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Proakis-50210 proa-fm August 9, 2001 14:2 COMMUNICATION SYSTEMS ENGINEERING John G. Proakis Masoud Salehi 2nd Ed. Upper Saddle River, New Jersey 07458 i

Proakis-50210 proa-fm August 9, 2001 14:2 To Felia, George, and Elena. —John G. Proakis To Fariba, Omid, Sina, and my parents. —Masoud Salehi Library of Congress Cataloging-in-Publication Data CIP data available on ﬁle. Vice President and Editorial Director, ECS: Marcia J. Horton Publisher: Tom Robbins Editorial Assistant: Jody McDonnell Vice President and Director of Production and Manufacturing, ESM: David W. Riccardi Executive Managing Editor: Vince O’Brien Managing Editor: David A. George Production Editor: Chanda Wakeﬁeld Director of Creative Services: Paul Belfanti Creative Director: Carole Anson Art Director: Jayne Conte Art Editor: Greg Dulles Manufacturing Manager: Trudy Pisciotti Manufacturing Buyer: Lynda Castillo Marketing Manager: Holly Stark Marketing Assistant: Karen Moon c 2002 by Prentice-Hall, Inc. Upper Saddle River, New Jersey All rights reserved. No part of this book may be reproduced, in any form or by any means without permission in writing from the publisher. Printed in the United States of America 10 9 8 7 5 4 3 6 2 1 ISBN 0-13-061793-8 Pearson Education Ltd., London Pearson Education Australia Pty. Ltd., Sydney Pearson Education Singapore, Pte. Ltd. Pearson Education North Asia Ltd., Hong Kong Pearson Education Canada, Inc., Toronto Pearson Educacíon de Mexico, S.A. de C.V. Pearson Education—Japan, Tokyo Pearson Education Malaysia, Pte. Ltd. ii

Proakis-50210 proa-fm August 3, 2001 15:53 Contents PREFACE 1 INTRODUCTION 1.1 1.2 1.3 1.4 1.5 1.6 Historical Review 1 Elements of an Electrical Communication System 4 1.2.1 Digital Communication System, 7 1.2.2 Early Work in Digital Communications, 10 Communication Channels and Their Characteristics Mathematical Models for Communication Channels 12 19 Organization of the Book 22 Further Reading 23 2 FREQUENCY DOMAIN ANALYSIS OF SIGNALS AND SYSTEMS 2.1 2.2 Fourier Series 2.1.1 Fourier Series for Real Signals: the Trigonometric Fourier Series, 29 24 Fourier Transforms 2.2.1 Fourier Transform of Real, Even, and Odd Signals, 35 31 xi 1 24 iii

Proakis-50210 proa-fm August 3, 2001 15:53 iv Contents 2.3 2.4 2.5 2.6 2.2.2 Basic Properties of the Fourier Transform, 36 2.2.3 Fourier Transform for Periodic Signals, 39 Power and Energy 2.3.1 Energy-Type Signals, 41 2.3.2 Power-Type Signals, 42 40 Sampling of Bandlimited Signals 45 Bandpass Signals 49 Further Reading 57 Problems 57 3 ANALOG SIGNAL TRANSMISSION AND RECEPTION 70 3.1 3.2 3.3 3.4 3.5 3.6 Introduction to Modulation 70 71 Amplitude Modulation (AM) 3.2.1 Double-Sideband Suppressed Carrier AM, 71 3.2.2 Conventional Amplitude Modulation, 78 3.2.3 Single-Sideband AM, 81 3.2.4 Vestigial-Sideband AM, 85 3.2.5 Implementation of AM Modulators and Demodulators, 88 3.2.6 Signal Multiplexing, 94 Angle Modulation 96 3.3.1 Representation of FM and PM Signals, 97 3.3.2 Spectral Characteristics of Angle-Modulated Signals, 101 3.3.3 Implementation of Angle Modulators and Demodulators, 107 Radio and Television Broadcasting 3.4.1 AM Radio Broadcasting, 115 3.4.2 FM Radio Broadcasting, 116 3.4.3 Television Broadcasting, 120 115 Mobile Radio Systems 128 Further Reading 131 Problems 131 4 RANDOM PROCESSES 144 4.1 4.2 Probability and Random Variables 144 159 Random Processes: Basic Concepts 4.2.1 Description of Random Processes, 162 4.2.2 Statistical Averages, 164 4.2.3 Stationary Processes, 166 4.2.4 Random Processes and Linear Systems, 174

Proakis-50210 proa-fm August 3, 2001 15:53 Contents v 4.3 4.4 4.5 4.6 4.7 Random Processes in the Frequency Domain 4.3.1 Power Spectrum of Stochastic Processes, 177 4.3.2 Transmission over LTI Systems, 183 177 Gaussian and White Processes 4.4.1 Gaussian Processes, 186 4.4.2 White Processes, 188 186 Bandlimited Processes and Sampling 192 Bandpass Processes 194 Further Reading 201 Problems 202 5 EFFECT OF NOISE ON ANALOG COMMUNICATION SYSTEMS 217 5.1 5.2 5.3 5.4 5.5 Effect of Noise on Linear-Modulation Systems 5.1.1 Effect of Noise on a Baseband System, 218 5.1.2 Effect of Noise on DSB-SC AM, 218 5.1.3 Effect of Noise on SSB AM, 220 5.1.4 Effect of Noise on Conventional AM, 221 217 Carrier-Phase Estimation with a Phase-Locked Loop (PLL) 225 5.2.1 The Phase-Locked Loop (PLL), 226 5.2.2 Effect of Additive Noise on Phase Estimation, 229 Effect of Noise on Angle Modulation 5.3.1 Threshold Effect in Angle Modulation, 244 5.3.2 Pre-emphasis and De-emphasis Filtering, 248 234 Comparison of Analog-Modulation Systems 251 Effects of Transmission Losses and Noise in Analog Communication Systems 5.5.1 Characterization of Thermal Noise Sources, 253 5.5.2 Effective Noise Temperature and Noise Figure, 254 5.5.3 Transmission Losses, 257 5.5.4 Repeaters for Signal Transmission, 258 252 5.6 Further Reading 261 Problems 261 6 INFORMATION SOURCES AND SOURCE CODING 267 6.1 Modeling of Information Sources 6.1.1 Measure of Information, 269 6.1.2 Joint and Conditional Entropy, 271 268

Proakis-50210 proa-fm August 3, 2001 15:53 vi Contents 6.2 6.3 6.4 6.5 6.6 6.7 6.8 Source-Coding Theorem 273 Source-Coding Algorithms 276 6.3.1 The Huffman Source-Coding Algorithm, 276 6.3.2 The Lempel-Ziv Source-Coding Algorithm, 280 Rate-Distortion Theory 282 6.4.1 Mutual Information, 283 6.4.2 Differential Entropy, 284 6.4.3 Rate-Distortion Function, 285 Quantization 290 6.5.1 Scalar Quantization, 291 6.5.2 Vector Quantization, 300 302 Waveform Coding 6.6.1 Pulse-Code Modulation (PCM), 302 6.6.2 Differential Pulse-Code Modulation (DPCM), 307 6.6.3 Delta Modulation (M), 310 Analysis-Synthesis Techniques 312 Digital Audio Transmission and Digital Audio Recording 6.8.1 Digital Audio in Telephone Transmission Systems, 317 6.8.2 Digital Audio Recording, 319 316 6.9 The JPEG Image-Coding Standard 323 6.10 Further Reading 327 Problems 327 7 DIGITAL TRANSMISSION THROUGH THE ADDITIVE WHITE GAUSSIAN NOISE CHANNEL 340 7.1 7.2 7.3 7.4 Geometric Representation of Signal Waveforms 341 Pulse Amplitude Modulation 345 Two-dimensional Signal Waveforms 7.3.1 Baseband Signals, 350 7.3.2 Two-dimensional Bandpass Signals—Carrier-Phase Modulation, 354 7.3.3 Two-dimensional Bandpass Signals—Quadrature Amplitude 350 Modulation, 357 Multidimensional Signal Waveforms 7.4.1 Orthogonal Signal Waveforms, 360 7.4.2 Biorthogonal Signal Waveforms, 365 7.4.3 Simplex Signal Waveforms, 366 7.4.4 Binary-Coded Signal Waveforms, 367 360

Proakis-50210 proa-fm August 3, 2001 15:53 Contents 7.5 7.6 7.7 7.8 vii 370 Optimum Receiver for Digitally Modulated Signals in Additive White Gaussian Noise 7.5.1 Correlation-Type Demodulator, 370 7.5.2 Matched-Filter-Type Demodulator, 375 7.5.3 The Optimum Detector, 381 7.5.4 Demodulation and Detection of Carrier-Amplitude Modulated Signals, 386 7.5.5 Demodulation and Detection of Carrier-Phase Modulated Signals, 388 7.5.6 Demodulation and Detection of Quadrature Amplitude Modulated Signals, 396 7.5.7 Demodulation and Detection of Frequency-Modulated Signals, 398 405 Probability of Error for Signal Detection in Additive White Gaussian Noise 7.6.1 7.6.2 7.6.3 7.6.4 7.6.5 7.6.6 7.6.7 7.6.8 7.6.9 7.6.10 Comparison of Modulation Methods, 432 Probability of Error for Binary Modulation, 405 Probability of Error for M-ary PAM, 408 Probability of Error for Phase-Coherent PSK Modulation, 413 Probability of Error for DPSK, 417 Probability of Error for QAM, 418 Probability of Error for M-ary Orthogonal Signals, 423 Probability of Error for M-ary Biorthogonal Signals, 428 Probability of Error for M-ary Simplex Signals, 429 Probability of Error for Noncoherent Detection of FSK, 430 Performance Analysis for Wireline and Radio Communication Channels 436 7.7.1 Regenerative Repeaters, 437 7.7.2 Link Budget Analysis for Radio Channels, 438 Symbol Synchronization 442 7.8.1 Early–Late Gate Synchronizers, 443 7.8.2 Minimum Mean-Square-Error Method, 445 7.8.3 Maximum-Likelihood Methods, 448 7.8.4 Spectral Line Methods, 449 7.8.5 Symbol Synchronization for Carrier-Modulated Signals, 451 7.9 Further Reading 452 Problems 453 8 DIGITAL TRANSMISSION THROUGH BANDLIMITED AWGN CHANNELS 474 8.1 Digital Transmission through Bandlimited Channels 474 8.1.1 Digital PAM Transmission through Bandlimited Baseband Channels, 478 8.1.2 Digital Transmission through Bandlimited Bandpass Channels, 480

Proakis-50210 proa-fm August 3, 2001 15:53 viii Contents 8.2 8.3 8.4 8.5 8.6 8.7 8.8 The Power Spectrum of Digitally Modulated Signals 482 8.2.1 The Power Spectrum of the Baseband Signal, 483 8.2.2 The Power Spectrum of a Carrier-Modulated Signal, 488 Signal Design for Bandlimited Channels 8.3.1 Design of Bandlimited Signals for Zero ISI—The Nyquist Criterion, 492 8.3.2 Design of Bandlimited Signals with Controlled ISI—Partial Response 490 Signals, 497 Probability of Error in Detection of Digital PAM 499 8.4.1 Probability of Error for Detection of Digital PAM with Zero ISI, 500 8.4.2 Symbol-by-Symbol Detection of Data with Controlled ISI, 501 8.4.3 Probability of Error for Detection of Partial Response Signals, 504 Digitally Modulated Signals with Memory 8.5.1 Modulation Codes and Modulation Signals with Memory, 508 8.5.2 The Maximum-Likelihood Sequence Detector, 521 8.5.3 Maximum-Likelihood Sequence Detection of Partial Response 507 Signals, 525 8.5.4 The Power Spectrum of Digital Signals with Memory, 530 System Design in the Presence of Channel Distortion 8.6.1 Design of Transmitting and Receiving Filters for a Known Channel, 535 8.6.2 Channel Equalization, 538 534 Multicarrier Modulation and OFDM 556 8.7.1 An OFDM System Implemented via the FFT Algorithm, 557 Further Reading 560 Problems 561 9 CHANNEL CAPACITY AND CODING 576 9.1 9.2 9.3 9.4 9.5 9.6 Modeling of Communication Channels 576 Channel Capacity 9.2.1 Gaussian Channel Capacity, 583 579 Bounds on Communication 586 9.3.1 Transmission of Analog Sources by PCM, 590 Coding for Reliable Communication 591 9.4.1 A Tight Bound on Error Probability of Orthogonal Signals, 592 9.4.2 The Promise of Coding, 595 Linear Block Codes 9.5.1 Decoding and Performance of Linear Block Codes, 606 9.5.2 Burst-Error-Correcting-Codes, 614 601 Cyclic Codes 9.6.1 The Structure of Cyclic Codes, 615 615

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