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Proakis digital communications 5th edition text

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

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DIGITAL COMMUNICATIONS, FIFTH EDITION
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Library of Congress Cataloging-in-Publication Data
Proakis, John G.
Digital communications
p.

/

John G. Proakis, Masoud Salehi.



5th ed.

cm.

Includes index.

ISBN 978-0-07-295716-7
Masoud. II.
TK5103.7.P76 2008
621.382— dc22
I.

Salehi,

—ISBN 0-07-295716-6

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 Band-Limited

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

2.22.7-7 Bandpass and Lowpass Signals / 2.1-2 Lowpass

Equivalent of Bandpass Signals /

2.

1-3 Energy

Considerations / 2.1-4 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 / 2.2-3 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

Wide-Sense Stationary

66

Random Processes /

2.

7-2

Random Processes / 2. 7-3 Proper and
Random Processes / 2. 7-4 Markov Chains
Series Expansion of Random Processes
1 Sampling Theorem for Band-Limited Random
Cyclostationary
Circular

2.8

74

Processes / 2.8—2 The Karhunen-Loeve 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) / 3.2-2 Phase

3.3Modulation
/ 3.2-3 Quadrature Amplitude

Modulation / 3.2-4 Multidimensional Signaling
3.3

3.4

Signaling Schemes with Memory
3.41 Continuous -Phase Frequency-Shift Keying

114

(CPFSK) / 3.3-2 Continuous-Phase Modulation (CPM)
Power Spectrum of Digitally Modulated Signals
1 Power Spectral Density of a Digitally Modulated Signal
with

Memory

/ 3.4-2

131

Power Spectral Density of Linearly

Modulated Signals / 3.4-3 Power Spectral Density of
Digitally Modulated Signals with Finite Memory / 3.4-4

Power Spectral Density of Modulation Schemes with a Markov
Structure / 3.4-5 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

4.3-1 Optimal Detection for a General Vector Channel
4.2

Waveform and Vector AWGN Channels
1

167

Optimal Detection for the Vector AWGN

Channel / 4.2-2 Implementation of the Optimal Receiver for
/ 4.2-3 A Union Bound on the Probability of

AWGN Channels
4.3

Error of Maximum Likelihood Detection
4.4Optimal Detection and Error Probability for B and-Limited
188

Signaling
1

Optimal Detection and Error Probability for ASK or

PAM Signaling
Probability for

/ 4.3-2 Optimal Detection and Error

PSK Signaling

Error Probability for

/ 4.3-3 Optimal Detection

QAM Signaling

and

/ 4.3-4 Demodulation

and Detection
4.4

Optimal Detection and Error Probability for Power-Limited
Signaling
1

Optimal Detection and Error Probability for Orthogonal

Signaling / 4.4-2 Optimal Detection and Error Probability

for Biortho gonal Signaling / 4.4-3 Optimal Detection and

Error Probability for Simplex Signaling

203


Contents
4.5

Optimal Detection in Presence of Uncertainty:

N oncoherent Detection

210

4.5-1 Noncoherent Detection of Carrier Modulated

7-

Signals / 4.5-2 Optimal Noncoherent Detection of FSK

Modulated Signals / 4.5-3 Error Probability of Orthogonal
Signaling with Noncoherent Detection / 4.5-4 Probability of
Error for Envelope Detection of Correlated Binary
4.6-

PSK (DPSK)
A Comparison of Digital Signaling Methods
Signals / 4.5-5 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

7-2 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 / 4.9-3 Suboptimum

Demodulation and Detection of CPM Signals
Performance Analysis for Wireline and Radio

Communication Systems

259

4.10-1 Regenerative Repeaters / 4.10-2 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
5.35.1-1 The Likelihood Function / 5.1-2 Carrier Recovery and
5.3Symbol Synchronization in Signal Demodulation

290

5.2

Carrier Phase Estimation

295

1

Maximum-Likelihood Carrier Phase Estimation /

2 The Phase-Locked Loop / 5.2-3 Effect of Additive

Noise on the Phase Estimate / 5.2-4 Decision-Directed

Loops / 5.2-5 Non-Decision-Directed Loops
5.3

Symbol Timing Estimation
1

315

Maximum-Likelihood Timing Estimation /

2 Non-Decision-Directed 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 / 6.3-2 Lossless

6.4Coding Algorithms
6.4

Lossy Data Compression
6.5-

1

Random
6.5

348

Entropy and Mutual Information for Continuous
Variables / 6.4-2 The Rate Distortion Function

Channel Models and Channel Capacity
1

354

Channel Models / 6.5-2 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

6.8-1 Bhattacharyya and Chernov Bounds / 6.8-2

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 / 7.1-2 Vector Spaces
7.3General Properties of Linear Block Codes
7.31

7.2

1

411

Generator and Parity Check Matrices / 7.2-2 Weight

and Distance for Linear Block Codes / 7.2-3 The Weight
Distribution
Polynomial / 7.2-4 Error Probability of Linear
7-

Block Codes
7.5-

7.3

Some

Specific Linear

1 Repetition

420

Block Codes

Codes / 7.3-2 Hamming Codes /

3 Maximum-Length Codes / 7.3-4 Reed-Muller

Codes / 7.3-5 Hadamard Codes / 7.3-6 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 / 7.5-2 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.

7-2

7-4 Elias Bound /

McEliece-Rodemich-Rumsey-Welch

7.8

440

Hamming Bound /
7.

7-5

(MRRW) Bound

/

6 Varshamov -Gilbert Bound
Modified Linear Block Codes
1 Shortening and Lengthening / 7.8-2 Puncturing and
Extending / 7.8-3 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 / 7.9-3 Encoders for Cyclic

Codes / 7.9-4 Decoding Cyclic Codes / 7.9-5 Examples of
Cyclic Codes
7.10

Bose-Chaudhuri-Hocquenghem (BCH) Codes

463

7.10-1 The Structure of BCH Codes / 7.10-2 Decoding

BCH Codes
7.11

Reed-Solomon Codes

471

7.12

Coding

475

7.13

Combining Codes

for Channels with Burst Errors

477

7.13-1 Product Codes / 7.13-2 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 / 8.1-2 The Transfer
Convolutional
Code / 8.1-3 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

Maximum-Likelihood Decoding of Convolutional
Codes
The Viterbi Algorithm / 8.2-2 Probability of
1



Error for Maximum-Likelihood Decoding of Convolutional

Codes
8.3

Distance Properties of Binary Convolutional Codes

516

8.4

Punctured Convolutional Codes

516

8.4-1 Rate-Compatible 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

8.9-1 Performance Bounds for Turbo Codes / 8.9-2 Iterative

Decoding for Turbo Codes / 8.9-3 EXIT Chart Study of
Iterative Decoding
8.10

Factor Graphs and the Sum-Product Algorithm

558

8.10-1 Tanner Graphs / 8.10-2 Factor Graphs / 8.10-3 The

Sum-Product Algorithm / 8.10-4
Sum-Product Algorithm

MAP Decoding

Using the


1

xi

Contents

8.11

8.11-Density Parity Check Codes
Low

Decoding

1

8.12

Coding
8.12-

for

568

LDPC Codes

Bandwidth-Constrained Channels

Coded
8.12- Modulation
1 Lattices and



Trellis

571
Trellis

Coded Modulation /

2 Turbo-Coded Bandwidth Efficient Modulation
8.13

Chapter 9

Bibliographical Notes and References

589

Problems

590

Digital

Communication Through Band-Limited

9.2-

Channels

597

9.1

Characterization of Band-Limited Channels

598

9.2

Signal Design for Band-Limited Channels
9.21 Design of Band-Limited Signals for No Intersymbol

602

9.3Interference

— The Nyquist Criterion

/ 9.2-2 Design of

9.3Band-Limited
Signals with Controlled ISI



Partial-Response
9.3Signals / 9.2-3 Data Detection for Controlled ISI /

9.3-4 Signal Design for Channels with Distortion
9.3

Optimum Receiver for Channels with ISI and AWGN
9.4-1 Optimum Maximum-Likelihood Receiver /
2 A Discrete-Time Model for a Channel with ISI /
3 Maximum-Likelihood Sequence Estimation (MLSE) for
the Discrete-Time White Noise Filter

623

Model /

9.5-4 Performance
of MLSE for Channels with ISI
9.4

640

Linear Equalization
1

Peak Distortion Criterion / 9.4-2 Mean-Square-Error

(MSE)

Criterion / 9.4-3 Performance Characteristics of the

MSE Equalizer

/ 9.4-4 Fractionally Spaced

Equalizers / 9.4-5 Baseband and Passband Linear Equalizers
9.5

661

Decision-Feedback Equalization
1 Coefficient Optimization / 9.5-2 Performance

Characteristics of

DEE

/ 9.5-3 Predictive Decision-Feedback

Equalizer / 9.5-4 Equalization at the
Transmitter

— Tomlinson-Harashima 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

10.1-1 The Zero-Forcing Algorithm / 10.1-2 The

Algorithm / 10.1-3

689
689


)

Contents

xii

Algorithm / 10.1-4 Excess

MSE due

to

Noisy Gradient

Estimates / 10.1-5 Accelerating the Initial Convergence Rate
in the

LMS Algorithm

Equalizer

/ 10.1-6 Adaptive Fractionally Spaced

— The Tap Leakage Algorithm

/ 10.1-7 An Adaptive

Channel Estimator for ML Sequence Detection
10.2

Adaptive Decision-Feedback Equalizer

705

10.3

Adaptive Equalization of Trellis-Coded Signals

706

10.4

Recursive Least-Squares Algorithms for Adaptive
Equalization

710

10.4-1 Recursive Least-Squares ( Kalman
10.5-

10.5

Algorithm / 10.4-2 Linear Prediction and the Lattice Filter
10.5Self-Recovering (Blind) Equalization
1

721

Blind Equalization Based on the Maximum-Likelihood

Criterion / 10.5-2 Stochastic Gradient Algorithms /

3 Blind Equalization Algorithms Based on Second- and

Higher-Order 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 / 11.1-2 M-ary Orthogonal Signals

Multicarrier Communications

743

1 Single-Carrier Versus Multicarrier

Modulation / 11.2-2 Capacity of a Nonideal Linear Filter
Channel / 11.2-3 Orthogonal Frequency Division
Multiplexing

(OFDM)

/ 11.2-4 Modulation and

OFDM System / 11.2-5 An FFT
Algorithm Implementation of an OFDM System / 11.2-6
Demodulation

in

an

Spectral Characteristics of Multicarrier Signals / 11.2-7 Bit

and Power Allocation
Peak-to-Average Ratio

in

Multicarrier Modulation / 11.2-8

in

Multicarrier Modulation / 11.2-9

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 / 12.2-3 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

Frequency-Hopped Spread Spectrum Signals
1

AWGN

802

Performance of FH Spread Spectrum Signals in an
Channel / 12.3-2 Performance of FH Spread

Spectrum Signals

in

Partial-Band Interference / 12.3-3

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

13.1-1 Channel Correlation Functions and Power
Spectra / 13.1-2 Statistical Models for Fading Channels
13.2

The

Effect of Signal Characteristics on the Choice of a

Channel Model

844

13.3

Frequency-Nonselective, Slowly Fading Channel

846

13.4

Diversity Techniques for Fading Multipath Channels

850

13.4-1 Binary Signals / 13.4-2 Multiphase Signals / 13.4-3

M-ary Orthogonal Signals
13.5

Signaling over a Frequency-Selective, Slowly Fading

Channel: The
13.5-1

A

RAKE Demodulator

869

Tapped-Delay-Line Channel Model / 13.5-2 The

RAKE Demodulator

/ 13.5-3 Performance of RAKE

Demodulator / 13.5^1 Receiver Structures for Channels with
Intersymbol Interference
13.6

Multicarrier Modulation

(OFDM)

884

OFDM

13.6-1 Performance Degradation of an
System due to
14.1Doppler
Spreading / 13.6-2 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 Finite-State Channels

Ergodic and Outage Capacity
1

899

905

The Ergodic Capacity of the Rayleigh Fading

Channel / 14.2-2 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

14.5Trellis-Coded Modulation for Fading Channels

TCM Systems for Fading Channels

1

Trellis-Coded Modulation

929

/ 14.5-2 Multiple

(MTCM)

Coded Modulation
Frequency Domain

14.6

Bit-Interleaved

936

14.7

Coding

942

in the

14.7-1 Probability of Error for Soft Decision Decoding of
14. 7-2 Probability of Error for

Linear Binary Block Codes /

Hard-Decision Decoding of Linear Block Codes /

Upper Bounds on

14.

7-3

Performance of Convolutional Codes for
a Rayleigh Fading Channel / 14.7^1 Use of Constant-Weight
14.8

the

Codes and Concatenated Codes for a Fading Channel
The Channel Cutoff Rate for Fading Channels

957

14.8-1 Channel Cutoff Rate for Fully Interleaved Fading

Channels with CSI at Receiver
14.9

Bibliographical Notes and References

960

Problems

961

Chapter 15 Multiple-Antenna Systems
15.1

Channel Models

966

for Multiple- Antenna

Systems

966

15.1-1 Signal Transmission Through a Slow Fading
15.2Frequency -Nonselective MIMO Channel / 15.1-2 Detection

of Data Symbols

in

a

MIMO System

/ 15.1-3 Signal

Transmission Through a Slow Fading Frequency-Selective

MIMO
15.2

Channel

Capacity of MIMO Channels
1

981

Mathematical Preliminaries / 15.2-2 Capacity of a

15.3Frequency-Nonselective Deterministic

MIMO

Channel / 15.2-3 Capacity of a Frequency-Nonselective
Ergodic Random MIMO Channel / 15.2-4 Outage
15.4Capacity / 15.2-5 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 / 15.3-2

Multiplexing Gain Versus Diversity Gain / 15.3-3 Multicode

15.4

MIMO Systems
Coding for MIMO Channels

1001

Performance of Temporally Coded SISO Systems in
Rayleigh Fading Channels / 15.4-2 Bit-Interleaved Temporal
1

Coding for MIMO Channels / 15.4-3 Space-Time Block

Codes for MIMO Channels /
Probability for a Space-Time
Trellis

15. 4-^4 Pairwise

Error

Code / 15.4-5 Space-Time

Codes for MIMO Channels / 15.4-6 Concatenated

Space-Time 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
/ 16.3-2 The

Optimum Multiuser Receiver / 16.3-3 Suboptimum
Detectors / 16.3-4 Successive Interference

16.4Cancellation / 16.3-5 Other Types of Multiuser
Detectors / 16.3-6 Performance Characteristics of Detectors

Multiuser

16.4

1

MIMO Systems for Broadcast Channels

1053

Linear Precoding of the Transmitted Signals / 16.4-2

Nonlinear Precoding of the Transmitted Signals
Decomposition / 16.4-3 Nonlinear Vector

— The QR

Precoding / 16.4-4 Lattice Reduction Technique for
Precoding

Random Access Methods

16.5

16.5-1

ALOHA

1068

Systems and Protocols / 16.5-2 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 Moore-Penrose Pseudoinverse

Norm and

Condition

Error Probability for Multichannel Binary Signals

1088

1088

1090

Error Probabilities for Adaptive Reception
of

M-Phase

C.l

1096

Signals

Mathematical Model for an M-Phase 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 Time-Invariant 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 multiple-antenna systems has been added as well.

The book

is

designed to serve as a text for a first-year graduate-level course for
It is also designed to serve as a text for self-study

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 maximum-likelihood criterion. Both decision-directed and non-decisiondirected 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, Reed-Solomon 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 graph-based codes, includ-

ing convolutional codes, turbo codes, low density parity check
lis

codes for band-limited 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 sum-product
algorithm.

Chapter 9

is

focused on digital communication through band-limited 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 peak-to-average power ratio in

OFDM.
Chapter 12 is focused on spread spectrum signals and systems, with emphasis
on direct sequence and frequency-hopped 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 bit-interleaved coded modulation are treated, and the performance
of coded systems in Rayleigh and Ricean fading is derived.
Chapter 15 provides a treatment of multiple-antenna systems, generally called
multiple-input, multiple-output (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 space-time coding.
Chapter 16 treats multiuser communications, including the topics of the capacity
of multiple-access methods, multiuser detection methods for the uplink in CDMA
systems, interference mitigation in multiuser broadcast channels, and random access
methods such as ALOHA and carrier-sense multiple access (CSMA).
With 16 chapters and a variety of topics, the instructor has the flexibility to design
either a one- or two-semester 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 one-semester 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, multiple-antenna systems, and multiuser communications.

The authors and McGraw-Hill 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 1.1-1 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

1.1-1

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

M-ary 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;

man-made

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 channel-corrupted transmitted waveform and reduces the waveforms to
a sequence of numbers that represent estimates of the transmitted data symbols (binary

or M-ary). 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 bit-error at the output of the decoder

demodulator-decoder 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 information-bearing 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
solid-state 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. Twisted-pair 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 1.2-1 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. Twisted-pair 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.

Fiber-Optic 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 fiber-optic
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 fiber-optic communication system is a light
several orders of

source, either a light-emitting 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

1.2-1

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 fiber-optic
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 1.2-2 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

Earth-satellite

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

1.2-2

Frequency range for wireless electromagnetic channels. [Adapted from Carlson (1975), 2nd
edition,
McGraw-Hill Book Company Co. Reprinted with permission of the publisher. ]

©


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