DIGITAL AND ANALOG COMMUNICATION SYSTEMS K. SAM SHANMUGAM Wichita State University John Wiley & Sons New York I Chichester I Brisbane / Toronto Copyright © 1979, by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Sections 107 and 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons. Library of Congress Cataloging in Publication Data: Shanmugam, K. Sam. Digital and analog communication systems. Includes bibliographical references and index. 1. Telecommunication. 2. Digital communications. 3. Information theory. 4. Signal theory (Tf.!iecommunication) I. Title. TK5101.S445 621.38 78-26191 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 To Radha, Kannon, and Ravi PREFACE With the increasing importance of digital communication, there is a need for a communication theory text that emphasizes the basic aspects of ~nformation theory, discrete modulation techniques, and coding theory at a level ap propriate for advanced undergraduates and first-year graduate students. The purpose of this book is to present an introductory level treatment of digital and analog communication systems with an emphasis on digital com munication systems. A study of communication systems covers many varied aspects-from the mathematical and statistical abstraction of information theory, modulation theory, and coding theory, to the electronic considerations associated with the building of functional blocks to perform various signal processing tasks. I have attempted to present in this book a unified treatment of these many diverse aspects of communication systems. Throughout the book we consider the process of electrical communication as consisting of a sequence of signal processing operations. Each functional block in the system performs a specifi<; signal processing operation. For each functional block, we define the input/output requirements and the parameters we have at our disposal. We derive expressions that relate the performance of each functional block to its parameters and use these relationships to optimize the design of the functional block. While we occasionally present examples of physical blocks (or circuits) that correspond to specific functional blocks, less emphasis is placed on this aspect of the problem-namely, the physical realization of functional blocks. The major reasons for neglecting this prob- vii viii Preface lem are: (1) specific circuits and devices become obsolete in a short time due to rapid technological developments, and (2) the design of circuits could be taught better in a circuit design course rather than in a communication systems course. The material presented in this book is arranged into three study areas: a review section, the study of digital communication systems, and the study of analog communication systems. The review section (Chapters 2 and 3) covers signal models, systems analysis, random variables, and random pro cesses. A cursory treatment of modulation and demodulation techniques and signal-to-noise ratios are included in the review. These topics are covered in detail in later chapters. Chapters 4, 5, 8, and 9 deal with the analysis and design of digital communication systems. Chapter 4 presents information theory and its im plications for digital communication systems. Discrete pulse and carrier wave modulation schemes are discussed in Chapters 5 and 8. Finally, basic ideas in coding theory are dealt with in Chapter 9. Analog communication systems are discussed in Chapters 6 and 7. Base band analog signal transmission and continuous wave (CW) modulation tech niques for analog signal transmission are covered in Chapter 6. The effect of noise in CW modulation schemes is discussed in Chapter 7. This chapter also contains a comparison of various CW modulation schemes. Finally, Chapter 10 deals with digital transmission methods for analog signals. Sampling, quantizing, and encoding of analog signals for transmission over digital systems are described here. It is assumed that the student has some knowledge of circuit analysis and linear systems analysis. Prior exposure to Fourier transforms, random vari ables, and random processes would be helpful, but not essential. With this background, it should be possible to organize and teach several possible courses out of this text. First, this book can be used, as a whole, for a two-semester course on digital and analog communication systems. It is also possible to teach a one-semester course on digital and analog communication systems by covering Chapters 2 and 3 rapidly and selecting materials from Chapters 5, 6, 7, and 8. Finally, an elective course in digital communication systems may be taught using the material in Chapters 4, 5, 8. 9, and 10. Selective double coverage of topics in the book will allow the instructor considerable flexibility in structuring these courses. Considerable effort has been made to present material at such a level that there is consistent progression from concepts to design considerations without getting mired in too much theoretical details. Proofs of theorems and statements are included only when it is felt that they contribute sufficient insight into the problem being addressed. Proofs are omitted when they Preface ix involve lengthy theoretical discourse of material at a level beyond the scope of this text. In such cases, outlines of proofs with adequate references to outside material is presented so that the ambitious reader can labor through the details. Each chapter contains a number of examples and problems. The examples and problems cover practical and theoretical aspects of analysis and design of communication systems. An instructor's manual giving complete solutions to the problems is available from the publisher on request. ACKNOWLEDGMENTS I am indebted to many people for their advice, assistance, and contributions to the development of this text. First, I wish to thank the Air Force Communication Service and the U.S. Air Force Rome Air Development Center for their support of my research activities in the field of com munication systems. Several problems and concepts presented in this text came out of these research activities and I am deeply indebted to these and other agencies, including the National Science Foundation, NASA, and the Department of Energy, for their research support. Several individuals have read the manuscript and their comments have helped me considerably to improve the accuracy and clarity of the text. I am pleased to acknowledge the assistance of Professor Arthur M. Breipohl, University of Kansas, and Professor M. Lal, Wichita State University, who supplied many helpful suggestions while teaching from the earlier drafts of the manuscript. The comments and suggestions from the reviewers, Profes sors Arthur M. Breipohl (University of Kansas), R. Frank Quick, Jr. (Car negie Mellon University), Robert A. Gabel (University of Colorado), and Gene A. Davenport, Editor, John Wiley and Sons, have also been very helpful. I am also grateful to my graduate students, J. M. Naik, Art Frankowski, and Mark A. Miller for proofreading the final manuscript. I also wish to thank the staff and administration of the College of Engineer ing at Wichita State University for providing me with typing and other help in the earlier stages of the development of the manuscript. In particular, I wish to thank Marta Manny who typed the entire manuscript in expert fashion, not once, but several times. Finally, I am grateful to my wife and children for their patience and understanding during the time I devoted to writing this book. K. Sam Shanmugam CONTENTS 1 INTRODUCTION 1 1.1 Model of a Communication System 2 1.2 Elements of a Digital Communication System 4 1.2.1 Information Source 5 1.2.2 Source Encoder/Decoder 6 1.2.3 Communication Channel 7 1.2.4 Modulator 8 1.2.5 Demodulator 9 1.2.6 Channel Encoder/Decoder 10 1.2.7 Other Functional Blocks 11 1.3 Analysis and Design of Communication Systems 12 1.3.1 Analysis of Communication Systems 12 1.3.2 Design of Communication Systems 12 1.4 Organization of the Book 14 2 SYSTEMS AND SIGNAL ANALYSIS 16 2.1 Systems and Signals 17 2.1.1 Classification of Sig nals 17 2.1.2 Classification of Systems 20 2.2 Signal Representation Using Fourier Series 21 2.2.1 Complex Exponential Fourier Series 21 2.2.2 Fourier Series Representation of Periodic Signals 22 xi xii Contents 2.3 Signal Representation Using Fourier Transforms 26 2.3.1 Fourier Transform Representation of Aperiodic Sig- nals 26 2.3.2 Fourier Transform of Periodic Power Signals 30 2.3.3 Transform Theorems 31 2.4 Power Spectral Density 36 2.5 System Response and Filters 41 2.5.1 Impulse Response, Step Response, and Time Domain Analysis 41 2.5.2 Transfer Function and Frequency Domain Analysis 42 2.5.3 Effect of Transfer Function on Spectral Densities 43 2.5.4 Real and Ideal Filters 43 2.6 Spectral Analysis of Modulation and Demodulation Opera- tions 47 2.6.1 Analysis of a Linear Modulation System 47 2.7 Spectral Measurements and Computations 50 2.7.1 Spectrum Analyzer 50 2.7.2 Numerical Computation of Fourier series Coefficients 51 2.7.3 Numerical Computation of Fourier Transforms 54 2.8 Summary 55 References 57 Problems 58 3 RANDOM SIGNAL THEORY 68 3.1 Introduction 68 3.2 Introduction to Probabilities 70 3.2.1 Definitions 70 3.2.2 Probabilities of Random Events 70 3.2.3 Joint and Conditional Probabilities 72 3.3 Discrete Random Variables 74 3.3.1 Probability Mass Functions 74 3.3.2 Statistical Averages 76 3.3.3 Examples of Probability Mass Functions 77 3.4 Continuous Random Variables 79 3.4.1 Probability Density Functions and Statistical Aver- ages 79 3.4.2 Examples of Probability Density Functions 80 3.4.3 Transformation of Random Variables 83 3.5 Random Processes 86 3.5.1 Definitions and Notations 88