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Keeping up to date with the most current technologies in the field is essential for all effective electrical and computer engineers. The updated 7th edition of Principles of Communications presents the reader with more in-chapter examples, providing for a more supportive framework for learning.
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Keeping up to date with the most current technologies in the field is essential for all effective electrical and computer engineers. The updated 7th edition of Principles of Communications presents the reader with more in-chapter examples, providing for a more supportive framework for learning.
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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons Inc
- 7 ed
- Seitenzahl: 752
- Erscheinungstermin: 10. Juni 2014
- Englisch
- Abmessung: 235mm x 191mm x 40mm
- Gewicht: 1406g
- ISBN-13: 9781118078914
- ISBN-10: 1118078918
- Artikelnr.: 38481284
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
- Verlag: John Wiley & Sons Inc
- 7 ed
- Seitenzahl: 752
- Erscheinungstermin: 10. Juni 2014
- Englisch
- Abmessung: 235mm x 191mm x 40mm
- Gewicht: 1406g
- ISBN-13: 9781118078914
- ISBN-10: 1118078918
- Artikelnr.: 38481284
- Herstellerkennzeichnung
- Libri GmbH
- Europaallee 1
- 36244 Bad Hersfeld
- 06621 890
Dr. Rodger E. Ziemer recieved his B.S., M.S., and Ph.D. degrees from the University of Minnesota from 1960 to 1965. He joined the University of Colorado at Colorado Springs in 1984 as Chairman and Professor in the ECE Department. In conjunction, Dr. Ziemer worked as the Program director for Communications Research for the National Science Foundation from 1998 to 2001. In May of 2008 he was appointed Professor Emeritus. William H. Tranter is the author of Principles of Communications, 7th Edition, published by Wiley.
CHAPTER 1 INTRODUCTION 1 1.1 The Block Diagram of a Communication System 4 1.2 Channel Characteristics 5 1.2.1 Noise Sources 5 1.2.2 Types of Transmission Channels 7 1.3 Summary of Systems-Analysis Techniques 13 1.3.1 Time and Frequency-Domain Analyses 13 1.3.2 Modulation and Communication Theories 13 1.4 Probabilistic Approaches to System Optimization 14 1.4.1 Statistical Signal Detection and EstimationTheory 14 1.4.2 Information Theory and Coding 15 1.4.3 Recent Advances 16 1.5 Preview of This Book 16 Further Reading 16 CHAPTER 2 SIGNAL AND LINEAR SYSTEM ANALYSIS 17 2.1 Signal Models 17 2.1.1 Deterministic and Random Signals 17 2.1.2 Periodic and Aperiodic Signals 18 2.1.3 Phasor Signals and Spectra 18 2.1.4 Singularity Functions 21 2.2 Signal Classifications 24 2.3 Fourier Series 26 2.3.1 Complex Exponential Fourier Series 26 2.3.2 Symmetry Properties of the Fourier Coefficients 27 2.3.3 Trigonometric Form of the Fourier Series 28 2.3.4 Parseval's Theorem 28 2.3.5 Examples of Fourier Series 29 2.3.6 Line Spectra 30 2.4 The Fourier Transform 34 2.4.1 Amplitude and Phase Spectra 35 2.4.2 Symmetry Properties 36 2.4.3 Energy Spectral Density 37 2.4.4 Convolution 38 2.4.5 Transform Theorems: Proofs and Applications 40 2.4.6 Fourier Transforms of Periodic Signals 48 2.4.7 Poisson Sum Formula 50 2.5 Power Spectral Density and Correlation 50 2.5.1 The Time-Average Autocorrelation Function 51 2.5.2 Properties of
(
) 52 2.6 Signals and Linear Systems 55 2.6.1 Definition of a Linear Time-Invariant System 56 2.6.2 Impulse Response and the SuperpositionIntegral 56 2.6.3 Stability 58 2.6.4 Transfer (Frequency Response) Function 58 2.6.5 Causality 58 2.6.6 Symmetry Properties of
(
) 59 2.6.7 Input-Output Relationships for Spectral Densities 62 2.6.8 Response to Periodic Inputs 62 2.6.9 Distortionless Transmission 64 2.6.10 Group and Phase Delay 64 2.6.11 Nonlinear Distortion 67 2.6.12 Ideal Filters 68 2.6.13 Approximation of Ideal Lowpass Filters by Realizable Filters 70 2.6.14 Relationship of Pulse Resolution and Risetime to Bandwidth 75 2.7 Sampling Theory 78 2.8 The Hilbert Transform 82 2.8.1 Definition 82 2.8.2 Properties 83 2.8.3 Analytic Signals 85 2.8.4 Complex Envelope Representation of Bandpass Signals 87 2.8.5 Complex Envelope Representation of Bandpass Systems 89 2.9 The Discrete Fourier Transform and Fast Fourier Transform 91 Further Reading 95 Summary 95 Drill Problems 98 Problems 100 Computer Exercises 111 CHAPTER 3 LINEAR MODULATION TECHNIQUES 112 3.1 Double-Sideband Modulation 113 3.2 Amplitude Modulation (AM) 116 3.2.1 Envelope Detection 118 3.2.2 The Modulation Trapezoid 122 3.3 Single-Sideband (SSB) Modulation 124 3.4 Vestigial-Sideband (VSB) Modulation 133 3.5 Frequency Translation and Mixing 136 3.6 Interference in Linear Modulation 139 3.7 Pulse Amplitude Modulation---PAM 142 3.8 Digital Pulse Modulation 144 3.8.1 Delta Modulation 144 3.8.2 Pulse-Code Modulation 146 3.8.3 Time-Division Multiplexing 147 3.8.4 An Example: The Digital Telephone System 149 Further Reading 150 Summary 150 Drill Problems 151 Problems 152 Computer Exercises 155 CHAPTER 4 ANGLE MODULATION ANDMULTIPLEXING 156 4.1 Phase and Frequency Modulation Defined 156 4.1.1 Narrowband Angle Modulation 157 4.1.2 Spectrum of an Angle-Modulated Signal 161 4.1.3 Power in an Angle-Modulated Signal 168 4.1.4 Bandwidth of Angle-Modulated Signals 168 4.1.5 Narrowband-to-Wideband Conversion 173 4.2 Demodulation of Angle-Modulated Signals 175 4.3 Feedback Demodulators: The Phase-Locked Loop 181 4.3.1 Phase-Locked Loops for FM and PM Demodulation 181 4.3.2 Phase-Locked Loop Operation in the Tracking Mode: The Linear Model 184 4.3.3 Phase-Locked Loop Operation in the Acquisition Mode 189 4.3.4 Costas PLLs 194 4.3.5 Frequency Multiplication and Frequency Division 195 4.4 Interference in Angle Modulation 196 4.5 Analog Pulse Modulation 201 4.5.1 Pulse-Width Modulation (PWM) 201 4.5.2 Pulse-Position Modulation (PPM) 203 4.6 Multiplexing 204 4.6.1 Frequency-Division Multiplexing 204 4.6.2 Example of FDM: Stereophonic FM Broadcasting 205 4.6.3 Quadrature Multiplexing 206 4.6.4 Comparison of Multiplexing Schemes 207 Further Reading 208 Summary 208 Drill Problems 209 Problems 210 Computer Exercises 213 CHAPTER 5 PRINCIPLES OF BASEBAND DIGITAL DATATRANSMISSION 215 5.1 Baseband Digital Data Transmission Systems 215 5.2 Line Codes and Their Power Spectra 216 5.2.1 Description of Line Codes 216 5.2.2 Power Spectra for Line-Coded Data 218 5.3 Effects of Filtering of Digital Data---ISI 225 5.4 Pulse Shaping: Nyquist's Criterion for Zero ISI 227 5.4.1 Pulses Having the Zero ISI Property 228 5.4.2 Nyquist's Pulse-Shaping Criterion 229 5.4.3 Transmitter and Receiver Filters for Zero ISI 231 5.5 Zero-Forcing Equalization 233 5.6 Eye Diagrams 237 5.7 Synchronization 239 5.8 Carrier Modulation of Baseband Digital Signals 243 Further Reading 244 Summary 244 Drill Problems 245 Problems 246 Computer Exercises 249 CHAPTER 6 OVERVIEW OF PROBABILITY AND RANDOMVARIABLES 250 6.1 What is Probability? 250 6.1.1 Equally Likely Outcomes 250 6.1.2 Relative Frequency 251 6.1.3 Sample Spaces and the Axioms of Probability 252 6.1.4 Venn Diagrams 253 6.1.5 Some Useful Probability Relationships 253 6.1.6 Tree Diagrams 257 6.1.7 Some More General Relationships 259 6.2 Random Variables and Related Functions 260 6.2.1 Random Variables 260 6.2.2 Probability (Cumulative) Distribution Functions 262 6.2.3 Probability-Density Function 263 6.2.4 Joint cdfs and pdfs 265 6.2.5 Transformation of Random Variables 270 6.3 Statistical Averages 274 6.3.1 Average of a Discrete Random Variable 274 6.3.2 Average of a Continuous Random Variable 275 6.3.3 Average of a Function of a Random Variable 275 6.3.4 Average of a Function of More Than One Random Variable 277 6.3.5 Variance of a Random Variable 279 6.3.6 Average of a Linear Combination of
Random Variables 280 6.3.7 Variance of a Linear Combination of Independent Random Variables 281 6.3.8 Another Special Average---The Characteristic Function 282 6.3.9 The pdf of the Sum of Two Independent Random Variables 283 6.3.10 Covariance and the Correlation Coefficient 285 6.4 Some Useful pdfs 286 6.4.1 Binomial Distribution 286 6.4.2 Laplace Approximation to the Binomial Distribution 288 6.4.3 Poisson Distribution and Poisson Approximation to the Binomial Distribution 289 6.4.4 Geometric Distribution 290 6.4.5 Gaussian Distribution 291 6.4.6 Gaussian
-Function 295 6.4.7 Chebyshev's Inequality 296 6.4.8 Collection of Probability Functions and Their Means and Variances 296 Further Reading 298 Summary 298 Drill Problems 300 Problems 301 Computer Exercises 307 CHAPTER 7 RANDOM SIGNALS AND NOISE 308 7.1 A Relative-Frequency Description of Random Processes 308 7.2 Some Terminology of Random Processes 310 7.2.1 Sample Functions and Ensembles 310 7.2.2 Description of Random Processes in Terms of Joint pdfs 311 7.2.3 Stationarity 311 7.2.4 Partial Description of Random Processes: Ergodicity 312 7.2.5 Meanings of Various Averages for Ergodic Processes 315 7.3 Correlation and Power Spectral Density 316 7.3.1 Power Spectral Density 316 7.3.2 The Wiener--Khinchine Theorem 318 7.3.3 Properties of the Autocorrelation Function 320 7.3.4 Autocorrelation Functions for Random Pulse Trains 321 7.3.5 Cross-Correlation Function and Cross-Power Spectral Density 324 7.4 Linear Systems and Random Processes 325 7.4.1 Input-Output Relationships 325 7.4.2 Filtered Gaussian Processes 327 7.4.3 Noise-Equivalent Bandwidth 329 7.5 Narrowband Noise 333 7.5.1 Quadrature-Component and Envelope-Phase Representation 333 7.5.2 The Power Spectral Density Function of
(
) and
(
) 335 7.5.3 Ricean Probability Density Function 338 Further Reading 340 Summary 340 Drill Problems 341 Problems 342 Computer Exercises 348 CHAPTER 8 NOISE IN MODULATION SYSTEMS 349 8.1 Signal-to-Noise Ratios 350 8.1.1 Baseband Systems 350 8.1.2 Double-Sideband Systems 351 8.1.3 Single-Sideband Systems 353 8.1.4 Amplitude Modulation Systems 355 8.1.5 An Estimator for Signal-to-Noise Ratios 361 8.2 Noise and Phase Errors in Coherent Systems 366 8.3 Noise in Angle Modulation 370 8.3.1 The Effect of Noise on the Receiver Input 370 8.3.2 Demodulation of PM 371 8.3.3 Demodulation of FM: Above Threshold Operation 372 8.3.4 Performance Enhancement through the Use ofDe-emphasis 374 8.4 Threshold Effect in FM Demodulation 376 8.4.1 Threshold Effects in FM Demodulators 376 8.5 Noise in Pulse-Code Modulation 384 8.5.1 Postdetection SNR 384 8.5.2 Companding 387 Further Reading 389 Summary 389 Drill Problems 391 Problems 391 Computer Exercises 394 CHAPTER 9 PRINCIPLES OF DIGITAL DATA TRANSMISSIONIN NOISE 396 9.1 Baseband Data Transmission in White Gaussian Noise 398 9.2 Binary Synchronous Data Transmission with Arbitrary Signal Shapes 404 9.2.1 Receiver Structure and Error Probability 404 9.2.2 The Matched Filter 407 9.2.3 Error Probability for the Matched-Filter Receiver 410 9.2.4 Correlator Implementation of the Matched-Filter Receiver 413 9.2.5 Optimum Threshold 414 9.2.6 Nonwhite (Colored) Noise Backgrounds 414 9.2.7 Receiver Implementation Imperfections 415 9.2.8 Error Probabilities for Coherent Binary Signaling 415 9.3 Modulation Schemes not Requiring Coherent References 421 9.3.1 Differential Phase-Shift Keying (DPSK) 422 9.3.2 Differential Encoding and Decoding of Data 427 9.3.3 Noncoherent FSK 429 9.4 M-ary Pulse-Amplitude Modulation (PAM) 431 9.5 Comparison of Digital Modulation Systems 435 9.6 Noise Performance of Zero-ISI Digital Data Transmission Systems 438 9.7 Multipath Interference 443 9.8 Fading Channels 449 9.8.1 Basic Channel Models 449 9.8.2 Flat-Fading Channel Statistics and Error Probabilities 450 9.9 Equalization 455 9.9.1 Equalization by Zero-Forcing 455 9.9.2 Equalization by MMSE 459 9.9.3 Tap Weight Adjustment 463 Further Reading 466 Summary 466 Drill Problems 468 Problems 469 Computer Exercises 476 CHAPTER 10 ADVANCED DATA COMMUNICATIONSTOPICS 477 10.1 M-ary Data Communications Systems 477 10.1.1 M-ary Schemes Based on Quadrature Multiplexing 477 10.1.2 OQPSK Systems 481 10.1.3 MSK Systems 482 10.1.4 M-ary Data Transmission in Terms of Signal Space 489 10.1.5 QPSK in Terms of Signal Space 491 10.1.6 M-ary Phase-Shift Keying 493 10.1.7 Quadrature-Amplitude Modulation (QAM) 495 10.1.8 Coherent FSK 497 10.1.9 Noncoherent FSK 498 10.1.10 Differentially Coherent Phase-Shift Keying 502 10.1.11 Bit Error Probability from Symbol Error Probability 503 10.1.12 Comparison of M-ary Communications Systems on the Basis of Bit Error Probability 505 10.1.13 Comparison of M-ary Communications Systems on the Basis of Bandwidth Efficiency 508 10.2 Power Spectra for Digital Modulation 510 10.2.1 Quadrature Modulation Techniques 510 10.2.2 FSK Modulation 514 10.2.3 Summary 516 10.3 Synchronization 516 10.3.1 Carrier Synchronization 517 10.3.2 Symbol Synchronization 520 10.3.3 Word Synchronization 521 10.3.4 Pseudo-Noise (PN) Sequences 524 10.4 Spread-Spectrum Communication Systems 528 10.4.1 Direct-Sequence Spread Spectrum 530 10.4.2 Performance of DSSS in CW Interference Environments 532 10.4.3 Performance of Spread Spectrum in Multiple User Environments 533 10.4.4 Frequency-Hop Spread Spectrum 536 10.4.5 Code Synchronization 537 10.4.6 Conclusion 539 10.5 Multicarrier Modulation and Orthogonal Frequency-Division Multiplexing 540 10.6 Cellular Radio Communication Systems 545 10.6.1 Basic Principles of Cellular Radio 546 10.6.2 Channel Perturbations in Cellular Radio 550 10.6.3 Multiple-Input Multiple-Output (MIMO) Systems---Protection Against Fading 551 10.6.4 Characteristics of 1G and 2G Cellular Systems 553 10.6.5 Characteristics of cdma2000 and W-CDMA 553 10.6.6 Migration to 4G 555 Further Reading 556 Summary 556 Drill Problems 557 Problems 558 Computer Exercises 563 CHAPTER 11 OPTIMUM RECEIVERS AND SIGNAL-SPACECONCEPTS 564 11.1 Bayes Optimization 564 11.1.1 Signal Detection versus Estimation 564 11.1.2 Optimization Criteria 565 11.1.3 Bayes Detectors 565 11.1.4 Performance of Bayes Detectors 569 11.1.5 The Neyman-Pearson Detector 572 11.1.6 Minimum Probability of Error Detectors 573 11.1.7 The Maximum a Posteriori (MAP) Detector 573 11.1.8 Minimax Detectors 573 11.1.9 The M-ary Hypothesis Case 573 11.1.10 Decisions Based on Vector Observations 574 11.2 Vector Space Representation of Signals 574 11.2.1 Structure of Signal Space 575 11.2.2 Scalar Product 575 11.2.3 Norm 576 11.2.4 Schwarz's Inequality 576 11.2.5 Scalar Product of Two Signals in Terms of Fourier Coefficients 578 11.2.6 Choice of Basis Function Sets---The Gram--Schmidt Procedure 579 11.2.7 Signal Dimensionality as a Function of Signal Duration 581 11.3 Map Receiver for Digital Data Transmission 583 11.3.1 Decision Criteria for Coherent Systems in Terms of Signal Space 583 11.3.2 Sufficient Statistics 589 11.3.3 Detection of
-ary Orthogonal Signals 590 11.3.4 A Noncoherent Case 592 11.4 Estimation Theory 596 11.4.1 Bayes Estimation 596 11.4.2 Maximum-Likelihood Estimation 598 11.4.3 Estimates Based onMultiple Observations 599 11.4.4 Other Properties of ML Estimates 601 11.4.5 Asymptotic Qualities of ML Estimates 602 11.5 Applications of Estimation Theory to Communications 602 11.5.1 Pulse-Amplitude Modulation (PAM) 603 11.5.2 Estimation of Signal Phase: The PLL Revisited 604 Further Reading 606 Summary 607 Drill Problems 607 Problems 608 Computer Exercises 614 CHAPTER 12 INFORMATION THEORY AND CODING 615 12.1 Basic Concepts 616 12.1.1 Information 616 12.1.2 Entropy 617 12.1.3 Discrete Channel Models 618 12.1.4 Joint and Conditional Entropy 621 12.1.5 Channel Capacity 622 12.2 Source Coding 626 12.2.1 An Example of Source Coding 627 12.2.2 Several Definitions 630 12.2.3 Entropy of an Extended Binary Source 631 12.2.4 Shannon--Fano Source Coding 632 12.2.5 Huffman Source Coding 632 12.3 Communication in Noisy Environments: Basic Ideas 634 12.4 Communication in Noisy Channels: Block Codes 636 12.4.1 Hamming Distances and Error Correction 637 12.4.2 Single-Parity-Check Codes 638 12.4.3 Repetition Codes 639 12.4.4 Parity-Check Codes for Single Error Correction 640 12.4.5 Hamming Codes 644 12.4.6 Cyclic Codes 645 12.4.7 The Golay Code 647 12.4.8 Bose--Chaudhuri--Hocquenghem (BCH) Codes and Reed Solomon Codes 648 12.4.9 Performance Comparison Techniques 648 12.4.10 Block Code Examples 650 12.5 Communication in Noisy Channels: Convolutional Codes 657 12.5.1 Tree and Trellis Diagrams 659 12.5.2 The Viterbi Algorithm 661 12.5.3 Performance Comparisons for Convolutional Codes 664 12.6 Bandwidth and Power Efficient Modulation (TCM) 668 12.7 Feedback Channels 672 12.8 Modulation and Bandwidth Efficiency 676 12.8.1 Bandwidth and SNR 677 12.8.2 Comparison of Modulation Systems 678 12.9 Quick Overviews 679 12.9.1 Interleaving and Burst-Error Correction 679 12.9.2 Turbo Coding 681 12.9.3 Source Coding Examples 683 12.9.4 Digital Television 685 Further Reading 686 Summary 686 Drill Problems 688 Problems 688 Computer Exercises 692 APPENDIX A PHYSICAL NOISE SOURCES 693 A.1 Physical Noise Sources 693 A.1.1 Thermal Noise 693 A.1.2 Nyquist's Formula 695 A.1.3 Shot Noise 695 A.1.4 Other Noise Sources 696 A.1.5 Available Power 696 A.1.6 Frequency Dependence 697 A.1.7 Quantum Noise 697 A.2 Characterization of Noise in Systems 698 A.2.1 Noise Figure of a System 699 A.2.2 Measurement of Noise Figure 700 A.2.3 Noise Temperature 701 A.2.4 Effective Noise Temperature 702 A.2.5 Cascade of Subsystems 702 A.2.6 Attenuator Noise Temperature and Noise Figure 704 A.3 Free-Space Propagation Example 705 Further Reading 708 Problems 708 APPENDIX B JOINTLY GAUSSIAN RANDOM VARIABLES 710 B.1 The pdf 710 B.2 The Characteristic Function 711 B.3 Linear Transformations 711 APPENDIX C PROOF OF THE NARROWBAND NOISEMODEL 712 APPENDIX D ZERO-CROSSING AND ORIGIN ENCIRCLEMENTSTATISTICS 714 D.1 The Zero-Crossing Problem 714 D.2 Average Rate of Zero Crossings 716 Problems 719 APPENDIX E CHI-SQUARE STATISTICS 720 APPENDIX F MATHEMATICAL AND NUMERICAL TABLES 722 F.1 The Gaussian Q-Function 722 F.2 Trigonometric Identities 724 F.3 Series Expansions 724 F.4 Integrals 725 F.4.1 Indefinite 725 F.4.2 Definite 726 F.5 Fourier-Transform Pairs 727 F.6 Fourier-Transform Theorems 727 APPENDIX G ANSWERS TO DRILL PROBLEMS www.wiley.com/college/ziemer BIBLIOGRAPHY www.wiley.com/college/ziemer INDEX 728
(
) 52 2.6 Signals and Linear Systems 55 2.6.1 Definition of a Linear Time-Invariant System 56 2.6.2 Impulse Response and the SuperpositionIntegral 56 2.6.3 Stability 58 2.6.4 Transfer (Frequency Response) Function 58 2.6.5 Causality 58 2.6.6 Symmetry Properties of
(
) 59 2.6.7 Input-Output Relationships for Spectral Densities 62 2.6.8 Response to Periodic Inputs 62 2.6.9 Distortionless Transmission 64 2.6.10 Group and Phase Delay 64 2.6.11 Nonlinear Distortion 67 2.6.12 Ideal Filters 68 2.6.13 Approximation of Ideal Lowpass Filters by Realizable Filters 70 2.6.14 Relationship of Pulse Resolution and Risetime to Bandwidth 75 2.7 Sampling Theory 78 2.8 The Hilbert Transform 82 2.8.1 Definition 82 2.8.2 Properties 83 2.8.3 Analytic Signals 85 2.8.4 Complex Envelope Representation of Bandpass Signals 87 2.8.5 Complex Envelope Representation of Bandpass Systems 89 2.9 The Discrete Fourier Transform and Fast Fourier Transform 91 Further Reading 95 Summary 95 Drill Problems 98 Problems 100 Computer Exercises 111 CHAPTER 3 LINEAR MODULATION TECHNIQUES 112 3.1 Double-Sideband Modulation 113 3.2 Amplitude Modulation (AM) 116 3.2.1 Envelope Detection 118 3.2.2 The Modulation Trapezoid 122 3.3 Single-Sideband (SSB) Modulation 124 3.4 Vestigial-Sideband (VSB) Modulation 133 3.5 Frequency Translation and Mixing 136 3.6 Interference in Linear Modulation 139 3.7 Pulse Amplitude Modulation---PAM 142 3.8 Digital Pulse Modulation 144 3.8.1 Delta Modulation 144 3.8.2 Pulse-Code Modulation 146 3.8.3 Time-Division Multiplexing 147 3.8.4 An Example: The Digital Telephone System 149 Further Reading 150 Summary 150 Drill Problems 151 Problems 152 Computer Exercises 155 CHAPTER 4 ANGLE MODULATION ANDMULTIPLEXING 156 4.1 Phase and Frequency Modulation Defined 156 4.1.1 Narrowband Angle Modulation 157 4.1.2 Spectrum of an Angle-Modulated Signal 161 4.1.3 Power in an Angle-Modulated Signal 168 4.1.4 Bandwidth of Angle-Modulated Signals 168 4.1.5 Narrowband-to-Wideband Conversion 173 4.2 Demodulation of Angle-Modulated Signals 175 4.3 Feedback Demodulators: The Phase-Locked Loop 181 4.3.1 Phase-Locked Loops for FM and PM Demodulation 181 4.3.2 Phase-Locked Loop Operation in the Tracking Mode: The Linear Model 184 4.3.3 Phase-Locked Loop Operation in the Acquisition Mode 189 4.3.4 Costas PLLs 194 4.3.5 Frequency Multiplication and Frequency Division 195 4.4 Interference in Angle Modulation 196 4.5 Analog Pulse Modulation 201 4.5.1 Pulse-Width Modulation (PWM) 201 4.5.2 Pulse-Position Modulation (PPM) 203 4.6 Multiplexing 204 4.6.1 Frequency-Division Multiplexing 204 4.6.2 Example of FDM: Stereophonic FM Broadcasting 205 4.6.3 Quadrature Multiplexing 206 4.6.4 Comparison of Multiplexing Schemes 207 Further Reading 208 Summary 208 Drill Problems 209 Problems 210 Computer Exercises 213 CHAPTER 5 PRINCIPLES OF BASEBAND DIGITAL DATATRANSMISSION 215 5.1 Baseband Digital Data Transmission Systems 215 5.2 Line Codes and Their Power Spectra 216 5.2.1 Description of Line Codes 216 5.2.2 Power Spectra for Line-Coded Data 218 5.3 Effects of Filtering of Digital Data---ISI 225 5.4 Pulse Shaping: Nyquist's Criterion for Zero ISI 227 5.4.1 Pulses Having the Zero ISI Property 228 5.4.2 Nyquist's Pulse-Shaping Criterion 229 5.4.3 Transmitter and Receiver Filters for Zero ISI 231 5.5 Zero-Forcing Equalization 233 5.6 Eye Diagrams 237 5.7 Synchronization 239 5.8 Carrier Modulation of Baseband Digital Signals 243 Further Reading 244 Summary 244 Drill Problems 245 Problems 246 Computer Exercises 249 CHAPTER 6 OVERVIEW OF PROBABILITY AND RANDOMVARIABLES 250 6.1 What is Probability? 250 6.1.1 Equally Likely Outcomes 250 6.1.2 Relative Frequency 251 6.1.3 Sample Spaces and the Axioms of Probability 252 6.1.4 Venn Diagrams 253 6.1.5 Some Useful Probability Relationships 253 6.1.6 Tree Diagrams 257 6.1.7 Some More General Relationships 259 6.2 Random Variables and Related Functions 260 6.2.1 Random Variables 260 6.2.2 Probability (Cumulative) Distribution Functions 262 6.2.3 Probability-Density Function 263 6.2.4 Joint cdfs and pdfs 265 6.2.5 Transformation of Random Variables 270 6.3 Statistical Averages 274 6.3.1 Average of a Discrete Random Variable 274 6.3.2 Average of a Continuous Random Variable 275 6.3.3 Average of a Function of a Random Variable 275 6.3.4 Average of a Function of More Than One Random Variable 277 6.3.5 Variance of a Random Variable 279 6.3.6 Average of a Linear Combination of
Random Variables 280 6.3.7 Variance of a Linear Combination of Independent Random Variables 281 6.3.8 Another Special Average---The Characteristic Function 282 6.3.9 The pdf of the Sum of Two Independent Random Variables 283 6.3.10 Covariance and the Correlation Coefficient 285 6.4 Some Useful pdfs 286 6.4.1 Binomial Distribution 286 6.4.2 Laplace Approximation to the Binomial Distribution 288 6.4.3 Poisson Distribution and Poisson Approximation to the Binomial Distribution 289 6.4.4 Geometric Distribution 290 6.4.5 Gaussian Distribution 291 6.4.6 Gaussian
-Function 295 6.4.7 Chebyshev's Inequality 296 6.4.8 Collection of Probability Functions and Their Means and Variances 296 Further Reading 298 Summary 298 Drill Problems 300 Problems 301 Computer Exercises 307 CHAPTER 7 RANDOM SIGNALS AND NOISE 308 7.1 A Relative-Frequency Description of Random Processes 308 7.2 Some Terminology of Random Processes 310 7.2.1 Sample Functions and Ensembles 310 7.2.2 Description of Random Processes in Terms of Joint pdfs 311 7.2.3 Stationarity 311 7.2.4 Partial Description of Random Processes: Ergodicity 312 7.2.5 Meanings of Various Averages for Ergodic Processes 315 7.3 Correlation and Power Spectral Density 316 7.3.1 Power Spectral Density 316 7.3.2 The Wiener--Khinchine Theorem 318 7.3.3 Properties of the Autocorrelation Function 320 7.3.4 Autocorrelation Functions for Random Pulse Trains 321 7.3.5 Cross-Correlation Function and Cross-Power Spectral Density 324 7.4 Linear Systems and Random Processes 325 7.4.1 Input-Output Relationships 325 7.4.2 Filtered Gaussian Processes 327 7.4.3 Noise-Equivalent Bandwidth 329 7.5 Narrowband Noise 333 7.5.1 Quadrature-Component and Envelope-Phase Representation 333 7.5.2 The Power Spectral Density Function of
(
) and
(
) 335 7.5.3 Ricean Probability Density Function 338 Further Reading 340 Summary 340 Drill Problems 341 Problems 342 Computer Exercises 348 CHAPTER 8 NOISE IN MODULATION SYSTEMS 349 8.1 Signal-to-Noise Ratios 350 8.1.1 Baseband Systems 350 8.1.2 Double-Sideband Systems 351 8.1.3 Single-Sideband Systems 353 8.1.4 Amplitude Modulation Systems 355 8.1.5 An Estimator for Signal-to-Noise Ratios 361 8.2 Noise and Phase Errors in Coherent Systems 366 8.3 Noise in Angle Modulation 370 8.3.1 The Effect of Noise on the Receiver Input 370 8.3.2 Demodulation of PM 371 8.3.3 Demodulation of FM: Above Threshold Operation 372 8.3.4 Performance Enhancement through the Use ofDe-emphasis 374 8.4 Threshold Effect in FM Demodulation 376 8.4.1 Threshold Effects in FM Demodulators 376 8.5 Noise in Pulse-Code Modulation 384 8.5.1 Postdetection SNR 384 8.5.2 Companding 387 Further Reading 389 Summary 389 Drill Problems 391 Problems 391 Computer Exercises 394 CHAPTER 9 PRINCIPLES OF DIGITAL DATA TRANSMISSIONIN NOISE 396 9.1 Baseband Data Transmission in White Gaussian Noise 398 9.2 Binary Synchronous Data Transmission with Arbitrary Signal Shapes 404 9.2.1 Receiver Structure and Error Probability 404 9.2.2 The Matched Filter 407 9.2.3 Error Probability for the Matched-Filter Receiver 410 9.2.4 Correlator Implementation of the Matched-Filter Receiver 413 9.2.5 Optimum Threshold 414 9.2.6 Nonwhite (Colored) Noise Backgrounds 414 9.2.7 Receiver Implementation Imperfections 415 9.2.8 Error Probabilities for Coherent Binary Signaling 415 9.3 Modulation Schemes not Requiring Coherent References 421 9.3.1 Differential Phase-Shift Keying (DPSK) 422 9.3.2 Differential Encoding and Decoding of Data 427 9.3.3 Noncoherent FSK 429 9.4 M-ary Pulse-Amplitude Modulation (PAM) 431 9.5 Comparison of Digital Modulation Systems 435 9.6 Noise Performance of Zero-ISI Digital Data Transmission Systems 438 9.7 Multipath Interference 443 9.8 Fading Channels 449 9.8.1 Basic Channel Models 449 9.8.2 Flat-Fading Channel Statistics and Error Probabilities 450 9.9 Equalization 455 9.9.1 Equalization by Zero-Forcing 455 9.9.2 Equalization by MMSE 459 9.9.3 Tap Weight Adjustment 463 Further Reading 466 Summary 466 Drill Problems 468 Problems 469 Computer Exercises 476 CHAPTER 10 ADVANCED DATA COMMUNICATIONSTOPICS 477 10.1 M-ary Data Communications Systems 477 10.1.1 M-ary Schemes Based on Quadrature Multiplexing 477 10.1.2 OQPSK Systems 481 10.1.3 MSK Systems 482 10.1.4 M-ary Data Transmission in Terms of Signal Space 489 10.1.5 QPSK in Terms of Signal Space 491 10.1.6 M-ary Phase-Shift Keying 493 10.1.7 Quadrature-Amplitude Modulation (QAM) 495 10.1.8 Coherent FSK 497 10.1.9 Noncoherent FSK 498 10.1.10 Differentially Coherent Phase-Shift Keying 502 10.1.11 Bit Error Probability from Symbol Error Probability 503 10.1.12 Comparison of M-ary Communications Systems on the Basis of Bit Error Probability 505 10.1.13 Comparison of M-ary Communications Systems on the Basis of Bandwidth Efficiency 508 10.2 Power Spectra for Digital Modulation 510 10.2.1 Quadrature Modulation Techniques 510 10.2.2 FSK Modulation 514 10.2.3 Summary 516 10.3 Synchronization 516 10.3.1 Carrier Synchronization 517 10.3.2 Symbol Synchronization 520 10.3.3 Word Synchronization 521 10.3.4 Pseudo-Noise (PN) Sequences 524 10.4 Spread-Spectrum Communication Systems 528 10.4.1 Direct-Sequence Spread Spectrum 530 10.4.2 Performance of DSSS in CW Interference Environments 532 10.4.3 Performance of Spread Spectrum in Multiple User Environments 533 10.4.4 Frequency-Hop Spread Spectrum 536 10.4.5 Code Synchronization 537 10.4.6 Conclusion 539 10.5 Multicarrier Modulation and Orthogonal Frequency-Division Multiplexing 540 10.6 Cellular Radio Communication Systems 545 10.6.1 Basic Principles of Cellular Radio 546 10.6.2 Channel Perturbations in Cellular Radio 550 10.6.3 Multiple-Input Multiple-Output (MIMO) Systems---Protection Against Fading 551 10.6.4 Characteristics of 1G and 2G Cellular Systems 553 10.6.5 Characteristics of cdma2000 and W-CDMA 553 10.6.6 Migration to 4G 555 Further Reading 556 Summary 556 Drill Problems 557 Problems 558 Computer Exercises 563 CHAPTER 11 OPTIMUM RECEIVERS AND SIGNAL-SPACECONCEPTS 564 11.1 Bayes Optimization 564 11.1.1 Signal Detection versus Estimation 564 11.1.2 Optimization Criteria 565 11.1.3 Bayes Detectors 565 11.1.4 Performance of Bayes Detectors 569 11.1.5 The Neyman-Pearson Detector 572 11.1.6 Minimum Probability of Error Detectors 573 11.1.7 The Maximum a Posteriori (MAP) Detector 573 11.1.8 Minimax Detectors 573 11.1.9 The M-ary Hypothesis Case 573 11.1.10 Decisions Based on Vector Observations 574 11.2 Vector Space Representation of Signals 574 11.2.1 Structure of Signal Space 575 11.2.2 Scalar Product 575 11.2.3 Norm 576 11.2.4 Schwarz's Inequality 576 11.2.5 Scalar Product of Two Signals in Terms of Fourier Coefficients 578 11.2.6 Choice of Basis Function Sets---The Gram--Schmidt Procedure 579 11.2.7 Signal Dimensionality as a Function of Signal Duration 581 11.3 Map Receiver for Digital Data Transmission 583 11.3.1 Decision Criteria for Coherent Systems in Terms of Signal Space 583 11.3.2 Sufficient Statistics 589 11.3.3 Detection of
-ary Orthogonal Signals 590 11.3.4 A Noncoherent Case 592 11.4 Estimation Theory 596 11.4.1 Bayes Estimation 596 11.4.2 Maximum-Likelihood Estimation 598 11.4.3 Estimates Based onMultiple Observations 599 11.4.4 Other Properties of ML Estimates 601 11.4.5 Asymptotic Qualities of ML Estimates 602 11.5 Applications of Estimation Theory to Communications 602 11.5.1 Pulse-Amplitude Modulation (PAM) 603 11.5.2 Estimation of Signal Phase: The PLL Revisited 604 Further Reading 606 Summary 607 Drill Problems 607 Problems 608 Computer Exercises 614 CHAPTER 12 INFORMATION THEORY AND CODING 615 12.1 Basic Concepts 616 12.1.1 Information 616 12.1.2 Entropy 617 12.1.3 Discrete Channel Models 618 12.1.4 Joint and Conditional Entropy 621 12.1.5 Channel Capacity 622 12.2 Source Coding 626 12.2.1 An Example of Source Coding 627 12.2.2 Several Definitions 630 12.2.3 Entropy of an Extended Binary Source 631 12.2.4 Shannon--Fano Source Coding 632 12.2.5 Huffman Source Coding 632 12.3 Communication in Noisy Environments: Basic Ideas 634 12.4 Communication in Noisy Channels: Block Codes 636 12.4.1 Hamming Distances and Error Correction 637 12.4.2 Single-Parity-Check Codes 638 12.4.3 Repetition Codes 639 12.4.4 Parity-Check Codes for Single Error Correction 640 12.4.5 Hamming Codes 644 12.4.6 Cyclic Codes 645 12.4.7 The Golay Code 647 12.4.8 Bose--Chaudhuri--Hocquenghem (BCH) Codes and Reed Solomon Codes 648 12.4.9 Performance Comparison Techniques 648 12.4.10 Block Code Examples 650 12.5 Communication in Noisy Channels: Convolutional Codes 657 12.5.1 Tree and Trellis Diagrams 659 12.5.2 The Viterbi Algorithm 661 12.5.3 Performance Comparisons for Convolutional Codes 664 12.6 Bandwidth and Power Efficient Modulation (TCM) 668 12.7 Feedback Channels 672 12.8 Modulation and Bandwidth Efficiency 676 12.8.1 Bandwidth and SNR 677 12.8.2 Comparison of Modulation Systems 678 12.9 Quick Overviews 679 12.9.1 Interleaving and Burst-Error Correction 679 12.9.2 Turbo Coding 681 12.9.3 Source Coding Examples 683 12.9.4 Digital Television 685 Further Reading 686 Summary 686 Drill Problems 688 Problems 688 Computer Exercises 692 APPENDIX A PHYSICAL NOISE SOURCES 693 A.1 Physical Noise Sources 693 A.1.1 Thermal Noise 693 A.1.2 Nyquist's Formula 695 A.1.3 Shot Noise 695 A.1.4 Other Noise Sources 696 A.1.5 Available Power 696 A.1.6 Frequency Dependence 697 A.1.7 Quantum Noise 697 A.2 Characterization of Noise in Systems 698 A.2.1 Noise Figure of a System 699 A.2.2 Measurement of Noise Figure 700 A.2.3 Noise Temperature 701 A.2.4 Effective Noise Temperature 702 A.2.5 Cascade of Subsystems 702 A.2.6 Attenuator Noise Temperature and Noise Figure 704 A.3 Free-Space Propagation Example 705 Further Reading 708 Problems 708 APPENDIX B JOINTLY GAUSSIAN RANDOM VARIABLES 710 B.1 The pdf 710 B.2 The Characteristic Function 711 B.3 Linear Transformations 711 APPENDIX C PROOF OF THE NARROWBAND NOISEMODEL 712 APPENDIX D ZERO-CROSSING AND ORIGIN ENCIRCLEMENTSTATISTICS 714 D.1 The Zero-Crossing Problem 714 D.2 Average Rate of Zero Crossings 716 Problems 719 APPENDIX E CHI-SQUARE STATISTICS 720 APPENDIX F MATHEMATICAL AND NUMERICAL TABLES 722 F.1 The Gaussian Q-Function 722 F.2 Trigonometric Identities 724 F.3 Series Expansions 724 F.4 Integrals 725 F.4.1 Indefinite 725 F.4.2 Definite 726 F.5 Fourier-Transform Pairs 727 F.6 Fourier-Transform Theorems 727 APPENDIX G ANSWERS TO DRILL PROBLEMS www.wiley.com/college/ziemer BIBLIOGRAPHY www.wiley.com/college/ziemer INDEX 728
CHAPTER 1 INTRODUCTION 1 1.1 The Block Diagram of a Communication System 4 1.2 Channel Characteristics 5 1.2.1 Noise Sources 5 1.2.2 Types of Transmission Channels 7 1.3 Summary of Systems-Analysis Techniques 13 1.3.1 Time and Frequency-Domain Analyses 13 1.3.2 Modulation and Communication Theories 13 1.4 Probabilistic Approaches to System Optimization 14 1.4.1 Statistical Signal Detection and EstimationTheory 14 1.4.2 Information Theory and Coding 15 1.4.3 Recent Advances 16 1.5 Preview of This Book 16 Further Reading 16 CHAPTER 2 SIGNAL AND LINEAR SYSTEM ANALYSIS 17 2.1 Signal Models 17 2.1.1 Deterministic and Random Signals 17 2.1.2 Periodic and Aperiodic Signals 18 2.1.3 Phasor Signals and Spectra 18 2.1.4 Singularity Functions 21 2.2 Signal Classifications 24 2.3 Fourier Series 26 2.3.1 Complex Exponential Fourier Series 26 2.3.2 Symmetry Properties of the Fourier Coefficients 27 2.3.3 Trigonometric Form of the Fourier Series 28 2.3.4 Parseval's Theorem 28 2.3.5 Examples of Fourier Series 29 2.3.6 Line Spectra 30 2.4 The Fourier Transform 34 2.4.1 Amplitude and Phase Spectra 35 2.4.2 Symmetry Properties 36 2.4.3 Energy Spectral Density 37 2.4.4 Convolution 38 2.4.5 Transform Theorems: Proofs and Applications 40 2.4.6 Fourier Transforms of Periodic Signals 48 2.4.7 Poisson Sum Formula 50 2.5 Power Spectral Density and Correlation 50 2.5.1 The Time-Average Autocorrelation Function 51 2.5.2 Properties of
(
) 52 2.6 Signals and Linear Systems 55 2.6.1 Definition of a Linear Time-Invariant System 56 2.6.2 Impulse Response and the SuperpositionIntegral 56 2.6.3 Stability 58 2.6.4 Transfer (Frequency Response) Function 58 2.6.5 Causality 58 2.6.6 Symmetry Properties of
(
) 59 2.6.7 Input-Output Relationships for Spectral Densities 62 2.6.8 Response to Periodic Inputs 62 2.6.9 Distortionless Transmission 64 2.6.10 Group and Phase Delay 64 2.6.11 Nonlinear Distortion 67 2.6.12 Ideal Filters 68 2.6.13 Approximation of Ideal Lowpass Filters by Realizable Filters 70 2.6.14 Relationship of Pulse Resolution and Risetime to Bandwidth 75 2.7 Sampling Theory 78 2.8 The Hilbert Transform 82 2.8.1 Definition 82 2.8.2 Properties 83 2.8.3 Analytic Signals 85 2.8.4 Complex Envelope Representation of Bandpass Signals 87 2.8.5 Complex Envelope Representation of Bandpass Systems 89 2.9 The Discrete Fourier Transform and Fast Fourier Transform 91 Further Reading 95 Summary 95 Drill Problems 98 Problems 100 Computer Exercises 111 CHAPTER 3 LINEAR MODULATION TECHNIQUES 112 3.1 Double-Sideband Modulation 113 3.2 Amplitude Modulation (AM) 116 3.2.1 Envelope Detection 118 3.2.2 The Modulation Trapezoid 122 3.3 Single-Sideband (SSB) Modulation 124 3.4 Vestigial-Sideband (VSB) Modulation 133 3.5 Frequency Translation and Mixing 136 3.6 Interference in Linear Modulation 139 3.7 Pulse Amplitude Modulation---PAM 142 3.8 Digital Pulse Modulation 144 3.8.1 Delta Modulation 144 3.8.2 Pulse-Code Modulation 146 3.8.3 Time-Division Multiplexing 147 3.8.4 An Example: The Digital Telephone System 149 Further Reading 150 Summary 150 Drill Problems 151 Problems 152 Computer Exercises 155 CHAPTER 4 ANGLE MODULATION ANDMULTIPLEXING 156 4.1 Phase and Frequency Modulation Defined 156 4.1.1 Narrowband Angle Modulation 157 4.1.2 Spectrum of an Angle-Modulated Signal 161 4.1.3 Power in an Angle-Modulated Signal 168 4.1.4 Bandwidth of Angle-Modulated Signals 168 4.1.5 Narrowband-to-Wideband Conversion 173 4.2 Demodulation of Angle-Modulated Signals 175 4.3 Feedback Demodulators: The Phase-Locked Loop 181 4.3.1 Phase-Locked Loops for FM and PM Demodulation 181 4.3.2 Phase-Locked Loop Operation in the Tracking Mode: The Linear Model 184 4.3.3 Phase-Locked Loop Operation in the Acquisition Mode 189 4.3.4 Costas PLLs 194 4.3.5 Frequency Multiplication and Frequency Division 195 4.4 Interference in Angle Modulation 196 4.5 Analog Pulse Modulation 201 4.5.1 Pulse-Width Modulation (PWM) 201 4.5.2 Pulse-Position Modulation (PPM) 203 4.6 Multiplexing 204 4.6.1 Frequency-Division Multiplexing 204 4.6.2 Example of FDM: Stereophonic FM Broadcasting 205 4.6.3 Quadrature Multiplexing 206 4.6.4 Comparison of Multiplexing Schemes 207 Further Reading 208 Summary 208 Drill Problems 209 Problems 210 Computer Exercises 213 CHAPTER 5 PRINCIPLES OF BASEBAND DIGITAL DATATRANSMISSION 215 5.1 Baseband Digital Data Transmission Systems 215 5.2 Line Codes and Their Power Spectra 216 5.2.1 Description of Line Codes 216 5.2.2 Power Spectra for Line-Coded Data 218 5.3 Effects of Filtering of Digital Data---ISI 225 5.4 Pulse Shaping: Nyquist's Criterion for Zero ISI 227 5.4.1 Pulses Having the Zero ISI Property 228 5.4.2 Nyquist's Pulse-Shaping Criterion 229 5.4.3 Transmitter and Receiver Filters for Zero ISI 231 5.5 Zero-Forcing Equalization 233 5.6 Eye Diagrams 237 5.7 Synchronization 239 5.8 Carrier Modulation of Baseband Digital Signals 243 Further Reading 244 Summary 244 Drill Problems 245 Problems 246 Computer Exercises 249 CHAPTER 6 OVERVIEW OF PROBABILITY AND RANDOMVARIABLES 250 6.1 What is Probability? 250 6.1.1 Equally Likely Outcomes 250 6.1.2 Relative Frequency 251 6.1.3 Sample Spaces and the Axioms of Probability 252 6.1.4 Venn Diagrams 253 6.1.5 Some Useful Probability Relationships 253 6.1.6 Tree Diagrams 257 6.1.7 Some More General Relationships 259 6.2 Random Variables and Related Functions 260 6.2.1 Random Variables 260 6.2.2 Probability (Cumulative) Distribution Functions 262 6.2.3 Probability-Density Function 263 6.2.4 Joint cdfs and pdfs 265 6.2.5 Transformation of Random Variables 270 6.3 Statistical Averages 274 6.3.1 Average of a Discrete Random Variable 274 6.3.2 Average of a Continuous Random Variable 275 6.3.3 Average of a Function of a Random Variable 275 6.3.4 Average of a Function of More Than One Random Variable 277 6.3.5 Variance of a Random Variable 279 6.3.6 Average of a Linear Combination of
Random Variables 280 6.3.7 Variance of a Linear Combination of Independent Random Variables 281 6.3.8 Another Special Average---The Characteristic Function 282 6.3.9 The pdf of the Sum of Two Independent Random Variables 283 6.3.10 Covariance and the Correlation Coefficient 285 6.4 Some Useful pdfs 286 6.4.1 Binomial Distribution 286 6.4.2 Laplace Approximation to the Binomial Distribution 288 6.4.3 Poisson Distribution and Poisson Approximation to the Binomial Distribution 289 6.4.4 Geometric Distribution 290 6.4.5 Gaussian Distribution 291 6.4.6 Gaussian
-Function 295 6.4.7 Chebyshev's Inequality 296 6.4.8 Collection of Probability Functions and Their Means and Variances 296 Further Reading 298 Summary 298 Drill Problems 300 Problems 301 Computer Exercises 307 CHAPTER 7 RANDOM SIGNALS AND NOISE 308 7.1 A Relative-Frequency Description of Random Processes 308 7.2 Some Terminology of Random Processes 310 7.2.1 Sample Functions and Ensembles 310 7.2.2 Description of Random Processes in Terms of Joint pdfs 311 7.2.3 Stationarity 311 7.2.4 Partial Description of Random Processes: Ergodicity 312 7.2.5 Meanings of Various Averages for Ergodic Processes 315 7.3 Correlation and Power Spectral Density 316 7.3.1 Power Spectral Density 316 7.3.2 The Wiener--Khinchine Theorem 318 7.3.3 Properties of the Autocorrelation Function 320 7.3.4 Autocorrelation Functions for Random Pulse Trains 321 7.3.5 Cross-Correlation Function and Cross-Power Spectral Density 324 7.4 Linear Systems and Random Processes 325 7.4.1 Input-Output Relationships 325 7.4.2 Filtered Gaussian Processes 327 7.4.3 Noise-Equivalent Bandwidth 329 7.5 Narrowband Noise 333 7.5.1 Quadrature-Component and Envelope-Phase Representation 333 7.5.2 The Power Spectral Density Function of
(
) and
(
) 335 7.5.3 Ricean Probability Density Function 338 Further Reading 340 Summary 340 Drill Problems 341 Problems 342 Computer Exercises 348 CHAPTER 8 NOISE IN MODULATION SYSTEMS 349 8.1 Signal-to-Noise Ratios 350 8.1.1 Baseband Systems 350 8.1.2 Double-Sideband Systems 351 8.1.3 Single-Sideband Systems 353 8.1.4 Amplitude Modulation Systems 355 8.1.5 An Estimator for Signal-to-Noise Ratios 361 8.2 Noise and Phase Errors in Coherent Systems 366 8.3 Noise in Angle Modulation 370 8.3.1 The Effect of Noise on the Receiver Input 370 8.3.2 Demodulation of PM 371 8.3.3 Demodulation of FM: Above Threshold Operation 372 8.3.4 Performance Enhancement through the Use ofDe-emphasis 374 8.4 Threshold Effect in FM Demodulation 376 8.4.1 Threshold Effects in FM Demodulators 376 8.5 Noise in Pulse-Code Modulation 384 8.5.1 Postdetection SNR 384 8.5.2 Companding 387 Further Reading 389 Summary 389 Drill Problems 391 Problems 391 Computer Exercises 394 CHAPTER 9 PRINCIPLES OF DIGITAL DATA TRANSMISSIONIN NOISE 396 9.1 Baseband Data Transmission in White Gaussian Noise 398 9.2 Binary Synchronous Data Transmission with Arbitrary Signal Shapes 404 9.2.1 Receiver Structure and Error Probability 404 9.2.2 The Matched Filter 407 9.2.3 Error Probability for the Matched-Filter Receiver 410 9.2.4 Correlator Implementation of the Matched-Filter Receiver 413 9.2.5 Optimum Threshold 414 9.2.6 Nonwhite (Colored) Noise Backgrounds 414 9.2.7 Receiver Implementation Imperfections 415 9.2.8 Error Probabilities for Coherent Binary Signaling 415 9.3 Modulation Schemes not Requiring Coherent References 421 9.3.1 Differential Phase-Shift Keying (DPSK) 422 9.3.2 Differential Encoding and Decoding of Data 427 9.3.3 Noncoherent FSK 429 9.4 M-ary Pulse-Amplitude Modulation (PAM) 431 9.5 Comparison of Digital Modulation Systems 435 9.6 Noise Performance of Zero-ISI Digital Data Transmission Systems 438 9.7 Multipath Interference 443 9.8 Fading Channels 449 9.8.1 Basic Channel Models 449 9.8.2 Flat-Fading Channel Statistics and Error Probabilities 450 9.9 Equalization 455 9.9.1 Equalization by Zero-Forcing 455 9.9.2 Equalization by MMSE 459 9.9.3 Tap Weight Adjustment 463 Further Reading 466 Summary 466 Drill Problems 468 Problems 469 Computer Exercises 476 CHAPTER 10 ADVANCED DATA COMMUNICATIONSTOPICS 477 10.1 M-ary Data Communications Systems 477 10.1.1 M-ary Schemes Based on Quadrature Multiplexing 477 10.1.2 OQPSK Systems 481 10.1.3 MSK Systems 482 10.1.4 M-ary Data Transmission in Terms of Signal Space 489 10.1.5 QPSK in Terms of Signal Space 491 10.1.6 M-ary Phase-Shift Keying 493 10.1.7 Quadrature-Amplitude Modulation (QAM) 495 10.1.8 Coherent FSK 497 10.1.9 Noncoherent FSK 498 10.1.10 Differentially Coherent Phase-Shift Keying 502 10.1.11 Bit Error Probability from Symbol Error Probability 503 10.1.12 Comparison of M-ary Communications Systems on the Basis of Bit Error Probability 505 10.1.13 Comparison of M-ary Communications Systems on the Basis of Bandwidth Efficiency 508 10.2 Power Spectra for Digital Modulation 510 10.2.1 Quadrature Modulation Techniques 510 10.2.2 FSK Modulation 514 10.2.3 Summary 516 10.3 Synchronization 516 10.3.1 Carrier Synchronization 517 10.3.2 Symbol Synchronization 520 10.3.3 Word Synchronization 521 10.3.4 Pseudo-Noise (PN) Sequences 524 10.4 Spread-Spectrum Communication Systems 528 10.4.1 Direct-Sequence Spread Spectrum 530 10.4.2 Performance of DSSS in CW Interference Environments 532 10.4.3 Performance of Spread Spectrum in Multiple User Environments 533 10.4.4 Frequency-Hop Spread Spectrum 536 10.4.5 Code Synchronization 537 10.4.6 Conclusion 539 10.5 Multicarrier Modulation and Orthogonal Frequency-Division Multiplexing 540 10.6 Cellular Radio Communication Systems 545 10.6.1 Basic Principles of Cellular Radio 546 10.6.2 Channel Perturbations in Cellular Radio 550 10.6.3 Multiple-Input Multiple-Output (MIMO) Systems---Protection Against Fading 551 10.6.4 Characteristics of 1G and 2G Cellular Systems 553 10.6.5 Characteristics of cdma2000 and W-CDMA 553 10.6.6 Migration to 4G 555 Further Reading 556 Summary 556 Drill Problems 557 Problems 558 Computer Exercises 563 CHAPTER 11 OPTIMUM RECEIVERS AND SIGNAL-SPACECONCEPTS 564 11.1 Bayes Optimization 564 11.1.1 Signal Detection versus Estimation 564 11.1.2 Optimization Criteria 565 11.1.3 Bayes Detectors 565 11.1.4 Performance of Bayes Detectors 569 11.1.5 The Neyman-Pearson Detector 572 11.1.6 Minimum Probability of Error Detectors 573 11.1.7 The Maximum a Posteriori (MAP) Detector 573 11.1.8 Minimax Detectors 573 11.1.9 The M-ary Hypothesis Case 573 11.1.10 Decisions Based on Vector Observations 574 11.2 Vector Space Representation of Signals 574 11.2.1 Structure of Signal Space 575 11.2.2 Scalar Product 575 11.2.3 Norm 576 11.2.4 Schwarz's Inequality 576 11.2.5 Scalar Product of Two Signals in Terms of Fourier Coefficients 578 11.2.6 Choice of Basis Function Sets---The Gram--Schmidt Procedure 579 11.2.7 Signal Dimensionality as a Function of Signal Duration 581 11.3 Map Receiver for Digital Data Transmission 583 11.3.1 Decision Criteria for Coherent Systems in Terms of Signal Space 583 11.3.2 Sufficient Statistics 589 11.3.3 Detection of
-ary Orthogonal Signals 590 11.3.4 A Noncoherent Case 592 11.4 Estimation Theory 596 11.4.1 Bayes Estimation 596 11.4.2 Maximum-Likelihood Estimation 598 11.4.3 Estimates Based onMultiple Observations 599 11.4.4 Other Properties of ML Estimates 601 11.4.5 Asymptotic Qualities of ML Estimates 602 11.5 Applications of Estimation Theory to Communications 602 11.5.1 Pulse-Amplitude Modulation (PAM) 603 11.5.2 Estimation of Signal Phase: The PLL Revisited 604 Further Reading 606 Summary 607 Drill Problems 607 Problems 608 Computer Exercises 614 CHAPTER 12 INFORMATION THEORY AND CODING 615 12.1 Basic Concepts 616 12.1.1 Information 616 12.1.2 Entropy 617 12.1.3 Discrete Channel Models 618 12.1.4 Joint and Conditional Entropy 621 12.1.5 Channel Capacity 622 12.2 Source Coding 626 12.2.1 An Example of Source Coding 627 12.2.2 Several Definitions 630 12.2.3 Entropy of an Extended Binary Source 631 12.2.4 Shannon--Fano Source Coding 632 12.2.5 Huffman Source Coding 632 12.3 Communication in Noisy Environments: Basic Ideas 634 12.4 Communication in Noisy Channels: Block Codes 636 12.4.1 Hamming Distances and Error Correction 637 12.4.2 Single-Parity-Check Codes 638 12.4.3 Repetition Codes 639 12.4.4 Parity-Check Codes for Single Error Correction 640 12.4.5 Hamming Codes 644 12.4.6 Cyclic Codes 645 12.4.7 The Golay Code 647 12.4.8 Bose--Chaudhuri--Hocquenghem (BCH) Codes and Reed Solomon Codes 648 12.4.9 Performance Comparison Techniques 648 12.4.10 Block Code Examples 650 12.5 Communication in Noisy Channels: Convolutional Codes 657 12.5.1 Tree and Trellis Diagrams 659 12.5.2 The Viterbi Algorithm 661 12.5.3 Performance Comparisons for Convolutional Codes 664 12.6 Bandwidth and Power Efficient Modulation (TCM) 668 12.7 Feedback Channels 672 12.8 Modulation and Bandwidth Efficiency 676 12.8.1 Bandwidth and SNR 677 12.8.2 Comparison of Modulation Systems 678 12.9 Quick Overviews 679 12.9.1 Interleaving and Burst-Error Correction 679 12.9.2 Turbo Coding 681 12.9.3 Source Coding Examples 683 12.9.4 Digital Television 685 Further Reading 686 Summary 686 Drill Problems 688 Problems 688 Computer Exercises 692 APPENDIX A PHYSICAL NOISE SOURCES 693 A.1 Physical Noise Sources 693 A.1.1 Thermal Noise 693 A.1.2 Nyquist's Formula 695 A.1.3 Shot Noise 695 A.1.4 Other Noise Sources 696 A.1.5 Available Power 696 A.1.6 Frequency Dependence 697 A.1.7 Quantum Noise 697 A.2 Characterization of Noise in Systems 698 A.2.1 Noise Figure of a System 699 A.2.2 Measurement of Noise Figure 700 A.2.3 Noise Temperature 701 A.2.4 Effective Noise Temperature 702 A.2.5 Cascade of Subsystems 702 A.2.6 Attenuator Noise Temperature and Noise Figure 704 A.3 Free-Space Propagation Example 705 Further Reading 708 Problems 708 APPENDIX B JOINTLY GAUSSIAN RANDOM VARIABLES 710 B.1 The pdf 710 B.2 The Characteristic Function 711 B.3 Linear Transformations 711 APPENDIX C PROOF OF THE NARROWBAND NOISEMODEL 712 APPENDIX D ZERO-CROSSING AND ORIGIN ENCIRCLEMENTSTATISTICS 714 D.1 The Zero-Crossing Problem 714 D.2 Average Rate of Zero Crossings 716 Problems 719 APPENDIX E CHI-SQUARE STATISTICS 720 APPENDIX F MATHEMATICAL AND NUMERICAL TABLES 722 F.1 The Gaussian Q-Function 722 F.2 Trigonometric Identities 724 F.3 Series Expansions 724 F.4 Integrals 725 F.4.1 Indefinite 725 F.4.2 Definite 726 F.5 Fourier-Transform Pairs 727 F.6 Fourier-Transform Theorems 727 APPENDIX G ANSWERS TO DRILL PROBLEMS www.wiley.com/college/ziemer BIBLIOGRAPHY www.wiley.com/college/ziemer INDEX 728
(
) 52 2.6 Signals and Linear Systems 55 2.6.1 Definition of a Linear Time-Invariant System 56 2.6.2 Impulse Response and the SuperpositionIntegral 56 2.6.3 Stability 58 2.6.4 Transfer (Frequency Response) Function 58 2.6.5 Causality 58 2.6.6 Symmetry Properties of
(
) 59 2.6.7 Input-Output Relationships for Spectral Densities 62 2.6.8 Response to Periodic Inputs 62 2.6.9 Distortionless Transmission 64 2.6.10 Group and Phase Delay 64 2.6.11 Nonlinear Distortion 67 2.6.12 Ideal Filters 68 2.6.13 Approximation of Ideal Lowpass Filters by Realizable Filters 70 2.6.14 Relationship of Pulse Resolution and Risetime to Bandwidth 75 2.7 Sampling Theory 78 2.8 The Hilbert Transform 82 2.8.1 Definition 82 2.8.2 Properties 83 2.8.3 Analytic Signals 85 2.8.4 Complex Envelope Representation of Bandpass Signals 87 2.8.5 Complex Envelope Representation of Bandpass Systems 89 2.9 The Discrete Fourier Transform and Fast Fourier Transform 91 Further Reading 95 Summary 95 Drill Problems 98 Problems 100 Computer Exercises 111 CHAPTER 3 LINEAR MODULATION TECHNIQUES 112 3.1 Double-Sideband Modulation 113 3.2 Amplitude Modulation (AM) 116 3.2.1 Envelope Detection 118 3.2.2 The Modulation Trapezoid 122 3.3 Single-Sideband (SSB) Modulation 124 3.4 Vestigial-Sideband (VSB) Modulation 133 3.5 Frequency Translation and Mixing 136 3.6 Interference in Linear Modulation 139 3.7 Pulse Amplitude Modulation---PAM 142 3.8 Digital Pulse Modulation 144 3.8.1 Delta Modulation 144 3.8.2 Pulse-Code Modulation 146 3.8.3 Time-Division Multiplexing 147 3.8.4 An Example: The Digital Telephone System 149 Further Reading 150 Summary 150 Drill Problems 151 Problems 152 Computer Exercises 155 CHAPTER 4 ANGLE MODULATION ANDMULTIPLEXING 156 4.1 Phase and Frequency Modulation Defined 156 4.1.1 Narrowband Angle Modulation 157 4.1.2 Spectrum of an Angle-Modulated Signal 161 4.1.3 Power in an Angle-Modulated Signal 168 4.1.4 Bandwidth of Angle-Modulated Signals 168 4.1.5 Narrowband-to-Wideband Conversion 173 4.2 Demodulation of Angle-Modulated Signals 175 4.3 Feedback Demodulators: The Phase-Locked Loop 181 4.3.1 Phase-Locked Loops for FM and PM Demodulation 181 4.3.2 Phase-Locked Loop Operation in the Tracking Mode: The Linear Model 184 4.3.3 Phase-Locked Loop Operation in the Acquisition Mode 189 4.3.4 Costas PLLs 194 4.3.5 Frequency Multiplication and Frequency Division 195 4.4 Interference in Angle Modulation 196 4.5 Analog Pulse Modulation 201 4.5.1 Pulse-Width Modulation (PWM) 201 4.5.2 Pulse-Position Modulation (PPM) 203 4.6 Multiplexing 204 4.6.1 Frequency-Division Multiplexing 204 4.6.2 Example of FDM: Stereophonic FM Broadcasting 205 4.6.3 Quadrature Multiplexing 206 4.6.4 Comparison of Multiplexing Schemes 207 Further Reading 208 Summary 208 Drill Problems 209 Problems 210 Computer Exercises 213 CHAPTER 5 PRINCIPLES OF BASEBAND DIGITAL DATATRANSMISSION 215 5.1 Baseband Digital Data Transmission Systems 215 5.2 Line Codes and Their Power Spectra 216 5.2.1 Description of Line Codes 216 5.2.2 Power Spectra for Line-Coded Data 218 5.3 Effects of Filtering of Digital Data---ISI 225 5.4 Pulse Shaping: Nyquist's Criterion for Zero ISI 227 5.4.1 Pulses Having the Zero ISI Property 228 5.4.2 Nyquist's Pulse-Shaping Criterion 229 5.4.3 Transmitter and Receiver Filters for Zero ISI 231 5.5 Zero-Forcing Equalization 233 5.6 Eye Diagrams 237 5.7 Synchronization 239 5.8 Carrier Modulation of Baseband Digital Signals 243 Further Reading 244 Summary 244 Drill Problems 245 Problems 246 Computer Exercises 249 CHAPTER 6 OVERVIEW OF PROBABILITY AND RANDOMVARIABLES 250 6.1 What is Probability? 250 6.1.1 Equally Likely Outcomes 250 6.1.2 Relative Frequency 251 6.1.3 Sample Spaces and the Axioms of Probability 252 6.1.4 Venn Diagrams 253 6.1.5 Some Useful Probability Relationships 253 6.1.6 Tree Diagrams 257 6.1.7 Some More General Relationships 259 6.2 Random Variables and Related Functions 260 6.2.1 Random Variables 260 6.2.2 Probability (Cumulative) Distribution Functions 262 6.2.3 Probability-Density Function 263 6.2.4 Joint cdfs and pdfs 265 6.2.5 Transformation of Random Variables 270 6.3 Statistical Averages 274 6.3.1 Average of a Discrete Random Variable 274 6.3.2 Average of a Continuous Random Variable 275 6.3.3 Average of a Function of a Random Variable 275 6.3.4 Average of a Function of More Than One Random Variable 277 6.3.5 Variance of a Random Variable 279 6.3.6 Average of a Linear Combination of
Random Variables 280 6.3.7 Variance of a Linear Combination of Independent Random Variables 281 6.3.8 Another Special Average---The Characteristic Function 282 6.3.9 The pdf of the Sum of Two Independent Random Variables 283 6.3.10 Covariance and the Correlation Coefficient 285 6.4 Some Useful pdfs 286 6.4.1 Binomial Distribution 286 6.4.2 Laplace Approximation to the Binomial Distribution 288 6.4.3 Poisson Distribution and Poisson Approximation to the Binomial Distribution 289 6.4.4 Geometric Distribution 290 6.4.5 Gaussian Distribution 291 6.4.6 Gaussian
-Function 295 6.4.7 Chebyshev's Inequality 296 6.4.8 Collection of Probability Functions and Their Means and Variances 296 Further Reading 298 Summary 298 Drill Problems 300 Problems 301 Computer Exercises 307 CHAPTER 7 RANDOM SIGNALS AND NOISE 308 7.1 A Relative-Frequency Description of Random Processes 308 7.2 Some Terminology of Random Processes 310 7.2.1 Sample Functions and Ensembles 310 7.2.2 Description of Random Processes in Terms of Joint pdfs 311 7.2.3 Stationarity 311 7.2.4 Partial Description of Random Processes: Ergodicity 312 7.2.5 Meanings of Various Averages for Ergodic Processes 315 7.3 Correlation and Power Spectral Density 316 7.3.1 Power Spectral Density 316 7.3.2 The Wiener--Khinchine Theorem 318 7.3.3 Properties of the Autocorrelation Function 320 7.3.4 Autocorrelation Functions for Random Pulse Trains 321 7.3.5 Cross-Correlation Function and Cross-Power Spectral Density 324 7.4 Linear Systems and Random Processes 325 7.4.1 Input-Output Relationships 325 7.4.2 Filtered Gaussian Processes 327 7.4.3 Noise-Equivalent Bandwidth 329 7.5 Narrowband Noise 333 7.5.1 Quadrature-Component and Envelope-Phase Representation 333 7.5.2 The Power Spectral Density Function of
(
) and
(
) 335 7.5.3 Ricean Probability Density Function 338 Further Reading 340 Summary 340 Drill Problems 341 Problems 342 Computer Exercises 348 CHAPTER 8 NOISE IN MODULATION SYSTEMS 349 8.1 Signal-to-Noise Ratios 350 8.1.1 Baseband Systems 350 8.1.2 Double-Sideband Systems 351 8.1.3 Single-Sideband Systems 353 8.1.4 Amplitude Modulation Systems 355 8.1.5 An Estimator for Signal-to-Noise Ratios 361 8.2 Noise and Phase Errors in Coherent Systems 366 8.3 Noise in Angle Modulation 370 8.3.1 The Effect of Noise on the Receiver Input 370 8.3.2 Demodulation of PM 371 8.3.3 Demodulation of FM: Above Threshold Operation 372 8.3.4 Performance Enhancement through the Use ofDe-emphasis 374 8.4 Threshold Effect in FM Demodulation 376 8.4.1 Threshold Effects in FM Demodulators 376 8.5 Noise in Pulse-Code Modulation 384 8.5.1 Postdetection SNR 384 8.5.2 Companding 387 Further Reading 389 Summary 389 Drill Problems 391 Problems 391 Computer Exercises 394 CHAPTER 9 PRINCIPLES OF DIGITAL DATA TRANSMISSIONIN NOISE 396 9.1 Baseband Data Transmission in White Gaussian Noise 398 9.2 Binary Synchronous Data Transmission with Arbitrary Signal Shapes 404 9.2.1 Receiver Structure and Error Probability 404 9.2.2 The Matched Filter 407 9.2.3 Error Probability for the Matched-Filter Receiver 410 9.2.4 Correlator Implementation of the Matched-Filter Receiver 413 9.2.5 Optimum Threshold 414 9.2.6 Nonwhite (Colored) Noise Backgrounds 414 9.2.7 Receiver Implementation Imperfections 415 9.2.8 Error Probabilities for Coherent Binary Signaling 415 9.3 Modulation Schemes not Requiring Coherent References 421 9.3.1 Differential Phase-Shift Keying (DPSK) 422 9.3.2 Differential Encoding and Decoding of Data 427 9.3.3 Noncoherent FSK 429 9.4 M-ary Pulse-Amplitude Modulation (PAM) 431 9.5 Comparison of Digital Modulation Systems 435 9.6 Noise Performance of Zero-ISI Digital Data Transmission Systems 438 9.7 Multipath Interference 443 9.8 Fading Channels 449 9.8.1 Basic Channel Models 449 9.8.2 Flat-Fading Channel Statistics and Error Probabilities 450 9.9 Equalization 455 9.9.1 Equalization by Zero-Forcing 455 9.9.2 Equalization by MMSE 459 9.9.3 Tap Weight Adjustment 463 Further Reading 466 Summary 466 Drill Problems 468 Problems 469 Computer Exercises 476 CHAPTER 10 ADVANCED DATA COMMUNICATIONSTOPICS 477 10.1 M-ary Data Communications Systems 477 10.1.1 M-ary Schemes Based on Quadrature Multiplexing 477 10.1.2 OQPSK Systems 481 10.1.3 MSK Systems 482 10.1.4 M-ary Data Transmission in Terms of Signal Space 489 10.1.5 QPSK in Terms of Signal Space 491 10.1.6 M-ary Phase-Shift Keying 493 10.1.7 Quadrature-Amplitude Modulation (QAM) 495 10.1.8 Coherent FSK 497 10.1.9 Noncoherent FSK 498 10.1.10 Differentially Coherent Phase-Shift Keying 502 10.1.11 Bit Error Probability from Symbol Error Probability 503 10.1.12 Comparison of M-ary Communications Systems on the Basis of Bit Error Probability 505 10.1.13 Comparison of M-ary Communications Systems on the Basis of Bandwidth Efficiency 508 10.2 Power Spectra for Digital Modulation 510 10.2.1 Quadrature Modulation Techniques 510 10.2.2 FSK Modulation 514 10.2.3 Summary 516 10.3 Synchronization 516 10.3.1 Carrier Synchronization 517 10.3.2 Symbol Synchronization 520 10.3.3 Word Synchronization 521 10.3.4 Pseudo-Noise (PN) Sequences 524 10.4 Spread-Spectrum Communication Systems 528 10.4.1 Direct-Sequence Spread Spectrum 530 10.4.2 Performance of DSSS in CW Interference Environments 532 10.4.3 Performance of Spread Spectrum in Multiple User Environments 533 10.4.4 Frequency-Hop Spread Spectrum 536 10.4.5 Code Synchronization 537 10.4.6 Conclusion 539 10.5 Multicarrier Modulation and Orthogonal Frequency-Division Multiplexing 540 10.6 Cellular Radio Communication Systems 545 10.6.1 Basic Principles of Cellular Radio 546 10.6.2 Channel Perturbations in Cellular Radio 550 10.6.3 Multiple-Input Multiple-Output (MIMO) Systems---Protection Against Fading 551 10.6.4 Characteristics of 1G and 2G Cellular Systems 553 10.6.5 Characteristics of cdma2000 and W-CDMA 553 10.6.6 Migration to 4G 555 Further Reading 556 Summary 556 Drill Problems 557 Problems 558 Computer Exercises 563 CHAPTER 11 OPTIMUM RECEIVERS AND SIGNAL-SPACECONCEPTS 564 11.1 Bayes Optimization 564 11.1.1 Signal Detection versus Estimation 564 11.1.2 Optimization Criteria 565 11.1.3 Bayes Detectors 565 11.1.4 Performance of Bayes Detectors 569 11.1.5 The Neyman-Pearson Detector 572 11.1.6 Minimum Probability of Error Detectors 573 11.1.7 The Maximum a Posteriori (MAP) Detector 573 11.1.8 Minimax Detectors 573 11.1.9 The M-ary Hypothesis Case 573 11.1.10 Decisions Based on Vector Observations 574 11.2 Vector Space Representation of Signals 574 11.2.1 Structure of Signal Space 575 11.2.2 Scalar Product 575 11.2.3 Norm 576 11.2.4 Schwarz's Inequality 576 11.2.5 Scalar Product of Two Signals in Terms of Fourier Coefficients 578 11.2.6 Choice of Basis Function Sets---The Gram--Schmidt Procedure 579 11.2.7 Signal Dimensionality as a Function of Signal Duration 581 11.3 Map Receiver for Digital Data Transmission 583 11.3.1 Decision Criteria for Coherent Systems in Terms of Signal Space 583 11.3.2 Sufficient Statistics 589 11.3.3 Detection of
-ary Orthogonal Signals 590 11.3.4 A Noncoherent Case 592 11.4 Estimation Theory 596 11.4.1 Bayes Estimation 596 11.4.2 Maximum-Likelihood Estimation 598 11.4.3 Estimates Based onMultiple Observations 599 11.4.4 Other Properties of ML Estimates 601 11.4.5 Asymptotic Qualities of ML Estimates 602 11.5 Applications of Estimation Theory to Communications 602 11.5.1 Pulse-Amplitude Modulation (PAM) 603 11.5.2 Estimation of Signal Phase: The PLL Revisited 604 Further Reading 606 Summary 607 Drill Problems 607 Problems 608 Computer Exercises 614 CHAPTER 12 INFORMATION THEORY AND CODING 615 12.1 Basic Concepts 616 12.1.1 Information 616 12.1.2 Entropy 617 12.1.3 Discrete Channel Models 618 12.1.4 Joint and Conditional Entropy 621 12.1.5 Channel Capacity 622 12.2 Source Coding 626 12.2.1 An Example of Source Coding 627 12.2.2 Several Definitions 630 12.2.3 Entropy of an Extended Binary Source 631 12.2.4 Shannon--Fano Source Coding 632 12.2.5 Huffman Source Coding 632 12.3 Communication in Noisy Environments: Basic Ideas 634 12.4 Communication in Noisy Channels: Block Codes 636 12.4.1 Hamming Distances and Error Correction 637 12.4.2 Single-Parity-Check Codes 638 12.4.3 Repetition Codes 639 12.4.4 Parity-Check Codes for Single Error Correction 640 12.4.5 Hamming Codes 644 12.4.6 Cyclic Codes 645 12.4.7 The Golay Code 647 12.4.8 Bose--Chaudhuri--Hocquenghem (BCH) Codes and Reed Solomon Codes 648 12.4.9 Performance Comparison Techniques 648 12.4.10 Block Code Examples 650 12.5 Communication in Noisy Channels: Convolutional Codes 657 12.5.1 Tree and Trellis Diagrams 659 12.5.2 The Viterbi Algorithm 661 12.5.3 Performance Comparisons for Convolutional Codes 664 12.6 Bandwidth and Power Efficient Modulation (TCM) 668 12.7 Feedback Channels 672 12.8 Modulation and Bandwidth Efficiency 676 12.8.1 Bandwidth and SNR 677 12.8.2 Comparison of Modulation Systems 678 12.9 Quick Overviews 679 12.9.1 Interleaving and Burst-Error Correction 679 12.9.2 Turbo Coding 681 12.9.3 Source Coding Examples 683 12.9.4 Digital Television 685 Further Reading 686 Summary 686 Drill Problems 688 Problems 688 Computer Exercises 692 APPENDIX A PHYSICAL NOISE SOURCES 693 A.1 Physical Noise Sources 693 A.1.1 Thermal Noise 693 A.1.2 Nyquist's Formula 695 A.1.3 Shot Noise 695 A.1.4 Other Noise Sources 696 A.1.5 Available Power 696 A.1.6 Frequency Dependence 697 A.1.7 Quantum Noise 697 A.2 Characterization of Noise in Systems 698 A.2.1 Noise Figure of a System 699 A.2.2 Measurement of Noise Figure 700 A.2.3 Noise Temperature 701 A.2.4 Effective Noise Temperature 702 A.2.5 Cascade of Subsystems 702 A.2.6 Attenuator Noise Temperature and Noise Figure 704 A.3 Free-Space Propagation Example 705 Further Reading 708 Problems 708 APPENDIX B JOINTLY GAUSSIAN RANDOM VARIABLES 710 B.1 The pdf 710 B.2 The Characteristic Function 711 B.3 Linear Transformations 711 APPENDIX C PROOF OF THE NARROWBAND NOISEMODEL 712 APPENDIX D ZERO-CROSSING AND ORIGIN ENCIRCLEMENTSTATISTICS 714 D.1 The Zero-Crossing Problem 714 D.2 Average Rate of Zero Crossings 716 Problems 719 APPENDIX E CHI-SQUARE STATISTICS 720 APPENDIX F MATHEMATICAL AND NUMERICAL TABLES 722 F.1 The Gaussian Q-Function 722 F.2 Trigonometric Identities 724 F.3 Series Expansions 724 F.4 Integrals 725 F.4.1 Indefinite 725 F.4.2 Definite 726 F.5 Fourier-Transform Pairs 727 F.6 Fourier-Transform Theorems 727 APPENDIX G ANSWERS TO DRILL PROBLEMS www.wiley.com/college/ziemer BIBLIOGRAPHY www.wiley.com/college/ziemer INDEX 728