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`

` COMMUNICATION SYSTEMS
`
`4TH EDITION
`
`2
`
`

`

` COMMUNICATION SYSTEMS
`
`4TH EDITION
`
`Simon Huykin
`McMaster University
`
`@ J
`
`OHN WILEY 8r SONS, INC.
`
`
`Singapore E Toronto
`New York 5 Chichester fi Weinheim E Brisbane
`
`
`3
`
`

`

`Editor
`Marketing Manager
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`Senior Production Editor
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`This book was set in 10/12 Times Roman by UG / GGS Information Services, Inc. and printed and bound
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`This book is printed on acid»free paper.
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`The paper in this book was manufactured by a mill whose forest management programs include sustained
`yield harvesting of its timberlands. Sustained yield harvesting principles ensure that the numbers of trees
`cut each year does not exceed the amount of new growth
`
`Copyright © 2001, John Wiley 8C Sons, Inc. All rights Reserved.
`No part of this publication may be reproduced, stored in a retrieval system or transmitted
`in any form or by any means, electronic, mechanical, photocopying, recording. scanning
`or otherwise, except as permitted under Sections 107 or 1089 of the 1976 United States
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`To order books or for customer service call 1-800-CALLWILEY {225-5 945).
`
`Library of Congress Catalaging—iml’ublimfion Data
`Haykin, Simon
`Communication systems / Simon Haykin.——4th ed.
`p. cm.
`ISBN 0471—1736971 {clothz alk paper)
`1. Telecommunication. 2. Signal theory (Telecommunication) I. Title.
`TK5101 .l-l37 2000
`621.332—dc21
`Printed in the United States of America
`1098765432
`
`99—04-2977
`
`4
`
`

`

`
`
`Electrical engineering education has undergone some radical changes during the past coue
`ple of decades and continues to do so. A modern undergraduate program in electrical
`engineering includes the following two introductory courses:
`
`b Signals and Systems, which provides a balanced and integrated treatment of contin-
`uous~time and discrete-time forms of signals and systems. The Fourier transform (in
`its different forms), Laplace transform, and z—transform are treated in detail. Typi-
`cally, the course also includes an elementary treatment of communication systems.
`F” Probability and Random Processes, which develops an intuitive grasp of discrete and
`continuous random variables and then introduces the notion of a random process
`and its characteristics
`
`Typically, these two introductory courses lead to a senior-level course on communication
`systems.
`The fourth edition of this book has been written with this background and primary
`objective in mind. Simply put, the book provides a modern treatment of communication
`systems at a level suitable for a one- or two-semester senior undergraduate course. The
`emphasis is on the statistical underpinnings of communication theory with applications.
`The material is presented in a logical manner, and it is illustrated with examples,
`with the overall aim being that of helping the student develop an intuitive grasp of the
`theory under discussion. Except for the Background and Preview chapter, each chapter
`ends with numerous problems designed not only to help the students test their understand—
`ing of the material covered in the chapter but also to challenge them to extend this material.
`Every chapter includes notes and references that provide suggestions for further reading.
`Sections or subsections that can be bypassed without loss of continuity are identified with
`a footnote.
`,
`A distinctive feature of the book is the inclusion of eight computer experiments using
`MATLAB. This set of experiments pr vides the basis of a “Software Laboratory”, with
`each experiment being designed to e end the material covered in the pertinent chapter.
`Most important, the experiments exploit the unique capabilities of MATLAB in an instruc-
`tive manner. The MATLAB codes for all these experiments are available on the Wiley Web
`site: http://www.wiley.com/college/hayki.u/.
`The Background and Preview chapter presents introductory and motivational ma-
`terial, paving the way for detailed treatment of the many facets of communication systems
`in the subsequent 10 chapters. The material in these chapters is organized as follows:
`
`> Chapter 1 develops a detailed treatment of random, or stochastic, processes, with
`particular emphasis on their partial characterization (i.e., second-order stafisdcs). In
`effect, the discussion is restricted to wide—sense stationary processes. The correlation
`Vll
`
`5
`
`

`

`u-I.
`
`PREFACE
`
`properties and power spectra of random processes are described in detail. Gaussian
`processes and narrowband noise feature prominently in the study of communication
`systems, hence their treatment in the latter part of the chapter. This treatment nat-
`urally leads to the consideration of the Rayleigh and Rician distributions that arise
`in a communications environment,
`
`Chapter 2 presents an integrated treatment of continuous—wave (CW) modulation
`(i.e., analog communications) and their different types, as outlined here:
`(i) Amplitude modulation, which itself can assume one of the following forms (de-
`pending on how the spectral characteristics of the modulated wave are specified):
`3" Full amplitude modulation
`9 Double sideband—suppressed carrier modulation
`5’ Quadrature amplitude modulation
`E" Single sideband modulation
`> Vestigial sideband modulation
`(ii) Angle modulation, which itself can assume one of two interrelated forms:
`it Phase modulation
`gr Frequency modulation
`The time-domain and spectral characteristics of these modulated waves, methods for
`their generation and detection, and the effects of channel noise on their performances
`are discussed.
`
`Chapter 3 covers pulse modulation and discusses the processes of sampling, quan—
`tization, and coding that are fundamental to the digital transmission of analog sig—
`nals. This chapter may be Viewed as the transition from analog to digital commu—
`nications. Specifically, the following types of pulse modulation are discussed:
`(i) Analog pulse modulation, where only time is represented in discrete form; it
`embodies the following special forms:
`P Pulse amplitude modulation
`5* Pulse width (duration) modulation
`B? Pule position modulation
`The characteristics of pulse amplitude modulation are discussed in detail, as it is
`basic to all forms of pulse modulation, be they of the analog or digital type.
`(ii) Digital pulse modulation, in which both time and signal amplitude are repre—
`sented in discrete form; it embodies the following special forms:
`3* Pulse»code modulation
`5 Delta modulation
`#5 Differential pulse-code modulation
`In delta modulation, the sampling rate is increased far in excess of that usedrin pulse—
`code modulation so as to simplify implementation of the system. In contrast, in
`differential pulse-code modulation, the sampling rate is reduced through the use of
`a predictor that exploits the correlation properties of the information—bearing signal.
`(iii) MPEG/audio coding standard, which includes a psychoacoustic model as a key
`element in the design of the encoder.
`P Chapter 4 covers baseband pulse transmission, which deals with the transmission of
`pulseeamplitude modulated signals in their baseband form. Two important issues are
`discussed: the effects of channel noise and limited channel bandwidth on the perfor—
`mance of a digital communication system. Assuming that the channel noise is additive ,
`
`‘
`
`6
`
`

`

`PREFACE
`
`ix
`
`and white, this effect is minimized by using a matched filter, which is basic to the
`design of communication receivers. As for limited channel bandwidth, it manifests
`itself in the form of a phenomenon known as intersymbol interference. To combat
`the degrading effects of this signal-dependent interference, we may use either a pulse-
`shaping filter or correlative encoder/decoder; both of these approaches are discussed.
`The chapter includes a discussion of digital subscriber lines for direct communication
`between a subscriber and an Internet service provider. This is followed by a deriva-
`tion of the optimum linear receiver for combatting the combined effects of channel
`noise and intersym bol interference, which, in turn, leads to an introductory treatment
`of adaptive equalization.
`Chapter 5 discusses signal-space analysis For an additive white Gaussian noise chan-
`nel. In particular, the foundations for the geometric representation of signals with
`finite energy are established The correlation receiver is derived, and its equivalence
`with the matched filter receiver is demonstrated. The chapter finishes with a discus-
`sion of the probability of error and its approximate calculation.
`Chapter 6 discusses passband data transmission, where a sinusoidal carrier wave is
`employed to facilitate the transmission of the digitally modulated wave over a band-
`pass channel. This chapter builds on the geometric interpretation of signals presented
`in Chapter 5. In particular, the effect of channel noise on the performance of digital
`communication systems is evaluated, using the following modulation techniques:
`(i) Phase-shift keying, which is the digital counterpart to phase modulation With
`the phase of the carrier wave taking‘on one of a prescribed set of discrete values.
`(ii) Hybrid amplitude/phase modulation schemes including quadrature-amplitude
`modulation {QAM), and carrierless amplitude/phase modulation (CAP).
`(iii) Frequency-shift keying, which is the digital counterpart of frequency modulation
`with the frequency of the carrier wave taking on one of a prescribed set of discrete
`values.
`
`(iv) Generic multichannel modulation, followed by discrete multitone, the use of
`which has been standardized in asymmetric digital subscriber lines.
`In a digital communication system, timing is everything, which means that the re—
`ceiver must be synchronized to the transmitter. In this context, we speak of the
`receiver being coherent or noncoherent, In a coherent receiver, provisions are made
`for the recovery of both the carrier phase and symbol timing. In a noncoherent
`receiver the carrier.phase is ignored and provision is only’made for symbol timing.
`Such a strategy is dictated by the fact that the carrier phase may be random, making
`phase recovery a costly proposition. Synchronization techniques are discussed in the
`latter part of the chapter, with particular emphasis on discrete-time signal processing.
`Chapter 7 introduces spread-spectrum modulation. Unlike traditional forms of mod-
`ulation discussed in earlier chapters, channel bandwidth is purposely sacrificed in
`spread—spectrum modulation for the sake of security or protection against interfering
`signals. The direct—sequence and frequency-hop forms of spread-spectrum modula-
`tion are discussed.
`
`Chapter 8 deals with multiuser radio communications, where a multitude of users
`have access to a common radio channel. This type of communication channel is well
`represented in satellite and wireless communication systems, both of which are dis-
`cussed. The chapter includes a presentation of link budget analysis, emphasizing the
`related antenna and propagation concepts, and noise calculations.
`Chapter 9 develops the fundamental limits in information theory, which are embod—
`ied in Shannon’s theorems for data compaction, data compression, and data trans-
`
`7
`
`

`

`X
`
`PREFACE
`
`mission. These theorems provide upper bounds on the performance of information
`sources and communication channels. Two concepts, basic to formulation of the
`theorems, are (1) the entropy of a source (whose definition is analogous to that of
`entropy in thermodynamics), and (2) channel capacity.
`9 Chapter 10 deals with error-control coding, which encompasses techniques for the
`encoding and decoding of digital data streams for their reliable transmission over
`noisy channels. Four types of error-control coding are discussed:
`(i) Linear block codes, which are completely described by sets of linearly indepen-
`dent code words, each of which consists of message bits and parity—check bits.
`The parity—check bits are included for the purpose of error control.
`(ii) Cyclic codes, which form a subclass of linear block codes.
`(iii) Convolutional codes, which involve operating on the message sequence contin-
`uously in a serial manner.
`(iv) Turbo codes, which provide a novel method of constructing good codes that
`approach Shannon’s channel capacity in a physically realizable manner.
`Methods for the generation of these codes and their decoding are discussed.
`
`The book also includes supplementary material in the form of six appendices as
`follows:
`
`i
`
`D Appendix 1 reviews probability theory.
`3* Appendix 2, on the representation of signals and systems, reviews the Fourier trans-
`form and its properties, the various definitions of bandwidth, the Hilbert transform,
`and the low-pass equivalents of narrowband signals and systems.
`5 Appendix 3 presents an introductory treatment of the Bessel function and its modified
`form. Bessel functions arise in the study of frequency modulation, noncoherent de—
`tection of signals in noise, and symbol timing synchronization.
`It Appendix 4 introduces the confluent hypergeometric function, the need for which
`arises ’in the envelope detection of amplitude—modulated signals in noise.
`W Appendix 5 provides an introduction to cryptography, which is basic to secure
`communications.
`5" Appendix 6 includes 12 useful tables of various kinds.
`
`As mentioned previously, the primary purpose of this book is to provide a modern
`treatment of communication systems suitable for use in a one— or two-semester under-
`graduate course at the senior level. The make-up of the material for the course is naturally
`determined by the background of the students and the interests of the teachers involved.
`The material covered in the book is both broad and deep enough to satisfy a variety of
`backgrounds and interests, thereby providing considerable flexibility in the choice of
`course material. As an aid to the teacher of the course, a detailed solutions manual for all
`the problems in the book is available from the publisher.
`
`‘
`
`E Acknowledgments
`I wish to express my deep gratitude to Dr. Gregory]. Pottie (University of California, Los
`Angeles), Dr. Santosh Venkatesh (University ofPennsylvania), Dr. Stephen G. Wilson (Uni—
`versity of Virginia), Dr. Gordon Stiiber (Georgia Institute of Technology), Dr. Venugopal
`Veeraralli (Cornell University), and Dr. Granville E. Ott (University of Texas at Austin)
`
`8
`
`

`

`PREFACE
`
`xi
`
`for critical reviews of an earlier version of the manuscript and for making numerous sug—
`gestions that‘have helped me shape the book into its present form. The treatment of the
`effect of noise on envelope detection presented in Chapter 2 is based on course notes made
`available to me by Dr. Santosh Venkatesh, for which I am grateful. I am grateful to Dr.
`Gordon Stiiber for giving permission to reproduce Figure 6.32.
`I am indebted to Dr. Michael Moher (Communications Research Centre, Ottawa)
`for reading five chapters of an earlier version of the manuscript and for making many
`constructive comments on turbo codes. I am equally indebted to Dr. Brendan Frey (Uni-
`versity of Waterloo, Ontario) for his invaluable help in refining the material on turbo
`codes, comments on low-density parity—check codes, for providing the software to plot
`Fig. 9.18, and giving me the permission to reproduce Figures 10.27 and 10.33. I am grate-
`ful to Dr. David Conn (McMaster University, Ontario) for his critical reading of the Back—
`ground and Preview Chapter and for making suggestions on how to improve the presen-
`tation of the material therein.
`
`I also wish to thank Dr. Jean-Jacque Werner (Lucent Technologies, Holmdel), Dr.
`James Mazo (Lucent Technologies, Murray Hill), Dr. Andrew Viterbi (Qualcom, San Di-
`ego), Dr. Radford Neal (University of Toronto, Ontario), Dr. Yitzhak (Irwin) Kalet (Tech-
`nion, Israel), Dr. Walter Chen (Motorola), Dr. John Cioffi (Stanford University), Dr. Jon
`Mark (University of Waterloo, Ontario), and Dr. Robert Dony (University of Guelph,
`Ontario); I thank them all for their helpful comments on selected sections in the book.
`Corrections and suggestions for improvements to the bookmade by Dr. Donald Wunsch
`II (University of Missouri) are also appreciated.
`I am grateful to my graduate student Mathini Sellathurai (McMaster University) for
`performing the computer experiments in the book, and Hugh Pasika (McMaster Univer-
`sity) for many useful comments on the Background and Preview Chapter and for doing
`the computations on some graphical plots in the book. Proofreading of the page proofs
`by Mathini Sellathurai and Alpesh Patel is much appreciated.
`I am particularly grateful to my editor at Wiley, Bill Zobrist, for his strong support
`and help throughout the writing of the book. I am indebted to Monique Calello, Senior
`Production Editor at Wiley, for her tireless effort in overseeing the production of the book
`in its various stages. I thank Katherine Hepburn for advertising and marketing the book.
`I thank Karen Tongish for her careful copyediting of the manuscript, Katrina Avery for
`her careful proofreading of the page proofs, and Kristen Maus for composing the index
`of the book.
`
`Last but by no means least, as always, I am grateful to my Technical Coordinator,
`Lola Brooks, for her tireless effort in typing the manuscript of the book. I also Wish to
`record my gratitude to Brigitte Maier, Assistant Librarian, and Regina Bendig, Reference
`Librarian, at McMaster University, for helping me on numerous occasions in tracing ref—
`erences for the bibliography.
`
`Simon Haykin
`Ancnster, Ontario
`January, 2000
`
`9
`
`

`

`
`
`a BACKGROUND AND PREVIEW
`1
`The Communication Process
`Primary Communication Resources
`Sources of Information
`3
`Communication Networks
`Communication Channels
`Modulation Process
`19
`
`’
`
`3
`
`10
`15
`
`Analog and Digital Types of Communication
`Shannon’s Information Capacity Theorem 23
`A Digital Communication Problem 24
`Historical Notes
`26
`Notes and References 29
`
`21
`
`misused-9e
`
`\l.
`
`99°
`10.
`
`32
`
`35
`
`g CHAPTER 1 Random Processes
`1.1
`Introduction
`31
`1.2
`Mathematical Definition of a Random Process
`1.3
`Stationary Processes
`33
`1.4
`Mean, Correlation, and Covariance Functions
`1.5
`Ergodic Processes
`41
`1.6
`Transmission of a Random Process Through a Linear Time-Invariant Filter
`1.7
`Power Spectral Density
`44
`1.8
`Gaussian Process
`54
`1.9
`Noise
`38
`1.10
`Narrowband Noise
`1.11
`
`64
`
`Representation of Narrowband Noise in Terms of In—phase and Quadrature
`Components
`64
`Representation of Narrowband Noise in Terms of Envelope and Phase
`Components
`67
`69
`Sine Wave Plus Narrowband Noise
`Computer Experiments: Flat-Fading Channel
`
`71
`
`1.12
`
`1.13
`1.14
`
`10
`
`1
`
`3 1
`
`42
`
`xiii
`
`10
`
`

`

`§CHAPIER 2 Continuous-Wave Modulation
`2.1
`Introduction
`88
`2.2
`90
`Amplitude Modulation
`2.3
`Linear Modulation Schemes
`2.4
`2.5
`2.6
`2.7
`2.8
`2.9
`2.10
`2.11
`2.12
`2.13
`2.14
`2.15
`
`105
`
`103
`Frequency Translation
`Frequency-Division Multiplexing
`Angle Modulation
`107
`109
`Frequency Modulation
`Nonlinear Effects in PM Systems
`Superheterodyne Receiver
`128
`130
`Noise in CW Modulation Systems
`Noise in Linear Receivers using Coherent Detection
`Noise in AM Receivers using Envelope Detection
`Noise in PM Receivers
`142
`
`88
`
`183
`
`132
`135
`
`xiv
`
`CONTENTS
`
`1.15 Summary and Discussion
`Notes and References
`77
`Problems
`78
`
`75
`
`93
`
`126
`
`Computer Experiments: Phase-locked Loop
`Surrunary and Discussion
`162
`Notes and References
`165
`Problems
`166
`
`157
`
`E CHAPTER 3 Pulse Modulation
`3.1
`Introduction
`183
`3.2
`184
`Sampling Process
`3.3
`1 8 8
`Pulse—Amplitude Modulation
`3.4
`Other Forms of Pulse Modulation
`3.5
`Bandwidth—Noise Trade—off
`193
`3.6
`Quantization Process
`193
`3.7
`Pulse-Code Modulation
`201
`3.8
`Noise Considerations in PCM Systems
`3.9
`Time-Division Multiplexing
`21 1
`3.10
`Digital Multiplexers
`214
`3.11
`Virtues, Limitations, and Modifications of PCM 217
`3.12
`Delta Modulation
`218
`3.13
`Linear Prediction
`223
`3.14
`227
`Differential Pulse-Code Modulation
`3.15
`Adaptive Differential Pulse-Code Modulation
`
`191
`
`209
`
`229
`
`11
`
`11
`
`

`

`CONTENTS
`
`XV
`
`3.16 Computer Experiment: Adaptive Delta Modulation
`3.17 MPEG Audio Coding Standard
`234
`3.18 Summary and Discussion
`236
`Notes and References
`238
`Problems
`239
`
`232
`
`'
`
`247
`
`26]
`
`g CHAPTER 4 Baseband Pulse Transmission
`4.1
`Introduction
`247
`4.2 Matched Filter
`248
`253
`4.3
`Error Rate Dueto Noise
`259
`4.4
`Intersyrnbol Interference
`4.5
`Nyquist’s Criterion for Distortionless Baseband Binary Transmission
`4.6
`Correlative-Level Coding
`267
`4.7
`Baseband M-ary PAM Transmission
`4.8
`Digital Subscriber Lines
`277
`4.9
`Optimum Linear Receiver
`282
`4.10 Adaptive Equalization
`287
`4.11 Computer Experiments: Eye Patterns
`4.12
`Summary and Discussion
`296
`Notes and References
`297
`Problems
`300
`
`275 f
`
`293
`
`
`EHAFTER 5 Signal-Space Analysis
`5.1
`Introduction
`309
`311
`5.2
`Geometric Representation of Signals
`5.3
`Conversion of the Continuous AWGN Channel into a Vector Channel
`5.4
`Likelihood Functions
`322
`
`309
`
`318
`
`5.5
`5.6
`
`5.7
`5.8
`
`Coherent Detection of Signals in Noise: Maximum Likelihood Decoding
`Correlation Receiver
`326
`
`322
`
`328
`Probability of Error
`337
`Summary and Discussion
`Notes and References
`33 7
`Problems
`338
`
`
`EBAPTER 6 Passband Digital Transmission
`6.1
`Introduction
`344
`6.2
`Passband Transmission Model
`6.3
`Coherent Phase—Shift Keying
`
`348
`349
`
`344
`
`12
`
`12
`
`

`

`xn'
`
`CONTENTS
`
`6.4
`6.5
`6.6
`6.7
`6.8
`6.9
`6.10
`6.11
`6.12
`6.13
`6.14
`6.15
`6.16
`
`368
`
`403
`
`413
`
`Hybrid Amplitude/Phase Modulation Schemes
`Coherent Frequency-Shift Keying
`380
`Detection of Signals with Unknown Phase
`Noncohercnt Orthogonal Modulation
`407
`Noncoherent Binary Frequency-Shift Keying
`Differential Phase-Shift Keying
`414
`Comparison of Digital Modulation Schemes Using a Single Carrier
`Voiceband Modems
`420
`Multichannel Modulation
`Discrete Multitone
`440
`
`431
`
`417
`
`448
`Synchronization
`Computer Experiments: Carrier Recovery and Symbol Timing
`Summary and Discussion
`464
`Notes and References
`465
`Problems
`468
`
`458
`
`3 CHAPTER 7 Spread-Spectrum Modulation
`7.1
`Introduction
`479
`7.2
`480
`Pseudo-Noise Sequences
`7.3
`A Notion of Spread Spectrum 488
`7.4
`Direct—Sequence Spread Spectrum with Coherent Binary Phase-Shift Keying
`7.5
`Signal-Space Dimensionality and Processing Gain
`493
`7.6
`Probability of Error
`497
`7.7
`Frequency-Hop Spread Spectrum 499
`7.8
`Computer Experiments: Maximal~Length and Gold Codes
`7.9
`Summary and Discussion
`508
`Notes and References
`509
`Problems
`509
`
`505
`
`479
`
`490
`
`
`
`Multiuser Radio Communications 5 12
`E CHAPTER 8
`8.1
`Introduction
`512
`8.2
`MultipleAccess Techniques
`8.3
`Satellite Communications
`8.4
`Radio Link Analysis
`517
`8.5
`Wireless Communications
`8.6
`8.7
`8.8
`8.9
`
`513
`514
`
`529
`
`535
`Statistical Characterization of Multipath Channels
`542
`Binary Signaling over a Rayleigh Fading Channel
`TDMA and CDMA Wireless Communication Systems
`Source Coding of Speech for Wireless Communications
`
`547
`55 D
`
`13
`
`13
`
`

`

`8.10 Adaptive Antenna Arrays for Wireless Communications
`8.11
`Summary and Discussion
`559
`Notes and References
`560
`Problems
`562
`
`553
`
`CONTENTS
`
`xvii
`
`567
`
`593
`
`626
`
`568
`
`
`§£IIAPTER 9 Fundamental Limits in Information Theory
`9.1
`Introduction 5 67
`9.2
`Uncertainty, Information, and Entropy
`9.3
`Source—Coding Theorem 574
`9.4
`Data Compaction
`575
`9.5
`Discrete Memoryless Channels
`9.6 Mutual Information
`584
`9.7
`Channel Capacity
`5 87
`9.8
`Channel-Coding Theorem 589 ~
`9.9
`Differential Entropy and Mutual Information for Continuous Ensembles
`9.10 Information Capacity Thenrem 597
`9.11
`Implications of the Information Capacity Theorem 601
`9.12 Information Capacity of Colored Noise Channel
`607
`9.13 Rate Distortion Theory
`611
`’
`9.14 Data Compression
`614
`616
`9.15 Summary and Discussion
`Nales and References
`61 7
`Problems
`618
`
`581
`
`gCHAPTER 10 Error-Control Coding
`10.1
`Introduction
`626
`10.2 Discrete-Memoryless Channels
`10.3 Linear Block Codes
`632
`
`629
`
`641
`10.4 Cyclic Codes
`654
`10.5 Convolutional Codes
`10.6 Maximum Likelihood Decoding of Convolutional Codes
`10.7 Trellis-Coded Modulation
`668
`10.8 Turbo Codes
`674
`10.9 Computer Experiment: Turbo Decoding
`10.10 Low-Density Parity-Check Codes
`683
`10.11 Irregular Codes
`691
`10.12 Summary and Discussion
`Notes and References
`694
`Problems
`696
`
`682
`
`693
`
`660
`
`14
`
`14
`
`

`

`xviii
`
`CONTENTS
`
`APPENDIX 1
`
`Probability Theory
`
`703
`
`APPENDIX 2
`APPENDIX 3
`
`APPENDIX 4
`APPENDIX 5
`APPENDIX 6
`
`Representation of Signals and Systems
`Bessel Functions
`735
`
`715
`
`Confluent Hypergeornetric Functions
`Cryptography
`742
`Tables
`761
`
`740
`
`GLOSSARY
`BIBLIOGRAPHY
`
`INDEX
`
`7 7 l
`7 7 7
`
`792
`
`15
`
`15
`
`

`

`2. 5
`
`Frequency-Division Multiplexing
`
`l 05
`
`The unshaded part of the spectrum in Figure 2.1719 defines the wanted modulated
`signal 52(1), and the shaded part of this spectrum defines the image signal associated
`with 5;”). For obvious reasons, the mixer in this case is referred to as a frequency—
`up converter.
`Down conversion. In this second case the translated carrier frequency f; is smaller
`than the incoming carrier frequency f1, and the required oscillator frequency f, is
`therefore defined by
`
`01‘
`
`fi=fl—fi
`
`fi=fi’fi
`
`The picture we have this time is the reverse of that pertaining to up conversion. In
`particular, the shaded part of the spectrum in Figure 2.17b defines the wanted mod-
`ulated signal 52(1), and the unshaded part of this spectrum defines the associated
`image signal. The mixer is now referred to as a frequency-dorm! converter. Note that
`in this case the translated carrier frequency )3 has to be larger than W (i.e., one half
`of the bandwidth of the modulated signal) to avoid sideband overlap.
`
`The purpose of the bandpass filter in the mixer of Figure 2.16 is to pass the wanted
`modulated signal slit) and eliminate the associated image signal. This objective is achieved
`by aligning the midband frequency of the filter with the translated carrier frequency fl and
`assigning it a bandwidth equal to that of die incoming modulated signal sllt).
`It is important to note that mixing is a linear operation. Accordingly, the relation of
`the sidebands of the incoming modulated wave to the carrier is completely preserved at
`the mixer output.
`
`[3. 5 Frequency-Dim'sion Multiplexing
`Another important signal processing operation is multiplexing, whereby a number of in-
`dependent signals can be combined into a composite signal suitable for transmission over
`a common channel. Voice frequencies transmitted over telephone systems, for example,
`range from 300 to 3100 Hz. To transmit a number of these signals over the same channel,
`the signals must be kept apart so that they do not interfere with each other, and thus they
`can be separated at the receiving end. This is accomplished by separating the signals either
`in frequency or in time. The technique of separating the signals in frequency is referred to
`as frequency-division multiplexing (FDM), whereas the technique of separating the signals
`in time is called time-division multiplexing (TDM). In this section, we discuss FDM sys—
`tems, and TDM systems are discussed in Chapter 3.
`A block diagram of an FDM system is shown in Figure 2.18. The incoming message
`signals are assumed to be of the low-pass type, but their spectra do not necessarily have
`nonzero values all the way down to zero frequency. Following each signal input, we have
`shown a low-pass filter, which is designed to remove high—frequency components that do
`not contribute significantly to signal representation but are capable of disturbing other
`message signals that share the common channel. These low-pass filters may be omitted
`only if the input signals are sufficiently band limited initially. The filtered signals are applied
`
`16
`
`16
`
`

`

`106
`
`Grumman 2 a CONTINUOUS-WAVE MODULATION
`
`Message
`inputs
`
`Low-pass
`Band—pass
`Band—pass
`Low-pass Message
`
`
` filters Modulators filters filters Demodulators filters
`
`
`outputs
`
`
`
`
`
`
`
`BP —> DEM —> LP L;1
`1——>-
`LF fl MOD —> BP
`
`29- LP
`BP
`BP
`———>
`LP ~94
`
`Common
`channel
`
`N—>-
`
`LP
`
`BF
`
`BF —>-
`
`LP —>-N
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Carrier
`
`supply
`
`
`Transmitter
`
`Carrier
`
`sunny
`
`
`Receiver
`
`FIGURE 2.18 Block diagram of FDM system.
`
`to modulators that shift the frequency ranges of the signals so as to occupy mutually
`exclusive frequency intervals. The necessary carrier frequencies needed to perform these
`frequency translations are obtained from a carrier supply. For the modulation, we may
`use any one of the methods described in previous sections of this chapter. However, the
`most widely used method of modulation in frequency-division multiplexing is single side-
`band modulation, which, in the case of voice signals, requires a bandwidth that is ap‘
`proximately equal to that of the original voice signal. In practice, each voice input is usually
`assigned a bandwidth of 4 kHz. The band-pass filters following the modulators are used
`to restrict the band of each modulated wave to its prescribed range. The resulting band-
`pass filter outputs are next combined in parallel to form the input to the common channel.
`At the receiving terminal, a bank of band-pass filters, with their inputs connected in par-
`allel, is used to separate the message signals on a frequency-occupancy basis. Finally, the
`original message signals are recovered by individual demodulators. Note that the FDM
`system shown in Figure 2.18 operates in only one direction. To provide for two—way
`transmission, as in telephony, for example, we have to completely duplicate the multi-
`plexing facilities, With the components connected in reverse order and with the signal
`waves proceeding from right to left.
`
`e EXAMPLE 2.1
`
`The practical implementation of an FDM system usually involves many steps of modulation
`and demodulation, as illustrated in Figure 2.19. The first multiplexing step combines 12 voict
`inputs into a basic group, which is formed by having the nth input modulate a carrier at
`frequency f5 = 60 + 4n kHz, where n = 1, 2, .
`.
`.
`, 12. The lower sidebands are then selected
`by baud-pass filtering and combined to form a group of 12 lower sidebands (one for with
`voice input). Thus the basic group occupies the frequency band 60 to 108 kHz. The next step
`in the FDM hierarchy involves the combination of five basic groups into a supcrgmup. This
`is accomplished by using the nth group to modulate a carrier of fi'equcncy fl. = 372 + 43”
`kHz, where n = 1, Z, .
`.
`. , 5. Here again the lower sidebands are selected by filtering and the“
`
`17
`
`17
`
`

`

`Carrier frequencies (in kHz)
`of voice inputs
`‘\
`
`,— ios
`1L.
`
`104 .-
`11
`
`’ 2°: ‘ 2°
`92 ——
`8
`as
`7 _
`34
`6
`7 80
`5
`76 — 4
`72 — 3
`
`68 — 2
`64 —-
`l.
`
`
`
`
`
`
`
`
`Voice band
`
`2.6 Angle inodulufilm
`
`107
`
`108 kHz
`
`Caryie' frequencies
`(in kHz) of groups
`‘— 552 kHz
`
`612 — 5
`504
`554 14_ 456
`2’22 ‘ 3F 360
`420 —-
`1
`312
`l
`Supergroup
`offigroups
`
`
`
`
`T60
`Basic group of 12
`voice inputs
`
`FIGURE 2.19 Illustrating the modulation steps in an FDM system.
`
`
`
`ination against noise and interference than amplitude modulation. As will be shown later
`in Section 2.7, however, this improvement in performance is achieved at the expense of
`increased transmission bandwidth; that is, angle modulation provides us with a practical
`
`5 BASIC DEFINITIONS
`
`Let 6,“) denote the angle of a modulated sinusoidal carrier, assumed to be a function of
`the message signal. We express the resulting angle-modulated wave as
`
`5“) = AC cos[6,-(t)]
`
`(2.19)
`
`18
`
`18
`
`

`

`3.9 Time-Division Mulllpleaving
`
`2 1 l
`
`ulfiplexing
`l 3,9 Time-Divisi
`The sampling theorem provides the basis for transmitting the information contained in a
`band-limited message signal m(t) as a sequence of samples of mlt) taken uniformly at a
`rate that is usually slightly higher than the Nyquist rate. An important feature of the
`sampling process is a conservation oftime. That is, the transmission of the message samples
`engages the communication channel for only a fraction of the sampling interval on a
`periodic basis, and in this way some of the time interval between adjacent samples is cleared
`for use by other independent message sources on a time-shared basis. We thereby obtain
`a time—division multiplex (TDM) system, which enables the joint utilization of a common
`communication channel by a plurality of independent message sources without mutual
`interfer