Communication Systems · PM and FM Signals 208 Narrowband PM and FM 212 Tone Modulation 213 Multitone and Periodic Modulation 220 5.2 Transmission Bandwidth and Distortion (5.1) 223

COMMUNICATION SYSTEMSAn Introduction to Signals and Noise

in Electrical Communication

FIFTH EDITION

A. Bruce CarlsonLate of Rensselaer Polytechnic Institute

Paul B. CrillyUniversity of Tennessee

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COMMUNICATION SYSTEMS: AN INTRODUCTION TO SIGNALS AND NOISE IN ELECTRICALCOMMUNICATION, FIFTH EDITION

Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of theAmericas, New York, NY 10020. Copyright © 2010 by The McGraw-Hill Companies, Inc. All rightsreserved. Previous editions © 2002, 1986, and 1975. No part of this publication may be reproduced ordistributed in any form or by any means, or stored in a database or retrieval system, without the priorwritten consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network orother electronic storage or transmission, or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside theUnited States.

This book is printed on acid-free paper.

1 2 3 4 5 6 7 8 9 0 DOC/DOC 0 9

ISBN 978–0–07–338040–7MHID 0–07–338040–7

Global Publisher: Raghothaman SrinivasanDirector of Development: Kristine TibbettsDevelopmental Editor: Lora NeyensSenior Marketing Manager: Curt ReynoldsProject Manager: Melissa M. LeickSenior Production Supervisor: Sherry L. KaneSenior Media Project Manager: Jodi K. BanowetzAssociate Design Coordinator: Brenda A. RolwesCover Designer: Studio Montage, St. Louis, MissouriCompositor: Laserwords Private LimitedTypeface: 10/12 Times RomanPrinter: R. R. Donnelley Crawfordsville, IN

All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.

Library of Congress Cataloging-in-Publication Data

Carlson, A. Bruce, 1937–Communication systems : an introduction to signals and noise in electrical communication /

A. Bruce Carlson, Paul B. Crilly.—5th ed.p. cm.

Includes index.ISBN 978–0–07–338040–7—ISBN 0–07–338040–7 (hard copy : alk. paper) 1. Signal theory

(Telecommunication) 2. Modulation (Electronics) 3. Digital communications. I. Crilly, Paul B. II. Title. TK5102.5.C3 2010621.382 ' 23—dc22

2008049008

www.mhhe.com

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To my wife and best friend,Alice Kathleen Eiland Crilly

To my parents,Lois Brown Crilly and Ira Benjamin Crilly

To my grandmother,Harriet Wilson Crilly

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Contents

The numbers in parentheses after section titles identify previous sections that contain the minimum prerequisitematerial.

Chapter 1

Introduction 11.1 Elements and Limitations

of Communication Systems 2Information, Messages, and Signals 2Elements of a Communication System 3Fundamental Limitations 5

1.2 Modulation and Coding 6Modulation Methods 6Modulation Benefits and Applications 8Coding Methods and Benefits 11

1.3 Electromagnetic Wave Propagation OverWireless Channels 12

RF Wave Deflection 14Skywave Propagation 14

1.4 Emerging Developments 171.5 Societal Impact and Historical

Perspective 20Historical Perspective 21

1.6 Prospectus 24

Chapter 2

Signals and Spectra 272.1 Line Spectra and Fourier Series 29

Phasors and Line Spectra 29Periodic Signals and Average Power 33Fourier Series 35Convergence Conditions and Gibbs

Phenomenon 39Parseval’s Power Theorem 42

2.2 Fourier Transforms and Continuous Spectra(2.1) 43

Fourier Transforms 43Symmetric and Causal Signals 47Rayleigh’s Energy Theorem 50Duality Theorem 52Transform Calculations 54

2.3 Time and Frequency Relations (2.2) 54Superposition 55Time Delay and Scale Change 55

Frequency Translation and Modulation 58Differentiation and Integration 60

2.4 Convolution (2.3) 62Convolution Integral 63Convolution Theorems 65

2.5 Impulses and Transforms in the Limit (2.4) 68

Properties of the Unit Impulse 68Impulses in Frequency 71Step and Signum Functions 74Impulses in Time 76

2.6 Discrete Time Signals and the DiscreteFourier Transform 80

Convolution Using the DFT (2.4) 83

Chapter 3

Signal Transmission and Filtering 913.1 Response of LTI Systems (2.4) 92

Impulse Response and the Superposition Integral 93

Transfer Functions and Frequency Response 96

Block-Diagram Analysis 1023.2 Signal Distortion in Transmission

(3.1) 105Distortionless Transmission 105Linear Distortion 107Equalization 110Nonlinear Distortion and Companding 113

3.3 Transmission Loss and Decibels (3.2) 116Power Gain 116Transmission Loss and Repeaters 118Fiber Optics 119Radio Transmission 122

3.4 Filters and Filtering (3.3) 126Ideal Filters 126Bandlimiting and Timelimiting 128Real Filters 129Pulse Response and Risetime 134

3.5 Quadrature Filters and Hilbert Transforms (3.4) 138

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3.6 Correlation and Spectral Density (3.4) 141Correlation of Power Signals 141Correlation of Energy Signals 145Spectral Density Functions 147

Chapter 4

Linear CW Modulation 1614.1 Bandpass Signals and Systems (3.4) 162

Analog Message Conventions 162Bandpass Signals 164Bandpass Transmission 168Bandwidth 172

4.2 Double-Sideband Amplitude Modulation (4.1) 173

AM Signals and Spectra 173DSB Signals and Spectra 176Tone Modulation and Phasor Analysis 178

4.3 Modulators and Transmitters (4.2) 179Product Modulators 180Square-Law and Balanced Modulators 180Switching Modulators 184

4.4 Suppressed-Sideband AmplitudeModulation (3.5, 4.3) 185

SSB Signals and Spectra 185SSB Generation 188VSB Signals and Spectra 191

4.5 Frequency Conversion and Demodulation (4.4) 193

Frequency Conversion 194Synchronous Detection 195Envelope Detection 198

Chapter 5

Angle CW Modulation 2075.1 Phase and Frequency Modulation

(4.3) 208PM and FM Signals 208Narrowband PM and FM 212Tone Modulation 213Multitone and Periodic Modulation 220

5.2 Transmission Bandwidth and Distortion (5.1) 223

Transmission Bandwidth Estimates 223Linear Distortion 226Nonlinear Distortion and Limiters 229

5.3 Generation and Detection of FM and PM (4.5, 5.2) 232

Direct FM and VCOs 233

Phase Modulators and Indirect FM 234Triangular-Wave FM 237Frequency Detection 239

5.4 Interference (5.3) 243Interfering Sinusoids 243Deemphasis and Preemphasis Filtering 245FM Capture Effect 247

Chapter 6

Sampling and Pulse Modulation 2576.1 Sampling Theory and Practice

(2.6, 4.2) 258Chopper Sampling 258Ideal Sampling and Reconstruction 263Practical Sampling and Aliasing 266

6.2 Pulse-Amplitude Modulation (6.1) 272Flat-Top Sampling and PAM 272

6.3 Pulse-Time Modulation (6.2) 275Pulse-Duration and Pulse-Position

Modulation 275PPM Spectral Analysis 278

Chapter 7

Analog Communication Systems 2877.1 Receivers for CW Modulation

(2.6, 4.5, 5.3) 288Superheterodyne Receivers 288Direct Conversion Receivers 292Special-Purpose Receivers 293Receiver Specifications 294Scanning Spectrum Analyzers 295

7.2 Multiplexing Systems (4.5, 6.1) 297Frequency-Division Multiplexing 297Quadrature-Carrier Multiplexing 302Time-Division Multiplexing 303Crosstalk and Guard Times 307Comparison of TDM and FDM 309

7.3 Phase-Locked Loops (7.1) 311PLL Operation and Lock-In 311Synchronous Detection and Frequency

Synthesizers 314Linearized PLL Models and FM

Detection 3177.4 Television Systems (7.1) 319

Video Signals, Resolution, and Bandwidth 319Monochrome Transmitters and Receivers 324Color Television 327HDTV 332

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vi Contents

Chapter 8

Probability and Random Variables 3458.1 Probability and Sample Space 346

Probabilities and Events 346Sample Space and Probability Theory 347Conditional Probability and Statistical

Independence 3518.2 Random Variables and Probability

Functions (8.1) 354Discrete Random Variables and CDFs 355Continuous Random Variables and PDFs 358Transformations of Random Variables 361Joint and Conditional PDFs 363

8.3 Statistical Averages (2.3, 8.2) 365Means, Moments, and Expectation 365Standard Deviation and Chebyshev’s

Inequality 366Multivariate Expectations 368Characteristic Functions 370

8.4 Probability Models (8.3) 371Binomial Distribution 371Poisson Distribution 373Gaussian PDF 374Rayleigh PDF 376Bivariate Gaussian Distribution 378Central Limit Theorem 379

Chapter 9

Random Signals and Noise 3919.1 Random Processes (3.6, 8.4) 392

Ensemble Averages and Correlation Functions 393

Ergodic and Stationary Processes 397Gaussian Processes 402

9.2 Random Signals (9.1) 403Power Spectrum 403Superposition and Modulation 408Filtered Random Signals 409

9.3 Noise (9.2) 412Thermal Noise and Available Power 413White Noise and Filtered Noise 416Noise Equivalent Bandwidth 419System Measurements Using White Noise 421

9.4 Baseband Signal Transmission With Noise (9.3) 422

Additive Noise and Signal-to-Noise Ratios 422Analog Signal Transmission 424

9.5 Baseband Pulse Transmission With Noise (9.4) 427

Pulse Measurements in Noise 427Pulse Detection and Matched

Filters 429

Chapter 10

Noise in Analog Modulation Systems 439

10.1 Bandpass Noise (4.4, 9.2) 440System Models 441Quadrature Components 443Envelope and Phase 445Correlation Functions 446

10.2 Linear CW Modulation With Noise (10.2) 448

Synchronous Detection 449Envelope Detection and Threshold Effect 451

10.3 Angle CW Modulation With Noise (5.3, 10.2) 454

Postdetection Noise 454Destination S/N 458FM Threshold Effect 460Threshold Extension by FM Feedback

Detection 46310.4 Comparison of CW Modulation Systems

(9.4, 10.3) 46410.5 Phase-Locked Loop Noise Performance

(7.3, 10.1) 46710.6 Analog Pulse Modulation With Noise

(6.3, 9.5) 468Signal-to-Noise Ratios 468False-Pulse Threshold Effect 471

Chapter 11

Baseband Digital Transmission 47911.1 Digital Signals and Systems (9.1) 481

Digital PAM Signals 481Transmission Limitations 484Power Spectra of Digital PAM 487Spectral Shaping by Precoding 490

11.2 Noise and Errors (9.4, 11.1) 491Binary Error Probabilities 492Regenerative Repeaters 496Matched Filtering 498Correlation Detector 501M-ary Error Probabilities 502

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11.3 Bandlimited Digital PAM Systems (11.2) 506

Nyquist Pulse Shaping 506Optimum Terminal Filters 509Equalization 513Correlative Coding 517

11.4 Synchronization Techniques (11.2) 523Bit Synchronization 524Scramblers and PN Sequence Generators 526Frame Synchronization 531

Chapter 12

Digitization Techniques for AnalogMessages and ComputerNetworks 543

12.1 Pulse-Code Modulation (6.2, 11.1) 544PCM Generation and Reconstruction 545Quantization Noise 548Nonuniform Quantizing and Companding 550

12.2 PCM With Noise (11.2, 12.1) 554Decoding Noise 555Error Threshold 557PCM Versus Analog Modulation 557

12.3 Delta Modulation and Predictive Coding (12.2) 559

Delta Modulation 560Delta-Sigma Modulation 565Adaptive Delta Modulation 566Differential PCM 567LPC Speech Synthesis 569

12.4 Digital Audio Recording (12.3) 571CD Recording 571CD Playback 574

12.5 Digital Multiplexing (12.1, 9.2) 575Multiplexers and Hierarchies 575Digital Subscriber Lines 579Synchronous Optical Network 580Data Multiplexers 582

Chapter 13

Channel Coding 59113.1 Error Detection and Correction (11.2) 592

Repetition and Parity-Check Codes 592Interleaving 595Code Vectors and Hamming Distance 595Forward Error-Correction (FEC) Systems 597ARQ Systems 600

13.2 Linear Block Codes (13.1) 604Matrix Representation of Block Codes 604Syndrome Decoding 608Cyclic Codes 611M-ary Codes 616

13.3 Convolutional Codes (13.2) 617Convolutional Encoding 617Free Distance and Coding Gain 623Decoding Methods 629Turbo Codes 635

Chapter 14

Bandpass Digital Transmission 64714.1 Digital CW Modulation

(4.5, 5.1, 11.1) 648Spectral Analysis of Bandpass Digital

Signals 649Amplitude Modulation Methods 650Phase Modulation Methods 653Frequency Modulation Methods 655Minimum-Shift Keying (MSK) and

Gaussian-Filtered MSK 65814.2 Coherent Binary Systems

(11.2, 14.1) 663Optimum Binary Detection 663Coherent OOK, BPSK, and FSK 668Timing and Synchronization 670Interference 671

14.3 Noncoherent Binary Systems (14.2) 673

Envelope of a Sinusoid Plus Bandpass Noise 673

Noncoherent OOK 674Noncoherent FSK 677Differentially Coherent PSK 679

14.4 Quadrature-Carrier and M-ary Systems (14.2) 682

Quadrature-Carrier Systems 682M-ary PSK Systems 685M-ary QAM Systems 689M-ary FSK Systems 690Comparison of Digital Modulation

Systems 69214.5 Orthogonal Frequency Division Multiplexing

(OFDM) (14.4, 7.2, 2.6) 696Generating OFDM Using the Inverse Discrete

Fourier Transform 697Channel Response and Cyclic Extensions 700

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viii Contents

14.6 Trellis-Coded Modulation (13.3, 14.4) 703TCM Basics 704Hard Versus Soft Decisions 712Modems 712

Chapter 15

Spread-Spectrum Systems 72115.1 Direct-Sequence Spread-Spectrum

(14.2) 723DSSS Signals 723DSSS Performance in Presence of

Interference 726Multiple Access 728Multipath and the Rake Receiver 729

15.2 Frequency-Hopping Spread-Spectrum (15.1) 733

FHSS Signals 733FHSS Performance in the Presence of

Interference 735Other SS Systems 737

15.3 Coding (15.1, 11.4) 73815.4 Synchronization (7.3) 743

Acquisition 743Tracking 745

15.5 Wireless Systems (15.2, 3.3, 14.5) 746Telephone Systems 746Wireless Networks 751

15.6 Ultra-Wideband Systems (6.3, 15.1) 754UWB Signals 754Coding Techniques 756Transmit-Reference System 758Multiple Access 759Comparison With Direct-Sequence Spread-

Spectrum 760

Chapter 16

Information and Detection Theory 767

16.1 Information Measure and Source Encoding (12.1) 769

Information Measure 769Entropy and Information Rate 771Coding for a Discrete Memoryless Channel 774Predictive Coding for Sources With Memory 778

16.2 Information Transmission on DiscreteChannels (16.1) 782

Mutual Information 782Discrete Channel Capacity 786Coding for the Binary Symmetric

Channel 78816.3 Continuous Channels and System

Comparisons (16.2) 791Continuous Information 791Continuous Channel Capacity 794Ideal Communication Systems 796System Comparisons 799

16.4 Signal Space 803Signals as Vectors 803The Gram-Schmidt Procedure 806

16.5 Optimum Digital Detection (16.3, 16.4) 808

Optimum Detection and MAP Receivers 809Error Probabilities 815Signal Selection and Orthogonal

Signaling 818

Appendix: Circuit and System Noise (9.4) 827Circuit and Device Noise 828Amplifier Noise 835System Noise Calculations 840Cable Repeater Systems 844

Tables 847T.1 Fourier Transforms 847T.2 Fourier Series 849T.3 Mathematical Relations 851T.4 The Sinc Function 854T.5 Probability Functions 855T.6 Gaussian Probabilities 857T.7 Glossary of Notation 859

Solutions to Exercises 861Answers to Selected Problems 904Index 911

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Preface

ix

This text, like its previous four editions, is an introduction to communication sys-tems written at a level appropriate for advanced undergraduates and first-year gradu-ate students in electrical or computer engineering.

An initial study of signal transmission and the inherent limitations of physicalsystems establishes unifying concepts of communication. Attention is then given toanalog communication systems, random signals and noise, digital systems, andinformation theory.

Mathematical techniques and models necessarily play an important rolethroughout the book, but always in the engineering context as means to an end.Numerous applications have been incorporated for their practical significance and asillustrations of concepts and design strategies. Some hardware considerations arealso included to justify various communication methods, to stimulate interest, and tobring out connections with other branches of the field.

PREREQUISITE BACKGROUNDThe assumed background is equivalent to the first two or three years of an electricalor computer engineering curriculum. Essential prerequisites are differential equa-tions, steady-state and transient circuit analysis, and a first course in electronics. Stu-dents should also have some familiarity with operational amplifiers, digital logic,and matrix notation. Helpful but not required are prior exposure to linear systemsanalysis, Fourier transforms, and probability theory.

CONTENTS AND ORGANIZATIONNew features of this fifth edition include (a) the addition of MATLAB† examples,exercises and problems that are available on the book’s website, www.mhhe.com/carlsoncrilly; (b) new end-of-chapter conceptual questions to reinforce the theory,provide practical application to what has been covered, and add to the students’problem-solving skills; (c) expanded coverage of wireless communications and anintroduction to radio wave propagation that enables the reader to better appreciate thechallenges of wireless systems; (d) expanded coverage of digital modulation systemssuch as the addition of orthogonal frequency division modulation and ultra widebandsystems; (e) expanded coverage of spread spectrum; (f) a discussion of wireless net-works; and (g) an easy-to-reference list of abbreviations and mathematical symbols.

Following an updated introductory chapter, this text has two chapters dealingwith basic tools. These tools are then applied in the next four chapters to analog com-munication systems, including sampling and pulse modulation. Probability, randomsignals, and noise are introduced in the following three chapters and applied to analogsystems. An appendix separately covers circuit and system noise. The remaining

†MATLAB is a registered trademark of MathWorks Inc.

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x Preface

six chapters are devoted to digital communication and information theory, whichrequire some knowledge of random signals and include coded pulse modulation.

All sixteen chapters can be presented in a yearlong undergraduate course withminimum prerequisites. Or a one-term undergraduate course on analog communica-tion might consist of material in the first seven chapters. If linear systems and prob-ability theory are covered in prerequisite courses, then most of the last eight chapterscan be included in a one-term senior/graduate course devoted primarily to digitalcommunication.

The modular chapter structure allows considerable latitude for other formats.As a guide to topic selection, the table of contents indicates the minimum prerequi-sites for each chapter section.

INSTRUCTIONAL AIDSEach chapter after the first one includes a list of instructional objectives to guide stu-dent study. Subsequent chapters also contain several examples and exercises. Theexercises are designed to help students master their grasp of new material presentedin the text, and exercise solutions are given at the back. The examples have been cho-sen to illuminate concepts and techniques that students often find troublesome.

Problems at the ends of chapters are numbered by text section. They range frombasic manipulations and computations to more advanced analysis and design tasks.A manual of problem solutions is available to instructors from the publisher.

Several typographical devices have been incorporated to serve as aids for students. Specifically,

• Technical terms are printed in boldface type when they first appear.

• Important concepts and theorems that do not involve equations are printedinside boxes.

• Asterisks (*) after problem numbers indicate that answers are provided at theback of the book.

• The symbol ‡ identifies the more challenging problems.

Tables at the back of the book include transform pairs, mathematical relations,and probability functions for convenient reference.

Communication system engineers use many abbreviations, so in addition to theindex, there is a section that lists common abbreviations. Also included is a list of themore commonly used mathematical symbols.

Online ResourcesThe website that accompanies this text can be found at www.mhhe.com/carlsoncrillyand features new MATLAB problems as well as material on computer networks(TCP/IP) and data encryption. The website also includes an annotated bibliographyin the form of a supplementary reading list and the list of references. The complete

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Preface xi

solutions manual, PowerPoint lecture notes, and image library are available onlinefor instructors. Contact your sales representative for additional information on thewebsite.

Electronic Textbook OptionsThis text is offered through CourseSmart for both instructors and students. Course-Smart is an online resource where students can purchase the complete text online atalmost half the cost of a traditional text. Purchasing the eTextbook allows students totake advantage of CourseSmart’s web tools for learning, which include full textsearch, notes and highlighting, and email tools for sharing notes between classmates.To learn more about CourseSmart options, contact your sales representative or visitwww.CourseSmart.com.

ACKNOWLEDGMENTSI am indebted to the many people who contributed to previous editions. I want tothank Professors Marshall Pace, Seddick Djouadi, and Aly Fathy for their feedbackand the use of their libraries; the University of Tennessee Electrical Engineering andComputer Science Department for support; Ms. Judy Evans, Ms. Dana Bryson,Messrs. Robert Armistead, Jerry Davis, Matthew Smith, and Tobias Mueller for theirassistance in manuscript preparation.

Thanks, too, for the wonderful feedback from our reviewers: Ali Abdi, New Jersey Institute of Technology; Venkatachalam Anantharam, University ofCalifornia–Berkeley; Nagwa Bekir, California State University–Northridge; Deva K. Borah, New Mexico State University; Sohail Dianat, Rochester Institute ofTechnology; David C. Farden, North Dakota State University; Raghvendra Gejji,Western Michigan University; Christoforos Hadjicostis, University of Illinois;Dr. James Kang, California State Polytechnic University–Pomona; K.R. Rao,University of Texas at Arlington; Jitendra K. Tugnait, Auburn University.

Thanks go to my friends Ms. Anissa Davis, Mrs. Alice LaFoy and Drs. StephenDerby, Samir ElGhazaly, Walter Green, Melissa Meyer, and John Sahr for theirencouragement; to my brother Peter Crilly for his encouragement; and to my childrenMargaret, Meredith, Benjamin, and Nathan Crilly for their support and sense ofhumor. Special thanks go to Dr. Stephen Smith of Oak Ridge National Laboratoryfor the many hours he spent reviewing the manuscript. I also want to thank Dr.Lonnie Ludeman, who as a role model demonstrated to me what a professor shouldbe. Finally, I am indebted to the late A. Bruce Carlson, who created within me thedesire and enthusiasm to continue my education and pursue graduate study in com-munication systems.

Paul B. Crilly

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List of Abbreviations

1� EV-DO evolution data optimized one time1G, 2G, 3G first-, second- and third-generation wireless phones3GPP third-generation partnership projectAC alternating currentACK positive acknowledgmentADC analog-to-digital converterADSL asynchronous DSLAFC automatic frequency controlAGC automatic gain controlAM amplitude modulationAMI alternate mark inversionAMPS Advanced Mobile Phone ServiceAPK amplitude-phase shift keyingARQ automatic repeat requestASK amplitude-shift keyingASCII American Standard Code for Information InterchangeAVC automatic volume controlAWGN additive white gaussian noiseBER bit error rate or bit error probabilityBJT bipolar junction transistorBPF bandpass filterBPSK binary PSKBSC binary symmetric channelCCD charge-coupled devicesCCIR International Radio Consultative CommitteeCCIT International Telegraph and Telephone Consultative Committee of the

Internationals UnionCD compact discCDF cumulative distribution functionCDMA code-division multiple accessCIRC cross-interleave Reed-Solomon error control codeCNR carrier-to-noise ratioCPFSK continuous-phase FSKCPS chipsCRC cyclic redundancy code or cyclic reduncancy checkCSMA carrier sense multiple accessCVSDM continuously variable slope delta modulationCW continuous-waveDAC digital-to-analog converterdB decibelsdBm decibel milliwattsdBW decibel wattsDC direct current, or direct conversion (receiver)

xii

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List of Abbreviations xiii

DCT discrete cosine transformDDS direct digital synthesisDFT discrete Fourier transformDLL delay-locked loopDM delta modulationDPCM differential pulse-code modulationDPSK differentially coherent PSKDSB or DSB-SC double-sideband-suppressed carrier modulationDSL digital subscriber lineDSM delta-sigma modulatorDSP digital signal processing or digital signal processorDSSS or DSS direct-sequence spread-spectrumDTV digital TVEIRP effective isotropic radiated powerEV-DV evolution, data, and voiceFCC Federal Communications Commission (USA)FDD frequency-division duplexFDM frequency-division multiplexingFDMA frequency-division multiple accessFDX full duplexFEC forward error correctionFET field effect transistorFFT fast Fourier transformFHSS frequency-hopping spread-spectrumFM frequency modulationFOH first order holdFSK frequency-shift keyingGMSK gaussian filtered MSKGPRS general packet radio systemGPS global positioning systemGSM Group Special Mobile, or Global System for Mobile

CommunicationsHDSL high bit rate DSLHDX half duplexHDTV high definition televisionHPF highpass filterHz hertzIDFT inverse discrete Fourier transformIFFT inverse fast Fourier transformIF intermediate frequencyIMT–2000 international mobile telecommunications–2000IP internet protocolIS-95 Interim Standard 95ISDN integrated services digital networkISI intersymbol interference

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xiv List of Abbreviations

ISM industrial, scientific, and medicalISO International Standards OrganizationITU International Telecommunications UnionJFET junction field-effect transistorkHz kilohertzkW kilowattLAN local area networkLC inductor/capacitor resonant circuitLO local oscillatorLOS line of sightLPC linear predictive codeLPF lowpass filterLSSB or LSB lower single-sideband modulationLTI linear time-invariant systemsMA multiple accessMAI multiple access interferenceMAP maximum a posterioriMC multicarrier modulationMHz megahertzMMSE minimum means-squared errormodem modulator/demodulatorMPEG motion picture expert groupMSK minimum shift keyingMTSO mobile telephone switching officeMUF maximum useable frequencyMUX multiplexerNAK negative acknowledgmentNAMPS narrowband advanced mobile phone serviceNBFM narrowband frequency modulationNBPM narrowband phase modulationNET networkNF noise figureNIST National Institute of Standards and TechnologyNRZ nonreturn-to-zeroNTSC National Television System CommitteeOFDM orthogonal frequency multiplexingOFDMA orthogonal frequency-division multiple accessOOK on-off keyingOQPSK offset quadrature phase shift keyingOSI open systems interconnectionPAM pulse-amplitude modulationPAR peak-to-average ratio (power)PCC parallel concatenated codesPCM pulse-code modulationPCS personal communications systems or services

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List of Abbreviations xv

PD phase discriminatorPDF probability density functionPEP peak envelope powerPLL phase-locked loopPM phase modulationPN pseudonoisePOT plain old telephonePPM pulse-position modulationPRK phase reverse keyingPSD power spectral densityPSK phase shift keyingPWM pulse width modulationQAM quadrature amplitude modulationQoS quality of serviceQPSK quadriphase PSKRC time constant: resistance-capacitanceRF radio frequencyRFC radio frequency chokeRFI radio frequency interferenceRMS root mean squaredRS Reed-SolomonRV random variableRZ return-to-zeroSDR software-defined radioSIR signal-to-interference ratioS/N, SNR signal-to-noise ratioSDSL symmetrical DSLSONET Synchronous Optical NetworkSS spread-spectrumSSB single-sideband modulationSX simplexTCM trellis-coded modulationTCP/IP transmission control protocol/Internet protocolTDD time division duplexTDM time-domain multiplexingTDMA time-domain multiple accessTH time-hoppingTHSS time-hopping spread-spectrumTH-UWB time-hopping ultra-widebandTR transmit referenceTRF tuned RF receiverUHF ultrahigh frequencyUMTS universal mobile telecommunications systems, or 3GUSSB or USB upper single-sideband modulationUWB ultra-wideband

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xvi List of Abbreviations

VCC voltage-controlled clockVCO voltage-controlled oscillatorVDSL very high-bit DSLVHDL VHSIC (very high speed integrated circuit) hardware

description languageVHF very high frequencyVLSI very large-scale integrationVOIP voice-over-Internet protocolVSB vestigial-sideband modulationW wattsWBFM wideband FMWCDMA wideband code division multiple accessWiLan wireless local area networkWiMAX Worldwide Interoperability for Microwave AccessWi-Fi Wireless Fidelity, or wireless local area networkWSS wide sense stationaryZOH zero-order hold

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xvii

Mathematical Symbols

A, Ac amplitude constant and carrier amplitude constantAe aperture areaAm tone amplitudeAv(t) envelope of a BP signalB bandwidth in hertz (Hz)BT transmission bandwidth, or bandwidth of a bandpass signalC channel capacity, bits per second, capacitance in Farads, or check vectorCvw(t1, t2) covariance function of signals v(t) and w(t)D deviation ratio, or pulse intervalDR dynamic rangeDFT[ ], IDFT[ ] discrete and inverse discrete Fourier transormE error vectorE, E1, E0, Eb signal energy, energy in bit 1, energy in bit 0, and bit energyE[ ] expected value operatorFX(x) cumulative distribution function of XFXY(x,y) joint cumulative distribution of X and YG generator vectorGx(f) power spectral density of signal x(t)Gvw(f) cross-spectral density functions of signals v(t), w(t)H(f) transfer or frequency-response function of a systemHC(f) channel’s frequency responseHeq(f) channel equalizer frequency responseHQ(f) transfer function of quadrature filterIR image rejectionJn(b) Bessell function of first kind, order n, argument bL,LdB loss in linear and decibel unitsLu, Ld uplink and downlink lossesM numerical base, such that q � Mv or message vectorND destination noise powerNR received noise powerN0 power spectral density or spectral density of white noiseNF, or F noise figureN(f) noise signal spectrumP power in wattsPc unmodulated carrier powerP(f) pulse spectrumPe, Pe0, Pe1 probability of error, probability of zero error, probability of 1 errorPbe, Pwe probability of bit and word errorsPout, Pin output and input power (watts)PdBW, PdBmW power in decibel watts and milliwattsPsb power per sidebandP(A), P(i,n) probability of event A occurring and probability of i errors in n-bit wordQ[ ] gaussian probability function

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xviii Mathematical Symbolsxviii Mathematical Symbols

R resistance in ohmsR(t) autocorrelation function for white noiseRc code rateRv (t1, t2) autocorrelation function of signal v(t)Rvw (t1, t2) cross-correlation function of signals v(t) and w(t)ST average transmitted powerSX message powerS/N, (S/N)R, (S/N)D signal-to-noise ratio (SNR), received SNR, and destination

SNRSD destination signal powerSR received signal powerTb bit durationT0, T repetition periodTc chip interval for DSSSTs sample interval or periodVbp (f) frequency domain version of a bandpass signalW message bandwidthX code vectorX, Y, Z random variablesY received code vectorX(f),Y(f) input and output spectrumsXbp (f) bandpass spectrumak kth symbolan, bn trigonometric Fourier series coefficientsc speed of light in kilometer per secondcn nth coefficient for exponential Fourier series, or transversal

filter weightcnk�1 (k � 1)th estimate of the nth tap coefficientc(t) output from PN generator or voltage-controlled clockd physical distancedmin code distancef frequency in hertzf(t) instantaneous frequencyfc carrier or center frequencyfc¿ image frequencyfd frequency interval fIF intermediate frequencyfLO local oscillator frequencyfk, fn discrete frequency fm tone frequency fD frequency deviation constantf0 center frequencyfs sample rateg, gT, gR power gain and transmitter and receiver power gainsgdB power gain in decibels (dB)

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Mathematical Symbols xixMathematical Symbols xix

h(t) impulse-response function of a systemhC(t) impulse-response function of a channelhk(t), hk(n) impulse-response function of kth portion of subchannelhQ(t) impulse-response function of a quadrature filterIm[x] and Re[x] imaginary and real components of xj imaginary number operatorl length in kilometersm number of repeater sectionsmk, k actual and estimated k message symboln(t) noise signalp(t) pulse signalp0(t), p1(t) gaussian and first-order monocycle pulses

output of transversal filter’s nth delay elementinput to equalizing filter

peq(tk) output of an equalizing filterpX(x) probability density function of XpXY(x) joint probability density function of X and Yq number of quantum levelsr, rb signal rate, bit rates(t) switching function for samplings0(t), s1(t) inputs to multiplier of correlation detectorsgn(t) signum functiont time in secondstd time delay in secondstk kth instant of timetr rise time in secondsu(t) unit step function, or output from rake diversity combinerv number of bitsv(t) input to a detectorvk (t) kth subcarrier function�v(t)� average value of v(t)vbp(t) time-domain expression of a bandpass signalw*(t) complex conjugate of w(t)

Hilbert transform of x, or estimate of xx(t), y(t) input and output time functionsx(t) message signalx(k), x(kTs) sampled version of x(t)X(n) discrete Fourier transform of x(k)xb(t) modulated signal at a subcarrier frequencyxc(t) modulated signalxq(k) quantized value for kth value of xy(t) detector outputxk(t), yk(t) subchannel signalyD(t) signal at destinationzm(t) output of matched filter or correlation detector

x̂

p& 1t 2p&n

m̂

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xx Mathematical Symbolsxx Mathematical Symbols

a loss coefficient in decibels per kilometer, or error probabilityg baseband signal to noise ratiog, gTH threshold signal to noise ratio (baseband) gb � Eb /N0 bit energy signal-to-noise ratiod incremental delayd(t) unit impulse, or Dirac delta functionE(t), E, Ek error, increment, and quantization error� quantization step sizel wavelength, meters, or time delaym modulation index, or packet rates standard deviationsY, sY2 standard deviation and variance of Yt pulse width, or time constantf phase anglef(t) instantaneous phasefD phase deviation constantfv(t) phase of a BP signalvc carrier frequency in radians per secondvm tone frequency in radians per second�(t/t) rectangular pulse�(t/t) triangle pulseL Laplace operatorF, F�1 Fourier transform operator and its inverse* convolution operatorℑ, ℑ0, ℑN noise temperatures

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1

chapter

1

Introduction

CHAPTER OUTLINE

1.1 Elements and Limitations of Communication Systems

Information, Messages, and Signals Elements of a Communication System Fundamental Limitations

1.2 Modulation and Coding

Modulation Methods Modulation Benefits and Applications Coding Methods and Benefits

1.3 Electromagnetic Wave Propagation Over Wireless Channels

RF Wave Deflection Skywave Propagation

1.4 Emerging Developments

1.5 Societal Impact and Historical Perspective

1.6 Prospectus

1.7 Questions

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2 CHAPTER 1 • Introduction

“ ttention, the Universe! By kingdoms, right wheel!” This prophetic phrase represents the first telegraph messageon record. Samuel F. B. Morse sent it over a 16 km line in 1838. Thus a new era was born: the era of electri-

cal communication.Now, over a century and a half later, communication engineering has advanced to the point that earthbound TV

viewers watch astronauts working in space. Telephone, radio, and television are integral parts of modern life. Long-distance circuits span the globe carrying text, data, voice, and images. Computers talk to computers via interconti-nental networks, and control virtually every electrical appliance in our homes. Wireless personal communicationdevices keep us connected wherever we go. Certainly great strides have been made since the days of Morse.Equally certain, coming decades will usher in many new achievements of communication engineering.

This textbook introduces electrical communication systems, including analysis methods, design principles, and hard-ware considerations. We begin with a descriptive overview that establishes a perspective for the chapters that follow.

1.1 ELEMENTS AND LIMITATIONS OF COMMUNICATION SYSTEMS

A communication system conveys information from its source to a destination somedistance away. There are so many different applications of communication systemsthat we cannot attempt to cover every type, nor can we discuss in detail all the indi-vidual parts that make up a specific system. A typical system involves numerouscomponents that run the gamut of electrical engineering—circuits, electronics, elec-tromagnetics, signal processing, microprocessors, and communication networks, toname a few of the relevant fields. Moreover, a piece-by-piece treatment wouldobscure the essential point that a communication system is an integrated whole thatreally does exceed the sum of its parts.

We therefore approach the subject from a more general viewpoint. Recognizingthat all communication systems have the same basic function of information trans-fer, we’ll seek out and isolate the principles and problems of conveying informationin electrical form. These will be examined in sufficient depth to develop analysis anddesign methods suited to a wide range of applications. In short, this text is concernedwith communication links as systems.

Information, Messages, and SignalsClearly, the concept of information is central to communication. But information isa loaded word, implying semantic and philosophical notions that defy precise defini-tion. We avoid these difficulties by dealing instead with the message, defined as thephysical manifestation of information as produced by the source. Whatever form themessage takes, the goal of a communication system is to reproduce at the destinationan acceptable replica of the source message.

There are many kinds of information sources, including machines as well aspeople, and messages appear in various forms. Nonetheless, we can identify two dis-tinct message categories, analog and digital. This distinction, in turn, determines thecriterion for successful communication.

A

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1.1 Elements and Limitations of Communication Systems 3

An analog message is a physical quantity that varies with time, usually in asmooth and continuous fashion. Examples of analog messages are the acoustic pres-sure produced when you speak, the angular position of an aircraft gyro, or the lightintensity at some point in a television image. Since the information resides in a time-varying waveform, an analog communication system should deliver this waveformwith a specified degree of fidelity.

A digital message is an ordered sequence of symbols selected from a finite setof discrete elements. Examples of digital messages are the letters printed on thispage, a listing of hourly temperature readings, or the keys you press on a computerkeyboard. Since the information resides in discrete symbols, a digital communica-tion system should deliver these symbols with a specified degree of accuracy in aspecified amount of time.

Whether analog or digital, few message sources are inherently electrical. Conse-quently, most communication systems have input and output transducers as shownin Fig. 1.1–1. The input transducer converts the message to an electrical signal, saya voltage or current, and another transducer at the destination converts the output sig-nal to the desired message form. For instance, the transducers in a voice communi-cation system could be a microphone at the input and a loudspeaker at the output.We’ll assume hereafter that suitable transducers exist, and we’ll concentrate primar-ily on the task of signal transmission. In this context the terms signal and messagewill be used interchangeably, since the signal, like the message, is a physical embod-iment of information.

Elements of a Communication SystemFigure 1.1–2 depicts the elements of a communication system, omitting transducersbut including unwanted contaminations. There are three essential parts of any com-munication system: the transmitter, transmission channel, and receiver. Each partplays a particular role in signal transmission, as follows.

The transmitter processes the input signal to produce a transmitted signalsuited to the characteristics of the transmission channel. Signal processing for trans-mission almost always involves modulation and may also include coding.

The transmission channel is the electrical medium that bridges the distancefrom source to destination. It may be a pair of wires, a coaxial cable, or a radio wave or laser beam. Every channel introduces some amount of transmission loss orattenuation, so the signal power, in general, progressively decreases with increasingdistance.

Figure 1.1–1 Communication system with input and output transducers.

Outputtransducer

Communicationsystem

Inputtransducer

Inputsignal

OutputsignalSource Destination

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The receiver operates on the output signal from the channel in preparation fordelivery to the transducer at the destination. Receiver operations include amplification,to compensate for transmission loss, and demodulation and decoding to reverse thesignal processing performed at the transmitter. Filtering is another important functionat the receiver, for reasons discussed next.

Various unwanted undesirable effects crop up in the course of signal transmis-sion. Attenuation is undesirable since it reduces signal strength at the receiver. Moreserious, however, are distortion, interference, and noise, which appear as alterationsof the signal’s waveshape or spectrum. Although such contaminations may occur atany point, the standard convention is to lump them entirely on the channel, treatingthe transmitter and receiver as being ideal. Figure 1.1–2 reflects this convention.Fig. 1.1–3a is a graph of an ideal 1101001 binary sequence as it leaves the transmit-ter. Note the sharp edges that define the signal’s values. Figures 1.1–3b through dshow the contaminating effects of distortion, interference, and noise respectively.

Distortion is waveform perturbation caused by imperfect response of the sys-tem to the desired signal itself. Unlike noise and interference, distortion disappearswhen the signal is turned off. If the channel has a linear but distorting response, thendistortion may be corrected, or at least reduced, with the help of special filters calledequalizers.

Interference is contamination by extraneous signals from human sources—othertransmitters, power lines and machinery, switching circuits, and so on. Interferenceoccurs most often in radio systems whose receiving antennas usually intercept sev-eral signals at the same time. Radio-frequency interference (RFI) also appears incable systems if the transmission wires or receiver circuitry pick up signals radiatedfrom nearby sources. With the exception of systems that employ code division mul-tiple access (CDMA), appropriate filtering removes interference to the extent thatthe interfering signals occupy different frequency bands than the desired signal.

Noise refers to random and unpredictable electrical signals produced by naturalprocesses both internal and external to the system. When such random variations are superimposed on an information-bearing signal, the message may be partially corrupted or totally obliterated. Filtering reduces noise contamination, but thereinevitably remains some amount of noise that cannot be eliminated. This noise con-stitutes one of the fundamental system limitations.

Figure 1.1–2 Elements of a communication system.

ReceiverTransmission

channel

Noise, interference,and distortion

Transmitter

Transmittedsignal

Inputsignal

Receivedsignal

Outputsignal

Source Destination

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1.1 Elements and Limitations of Communication Systems 5

Figure 1.1–3 Contamination of a signal transmitting a 1101001 sequence: (a) original signalas it leaves the transmitter, (b) effects of distortion, (c) effects of interference, (d) effects of noise.

(a)

(b)

(c)

(d)

1 1 1 10 0 0

t

t

t

t

Finally, it should be noted that Fig. 1.1–2 represents one-way, or simplex (SX),transmission. Two-way communication, of course, requires a transmitter and receiverat each end. A full-duplex (FDX) system has a channel that allows simultaneous transmission in both directions. A half-duplex (HDX) system allows transmission ineither direction but not at the same time.

Fundamental LimitationsAn engineer faces two general kinds of constraints when designing a communicationsystem. On the one hand are the technological problems, including such diverseconsiderations as hardware availability, economic factors, governmental regulations,and so on. These are problems of feasibility that can be solved in theory, even thoughperfect solutions may not be practical. On the other hand are the fundamental phys-ical limitations, the laws of nature as they pertain to the task in question. These lim-itations ultimately dictate what can or cannot be accomplished, irrespective of thetechnological problems. Two fundamental limitations of information transmissionby electrical means are bandwidth and noise.

The concept of bandwidth applies to both signals and systems as a measureof speed. When a signal changes rapidly with time, its frequency content, orspectrum, extends over a wide range, and we say that the signal has a large band-width. Similarly, the ability of a system to follow signal variations is reflected inits usable frequency response, or transmission bandwidth. Now all electricalsystems contain energy-storage elements, and stored energy cannot be changedinstantaneously. Consequently, every communication system has a finite band-width B that limits the rate of signal variations.

Communication under real-time conditions requires sufficient transmission band-width to accommodate the signal spectrum; otherwise, severe distortion will result.

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Thus, for example, a bandwidth of several megahertz is needed for a TV video signal,while the much slower variations of a voice signal fit into B � 3 kHz. For a digital sig-nal with r symbols per second, the bandwidth must be B � r/2. In the case of informa-tion transmission without a real-time constraint, the available bandwidth determinesthe maximum signal speed. The time required to transmit a given amount of informa-tion is therefore inversely proportional to B.

Noise imposes a second limitation on information transmission. Why is noiseunavoidable? Rather curiously, the answer comes from kinetic theory. At any tem-perature above absolute zero, thermal energy causes microscopic particles to exhibitrandom motion. The random motion of charged particles such as electrons generatesrandom currents or voltages called thermal noise. There are also other types ofnoise, but thermal noise appears in every communication system.

We measure noise relative to an information signal in terms of the signal-to-noise power ratio S/N (or SNR). Thermal noise power is ordinarily quite small, andS/N can be so large that the noise goes unnoticed. At lower values of S/N, however,noise degrades fidelity in analog communication and produces errors in digital communication. These problems become most severe on long-distance links whenthe transmission loss reduces the received signal power down close to the noise level.Amplification at the receiver is then to no avail, because the noise will be amplifiedalong with the signal.

Taking both limitations into account, Shannon (1948)† stated that the rate ofinformation transmission cannot exceed the channel capacity.

C � B log2 (1 � S/N) � 3.32 B log10 (1 � S/N)

This relationship, known as the Hartley-Shannon law, sets an upper limit on the per-formance of a communication system with a given bandwidth and signal-to-noiseratio. Note, this law assumes the noise is random with a gaussian distribution, and theinformation is randomly coded.

1.2 MODULATION AND CODINGModulation and coding are operations performed at the transmitter to achieve effi-cient and reliable information transmission. So important are these operations thatthey deserve further consideration here. Subsequently, we’ll devote several chaptersto modulating and coding techniques.

Modulation MethodsModulation involves two waveforms: a modulating signal that represents the messageand a carrier wave that suits the particular application. A modulator systematicallyalters the carrier wave in correspondence with the variations of the modulating signal.

†References are indicated in this fashion throughout the text. Complete citations are listed alphabeti-cally by author in the References at www.mhhe.com/carlsoncrilly.

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1.2 Modulation and Coding 7

(a)

(b)

(c)

t

t

t

The resulting modulated wave thereby “carries” the message information. We generallyrequire that modulation be a reversible operation, so the message can be retrieved by thecomplementary process of demodulation.

Figure 1.2–1 depicts a portion of an analog modulating signal (part a) and the cor-responding modulated waveform obtained by varying the amplitude of a sinusoidalcarrier wave (part b). This is the familiar amplitude modulation (AM) used for radiobroadcasting and other applications. A message may also be impressed on a sinusoidalcarrier by frequency modulation (FM) or phase modulation (PM). All methods forsinusoidal carrier modulation are grouped under the heading of continuous-wave(CW) modulation.

Incidentally, you act as a CW modulator whenever you speak. The transmissionof voice through air is accomplished by generating carrier tones in the vocal cordsand modulating these tones with muscular actions of the oral cavity. Thus, what theear hears as speech is a modulated acoustic wave similar to an AM signal.

Most long-distance transmission systems employ CW modulation with a carrierfrequency much higher than the highest frequency component of the modulating sig-nal. The spectrum of the modulated signal then consists of a band of frequency com-ponents clustered around the carrier frequency. Under these conditions, we say thatCW modulation produces frequency translation. In AM broadcasting, for example,the message spectrum typically runs from 100 Hz to 5 kHz; if the carrier frequency is600 kHz, then the spectrum of the modulated carrier covers 595–605 kHz.

Figure 1.2–1 (a) Modulating signal; (b) sinusoidal carrier with amplitude modulation; (c) pulse-train carrier with amplitude modulation.

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Another modulation method, called pulse modulation, has a periodic train ofshort pulses as the carrier wave. Figure 1.2–1c shows a waveform with pulse ampli-tude modulation (PAM). Notice that this PAM wave consists of short samplesextracted from the analog signal at the top of the figure. Sampling is an importantsignal-processing technique, and, subject to certain conditions, it’s possible toreconstruct an entire waveform from periodic samples.

But pulse modulation by itself does not produce the frequency translation neededfor efficient signal transmission. Some transmitters therefore combine pulse and CWmodulation. Other modulation techniques, described shortly, combine pulse modula-tion with coding.

Modulation Benefits and ApplicationsThe primary purpose of modulation in a communication system is to generate a mod-ulated signal suited to the characteristics of the transmission channel. Actually, thereare several practical benefits and applications of modulation briefly discussed below.

Modulation for Efficient Transmission Signal transmission over appreciable distancealways involves a traveling electromagnetic wave, with or without a guiding medium.The efficiency of any particular transmission method depends upon the frequency ofthe signal being transmitted. By exploiting the frequency-translation property of CWmodulation, message information can be impressed on a carrier whose frequency hasbeen selected for the desired transmission method.

As a case in point, efficient line-of-sight ratio propagation requires antennaswhose physical dimensions are at least 1/10 of the signal’s wavelength. Unmodu-lated transmission of an audio signal containing frequency components down to 100 Hz would thus call for antennas some 300 km long. Modulated transmission at100 MHz, as in FM broadcasting, allows a practical antenna size of about one meter.At frequencies below 100 MHz, other propagation modes have better efficiency withreasonable antenna sizes.

For reference purposes, Fig. 1.2–2 shows those portions of the electromagneticspectrum suited to signal transmission. The figure includes the free-space wavelength,frequency-band designations, and typical transmission media and propagation modes.Also indicated are representative applications authorized by the U.S. Federal Commu-nications Commission (FCC). See http://www.ntia.doc.gov/osmhome/chap04chart.pdffor a complete description of U.S. frequency allocations. It should be noted that,throughout the spectrum, the FCC has authorized industrial, scientific, and medical(ISM) bands.† These bands allow limited power transmission from various wirelessindustrial, medical, and experimental transmitting devices as well as unintentional radi-ators such as microwave ovens, etc. It is understood that ISM users in these bands musttolerate interference from inputs from other ISM radiators.

†ISM bands with center frequencies include 6.789 MHz, 13.560 MHz, 27.120 MHz, 40.68 MHz,

915 MHz, 2.45 GHz, 5.8 GHz, 24.125 GHz, 61.25 GHz, 122.5 GHz, and 245 GHz.

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http://www.ntia.doc.gov/osmhome/chap04chart.pdf


1014 Hz

1015 Hz

100 GHz

10 GHz

1 GHz

100 MHz

10 MHz

1 MHz

100 kHz

10 kHz

1 kHz

1 cm

10 cm

1 m

10 m

100 m

1 km

10 km

100 km

10–6 m

Frequencydesignations

Wavelength Frequency

Ultraviolet

Visible

Infrared

Extra highfrequency

(EHF)

Super highfrequency

(SHF)

Ultra highfrequency

(UHF)

Very highfrequency

(VHF)

Highfrequency

(HF)

Mediumfrequency

(MF)

Lowfrequency

(LF)

Very lowfrequency

(VLF)

Audio

Transmissionmedia

Opticalfibers

Laserbeams

Waveguide

Coaxialcable

Wire pairs

Line-of-sightradio

Skywaveradio

Groundwaveradio

Propagationmodes

Representativeapplications

Experimental

Wideband data

ExperimentalNavigation

Satellite-satelliteMicrowave relay

Earth-satelliteRadar

Broadband PCSWireless comm. services

Cellular, pagersNarrowband PCS, GPS signals.

UHF TVMobil, Aeronautical

VHF TV and FM

Mobile radio

CB radioBusiness

Amateur radioCivil defense

AM broadcasting

Aeronautical

Submarine cable

Navigation

Transoceanic radio

TelephoneTelegraph

Figure 1.2–2 The electromagnetic spectrum.*

*The U.S. Government’s National Institute of Standards and Technology (NIST) broadcasts timeand frequency standards at 60 kHz and 2.5, 5, 10, 15, and 20 MHz.

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Modulation to Overcome Hardware Limitations The design of a communication sys-tem may be constrained by the cost and availability of hardware, hardware whoseperformance often depends upon the frequencies involved. Modulation permits thedesigner to place a signal in some frequency range that avoids hardware limitations.A particular concern along this line is the question of fractional bandwidth, definedas absolute bandwidth divided by the center frequency. Hardware costs and compli-cations are minimized if the fractional bandwidth is kept within 1–10 percent.Fractional-bandwidth considerations account for the fact that modulation units arefound in receivers as well as in transmitters.

It likewise follows that signals with large bandwidth should be modulated on high-frequency carriers. Since information rate is proportional to bandwidth, according tothe Hartley-Shannon law, we conclude that a high information rate requires a highcarrier frequency. For instance, a 5 GHz microwave system can accommodate10,000 times as much information in a given time interval as a 500 kHz radio channel.Going even higher in the electromagnetic spectrum, one optical laser beam has abandwidth potential equivalent to 10 million TV channels.

Modulation to Reduce Noise and Interference A brute-force method for combatingnoise and interference is to increase the signal power until it overwhelms the con-taminations. But increasing power is costly and may damage equipment. (One of theearly transatlantic cables was apparently destroyed by high-voltage rupture in aneffort to obtain a usable received signal.) Fortunately, FM and certain other types ofmodulation have the valuable property of suppressing both noise and interference.

This property is called wideband noise reduction because it requires the trans-mission bandwidth to be much greater than the bandwidth of the modulating signal.Wideband modulation thus allows the designer to exchange increased bandwidth fordecreased signal power, a trade-off implied by the Hartley-Shannon law. Note that ahigher carrier frequency may be needed to accommodate wideband modulation.

Modulation for Frequency Assignment When you tune a radio or television set to aparticular station, you are selecting one of the many signals being received at thattime. Since each station has a different assigned carrier frequency, the desired signalcan be separated from the others by filtering. Were it not for modulation, only onestation could broadcast in a given area; otherwise, two or more broadcasting stationswould create a hopeless jumble of interference.

Modulation for Multiplexing Multiplexing is the process of combining several signalsfor simultaneous transmission on one channel. Frequency-division multiplexing(FDM) uses CW modulation to put each signal on a different carrier frequency, and abank of filters separates the signals at the destination. Time-division multiplexing(TDM) uses pulse modulation to put samples of different signals in nonoverlappingtime slots. Back in Fig. 1.2–1c, for instance, the gaps between pulses could be filledwith samples from other signals. A switching circuit at the destination then separatesthe samples for signal reconstruction. Applications of multiplexing include FM stereo-phonic broadcasting, cable TV, and long-distance telephone.

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A variation of multiplexing is multiple access (MA). Whereas multiplexinginvolves a fixed assignment of the common communications resource (such as fre-quency spectrum) at the local level, MA involves the remote sharing of the resource.For example, code-division multiple access (CDMA) assigns a unique code to eachdigital cellular user, and the individual transmissions are separated by correlationbetween the codes of the desired transmitting and receiving parties. Since CDMAallows different users to share the same frequency band simultaneously, it providesanother way of increasing communication efficiency.

Coding Methods and BenefitsWe’ve described modulation as a signal-processing operation for effective transmis-sion. Coding is a symbol-processing operation for improved communication when the information is digital or can be approximated in the form of discrete sym-bols. Both coding and modulation may be necessary for reliable long-distance digitaltransmission.

The operation of encoding transforms a digital message into a new sequence ofsymbols. Decoding converts an encoded sequence back to the original messagewith, perhaps, a few errors caused by transmission contaminations. Consider a com-puter or other digital source having M W 2 symbols. Uncoded transmission of amessage from this source would require M different waveforms, one for each sym-bol. Alternatively, each symbol could be represented by a binary codeword consist-ing of K binary digits. Since there are 2K possible codewords made up of K binarydigits, we need K � log2 M digits per codeword to encode M source symbols. If thesource produces r symbols per second, the binary code will have Kr digits per sec-ond, and the transmission bandwidth requirement is K times the bandwidth of anuncoded signal.

In exchange for increased bandwidth, binary encoding of M-ary source symbolsoffers two advantages. First, less complicated hardware is needed to handle a binarysignal composed of just two different waveforms. Second, everything else beingequal, contaminating noise has less effect on a binary signal than it does on a signalcomposed of M different waveforms, so there will be fewer errors caused by thenoise. Hence, this coding method is essentially a digital technique for widebandnoise reduction. The exception to the above rule would be if each of the M dif-ferent waveforms were transmitted on a different frequency, space, or were mutuallyorthogonal.

Channel coding is a technique used to introduce controlled redundancy to fur-ther improve the performance reliability in a noisy channel. Error-control codinggoes further in the direction of wideband noise reduction. By appending extra checkdigits to each binary codeword, we can detect, or even correct, most of the errors thatdo occur. Error-control coding increases both bandwidth and hardware complexity,but it pays off in terms of nearly error-free digital communication despite a low signal-to-noise ratio.

Now, let’s examine the other fundamental system limitation: bandwidth. Manycommunication systems rely on the telephone network for transmission. Since the

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bandwidth of the transmission system is limited by decades-old design specifica-tions, in order to increase the data rate, the signal bandwidth must be reduced. High-speed modems (data modulator/demodulators) are one application requiring suchdata reduction. Source-coding techniques take advantage of the statistical knowl-edge of the source signal to enable efficient encoding. Thus, source coding can beviewed as the dual of channel coding in that it reduces redundancy to achieve thedesired efficiency.

Finally, the benefits of digital coding can be incorporated in analog communi-cation with the help of an analog-to-digital conversion method such as pulse-code-modulation (PCM). A PCM signal is generated by sampling the analog message,digitizing (quantizing) the sample values, and encoding the sequence of digitizedsamples. In view of the reliability, versatility, and efficiency of digital transmission,PCM has become an important method for analog communication. Furthermore,when coupled with high-speed microprocessors, PCM makes it possible to substitutedigital signal processing for analog operations.

1.3 ELECTROMAGNETIC WAVE PROPAGATION OVER WIRELESS CHANNELS

Over 100 years ago, Marconi established the first wireless communication betweenNorth America and Europe. Today, wireless communication is more narrowly definedto primarily mean the ubiquitous cell phones, wireless computer networks, other personal communication devices, and wireless sensors.

Like light waves, radio signals by nature only travel in a straight line, and there-fore propagation beyond line-of-sight (LOS) requires a means of deflecting thewaves. Given that the earth is spherical, the practical distance for LOS communica-tion is approximately 48 kM, or 30 miles, depending on the terrain and the height ofthe antennas, as illustrated in Fig. 1.3–1. In order to maximize coverage, therefore,television broadcast antennas and cell-phone base antennas are usually located onhills, high towers, and/or mountains.

However, there are several effects that enable light as well as electromagnetic(EM) waves to propagate around obstructions or beyond the earth’s horizon. Theseare refraction, diffraction, reflection, and scattering. These mechanisms can be bothuseful and troublesome to the radio engineer. For example, before satellite technol-ogy, international broadcasts and military communications took advantage of thefact that the ionosphere’s F-layer reflects† short-wave radio signals, as shown inFig. 1.3–2. Here signals from Los Angeles (LA) travel 3900 km to New York City(NY). However, the ability to reach a specific destination using ionospheric reflec-tion is dependent on the frequency, type of antenna, solar activity, and other phe-nomena that affect the ionosphere. We also observe that, while our signal of interestwill propagate from LA to NY, it will likely skip over Salt Lake City and Chicago.Therefore, ionospheric propagation is a relatively unreliable means of radio frequency

†Radio waves actually refract off the ionosphere. See further discussion.

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1.3 Electromagnetic Wave Propagation Over Wireless Channels 13

Figure 1.3–1 Line-of-sight communication and the earth’s curve.

Figure 1.3–2 Earth’s atmosphere regions and skywave propagation via the E- and F-layers ofthe ionosphere. Distances are approximate, and for clarity, the figure is not toscale.

(RF) communication. Reliability can be improved, however, if we employ frequencydiversity, that is, send the same signal over several different frequencies to increasethe probability that one of them will reach the intended destination. On the otherhand, as shown in Fig. 1.3–3, reflection of radio signals may cause multipath inter-ference whereby the signal and a delayed version(s) interfere with each other at thedestination. This destructive addition of signals causes signal fading. If you observeFig. 1.3–3, the received signal is the sum of three components: the direct one plustwo multipath ones, or simply y(t) � a1 x(t) � a2 x(t � a) � a3 x(t � b). Dependingon values of a and b, we can have constructive or destructive interference, and thusthe amplitude of y(t) could be greatly reduced or increased.

Los Angeles

ChicagoSalt LakeCity

New York

D La

yer

E Lay

er

F2 Laye

r

F1 Laye

r

200–

400 k

m

100

km

70 km

10

km

Trop

ospher

e

~30 miles

earth

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Signal fading, or attenuation, can also be caused by losses in the medium. Let’s con-sider the various means by which RF signals can be deflected as well as provide abrief description of general radio propagation. We draw on material from E. Jordanand K. Balmain (1971) and the ARRL Handbook’s chapter on radio propagation.

RF Wave DeflectionIn addition to waves reflecting from buildings, they can also reflect off of hills, auto-mobiles, and even airplanes. For example, two stations 900 km apart can communi-cate via reflection from an airplane whose altitude is 12 km. Of course, this wouldonly be suitable for experimental systems.

Waves bend by refraction because their velocity changes when passing fromone medium to another with differing indices of refraction. This explains why anobject in water is not located where it appears to be.

Diffraction occurs when the wave front meets a sharp edge and is delayed thenreflected off to the other side, redirecting or bending the rays as shown in Fig. 1.3–4a. Insome cases, the edge doesn’t have to be sharp, and as shown in Figs. 1.3–4b and c, sig-nals can be diffracted from a building or mountain. Note Fig. 1.3–4b is another illustra-tion of multipath caused by diffraction and reflection. At wavelengths above 300 meters(i.e., below 1 MHz), the earth acts as a diffractor and enables ground-wave propagation.

If the medium contains reflective particles, light or radio waves may be scatteredand thus deflected. A common example is fog’s causing automobile headlight beamsto be scattered. Similarly, meteor showers will leave ionized trails in the earth’satmosphere that scatter radio waves and allow non-LOS propagation for signals in therange of 28–432 MHz. This, along with other propagation mechanisms, can be anextremely transient phenomenon.

Skywave PropagationSkywave propagation is where radio waves are deflected in the troposphere or ion-osphere to enable communication distances that well exceed the optical LOS.Figure 1.3–2 shows the regions of the earth’s atmosphere including the troposphere

a2x(t – a)

a3x(t – b )

y(t) = a1x (t) + a2x (t – a ) + a3x (t – b )a1x(t)

Figure 1.3–3 Multipath interference caused by a signal being reflected off the terrain and abuilding.

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1.3 Electromagnetic Wave Propagation Over Wireless Channels 15

(b) (c)

(a)

Reflection

Diffraction

Diffraction

Earth

Diffraction

Figure 1.3–4 Diffraction of waves: (a) optical, (b) off the top of a building, (c) off a hill or theearth.

and the ionosphere’s D-, E-, and F-layers. Also shown are their approximate respec-tive distances from the earth’s surface. The troposphere, which is 78 percent nitro-gen, 21 percent oxygen, and 1 percent other gases, is the layer immediately abovethe earth and where we get clouds and weather. Thus its density will vary accordingto the air temperature and moisture content. The ionosphere starts at about 70 kmand contains mostly hydrogen and helium gases. The behavior of these layersdepends on solar activity, ionized by the sun’s ultraviolet light, causing an increasingelectron density with altitude. The D-layer (70–80 km) is present only during the dayand, depending on the transmission angle, will strongly absorb radio signals belowabout 5–10 MHz. Therefore, signals below these frequencies are propagated beyondLOS primarily via ground wave. This is why you hear only local AM broadcast sig-nals during the day. The E-layer (about 100 km) also exists primarily during the day.Layers F1 and F2 exist during the day, but at night these combine to form a single F-layer. The E and F layers, as well as to a lesser extent the troposphere, are the basisfor skywave propagation.

While the primary mechanism for bending radio waves in the E and F layersappears to be reflection, it is actually refraction as shown in Fig. 1.3–5. The particu-lar layer has a refractive index that increases with altitude. This causes the enteringradio wave to be refracted in a downward curvature. The thickness of the layer andelectron density gradient may be such that the curvature is sufficient enough torefract the wave back to earth.

The geometry and altitude of the E- and F-layers are such that the maximum distance of one hop from these layers is 2500 and 4000 km respectively. Note, inobserving Fig. 1.3–2, the distance from LA to NY is 3900 km, and Salt Lake City toChicago is 2000 km (E-layer). As Fig. 1.3–6 indicates, multiple hops can occurbetween the earth and E- and F-layers, and/or the F- and E-layers. Multiple hopsmake it possible for signals to propagate halfway around the earth. Of course, thereis some loss of signal strength with each hop.

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During the day, and depending on solar activity, the E-layer is capable of deflectingsignals up to 20 MHz. At other times, aurora borealis (or australis), the northern (orsouthern) lights, will cause high-energy particles to ionize gasses in the E-layer,enabling propagation of signals up to 900 MHz. There is also Sporadic E skip, whichenables propagation for frequencies up to 220 MHz or so. The F-layer will enabledeflection of signals up to approximately 20 MHz, but during sunspot activity signalsabove 50 MHz have been propagated thousands of miles via the F-layer.

The maximum frequency at which the ionosphere is capable of refracting a per-pendicular signal back to earth is referred to as the maximum usable frequency(MUF). However, in reality the signal paths are not perpendicular to the ionosphere,and thus the ionosphere may refract even higher frequencies since a lower launch

Earth

Ionosphere

Figure 1.3–5 Radio wave refracting off the ionosphere.

Earth

F La

yer

E La

yer

Figure 1.3–6 Signal propagation via multi-hop paths.

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1.4 Emerging Developments 17

angle encounters a thicker layer. The MUF will vary depending on solar activity, butis usually at least 14 MHz, even if for a few hours each day.

Similarly, temperature inversions, moisture, and other weather conditions in thetroposphere may refract or scatter the radio wave. Even under normal circumstances,because air has a nonhomogenous index of refraction, horizontal waves will have adownward curvature and thus be capable of traveling just beyond LOS. In any case,troposphere bending, or tropo scatter, primarily affects signals above 30 MHz. Whilethis is a short-term effect, there have been cases where 220 and 432 MHz signalshave traveled more than 2500 miles.

We summarize with the following statements with respect to propagation via theatmosphere: (a) The ionosphere will enable signals below the MUF to propagategreat distances beyond LOS, but may skip over the intended destination; thus, wehave to employ frequency diversity and different antenna angles to increase the prob-ability of the signal’s reaching its destination. (b) There can be a great variation inthe MUF depending on solar activity. (c) Signal propagation beyond LOS for fre-quencies above 14–30 MHz is extremely transient and unreliable. This is why wenow use satellites for reliable communications for signals above 30 MHz. (d) Whilepropagation beyond LOS using the atmosphere as well as other objects is notdependable, when it does occur it can cause interference between different users aswell as multipath interference. The radio engineer needs to be aware of all of thementioned propagation modes and design a system accordingly.

1.4 EMERGING DEVELOPMENTSTraditional telephone communication has been implemented via circuit switching,as shown in Fig. 1.4–1a, in which a dedicated (or a virtual) line is assigned to con-nect the source and destination. The Internet, originally designed for efficient andfast text and data transmission, uses packet switching in which the data stream isbroken up into packets and then routed to the destination via a set of available chan-nels to be reconstructed at the destination. Fig. 1.4–1b shows how telephone and textinformation is sent via packet switching. Packet switching is more efficient than cir-cuit switching if the data are bursty or intermittent, as is the case with text, but wouldnot normally be tolerated for voice telephone. With the continued development ofhigh-speed data routers and with the existing cable television infrastructure, Internettelephone, or Voice-over-Internet Protocol (VoIP), is becoming a viable alternativeto standard telephone circuit switching. In fact, third-generation (3G) wirelessphones will primarily use packet switching.

3G wireless systems, or Universal Mobile Telecommunications Systems (UMTS),are the successor to the original first- and second-generation (1G and 2G) voice-onlycell-phone systems. 3G is now a global standard for wireless phone networks and has the following features: (a) voice and data, (b) packet-only switching (some systemsare compatible with circuit switching), (c) code division multiple access (CDMA), (d)full global roaming, and (e) evolutionary migration from the existing base of 2G sys-tems. For example, 2.5G cell phone systems are a combination of voice and data. See

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Goodman and Myers (2005) and Ames and Gabor (2000) for more information on 3Gstandards.

In addition to packet switching, there has been continued development of bettermultiple access methods to enable ways to more efficiently utilize an existing chan-nel. In the case of wireless or cell phones, this enables lower cost service and moreusers per cell without degradation in quality of service (QoS). The traditional meth-ods include frequency, time, and code division multiple access (FDMA, TDMA, andCDMA). FDMA and TDMA are covered in Chap. 7, and CDMA, which uses directsequence spread spectrum, is covered in Chap. 15. FDMA and TDMA share a chan-nel via an assigned frequency or time slot respectively. In both of these methods, toomany users on a channel will cause cross-talk such that one user may hear the other’sconversation in the background. Thus with FDMA and TDMA there is the proverbialtrade-off between interference and economics. This is particularly the case with cellphones, where we have to set a hard limit on the number of users per cell. This hardlimit prevents additional users from making calls even though some other existinguser will soon be hanging up and releasing the frequency or time slot. On the otherhand, with CDMA an unauthorized listener will hear only noise, and thus when some-one wants to make a phone call in an already busy cell area, the additional CDMAuser will temporarily raise the level of background noise since someone else is soonlikely to be hanging up. Therefore, we can set a soft limit to the number of CDMAusers per cell and allow more users per cell. This is one important reason why CDMA

VOIPRouter “Hey Mom!”

Router

“Hey Mom!”

t

y

e

m

x

M

x

o

T

H

!e

Digitized voice symbolsdivided up into packetsthat will flow over6 channels

Voice symbols reconstructed byputting packets in theirproper order

Packet flow

Channel1

2

3

7

5

6

(b)

Router

VOIPRouter

“Text” “Text”

Received textSent text

“Hey Mom!” “Hey Mom!”

(a)

Figure 1.4–1 (a) Standard telephone lines that use circuit switching, (b) Internet telephone(VoIP) using packet switching and someone else communicating via the Internet.

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1.4 Emerging Developments 19

is being used in 3G wireless systems. CDMA also reduces the multipath problemsince the multipath component is treated as another user.

Orthogonal frequency division multiplexing (OFDM) is a variation of fre-quency division multiplexing (FDM) in which we can reduce interference betweenusers by selecting a set of carrier frequencies that are orthogonal to each other.Another application of OFDM is that, instead of sending a message at a high rateover a single channel, we can send the same message over several channels at alower rate; this reduces the problem of multipath. OFDM is covered in Chap. 14 andis used widely in wireless computer networks such as Wi-Fi and WiMax.

Ultra-wideband (UWB) systems can operate at average power levels below theambient levels of existing RF interference, or in other words, the power output of aUWB is below such unintentional radiators as computer boards and other digitallogic hardware. Recent Federal Communications Commission (FCC) guidelinesallow for unlicensed UWB operation from approximately 3.1 to 10.6 GHz at powerlevels not to exceed –41 dBm. This combined with continued development of UWBtechnology will enable greater use of the RF spectrum and thus allow for even moreusers and services on the RF spectrum.

Computer networks Wi-Fi (or IEEE 802.11) and WiMax (or IEEE 802.16) aretwo wireless computer network systems that have proliferated due to the FCC’s mak-ing available portions of the 915 MHz, 2.45 GHz, and 5.8-GHz ISM as well as otherUHF and microwave bands available for communication purposes. Wi-Fi technologyis used in local area networks (LANs) such as those used by laptop computers seen incoffee shops, etc, hence the often-used term “hot spots.” Its range is approximately ahundred meters. WiMax is a mobile wireless system and often uses the existing cellphone tower infrastructure and has a range comparable to that of cell phones. WiMaxhas been touted as an alternative to wireless phones for data service and can be used asan alternative to cable to enable Internet access in buildings. In other words, WiMaxcan serve as the last mile for broadband connectivity. Note that WiMax, Wi-Fi, and cellphones all operate on separate frequencies and thus are separate systems.

Software radio, or software-defined radio (SDR), as shown in the receiver ofFig. 1.4–2a, is another relatively recent development in communication technologythat promises greater flexibility than is possible with standard analog circuit meth-ods. The signal at the antenna is amplified by a radio frequency (RF) amplifier anddigitized using an analog-to-digital converter (ADC). The ADC’s output is fed to thedigital signal processor (DSP), which does the appropriate demodulation, and so on,and then to the digital-to-analog converter (DAC), which changes it back to a formthe user can hear. A software radio transmitter would be the inverse. The flexibilityincludes varying the parameters of station frequency, filter characteristics, modula-tion types, gain, and so on, via software control. Note, in many cases, because oftechnological hardware limitations particularly in the GHz frequency range, theequipment is often a hybrid of analog and software radio. Software radios are oftenimplemented via field programmable gate arrays (FPGAs) wherein the transmitter orreceiver design is first developed in some high-level software language such asSimulink, converted to VHSIC (very high speed integrated circuits) hardwaredescription language (VHDL) to be compiled, and then downloaded to the FPGA asshown in Fig. 1.4–2b.

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1.5 SOCIETAL IMPACT AND HISTORICALPERSPECTIVE

The tremendous technological advances of communication systems once againaffirms that “Engineers are the agents of social change”† and are the driving forcebehind drastic changes in public policy, whether it be privacy, commerce, or intellec-tual property. These paradigm changes are all due to the diligence of engineers andinvestors who create and develop the next generation of communications technology.Let us cite some examples. At one time, telephone service was available only throughlandlines and was a government-regulated monopoly. You paid a premium for longdistance and it was priced by the minute. Today, the consumer has the additionalchoices of phone service through the Internet, simply Voice-Over-Internet Protocol(VOIP), and the cell phone. These new technologies have removed the distinctionbetween local and long distance, and usually both are available for a low, fixed rateregardless of the amount of time spent using the service, diminishing the role of gov-ernment utility commissions. Similarly, with digital subscriber lines (DSLs), the

†Daitch, P. B. “Introduction to College Engineering” (Reading, MA: Addison Wesley, 1973), p. 106.

(a)

ADCRF Amp.

Antenna

DS P DAC Destination

ADCRF Amp.

Antenna

FPGA

Compiler

Simulink

DAC Destination

(b)

Figure 1.4–2 (a) Software radio receiver, (b) software radio receiver implemented via anFPGA.

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1.5 Societal Impact and Historical Perspective 21

telephone companies can also provide both standard phone and video services. WiMaxand, to a lesser extent, Wi-Fi technologies are diminishing the need for wired access to the network. For example, just like cable can now provide a home or business withvideo, data, and voice services, WiMax is expected to do the same. What is even moreinteresting is that, unlike many cell phone providers that are part of a local telephonecompany, WiMax companies are often small independent startups. Some of the moti-vation for WiMax startups is to provide an alternative to the regulated local phone orcable company (Andrews et al., 2007). Finally, television via satellite is now availableusing dishes less than a meter in diameter, making it possible to receive satellite TVwithout running afoul of local zoning restrictions. You can observe on any collegecampus that most college students have a wireless phone service that can reach any-where in the United States at a quality and cost rivaling those of landlines. Phones cansend and receive voice, music, text, and video information. E-commerce sales via the Internet have forced state governments to rethink th

Documents

Communication Systems · PM and FM Signals 208 Narrowband PM and FM 212 Tone Modulation 213 Multitone and Periodic Modulation 220 5.2 Transmission Bandwidth and Distortion (5.1) 223