbert Bound
Modified Linear Block Codes
1 Shortening and Lengthening / 7.82 Puncturing and
Extending / 7.83 Expurgation and Augmentation
445
1
X
Contents
7.9
7.9Cyclic Codes
7.91 Cyclic Codes
447
— Definition and Basic Properties
/
2 Systematic Cyclic Codes / 7.93 Encoders for Cyclic
Codes / 7.94 Decoding Cyclic Codes / 7.95 Examples of
Cyclic Codes
7.10
BoseChaudhuriHocquenghem (BCH) Codes
463
7.101 The Structure of BCH Codes / 7.102 Decoding
BCH Codes
7.11
ReedSolomon Codes
471
7.12
Coding
475
7.13
Combining Codes
for Channels with Burst Errors
477
7.131 Product Codes / 7.132 Concatenated Codes
7.14
Bibliographical Notes and References
482
Problems
482
8.1
Chapter 8
Trellis
8.2
8.1
and Graph Based Codes
The
Structure of Convolutional
491
Codes
491
and State Diagrams / 8.12 The Transfer
Convolutional
Code / 8.13 Systematic,
Function of a
8.2 1 Tree,
Trellis,
Nonrecursive, and Recursive Convolutional Codes /
8.1^1 The Inverse of a Convolutional Encoder and
Catastrophic Codes
Decoding of Convolutional Codes
510
MaximumLikelihood Decoding of Convolutional
Codes
The Viterbi Algorithm / 8.22 Probability of
1
—
Error for MaximumLikelihood Decoding of Convolutional
Codes
8.3
Distance Properties of Binary Convolutional Codes
516
8.4
Punctured Convolutional Codes
516
8.41 RateCompatible Punctured Convolutional Codes
8.5
Other Decoding Algorithms for Convolutional Codes
8.6
Practical Considerations in the Application of
8.7
Nonbinary Dual k Codes and Concatenated Codes
537
8.8
Maximum a Posteriori Decoding
Codes
The B C JR Algorithm
54
8.9
Turbo Codes and
Convolutional Codes
—
Iterative
525
532
of Convolutional
Decoding
548
8.91 Performance Bounds for Turbo Codes / 8.92 Iterative
Decoding for Turbo Codes / 8.93 EXIT Chart Study of
Iterative Decoding
8.10
Factor Graphs and the SumProduct Algorithm
558
8.101 Tanner Graphs / 8.102 Factor Graphs / 8.103 The
SumProduct Algorithm / 8.104
SumProduct Algorithm
MAP Decoding
Using the
1
xi
Contents
8.11
8.11Density Parity Check Codes
Low
Decoding
1
8.12
Coding
8.12
for
568
LDPC Codes
BandwidthConstrained Channels
Coded
8.12 Modulation
1 Lattices and
—
Trellis
571
Trellis
Coded Modulation /
2 TurboCoded Bandwidth Efficient Modulation
8.13
Chapter 9
Bibliographical Notes and References
589
Problems
590
Digital
Communication Through BandLimited
9.2
Channels
597
9.1
Characterization of BandLimited Channels
598
9.2
Signal Design for BandLimited Channels
9.21 Design of BandLimited Signals for No Intersymbol
602
9.3Interference
— The Nyquist Criterion
/ 9.22 Design of
9.3BandLimited
Signals with Controlled ISI
—
PartialResponse
9.3Signals / 9.23 Data Detection for Controlled ISI /
9.34 Signal Design for Channels with Distortion
9.3
Optimum Receiver for Channels with ISI and AWGN
9.41 Optimum MaximumLikelihood Receiver /
2 A DiscreteTime Model for a Channel with ISI /
3 MaximumLikelihood Sequence Estimation (MLSE) for
the DiscreteTime White Noise Filter
623
Model /
9.54 Performance
of MLSE for Channels with ISI
9.4
640
Linear Equalization
1
Peak Distortion Criterion / 9.42 MeanSquareError
(MSE)
Criterion / 9.43 Performance Characteristics of the
MSE Equalizer
/ 9.44 Fractionally Spaced
Equalizers / 9.45 Baseband and Passband Linear Equalizers
9.5
661
DecisionFeedback Equalization
1 Coefficient Optimization / 9.52 Performance
Characteristics of
DEE
/ 9.53 Predictive DecisionFeedback
Equalizer / 9.54 Equalization at the
Transmitter
— TomlinsonHarashima Precoding
9.6
Reduced Complexity
ML Detectors
9.7
Iterative Equalization
and Decoding
9.8
669
—Turbo
Equalization
67
Bibliographical Notes and References
673
Problems
674
Chapter 10 Adaptive Equalization
10.1
Adaptive Linear Equalizer
LMS
Convergence Properties of the LMS
10.11 The ZeroForcing Algorithm / 10.12 The
Algorithm / 10.13
689
689
)
Contents
xii
Algorithm / 10.14 Excess
MSE due
to
Noisy Gradient
Estimates / 10.15 Accelerating the Initial Convergence Rate
in the
LMS Algorithm
Equalizer
/ 10.16 Adaptive Fractionally Spaced
— The Tap Leakage Algorithm
/ 10.17 An Adaptive
Channel Estimator for ML Sequence Detection
10.2
Adaptive DecisionFeedback Equalizer
705
10.3
Adaptive Equalization of TrellisCoded Signals
706
10.4
Recursive LeastSquares Algorithms for Adaptive
Equalization
710
10.41 Recursive LeastSquares ( Kalman
10.5
10.5
Algorithm / 10.42 Linear Prediction and the Lattice Filter
10.5SelfRecovering (Blind) Equalization
1
721
Blind Equalization Based on the MaximumLikelihood
Criterion / 10.52 Stochastic Gradient Algorithms /
3 Blind Equalization Algorithms Based on Second and
HigherOrder Signal
10.6
Statistics
Bibliographical Notes and References
731
Problems
732
11.1
Chapter 11 Multichannel
and Multicarrier Systems
11.211.1
Multichannel Digital Communications in
737
AWGN
Channels
1
11.2
737
Binary Signals / 11.12 Mary Orthogonal Signals
Multicarrier Communications
743
1 SingleCarrier Versus Multicarrier
Modulation / 11.22 Capacity of a Nonideal Linear Filter
Channel / 11.23 Orthogonal Frequency Division
Multiplexing
(OFDM)
/ 11.24 Modulation and
OFDM System / 11.25 An FFT
Algorithm Implementation of an OFDM System / 11.26
Demodulation
in
an
Spectral Characteristics of Multicarrier Signals / 11.27 Bit
and Power Allocation
PeaktoAverage Ratio
in
Multicarrier Modulation / 11.28
in
Multicarrier Modulation / 11.29
Channel Coding Considerations
11.3
in
Multicarrier Modulation
Bibliographical Notes and References
759
12.2Problems
12.2
760
Chapter 12 Spread Spectrum Signals for Digital
Communications
12.1
Model of Spread Spectrum
Digital
762
Communication
System
12.2
763
Direct Sequence Spread Spectrum Signals
1
Error Rate Performance of the Decoder /
2
Some Applications of DS Spread Spectrum
Signals / 12.23 Effect of Pulsed Interference on
765
DS Spread
Contents
xiii
12.3
Spectrum Systems / 12.2^1 Excision of Narrowband
12.2DS Spread Spectrum Systems /
Interference in
12.3
5 Generation of PN Sequences
FrequencyHopped Spread Spectrum Signals
1
AWGN
802
Performance of FH Spread Spectrum Signals in an
Channel / 12.32 Performance of FH Spread
Spectrum Signals
in
PartialBand Interference / 12.33
A
CDMA System Based on FH Spread Spectrum Signals
12.4
Other Types of Spread Spectrum Signals
814
12.5
Synchronization of Spread Spectrum Systems
815
12.6
Bibliographical Notes and References
823
Problems
823
Chapter 13 Fading Channels
and Signaling
13.1
I:
Characterization
830
Characterization of Fading Multipath Channels
831
13.11 Channel Correlation Functions and Power
Spectra / 13.12 Statistical Models for Fading Channels
13.2
The
Effect of Signal Characteristics on the Choice of a
Channel Model
844
13.3
FrequencyNonselective, Slowly Fading Channel
846
13.4
Diversity Techniques for Fading Multipath Channels
850
13.41 Binary Signals / 13.42 Multiphase Signals / 13.43
Mary Orthogonal Signals
13.5
Signaling over a FrequencySelective, Slowly Fading
Channel: The
13.51
A
RAKE Demodulator
869
TappedDelayLine Channel Model / 13.52 The
RAKE Demodulator
/ 13.53 Performance of RAKE
Demodulator / 13.5^1 Receiver Structures for Channels with
Intersymbol Interference
13.6
Multicarrier Modulation
(OFDM)
884
OFDM
13.61 Performance Degradation of an
System due to
14.1Doppler
Spreading / 13.62 Suppression ofICI in
OFDM
Systems
14.213.7
Bibliographical Notes and References
890
Problems
891
Chapter 14 Fading Channels
14.1
II:
Capacity of Fading Channels
1 Capacity
14.2
Capacity and Coding
900
of FiniteState Channels
Ergodic and Outage Capacity
1
899
905
The Ergodic Capacity of the Rayleigh Fading
Channel / 14.22 The Outage Capacity of Rayleigh Fading
Channels
14.3
Coding
for Fading
Channels
918
Contents
XIV
14.4
14.4of Coded Systems In Fading Channels
Performance
14.5
919
Coding for Fully Interleaved Channel Model
1
14.5TrellisCoded Modulation for Fading Channels
TCM Systems for Fading Channels
1
TrellisCoded Modulation
929
/ 14.52 Multiple
(MTCM)
Coded Modulation
Frequency Domain
14.6
BitInterleaved
936
14.7
Coding
942
in the
14.71 Probability of Error for Soft Decision Decoding of
14. 72 Probability of Error for
Linear Binary Block Codes /
HardDecision Decoding of Linear Block Codes /
Upper Bounds on
14.
73
Performance of Convolutional Codes for
a Rayleigh Fading Channel / 14.7^1 Use of ConstantWeight
14.8
the
Codes and Concatenated Codes for a Fading Channel
The Channel Cutoff Rate for Fading Channels
957
14.81 Channel Cutoff Rate for Fully Interleaved Fading
Channels with CSI at Receiver
14.9
Bibliographical Notes and References
960
Problems
961
Chapter 15 MultipleAntenna Systems
15.1
Channel Models
966
for Multiple Antenna
Systems
966
15.11 Signal Transmission Through a Slow Fading
15.2Frequency Nonselective MIMO Channel / 15.12 Detection
of Data Symbols
in
a
MIMO System
/ 15.13 Signal
Transmission Through a Slow Fading FrequencySelective
MIMO
15.2
Channel
Capacity of MIMO Channels
1
981
Mathematical Preliminaries / 15.22 Capacity of a
15.3FrequencyNonselective Deterministic
MIMO
Channel / 15.23 Capacity of a FrequencyNonselective
Ergodic Random MIMO Channel / 15.24 Outage
15.4Capacity / 15.25 Capacity of MIMO Channel
Channel
15.3
Is
Known
When
the
at the Transmitter
Spread Spectrum Signals and Multicode Transmission
1
992
Orthogonal Spreading Sequences / 15.32
Multiplexing Gain Versus Diversity Gain / 15.33 Multicode
15.4
MIMO Systems
Coding for MIMO Channels
1001
Performance of Temporally Coded SISO Systems in
Rayleigh Fading Channels / 15.42 BitInterleaved Temporal
1
Coding for MIMO Channels / 15.43 SpaceTime Block
Codes for MIMO Channels /
Probability for a SpaceTime
Trellis
15. 4^4 Pairwise
Error
Code / 15.45 SpaceTime
Codes for MIMO Channels / 15.46 Concatenated
SpaceTime Codes and Turbo Codes
xv
Contents
Bibliographical Notes and References
1021
Problems
1021
15.5
Chapter 16 Multiuser Communications
1028
16.1
Introduction to Multiple Access Techniques
1028
16.2
16.3of Multiple Access Methods
Capacity
1031
16.3
Multiuser Detection in
1
CDMA Systems
CDMA Signal and Channel Models
1036
/ 16.32 The
Optimum Multiuser Receiver / 16.33 Suboptimum
Detectors / 16.34 Successive Interference
16.4Cancellation / 16.35 Other Types of Multiuser
Detectors / 16.36 Performance Characteristics of Detectors
Multiuser
16.4
1
MIMO Systems for Broadcast Channels
1053
Linear Precoding of the Transmitted Signals / 16.42
Nonlinear Precoding of the Transmitted Signals
Decomposition / 16.43 Nonlinear Vector
— The QR
Precoding / 16.44 Lattice Reduction Technique for
Precoding
Random Access Methods
16.5
16.51
ALOHA
1068
Systems and Protocols / 16.52 Carrier
Sense Systems and Protocols
16.6
Appendix
A
Appendix B
Appendix
C
Bibliographical Notes and References
1077
Problems
1078
1085
Matrices
A.l
Eigenvalues and Eigenvectors of a Matrix
1086
A.2
Singular Value Decomposition
1087
A.3
Matrix
A.4
The MoorePenrose Pseudoinverse
Norm and
Condition
Error Probability for Multichannel Binary Signals
1088
1088
1090
Error Probabilities for Adaptive Reception
of
MPhase
C.l
1096
Signals
Mathematical Model for an MPhase Signaling Communication
1096
System
and Probability Density Function of
C.2
Characteristic Function
the Phase 6
1098
C.3
Error Probabilities for Slowly Fading Rayleigh Channels
1100
C.4
Error Probabilities for TimeInvariant and Ricean Fading
Channels
Appendix D
Number
Square Root Factorization
1104
1107
109
References and Bibliography
1
Index
1142
PREFACE
welcome Professor Masoud Salehi as a coauthor to the fifth edition
new edition has undergone a major revision and
reorganization of topics, especially in the area of channel coding and decoding. A new
It is
a pleasure to
of Digital Communications This
.
chapter on multipleantenna systems has been added as well.
The book
is
designed to serve as a text for a firstyear graduatelevel course for
It is also designed to serve as a text for selfstudy
students in electrical engineering.
and
as a reference
book
for the practicing engineer involved in the design and analysis
of digital communications systems.
As
to background,
we presume
that the reader has
a thorough understanding of basic calculus and elementary linear systems theory and
knowledge of probability and stochastic processes.
Chapter 1 is an introduction to the subject, including a historical perspective and
a description of channel characteristics and channel models.
Chapter 2 contains a review of deterministic and random signal analysis, including
bandpass and lowpass signal representations, bounds on the tail probabilities of random
variables, limit theorems for sums of random variables, and random processes.
Chapter 3 treats digital modulation techniques and the power spectrum of digitally
modulated signals.
Chapter 4 is focused on optimum receivers for additive white Gaussian noise
(AWGN) channels and their error rate performance. Also included in this chapter is
an introduction to lattices and signal constellations based on lattices, as well as link
budget analyses for wireline and radio communication systems.
Chapter 5 is devoted to carrier phase estimation and time synchronization methods
based on the maximumlikelihood criterion. Both decisiondirected and nondecisiondirected methods are described.
Chapter 6 provides an introduction to topics in information theory, including
prior
lossless source coding, lossy data compression, channel capacity for different channel
models, and the channel reliability function.
Chapter 7
of cyclic codes,
treats linear
block codes and their properties. Included
is
a treatment
BCH codes, ReedSolomon codes,
and concatenated codes. Both soft
decision and hard decision decoding methods are described, and their performance in
AWGN channels
is
evaluated.
Chapter 8 provides
a treatment of trellis codes and graphbased codes, includ
ing convolutional codes, turbo codes, low density parity check
lis
codes for bandlimited channels, and codes based on
rithms are also treated, including the Viterbi algorithm and
xvi
(LDPC)
its
codes,
trel
Decoding algoperformance on AWGN
lattices.
Preface
XVII
channels, the BCJR algorithm for iterative decoding of turbo codes, and the sumproduct
algorithm.
Chapter 9
is
focused on digital communication through bandlimited channels.
Topics treated in this chapter include the characterization and signal design for band
optimum receiver for channels with intersymbol interference and
and suboptimum equalization methods, namely, linear equalization, decisionfeedback equalization, and turbo equalization.
Chapter 10 treats adaptive channel equalization. The LMS and recursive leastlimited channels, the
AWGN,
squares algorithms are described together with their performance characteristics. This
chapter also includes a treatment of blind equalization algorithms.
Chapter 11 provides a treatment of multichannel and
multicarrier modulation.
Topics treated include the error rate performance of multichannel binary signal and
M ary orthogonal signals in AWGN channels; the capacity of a nonideal linear

channel with
tion in an
filter
AWGN; OFDM
OFDM
modulation and demodulation; bit and power allocasystem; and methods to reduce the peaktoaverage power ratio in
OFDM.
Chapter 12 is focused on spread spectrum signals and systems, with emphasis
on direct sequence and frequencyhopped spread spectrum systems and their performance. The benefits of coding in the design of spread spectrum signals is emphasized
throughout
this chapter.
Chapter 13
communication through fading channels, including the characand the key important parameters of multipath spread and
Doppler spread. Several channel fading statistical models are introduced, with emphasis placed on Rayleigh fading, Ricean fading, and Nakagami fading. An analysis of the
performance degradation caused by Doppler spread in an OFDM system is presented,
and a method for reducing this performance degradation is described.
Chapter 14 is focused on capacity and code design for fading channels. After introducing ergodic and outage capacities, coding for fading channels is studied. Bandwidthefficient coding and bitinterleaved coded modulation are treated, and the performance
of coded systems in Rayleigh and Ricean fading is derived.
Chapter 15 provides a treatment of multipleantenna systems, generally called
multipleinput, multipleoutput (MIMO) systems, which are designed to yield spatial
signal diversity and spatial multiplexing. Topics treated in this chapter include detection
treats
terization of fading channels
algorithms for
MIMO channels, the capacity of MIMO channels with AWGN without
and with signal fading, and spacetime coding.
Chapter 16 treats multiuser communications, including the topics of the capacity
of multipleaccess methods, multiuser detection methods for the uplink in CDMA
systems, interference mitigation in multiuser broadcast channels, and random access
methods such as ALOHA and carriersense multiple access (CSMA).
With 16 chapters and a variety of topics, the instructor has the flexibility to design
either a one or twosemester course. Chapters 3, 4, and 5 provide a basic treatment of
digital modulation/demodulation and detection methods. Channel coding and decoding
treated in Chapters 7, 8, and 9 can be included along with modulation/demodulation
in a onesemester course. Alternatively, Chapters 9 through 12 can be covered in place
of channel coding and decoding. A second semester course can cover the topics of
xviii
Preface
communication through fading channels, multipleantenna systems, and multiuser communications.
The authors and McGrawHill would like to thank the following reviewers
suggestions on selected chapters of the
fifth
for their
edition manuscript:
Paul Salama, Indiana University/Purdue University, Indianapolis; Dimitrios Hatzinakos, University of Toronto, and
Finally, the first author
Ender Ayanoglu, University of California,
Irvine.
wishes to thank Gloria Doukakis for her assistance in typing
We
also thank Patrick Amihood for preparing several graphs
and 16 and Apostolos Rizos and Kostas Stamatiou for preparing parts
of the Solutions Manual.
parts of the manuscript.
in Chapters 15
1
Introduction
we present the basic principles that underlie the analysis and design
communication systems. The subject of digital communications involves the
transmission of information in digital form from a source that generates the information
to one or more destinations. Of particular importance in the analysis and design of
communication systems are the characteristics of the physical channels through which
In
this
book,
of digital
the information
is
transmitted.
The
characteristics of the channel generally affect the
design of the basic building blocks of the communication system. Below,
we
describe
the elements of a communication system and their functions.
1.1
ELEMENTS OF A DIGITAL COMMUNICATION SYSTEM
Figure 1.11 illustrates the functional diagram and the basic elements of a digital
communication system. The source output may be
either
an analog signal, such as an
audio or video signal, or a digital signal, such as the output of a computer, that is discrete
and has a finite number of output characters. In a digital communication system,
by the source are converted into a sequence of binary digits.
Ideally, we should like to represent the source output (message) by as few binary digits
as possible. In other words, we seek an efficient representation of the source output
that results in little or no redundancy. The process of efficiently converting the output
of either an analog or digital source into a sequence of binary digits is called source
encoding or data compression.
The sequence of binary digits from the source encoder, which we call the information sequence is passed to the channel encoder. The purpose of the channel encoder
is to introduce, in a controlled manner, some redundancy in the binary information
sequence that can be used at the receiver to overcome the effects of noise and interin time
the messages produced
,
ference encountered in the transmission of the signal through the channel. Thus, the
added redundancy serves
to increase the reliability of the received data
and improves
1
,
2
Digital
Communications
Output
signal
FIGURE
1.11
Basic elements of a digital communication system.
the fidelity of the received signal. In effect, redundancy in the information sequence
aids the receiver in
decoding the desired information sequence. For example, a
(trivial)
form of encoding of the binary information sequence is simply to repeat each binary
digit m times, where m is some positive integer. More sophisticated (nontrivial) encoding involves taking k information bits at a time and mapping each k bit sequence into
a unique n bit sequence, called a code word. The amount of redundancy introduced by
encoding the data in this manner is measured by the ratio n/k. The reciprocal of this
ratio, namely k/n is called the rate of the code or, simply, the code rate.
The binary sequence at the output of the channel encoder is passed to the digital
modulator which serves as the interface to the communication channel. Since nearly
all the communication channels encountered in practice are capable of transmitting
,
,
electrical signals
(waveforms), the primary purpose of the digital modulator
the binary information sequence into signal waveforms.
us suppose that the coded information sequence
is to
To elaborate on
be transmitted one
is to
map
this point, let
bit at a
time
at
some uniform rate R bits per second (bits/s). The digital modulator may simply map the
binary digit 0 into a waveform so(t) and the binary digit 1 into a waveform s\ ( t ). In this
manner, each bit from the channel encoder is transmitted separately.
modulation. Alternatively, the modulator
time by using
M=2
for each of the 2
new
b
b
distinct
may
waveforms
possible b bit sequences.
We call this binary
transmit b coded information bits at a
Si(t),
i
=
We call
0, 1,
this
.
.
.
M—
1,
one waveform
Mary modulation
(
M
>
2).
modulator every b/R seconds. Hence, when
the channel bit rate R is fixed, the amount of time available to transmit one of the
waveforms corresponding to a b bit sequence is b times the time period in a system
Note
that a
b bit sequence enters the
M
that uses binary modulation.
The communication channel is the physical medium that is used to send the signal
from the transmitter to the receiver. In wireless transmission, the channel may be the
atmosphere (free space).
On the other hand, telephone channels usually employ a variety
of physical media, including wire lines, optical fiber cables, and wireless (microwave
radio).
Whatever the physical medium used for transmission of the information, the
random manner by a
essential feature is that the transmitted signal is corrupted in a
Chapter One: Introduction
3
variety of possible mechanisms, such as additive thermal noise generated
devices;
manmade
noise, e.g., automobile ignition noise;
by electronic
and atmospheric noise, e.g.,
electrical lightning discharges during thunderstorms.
At
the receiving
end of a
digital
communication system, the
digital
demodulator
processes the channelcorrupted transmitted waveform and reduces the waveforms to
a sequence of numbers that represent estimates of the transmitted data symbols (binary
or Mary). This sequence of numbers
is
passed to the channel decoder, which attempts
sequence from knowledge of the code used by
the channel encoder and the redundancy contained in the received data.
A measure of how well the demodulator and decoder perform is the frequency with
to reconstruct the original information
which
errors occur in the
decoded sequence. More precisely, the average probability
is a measure of the performance of the
of a biterror at the output of the decoder
demodulatordecoder combination. In general, the probability of error is a function of
the code characteristics, the types of waveforms used to transmit the information over
the channel, the transmitter power, the characteristics of the channel
(i.e.,
the
amount
of noise, the nature of the interference), and the method of demodulation and decoding.
These items and
their effect
on performance will be discussed in
detail in
subsequent
chapters.
As
a final step,
when an analog
output
is
desired, the source decoder accepts the
output sequence from the channel decoder and, from knowledge of the source encoding
method used, attempts
to reconstruct the original signal
from the source. Because of
channel decoding errors and possible distortion introduced by the source encoder,
and perhaps, the source decoder, the signal at the output of the source decoder is an
approximation to the original source output. The difference or some function of the
difference between the original signal and the reconstructed signal is a measure of the
distortion introduced
by the
digital
communication system.
1.2
COMMUNICATION CHANNELS AND THEIR CHARACTERISTICS
As
indicated in the preceding discussion, the communication channel provides the con
nection between the transmitter and the receiver.
The physical channel may be
a pair of
wires that carry the electrical signal, or an optical fiber that carries the information on a
modulated light beam, or an underwater ocean channel in which the information is transmitted acoustically, or free space over which the informationbearing signal
by use of an antenna. Other media that can be characterized
is
radiated
communication channels
are data storage media, such as magnetic tape, magnetic disks, and optical disks.
One common problem in signal transmission through any channel is additive noise.
In general, additive noise is generated internally by components such as resistors and
solidstate devices used to implement the communication system. This is sometimes
called thermal noise. Other sources of noise and interference may arise externally to
the system, such as interference from other users of the channel. When such noise
and interference occupy the same frequency band as the desired signal, their effect
can be minimized by the proper design of the transmitted signal and its demodulator at
as
4
Communications
Digital
the receiver. Other types of signal degradations that may be encountered in transmission
over the channel are signal attenuation, amplitude and phase distortion, and multipath
distortion.
effects of noise may be minimized by increasing the power in the transmitted
However, equipment and other practical constraints limit the power level in
the transmitted signal. Another basic limitation is the available channel bandwidth.
A bandwidth constraint is usually due to the physical limitations of the medium and
the electronic components used to implement the transmitter and the receiver. These
two limitations constrain the amount of data that can be transmitted reliably over any
communication channel as we shall observe in later chapters. Below, we describe some
of the important characteristics of several communication channels.
The
signal.
Wireline Channels
The telephone network makes extensive use of wire lines for voice
signal transmission,
and video transmission. Twistedpair wire lines and coaxial cable are
basically guided electromagnetic channels that provide relatively modest bandwidths.
Telephone wire generally used to connect a customer to a central office has a bandwidth
of several hundred kilohertz (kHz). On the other hand, coaxial cable has a usable
bandwidth of several megahertz (MHz). Figure 1.21 illustrates the frequency range of
guided electromagnetic channels, which include waveguides and optical fibers.
as well as data
Signals transmitted through such channels are distorted in both amplitude and
phase and further corrupted by additive noise. Twistedpair wireline channels are also
prone to crosstalk interference from physically adjacent channels. Because wireline
channels carry a large percentage of our daily communications around the country and
the world,
much
research has been performed on the characterization of their trans
mission properties and on methods for mitigating the amplitude and phase distortion
encountered in signal transmission. In Chapter
optimum
9,
we
describe methods for designing
transmitted signals and their demodulation; in Chapter 10,
we
consider the
design of channel equalizers that compensate for amplitude and phase distortion on
these channels.
FiberOptic Channels
Optical fibers offer the communication system designer a channel bandwidth that
is
magnitude larger than coaxial cable channels. During the past two
decades, optical fiber cables have been developed that have a relatively low signal attenuation, and highly reliable photonic devices have been developed for signal generation
and signal detection. These technological advances have resulted in a rapid deployment of optical fiber channels, both in domestic telecommunication systems as well as
for transcontinental communication. With the large bandwidth available on fiberoptic
channels, it is possible for telephone companies to offer subscribers a wide array of
telecommunication services, including voice, data, facsimile, and video.
The transmitter or modulator in a fiberoptic communication system is a light
several orders of
source, either a lightemitting diode
(LED)
or a laser. Information
is
transmitted by
varying (modulating) the intensity of the light source with the message signal. The light
propagates through the fiber as a light wave and
is
amplified periodically (in the case of
Chapter One: Introduction
5
FIGURE
1.21
Frequency range for guided wire
channel.
digital transmission,
it is
detected and regenerated by repeaters) along the transmission
path to compensate for signal attenuation. At the receiver, the light intensity
is
detected
by a photodiode, whose output is an electrical signal that varies in direct proportion
to the power of the light impinging on the photodiode. Sources of noise in fiberoptic
channels are photodiodes and electronic amplifiers.
Wireless Electromagnetic Channels
In wireless communication systems, electromagnetic energy
agation
medium by an antenna which
obtain efficient
is
coupled to the prop
The physical
size and
depend primarily on the frequency of operation. To
radiation of electromagnetic energy, the antenna must be longer than
the configuration of the antenna
serves as the radiator.
6
Digital
^
Communications
of the wavelength. Consequently, a radio station transmitting in the amplitude
modulated (AM) frequency band, say at fc = 1 MHz [corresponding to a wavelength
of k = c/fc = 300 meters (m)], requires an antenna of at least 30 m. Other important
characteristics and attributes of antennas for wireless transmission are described in
Chapter 4.
Figure 1.22 illustrates the various frequency bands of the electromagnetic spectrum. The mode of propagation of electromagnetic waves in the atmosphere and in
Frequency band
Use
Ultraviolet
10
15
Hz
14
Hz
Visible light
0~ b
1
Experimental
m
Infrared
10
Millimeter waves
(EHF)
h 100
GHz
Experimental
Navigation
Satellite to satellite
Super high frequency
(SHF)
10
Microwave
relay
h 10
radio
Radar
Mobile radio
cm
Ultra high frequency
Y
(UHF)
1
Microwave
GHz
Earthsatellite
1
GHz
UHF TV and mobile radio
m
Mobile, aeronautical
Very high frequency
(VHF)
VHF TV and FM broadcast
100
Shortwave
MHz
radio
mobile radio
10
m
>%
High frequency
(HF)
I
>
o
Business
Amateur
radio
10
MHz

International radio
100
Citizen's
r
Medium
frequency
(MF)
1
10
band
AM broadcast
hi
MHz
km
km
Longwave
Low frequency
Aeronautical
(LF)
Navigation
100
radio
Radio teletype
4
Very low frequency
10
(VLF)
100
kHz
kHz
km
Audio
band
FIGURE
1
kHz
1.22
Frequency range for wireless electromagnetic channels. [Adapted from Carlson (1975), 2nd
edition,
McGrawHill Book Company Co. Reprinted with permission of the publisher. ]
©