DIGITAL COMMUNICATION

Third Edition

DIGITAL COMMUNICATION

Third Edition

John R. Barry Georgia Institute of Technology

Edward A. Lee University of California at Berkeley

David G. Messerschmitt University of California at Berkeley

Volume I

SPRINGER SCIENCE+BUSINESS MEDIA, LLC

Library of Congress Cataloging-in-Publication Data

Barry, John R., 1963-Digital Communication/ John R. Barry, Edward A. Lee, and David G. Messerschmitt. -3 r d ed.

p.cm. Rev. ed. of: Digital Communication / Edward A. Lee, David G. Messerschmitt. 2nd ed. c 1994. Includes bibliographical references and index. I S B N 978-1-4613-4975-4 I S B N 978-1-4615-0227-2 (eBook) D O I 10.1007/978-1-4615-0227-2 1. Digital Communications. I. Lee, Edward A., 1957- II. Messerschmitt, David G. III.

Lee, Edward A . , 1957- Digital Communication. IV. Title.

TK5103.7.L44 2003 621.382—dc22

2003054667

Copyright © 2004 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2004 Softcover reprint of the hardcover 3rd edition 2004

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To Annis, Reid, and Neil Rhonda, Helen, and Katalina

Dody and Laura

CONTENTS

Preface xiii

Changes from the Second Edition xv

Notes to an Instructor xvii

1. Introduction 1 1.1. Applications of Digital Communication 2 1.2. Digital Networks 3 1.3. Digital vs. Analog Communications 4 1.4. Plan of the Book 6 1.5. Further Reading 7

2. Deterministic Signal Processing 11 2.1. Signals 11 2.2. LTI Systems and Fourier Transforms 13 2.3. The Nyquist Sampling Theorem 15 2.4. Downconversion and Complex Envelopes 17 2.5. Z Transforms and Rational Transfer Functions 21 2.6. Signals as Vectors 33 2-A Properties of the Fourier Transform 44 2-B Spectral Factorization 47

viii

3. Stochastic Signal Processing 57 3.1. Random Variables 58 3.2. Random Processes 67 3.3. Markov Chains 82 3.4. The Poisson Process and Queueing 89 3.5. Further Reading 99 3-A Power Spectrum of A Cyclostationary Process 100 3-B Power Spectrum of A Markov Chain 101 3-C Derivation of a Poisson Process 104 3-D Moment Generating Function of Shot Noise 105

4. Limits of Communication 113 4.1. Just Enough Information About Entropy 115 4.2. Capacity of Discrete-Time Channels 118 4.3. Further Reading 125 4-A Asymptotic Equipartition Theorem 126

5. Pulse-Amplitude Modulation 131 5.1. Baseband PAM 132 5.2. Passband PAM 143 5.3. The One-Shot Minimum-Distance Receiver 153 5.4. Minimum-Distance Sequence Detection 164 5.5. Performance Analysis in AWGN 184 5.6. Further Reading 194

6. Advanced Modulation 203 6.1. M-ary Modulation 204 6.2. Probability of Error 209 6.3. Orthogonal Modulation 215 6.4. Orthogonal Pulse-Amplitude Modulation (OPAM) 230 6.5. Modulation with Memory 248 6.6. Bandwidth and Signal Dimensionality 256 6.7. Capacity and Modulation 260 6.8. Further Reading 274 6-A The Generalized Nyquist Criterion 274

IX

7. Probabilistic Detection 285 7.1. Detection of a Single Real-Valued Symbol 287 7.2. Detection of a Signal Vector 291 7.3. Known Signals in Gaussian Noise 296 7.4. ML Sequence Detection with the Viterbi Algorithm 309 7.5. A Posteriori Probability Detection with BCJR 312 7.6. Symbol-Error Probability for MLSD 318 7.7. Incoherent Detection 324 7.8. Shot Noise Signal with Known Intensity 328 7.9. Further Reading 331 7-A Karhunen-Loeve Expansion 331 7-B Bit-Error Probability for Sequence Detectors 334 7-C BCJR Forward/Backward Recursions 339

8. Equalization 345 8.1. Optimal Zero-Forcing Equalization 348 8.2. Generalized Equalization Methods 369 8.3. Fractionally Spaced Equalizer 386 8.4. Transversal Filter Equalizers 390 8.5. lSI and Channel Capacity 391 8.6. Further Reading 414 8-A DFE Error Propagation 415

9. Adaptive Equalization 423 9.1. Constrained-Complexity Equalizers 425 9.2. Adaptive Linear Equalizer 437 9.3. Adaptive DFE 446 9.4. Fractionally Spaced Equalizer 448 9.5. Passband Equalization 450 9.6. Further Reading 453 9-A SG Algorithm Error Vector Norm 454

10. MIMO Communications 461 10.1. Basics of MIMO Systems 464 10.2. The Gaussian MIMO Channel 475 10.3. Memoryless MIMO Channels 485 10.4. MIMO Detection with Channel Memory 524 10.5. Further Reading 530 10-A Proof of Separability Result (10.45) 530

x

11. Fading and Diversity 11.1. Types of Diversity 11.2. Receiver Diversity 11.3. Performance Analysis for Rayleigh Fading 11.4. The Diversity-Interference Trade-Off 11.5. Transmit Diversity 11.6. Layered Space-Time Modems 11-A Proof of Conservation Theorem 11-B Bound on Pairwise Error Probability

12. Error Control 12.1. The Capacity Penalty of Binary Coding 12.2. Binary Linear Block Codes 12.3. Convolutional Codes 12.4. Low-Density Parity-Check Codes 12.5. Turbo Codes 12.6. Historical Notes and Further Reading 12-A Linear Codes 12-B Maximal-Length Feedback Shift Registers 12-C Path Enumerators 12-D Derivation of the Tanh Rule

13. Signal-Space Coding 13.1. Multidimensional Signal Constellations 13.2. Trellis Codes 13.3. Coset Codes 13.4. Signal-Space Coding and lSI 13.5. Further Reading

14. Phase-Locked Loops 14.1. Ideal Continuous-Time PLL 14.2. Discrete-Time PLLs 14.3. Phase Detectors 14.4. Variations on a Theme: VCOs 14.5. Further Reading

537 538 539 541 545 548 562 565 566

571 574 577 591 601 618 626 627 632 638 640

651 653 669 684 689 694

701 703 710 714 719 721

15. Carrier Recovery 15.1. Decision-Directed Carrier Recovery 15.2. Power of N Carrier Recovery 15.3. Further Reading

16. Timing Recovery 16.1. Timing Recovery Performance 16.2. Spectral-Line Methods 16.3. MMSE Timing Recovery and Approximations 16.4. Baud-Rate Timing Recovery 16.5. Accumulation of Timing Jitter 16.6. Further Reading 16-A The Poisson Sum Formula 16-B Discrete-Time Derivative

17. Multiple Access Alternatives 17.1. Medium Topology for Multiple Access 17.2. Multiple Access by Time Division 17.3. Multiple Access by Frequency Division 17.4. Multiple Access by Code Division 17.5. The Cellular Concept

Exercise Solutions

Index

Xl

727 728 734 736

739 741 743 750 755 758 760 760 761

767 769 772 788 790 793

799

831

Preface This book concerns digital communication. Specifically, we treat the transport of bit

streams from one geographical location to another over various physical media, such as wire pairs, coaxial cable, optical fiber, and radio. We also treat multiple-access channels, where there are potentially multiple transmitters and receivers sharing a common medium.

Ten years have elapsed since the Second Edition, and there have been remarkable advances in wireless communication, including cellular telephony and wireless local-area networks. This Third Edition expands treatment of communication theories underlying wireless, and especially advanced techniques involving multiple antennas, which tum the traditional single-input single-output channel into a multiple-input multiple-output (MIMO) channel. This is more than a trivial advance, as it stimulates many advanced techniques such as adaptive antennas and coding techniques that take advantage of space as well as time. This is reflected in the addition of two new chapters, one on the theory of MIMO channels, and the other on diversity techniques for mitigating fading. The field of error-control coding has similarly undergone tremendous changes in the past decade, brought on by the invention of turbo codes in 1993 and the subsequent rediscovery of Gallager's low-density parity-check codes. Our treatment of error-control coding has been rewritten to reflect the current state of the art. Other materials have been reorganized and reworked, and three chapters from the previous edition have been moved to the book's Web site to make room. For this third edition we have added a third author, John Barry, who carried the major burden of these revisions.

The general approach of this book is to extract the common principles underlying a range of media and applications and present them in a unified framework. It is relevant to the design of a variety of systems, including voice and video digital cellular telephone, digital CATV distribution, wireless LANs, digital subscriber loop, metallic ethernet, voiceband data modems, and satellite communication systems.

This book is intended for designers and would-be designers of digital communication systems. To limit the length we have been selective in topics covered and in the depth of coverage. For example, the coverage of advanced information, coding, and detection theory is limited to those aspects directly relevant to the design of digital communication systems. This

xiv

emphasis on topics important to designers results in more detailed treatment of some topics than is traditional in academic textbooks, for example in our coverage of synchronization (timing and carrier recovery).

This book is suitable as a first-year graduate textbook, and should also be of interest to many industry professionals. We have attempted to make the book attractive to both audiences through the inclusion of many practical examples and a practical flavor in the choice of topics. In addition, we have increased the readability by relegating many of the more detailed derivations to appendices and exercise solutions, both of which are included in the book.

The book has a Web site at http://www.ece.gatech.eduJ-barry/digitall, where the reader may find the chapters "Physical Media and Channels," "Spectrum Control," and "Echo Cancellation" from the Second Edition, other supplementary materials, useful links, a problem solutions manual, and errata.

For this third edition, we owe a debt of gratitude to Abdallah Said AI-Ahmari, Anuj Batra, Richard T. Causey, Elizabeth Chesnutt, Arumugam Kannan, Piya Kovintavewat, Renato da Rocha Lopes, Aravind R. Nayak, Faith Nilo, Joon Hyun Sung, Badri Varadarajan, Deric Waters, and to several anonymous reviewers. In addition we gratefully acknowledge the many people who helped shape the first two editions. Any remaining errors are the full responsibility of the authors.

We hope the result is a readable and useful book, and always appreciate comments and suggestions from the readers.

John R. Barry Edward A. Lee David G. Messerschmitt

Atlanta, Georgia Berkeley, California June 10, 2003

Changes from the Second Edition

The Third Edition differs from the Second Edition in three significant ways. First, chapters 6 through 9 from the Second Edition have been reorganized and streamlined to highlight pulse-amplitude modulation, becoming the new chapters 5 through 7. Second, new material on recent advances in wireless communications, error-control coding, and multiuser communications has been added. As a result, two new chapters have been added. Finally, the three chapters "Physical Media and Channels," "Spectrum Control," and "Echo Cancellation" from the Second Edition have been moved to the book Web site.

Here is a chapter-by-chapter summary of the major changes for this Third Edition:

Chapter 2. The up converter, downconverter, and complex envelope are defined in mathematical terms for later use. More details of linear waveform spaces, including orthonormal bases and the Gram-Schmidt procedure, are added.

Chapter 5. This chapter focuses exclusively on pulse-amplitude modulation (PAM), both passband and baseband. It consolidates material that was previously spread across four different chapters. The new organization retains the intuitive flow that characterized the Second Edition, with initial emphasis on the deterministic features of PAM systems. The minimum-distance receiver is proposed, first for an isolated pulse and then for dispersive channels with intersymbol interference, which leads to such concepts as the correlator, matched filter, whitened-matched filter and the Viterbi algorithm. The statistics of the noise do not enter into the picture until the very end, where we analyze the performance of various PAM techniques with minimum-distance detection in the presence of white Gaussian noise. Separating PAM like this offers two key advantages. First, PAM and its derivatives (like multicarrier modulation) are a preferred choice for many emerging applications, making PAM a worthy topic of study in its own right. A practicing engineer may wish to study PAM only, and the new organization makes this easy to do. Second, focusing on PAM allows us to

xvi

introduce important concepts (such as minimum-distance detection and power-bandwidth trade-offs) in a highly focused and motivated setting. In a sense, we use PAM as a case study, which facilitates the generalization to arbitrary M-ary modulation schemes that follows.

Chapter 6. This chapter moves beyond PAM to examine advanced modulation techniques such as orthogonal modulation and orthogonal pulse-amplitude modulation, which includes code-division multiple access and multicarrier modulation (such as OFDM) as special cases. Also covered are advanced topics such as modulation with memory, the relationship between bandwidth and dimensionality, and the normalized SNR as a means for comparing modulation to Shannon capacity.

Chapter 7. This chapter adopts a probabilistic approach to the detection problem, thus expanding our scope beyond white-Gaussian noise. The Viterbi algorithm is formulated in probabilistic terms, and it is related to the forward-backward (or BCJR) algorithm for a posteriori-probability detection, which plays a key role in turbo decoding.

Chapter 10. This new chapter examines the fundamentals of multiple-input multiple­output communications, with particular emphasis on the detection problem, also known as the multiuser detection problem.

Chapter 11. This new chapter describes diversity techniques for mitigating multipath fading, which exploit antenna arrays at either the transmitter or the receiver (or both). We examine beamforming and combining techniques as well as space-time codes and spatial multiplexing.

Chapter 12. New material on low-density parity-check codes has been added, including Tanner graphs, message-passing decoding, and density evolution. We also describe parallel­concatenated and serial-concatenated turbo codes and turbo-decoding algorithms, with repeat­accumulate codes and turbo equalization treated as special cases.

Notes to an Instructor This book can be used as a textbook for advanced undergraduates, or for a first course in

digital communication for graduate students. We presume a working knowledge oftransfonns, linear systems, and random processes, and review these topics in chapters 2 and 3 at a depth suitable only for establishing notation. This treatment also serves to delimit the background assumed in the remainder of the book, or with more advanced students can be omitted or made optional. We include a more detailed treatment of basic topics important to digital communication but which may not be familiar to a first-year graduate student, including signal space (chapter 2), Markov chains and their analysis (chapter 3), Poisson processes and shot noise (chapter 3), the basic boundaries of communication from infonnation theory (chapter 4), and maximum-likelihood detection and the Viterbi algorithm (chapter 7). These treatments are self-contained and assume only the basic background mentioned earlier. These basic topics can be covered at the beginning of the course, or delayed until the first time they are used. Our own preference is the latter, since the immediate application of the techniques serves as useful reinforcement.

The core of book is the treatment modulation, detection and equalization (chapters 5 through 9), MIMO channels (chapters 10 and 11), coding (chapters 12 and 13), and synchronization (chapters 14 through 16). These topics are covered in considerable depth. After completing a course based on this book, students should be highly motivated to take advanced courses in infonnation theory, algebraic coding, detection and estimation theory, and communication networks, and will have a prior appreciation of the utility of these topics.

There is sufficient material for two semesters, although it can easily be used for a single­semester course by selectively covering topics. At Georgia Tech we use this book for a one­semester graduate course that has as prerequisites undergraduate courses in systems and transfonns and probability and random processes. We do not presume any prior exposure to signal space, Markov chains, or the Poisson process. In this course we rely on the students to review Chapters 1 through 4, and we cover Chapters 5 through 8 and Chapter 10 and 11 in lecture. Chapters 9, 12 and 13 are skipped because adaptive filtering and error-control coding techniques are covered in other courses.