PRINCIPLES OF COMMUNICATIONS

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1 PRINCIPLES OF COMMUNICATIONS Systems, Modulation, and Noise SIXTH EDITION INTERNATIONAL STUDENT VERSION RODGER E. ZIEMER University of Colorado at Colorado Springs WILLIAM H. TRANTER Virginia Polytechnic Institute and State University WILEY John Wiley & Sons, Inc.

CONTENTS CHAPTER 1 OVERVIEW AND HISTORICAL PERSPECTIVES 1 1.1 The Block Diagram of a Communication System 3 1.2 Channel Characteristics 5 1.2.1 Noise Sources 5 1.2.2 Types of Transmission Channels 6 1.

2 CONTENTS CHAPTER 1 OVERVIEW AND HISTORICAL PERSPECTIVES The Block Diagram of a Communication System Channel Characteristics Noise Sources Types of Transmission Channels Summary of Systems Analysis Techniques Time-Domain and Frequency- Domain Analyses Modulation and Communication Theories Probabilistic Approaches to System Optimization Statistical Signal Detection and Estimation Theory Information Theory and Coding Recent Advances Preview of This Book 16 Further Reading 16 CHAPTER 2 FUNDAMENTALS OF SIGNAL AND SYSTEM ANALYSIS Signal Models Deterministic and Random Signals Periodic and Aperiodic Signals Phasor Signals and Spectra Singularity Functions Signal Classifications Generalized Fourier Series Fourier Series Complex Exponential Fourier Series Symmetry Properties of the Fourier Coefficients Trigonometric Form of the Fourier Series Parseval's Theorem Examples of Fourier Series Line Spectra The Fourier Transform Amplitude and Phase Spectra Symmetry Properties Energy Spectral Density Convolution Transform Theorems: Proofs and Applications Fourier Transforms of Periodic Signals Poisson Sum Formula Power Spectral Density and Correlation The Time-Average Autocorrelation Function Properties of R(x) Signals and Linear Systems Definition of a Linear Time-Invariant System 56 ix

X Contents 2.7.2 Impulse Response and the Superposition Integral 57 2.7.3 Stability 58 2.7.4 Transfer (Frequency Response) Function 58 2.7.5 Causality 59 2.7.6 Symmetry Properties of #(/) 59 2.7.7 Input-Output Relationships for Spectral Densities 62 2.

3 X Contents Impulse Response and the Superposition Integral Stability Transfer (Frequency Response) Function Causality Symmetry Properties of #(/) Input-Output Relationships for Spectral Densities Response to Periodic Inputs Distortionless Transmission Group and Phase Delay Nonlinear Distortion Ideal Filters Approximation of Ideal Lowpass Filters by Realizable Filters Relationship of Pulse Resolution and Risetime to Bandwidth Sampling Theory The Hubert Transform Definition Properties Analytic Signals Complex Envelope Representation of Bandpass Signals Complex Envelope Representation of Bandpass Systems Discrete Fourier Transform and Fast Fourier Transform 91 Summary 95 Further Reading 99 Problems 100 Computer Exercises 110 / CHAPTER 3 MODULATION TECHNIQUES WITH EMPHASIS ON ANALOG SYSTEMS Linear Modulation Double-Sideband Modulation Amplitude Modulation Single-Sideband Modulation Vestigial-Sideband Modulation Frequency Translation and Mixing Angle Modulation Narrowband Angle Modulation Spectrum of an Angle-Modulated Signal Power in an Angle-Modulated Signal Bandwidth of Angle-Modulated Signals Narrowband-to-Wideband Conversion Demodulation of Angle-Modulated Signals Interference Interference in Linear Modulation Interference in Angle Modulation Feedback Demodulators: The Phase-Locked Loop Phase-Locked Loops for FM and PM Demodulation Phase-Locked Loop Operation in the Tracking Mode: The Linear Model Phase-Locked Loop Operation in the Acquisition Mode Costas PLLs Frequency Multiplication and Frequency Division Analog Pulse Modulation Pulse-Amplitude Modulation Pulse-Width Modulation (PWM) Pulse-Position Modulation (PPM) Delta Modulation and PCM Delta Modulation Pulse-Code Modulation 190

Contents xi 3.7 Multiplexing 191 3.7.1 Frequency-Division Multiplexing 192 3.7.2 Example of FDM: Stereophonic FM Broadcasting 193 3.7.3 Quadrature Multiplexing 193 3.7.4 Time-Division Multiplexing 195 3.

4 Contents xi 3.7 Multiplexing Frequency-Division Multiplexing Example of FDM: Stereophonic FM Broadcasting Quadrature Multiplexing Time-Division Multiplexing An Example: The Digital Telephone System Comparison of Multiplexing Schemes 198 Summary 198 Further Reading 202 Problems 202 Computer Exercises 208 CHAPTER 4 BASEBAND COMMUNICATION SYSTEMS IN THE ABSENCE OF NOISE Baseband Digital Data Transmission Systems Line Codes and Their Power Spectra Description of Line Codes Power Spectra for Line Coded Data Effects of Filtering of Digital Data: ISI Pulse Shaping: Nyquist's Criterion for Zero ISI Pulses Having the Zero-ISI Property Nyquist's Pulse Shaping Criterion Transmitter and Receiver Filters for Zero ISI Zero-Forcing Equalization Eye Diagrams Synchronization Carrier Modulation of Baseband Digital Signals 238 Summary 239 Further Reading 240 Problems 241 Computer Exercises 243 CHAPTER 5 A BRIEF REVIEW OF PROBABILITY THEORY What is Probability? Equally Likely Outcomes Relative Frequency Sample Spaces and the Axioms of Probability Venn Diagrams Some Useful Probability Relationships Tree Diagrams Some More General Relationships Random Variables and Related Functions Random Variables Probability (Cumulative) Distribution Functions Probability Density Function Joint cdfs and pdfs Transformation of Random Variables Statistical Averages Average of a Discrete Random Variable Average of a Continuous Random Variable Average of a Function of a Random Variable Average of a Function of More Than One Random Variable Variance of a Random Variable Average of a Linear Combination of N Random Variables 273

ХМ Contents 5.3.7 Variance of a Linear Combination of Independent Random Variables 274 5.3.8 Another Special Average: The Characteristic Function 275 5.3.9 The pdf of the Sum of Two Independent Random Variables 276 5.

5 ХМ Contents Variance of a Linear Combination of Independent Random Variables Another Special Average: The Characteristic Function The pdf of the Sum of Two Independent Random Variables Covariance and the Correlation Coefficient Some Useful pdfs Binomial Distribution Laplace Approximation to the Binomial Distribution Poisson Distribution and Poisson Approximation to the Binomial Distribution Geometric Distribution Gaussian Distribution Gaussian g-function Chebyshev's Inequality Collection of Probability Functions and Their Means and Variances 289 Summary 290 Further Reading 293 Problems 294 Computer Exercises 299 CHAPTER 6 STOCHASTIC PROCESSES A Relative-Frequency Description of Random Processes Some Terminology of Random Processes Sample Functions and "~ Ensembles Description of Random Processes in Terms of Joint pdfs Stationarity Partial Description of Random Processes: Ergodicity Meanings of Various Averages for Ergodic Processes Correlation and Power Spectral Density Power Spectral Density The Wiener-Khinchine Theorem Properties of the Autocorrelation Function Autocorrelation Functions for Random Pulse Trains Cross-Correlation Function and Cross-Power Spectral Density Linear Systems and Random Processes Input-Output Relationships Filtered Gaussian Processes Noise-Equivalent Bandwidth Narrowband Noise Quadrature-Component and Envelope-Phase Representation The Power Spectral Density Function of n c {t) and n s (f) Ricean Probability Density Function 329 Summary 331 Further Reading 334 Problems 334 Computer Exercises 339 CHAPTER 7 NOISE EFFECTS IN SIMPLE MODULATION SYSTEMS Signal-to-Noise Ratios Baseband Systems Double-Sideband Systems Single-Sideband Systems Amplitude Modulation Systems Noise and Phase Errors in Coherent Systems 353

Contents XÜi 7.3 Noise in Angle Modulation 357 7.3.1 The Effect of Noise on the Receiver Input 357 7.3.2 Demodulation of PM 359 7.3.3 Demodulation of FM: Above Threshold Operation 360 7.3.4 Performance Enhancement Through the Use of De-emphasis 362 7.

6 Contents XÜi 7.3 Noise in Angle Modulation The Effect of Noise on the Receiver Input Demodulation of PM Demodulation of FM: Above Threshold Operation Performance Enhancement Through the Use of De-emphasis Threshold Effect in FM Demodulation Threshold Effects in FM Demodulators Noise in Pulse-Code Modulation Postdetection SNR Companding 375 Summary 376 Further Reading 378 Problems 379 Computer Exercises 382 CHAPTER 8 FUNDAMENTALS OF BASIC BINARY DIGITAL COMMUNICATION SYSTEMS Baseband Data Transmission in White Gaussian Noise Binary Data Transmission with Arbitrary Signal Shapes Receiver Structure and Error Probability The Matched Filter Error Probability for the Matched-Filter Receiver Correlator Implementation of the Matched-Filter Receiver Optimum Threshold Nonwhite (Colored) Noise Backgrounds Receiver Implementation Imperfections Error Probabilities for Coherent Binary Signaling Modulation Schemes Not Requiring Coherent References Differential Phase-Shift Keying (DPSK) Noncoherent FSK M-ary РАМ Comparison of Digital Modulation Systems Performance of Zero-ISI Digital Data Systems Multipath Interference Flat Fading Channels Equalization Equalization by Zero-Forcing Equalization by Minimum Mean-Squared Error Tap Weight Adjustment 449 Summary 450 Further Reading 453 Problems 453 Computer Exercises 459 CHAPTER 9 ADVANCED DIGITAL COMMUNICATIONS M-ary Data Communications Systems M-ary Schemes Based on Quadrature Multiplexing OQPSK Systems MSK Systems M-ary Data Transmission in Terms of Signal Space QPSK in Terms of Signal Space M-ary Phase-Shift Keying Quadrature-Amplitude Modulation Coherent (FSK) Noncoherent (FSK) 481

xiv Contents 9.1.10 Differentially Coherent Phase-Shift Keying 485 9.1.11 Bit-Error Probability from Symbol- Error Probability 486 9.1.12 Comparison of M-ary Communications Systems on the Basis of Bit Error Probability 488 9.

7 xiv Contents Differentially Coherent Phase-Shift Keying Bit-Error Probability from Symbol- Error Probability Comparison of M-ary Communications Systems on the Basis of Bit Error Probability Comparison of M-ary Communications Systems on the Basis of Bandwidth Efficiency Power Spectra for Quadrature Modulation Techniques Synchronization Carrier Synchronization Symbol Synchronization Word Synchronization Pseudo-Noise Sequences Spread-Spectrum Communication Systems Direct-Sequence Spread Spectrum Performance in Continuous-Wave (CW) Interference Environments Performance in Multiple User Environments Frequency-Hop Spread Spectrum Code Synchronization Conclusion Multicarrier Modulation and Orthogonal Frequency Division Multiplexing Satellite Communications Antenna Coverage Earth Stations and Transmission Methods Link Analysis: Bent-Pipe Relay Link Analysis: OBP Digital Transponder Cellular Radio Communication Systems Basic Principles of Cellular Radio Channel Perturbations in Cellular Radio Characteristics of IG and 2G Cellular Systems Characteristics of W-CDMA and cdma Summary 546 Further Reading 549 Problems 549 Computer Exercises 553 CHAPTER 10 THE APPLICATION OF DETECTION AND ESTIMATION THEORY TO COMMUNICATIONS Bayes Optimization Signal Detection Versus Estimation Optimization Criteria Bayes Detectors Performance of Bayes Detectors The Neyman-Pearson Detector Minimum Probability-of-Error Detectors The Maximum a Posteriori Detector Minimax Detectors The M-ary Hypothesis Case 563" Decisions Based on Vector Observations Vector Space Representation of Signals Structure of Signal Space Scalar Product Norm Schwarz's Inequality Scalar Product of Two Signals in Terms of Fourier Coefficients 567

Contents XV 10.2.6 Choice of Basis Function Sets: The Gram-Schmidt Procedure 569 10.2.7 Signal Dimensionality as a Function of Signal Duration 571 10.

8 Contents XV Choice of Basis Function Sets: The Gram-Schmidt Procedure Signal Dimensionality as a Function of Signal Duration Maximum A Posteriori Receiver for Digital Data Transmission Decision Criteria for Coherent Systems in Terms of Signal Space Sufficient Statistics Detection of M-ary Orthogonal Signals A Noncoherent Case Estimation Theory Bayes Estimation Maximum-Likelihood Estimation Estimates Based on Multiple Observations Other Properties of ML Estimates Asymptotic Qualities of ML Estimates Applications of Estimation Theory to Communications Pulse-Amplitude Modulation Estimation of Signal Phase: The PLL Revisited 594 Summary 597 Further Reading 598 Problems 598 Computer Exercises 605 CHAPTER 11 SOURCE CODING AND ERROR CORRECTION TECHNIQUES Basic Concepts Information Entropy Discrete Channel Models Joint and Conditional Entropy Channel Capacity Source Coding An Example of Source Coding Several Definitions Entropy of an Extended Binary Source Shannon-Fano Source Coding Huffman Source Coding Communication in Noisy Environments: Basic Ideas Communication in Noisy Channels: Block Codes Hamming Distances and Error Correction Single-Parity-Check Codes Repetition Codes Parity-Check Codes for Single Error Correction Hamming Codes Cyclic Codes Performance Comparison Techniques Block Code Examples Communication in Noisy Channels: Convolutional Codes Tree and Trellis Diagrams The Viterbi Algorithm Performance Comparisons for Convolutional Codes Communication in Noisy Channels: Other Techniques Burst-Error-Correcting Codes Turbo Coding Feedback Channels Modulation and Bandwidth Efficiency Bandwidth and SNR Comparison of Modulation Systems 666

9 XVi Contents 11.8 Bandwidth and Power Efficient Modulation (TCM) 668 Summary 672 Further Reading 675 Problems 675 Computer Exercises 679 APPENDIX A NOISE MODELING WITH APPLICATIONS TO COMMUNICATIONS 681 A.l Physical Noise Sources 681 A. 1.1 Thermal Noise 681 A. 1.2 Nyquist's Formula 683 A. 1.3 Shot Noise 684 A. 1.4 Other Noise Sources 684 A. 1.5 Available Power 685 A. 1.6 Frequency Dependence 686 A. 1.7 Quantum Noise 686 A.2 Characterization of Noise in Systems 687 A.2.1 Noise Figure of a System 687 A.2.2 Measurement of Noise Figure 689 A.2.3 Noise Temperature 691 A.2.4 Effective Noise Temperature 691 A.2.5 Cascade of Subsystems 692 A.2.6 Attenuator Noise Temperature and Noise Figure 694 A.3 Free-Space Propagation Example 695 A.4 Further Reading 698 A.5 Problems 699 APPENDIX С THE NARROWBAND NOISE MODEL 703 APPENDIX D FM THRESHOLDING AND RELATED ANALYSES 706 D.l The Zero-Crossing Problem 706 D.2 Average Rate of Zero Crossings 708 D.3 Problems 712 APPENDIX E THE CHI-SQUARE RANDOM VARIABLE 713 APPENDIX F USEFUL TABLES AND IDENTITIES 715 APPENDIX G MATHEMATICAL AND NUMERICAL TABLES 719 G.l The Gaussian ß-Function 719 G.2 Trigonometric Identities 721 G.3 Series Expansions 722 G.4 Integrals 722 G.4.1 Indefinite 722 G.4.2 Definite 723 G.5 Fourier Transform Pairs 724 G.6 Fourier Transform Theorems 725 REFERENCES 726 AUTHOR INDEX 729 SUBJECT INDEX 731 APPENDIX В MULTIVARIATE GAUSSIAN VARIABLES 701 B.l The Probability Density Function 701 B.2 The Characteristic Function 701 B.3 Linear Transformations 702

COMMUNICATION SYSTEMS

COMMUNICATION SYSTEMS 4TH EDITION Simon Hayhin McMaster University JOHN WILEY & SONS, INC. Ш.! [ BACKGROUND AND PREVIEW 1. The Communication Process 1 2. Primary Communication Resources 3 3. Sources of