Digital Transmission (eBook)

Digital Transmission with VisSim/Comm is a book where principles of digital transmission are emphasized, rather than modern technologies. These principles permit the reader to understand more advanced topics and the associated technology. In this book, each topic is addressed in two different and complimentary ways: theoretically and by simulation. The theoretical approach encompasses common subjects covering the principles of digital transmission, like notions of probability and stochastic processes, baseband and passband signaling, signal-space representation, spread spectrum, carrier and symbol-timing recovery, information theory and channel coding. The simulation approach deals with the same subjects with focus on the capabilities of VisSim/Comm to help the reader to understand the theoretical concepts. The files supplied in the accompanying CD run through an evaluation version of VisSim/Comm VisSim/Comm, a communication’s systems simulation software.

Preface 6
Contents 9
Structure of the Book 19
Acknowledgement 21
Author Disclaimer 24
1 A Review of Probability and Stochastic Processes 25
1.1 Set Theory Basics 25
1.1.1 The Venn Diagram and Basic Set Operations 26
1.1.2 Other Set Operations and Properties 27
1.2 Definitions and Axioms of Probability 27
1.3 Counting Methods for Determining Probabilities 29
1.3.1 Distinct Ordered k-Tuples 29
1.3.2 Sampling with Replacement and with Ordering 30
1.3.3 Sampling Without Replacement and with Ordering 30
1.3.4 Permutation of Distinct Objects 30
1.3.5 Sampling Without Replacement and Without Ordering 30
1.3.6 Sampling with Replacement and Without Ordering 31
1.4 Conditional Probability and Bayes Rule 31
Simulation 1.1 -- Conditional Probability 33
1.5 Random Variables 34
1.5.1 The Cumulative Distribution Function 34
1.5.2 Types of Random Variables 36
1.5.2.1 Discrete Random Variables 36
1.5.2.2 Continuous Random Variables 36
1.5.2.3 Mixed Random Variables 36
1.5.2.4 Probability Density Function of a Discrete Random Variable 37
1.5.2.5 Properties of the Probability Density Function 37
1.5.2.6 The Normalized Histogram as an Approximation for the PDF 38
1.6 Conditional Probability Densities and Mass Functions 40
1.6.1 The Bayes Rule Revisited 40
1.6.2 The Total Probability Theorem Revisited 41
1.7 Statistical Averages of Random Variables 41
1.7.1 Mean of Random Variables 41
1.7.2 Moments of Random Variables 43
1.7.3 Joint Moments of Random Variables 44
1.7.3.1 Correlation Between Random Variables 45
1.7.3.2 Covariance Between Random Variables 45
1.7.4 The Characteristic and the Moment-Generating Functions 45
1.7.5 Conditional Expected Value 47
1.8 Some Discrete Random Variables 47
1.8.1 Bernoulli Random Variable 47
1.8.2 Binomial Random Variable 48
1.8.3 Geometric Random Variable 48
1.8.4 Poisson Random Variable 49
Simulation 1.2 -- Discrete Random Variables 50
1.9 Some Continuous Random Variables 51
1.9.1 Uniform Random Variable 51
1.9.2 Exponential Random Variable 52
1.9.3 Gaussian Random Variable 53
1.9.4 Rayleigh Random Variable 55
Simulation 1.3 -- Continuous Random Variables 56
1.9.5 Multivariate Gaussian Random Variables 58
1.10 Sum of Random Variables and the Central Limit Theorem 59
1.10.1 Mean and Variance for the Sum of Random Variables 59
1.10.2 Moments of the Sum of Random Variables 60
1.10.3 PDF of the Sum of Random Variables 60
1.10.4 The Central Limit Theorem 61
1.11 Transformations of Random Variables 62
Simulation 1.4 -- A Communication System Analysis 70
1.12 Parameter Estimation via Sample Mean 71
1.12.1 The Sample Mean 72
1.12.2 The Confidence Interval on the Sample Mean 74
Simulation 1.5 -- Confidence Interval on BER Estimations 77
1.12.3 The Law of Large Numbers 78
1.13 Generation of Random Numbers 79
1.13.1 Congruential Methods 80
1.13.2 Inverse CDF Method 80
1.13.3 Acceptance/Rejection Methods 81
1.13.4 Box-Muller Method 82
Simulation 1.6 -- Random Numbers Generation 82
1.14 Random Processes 84
Simulation 1.7 -- The Concept of Random Process 86
1.14.1 Stationarity Classes for Random Processes 87
1.14.2 Averages of Stationary Random Processes 88
1.14.2.1 Mean and Variance 88
1.14.2.2 Autocovariance and Autocorrelation Functions 89
1.14.2.3 Power Spectral Density (PSD) 92
1.14.2.4 Cross-Covariance and Cross-Correlation Functions 94
Simulation 1.8 -- Estimating Averages of Random Processes 95
1.14.3 Random Processes Through Linear Systems 97
1.14.3.1 Mean 98
1.14.3.2 Autocorrelation 98
1.14.3.3 Power Spectral Density (PSD) 99
1.14.3.4 Cross-Spectral Density 99
1.14.4 The Gaussian Random Process 100
Simulation 1.9 -- Filtered Complex Gaussian Process 101
1.14.5 Thermal Noise Process 103
1.14.5.1 Additive White Gaussian Noise (AWGN) 104
1.14.5.2 Equivalent Noise Bandwidth 105
1.15 Summary and Further Reading 106
1.16 Additional Problems 107
References 109
2 Signals and Systems 110
2.1 Signals 110
2.1.1 Classification of Signals 110
2.1.1.1 Continuous and Discrete Signals 110
2.1.1.2 Periodic and Non-periodic Signals 111
2.1.1.3 Even and Odd Signals 112
2.1.1.4 Deterministic and Random Signals 112
2.1.1.5 Baseband and Passband Signals 112
2.1.1.6 Energy and Power Signals 112
2.1.2 Typical Deterministic Signals 113
2.1.2.1 Unit-Step Function 113
2.1.2.2 Dirac Delta and Kronecker Delta Functions 114
2.1.2.3 Rectangular Function 115
2.1.2.4 Sinc Function 116
2.2 Fourier Analysis of Signals 117
2.2.1 Fourier Series 117
2.2.1.1 Fourier Series for Continuous-Time Periodic Signals 117
2.2.1.2 Convergence of the Fourier Series for Continuous-Time Periodic Signals 118
Simulation 2.1 -- Gibbs Phenomenon 120
2.2.1.3 Power of a Continuous-Time Periodic Voltage or Current Signal 121
2.2.1.4 Properties of Fourier Series for Continuous-Time Periodic Signals 122
2.2.1.5 Fourier Series for Discrete-Time Periodic Signals 122
2.2.1.6 Convergence of the Fourier Series for Discrete-Time Periodic Signals 123
2.2.1.7 Power of a Discrete-Time Periodic Voltage or Current Signal 123
2.2.1.8 Properties of Fourier Series for Discrete-Time Periodic Signals 123
2.2.2 Continuous-Time Fourier Transform 123
2.2.2.1 Definition of the Continuous-Time Fourier Transform 125
2.2.2.2 Convergence of the Continuous-Time Fourier Transform 126
2.2.2.3 Continuous-Time Fourier Transform for Periodic Signals 126
2.2.2.4 Energy of a Continuous-Time Aperiodic Voltage or Current Signal 127
2.2.2.5 Properties and Pairs of the Continuous-Time Fourier Transform 127
2.2.3 Discrete-Time Fourier Transform 129
2.2.3.1 Definition of the Discrete-Time Fourier Transform 129
2.2.3.2 Periodicity of the Discrete-Time Fourier Transform 129
2.2.3.3 Convergence of the Discrete-Time Fourier Transform 130
2.2.3.4 Discrete-Time Fourier Transform for Periodic Signals 130
2.2.3.5 Energy of a Discrete-Time Aperiodic Voltage or Current Signal 130
2.2.3.6 Properties and Pairs of the Discrete-Time Fourier Transform 131
2.2.4 Discrete Fourier Transform 131
2.2.4.1 The DFT and the Discrete-Time Fourier Series 133
2.2.4.2 The DFT and the Fourier Transform 133
2.2.4.3 Mapping the Discrete-Frequency Index k into the Ordinary Frequency f 133
2.2.4.4 Parseval's Relation for the DFT 133
2.2.4.5 Direct and Inverse Numerical Fast Fourier Transforms (FFT and IFFT) 134
Simulation 2.2 -- The FFT via VisSim/Comm 134
2.2.5 Laplace and Z-Transforms 136
2.3 Sampling of Deterministic and Random Signals 138
2.3.1 Ideal Sampling of Deterministic Signals 138
2.3.2 Ideal Sampling of Stochastic Processes 140
2.3.3 Practical Sampling 140
Simulation 2.3 -- Sampling 143
2.3.3.1 Aliasing as a Desired Effect 144
2.3.3.2 Sampling of Discrete-Time Signals 145
2.3.3.3 Sampling of Passband Signals 145
2.3.4 Analog-to-Digital Conversion 145
2.3.4.1 Uniform Quantization 146
2.3.4.2 Non-uniform Quantization 148
Simulation 2.4 -- Uniform and Non-uniform Quantization 150
2.3.4.3 Other A/D Conversion Techniques 153
2.4 Linear Systems 153
2.4.1 Time-Domain Characterization of Linear Systems 153
2.4.2 Frequency-Domain Characterization of Linear Systems 155
2.4.2.1 Distortion-Free Linear System 156
2.4.2.2 Group Delay 157
2.4.3 Classifications and Properties of Linear Systems 158
2.4.3.1 Linear Time-Invariant (LTI) Continuous-Time Systems5 158
2.4.3.2 Linear Time-Variant (LTV) Continuous-Time Systems 158
2.4.3.3 Causal Continuous-Time LTI Systems 159
2.4.3.4 Stable Continuous-Time LTI Systems 159
2.4.3.5 Eigenfunctions of Continuous-Time LTI Systems 159
2.4.3.6 LTI Systems With and Without Memory 160
2.4.3.7 Frequency Response for Systems Characterized by Linear Differential Equations 161
2.4.3.8 Frequency Response for Systems Characterized by Linear Difference Equations 161
2.4.4 Mapping a Discrete-Time into a Continuous-Time Frequency 162
Simulation 2.5 -- Moving Average Filter 165
2.4.4.1 A Note on Discrete-Time Filtering 166
2.5 Complex Representation of Signals and Systems 169
Simulation 2.6 -- Real Versus Complex Simulation 171
2.6 The Power Spectral Density Revisited 173
2.6.1 The PSD of Passband Signals 173
Simulation 2.7 -- Estimating the PSD of Passband Signals 176
2.6.2 Estimation of the PSD via the Periodogram 178
Simulation 2.8 -- Periodogram Estimation of the PSD 179
2.6.3 The PSD of Baseband Digital Communication Signals 182
2.7 The Bandwidth of Communication Signals 185
2.7.1 Absolute Bandwidth 185
2.7.2 -3 dB (or Half Power) Bandwidth 186
2.7.3 Equivalent Noise Bandwidth 186
2.7.4 Root Mean Square (rms) Bandwidth 186
2.7.5 Null-to-Null or Main Lobe Bandwidth 187
2.7.6 Spectral Mask 188
2.8 Summary and Further Reading 189
2.9 Additional Problems 189
References 191
3 Communication Channels 193
3.1 Definitions 193
3.1.1 Communication Channel 193
3.1.2 Channel Modeling 196
3.1.3 Channel Sounding 196
3.1.4 Empirical, Deterministic and Stochastic Channel Models 197
3.2 AWGN Channel Model 197
3.2.1 Vector AWGN Channel 198
Simulation 3.1 -- Waveform and Vector Channel Simulation 200
3.3 Discrete Memoryless Channels 202
3.3.1 The Binary Symmetric Channel Revisited 203
Simulation 3.2 -- Waveform and BSC Channel Simulation 203
3.4 Discrete Channels with Memory 205
3.5 Wireline Channels 206
3.5.1 Twisted Pair 206
3.5.2 Coaxial Cable 209
3.5.3 Waveguide 211
3.5.4 Optical Fiber 212
3.5.5 Low-Voltage Power-Line 216
3.5.5.1 Frequency Response of the Indoor PLC Channel 217
3.5.5.2 Noise in the Indoor PLC Channel 218
3.5.5.3 Generalized Background Noise 219
3.5.5.4 Impulse Noise 220
3.6 Wireless Channels 221
3.6.1 Mobile Outdoor Channel 221
3.6.1.1 Large-Scale Propagation 222
3.6.1.2 Small-Scale Propagation 228
Simulation 3.3 -- Large-Scale and Small-Scale Propagation 230
3.6.1.3 Time-Variant Impulse Response of the Multipath Channel 232
3.6.1.4 Flat Fading -- Multiplicative Channel Model 233
3.6.1.5 Frequency Selective Fading -- tapped delay line Channel Model 236
3.6.1.6 Doppler Shift and Doppler Spread of an Unmodulated Signal 237
Simulation 3.4 -- Mobile Channel Simulator 239
3.6.1.7 Channel Correlation Functions and Related Parameters 241
3.6.1.8 Overall Classification of the Fading 246
3.6.1.9 Level Crossing Rate and Average Duration of a Ricean Fading Envelope 247
Simulation 3.5 -- Exploring the Coherence Bandwidth 248
Simulation 3.6 -- Exploring the Coherence Time 249
Simulation 3.7 -- Flat and Frequency Selective Channel 251
Simulation 3.8 -- A Modulated Signal Under Selective Fading 253
3.6.2 Mobile Indoor Channel 254
3.6.2.1 Large-Scale Propagation 255
3.6.2.2 Small-Scale Propagation 256
Simulation 3.9 -- Saleh-Valenzuela Indoor Channel Model 259
3.6.3 Terrestrial Microwave Channel 261
3.6.3.1 Propagation Losses in a Terrestrial Microwave Channel 262
3.6.3.2 Multipath Propagation in the Terrestrial Microwave Channel 266
3.6.3.3 Simplified Three-Path Terrestrial Microwave Channel Model 267
Simulation 3.10 -- Rummler Terrestrial Microwave Channel Model 269
3.6.4 Spatial Wireless Channel Models 272
3.6.5 Other Wireless Channels 274
3.6.5.1 Underwater Acoustic Channel 274
3.6.5.2 Free-Space Optical Channel 276
3.6.5.3 Underground Radio Channel 277
3.7 Summary and Further Reading 278
3.8 Additional Problems 280
References 282
4 Baseband Digital Transmission 286
4.1 Definitions and Typical Baseband Signals 286
4.1.1 Line Codes 287
4.1.1.1 Unipolar Non-return-to-Zero (NRZ-u) 288
4.1.1.2 Unipolar Return-to-Zero (RZ-u) 289
4.1.1.3 Bipolar Non-return-to-Zero (NRZ-b) 290
4.1.1.4 Bipolar Return to Zero (RZ-b) 290
4.1.1.5 Alternate Mark Inversion (AMI) 290
4.1.1.6 Manchester 291
4.1.1.7 Miller 292
4.1.1.8 Code Mark Inversion (CMI) 292
4.1.1.9 High Density Bipolar n(HDBn) 292
Simulation 4.1 -- Line Codes 293
4.1.2 M-ary PAM Signaling 294
Simulation 4.2 -- M-ary PAM Signaling 297
4.2 Detection of Baseband Pulses in Noise 299
4.2.1 Modeling and Motivation 299
Simulation 4.3 -- Motivation for Baseband Detection Analysis 300
4.2.2 The Matched Filter 305
Simulation 4.4 -- Pulse Signal-to-Noise Ratio Measurement 307
4.2.3 Equivalence Between the Matched Filter and the Correlator 310
Simulation 4.5 -- Equivalence Matched Filter Correlator 313
4.2.4 Error Probability Analysis 315
Simulation 4.6 -- Equivalence Matched Filter Correlator Revisited 323
4.2.5 MAP and ML Decision Rules for Binary Transmission 325
4.3 Intersymbol Interference (ISI) 328
4.3.1 Distortion-Free Channel and ISI Channel 328
Simulation 4.7 -- Distortion-Free Channel 331
4.3.2 Nyquist Criterion for ISI-Free Transmission 333
Simulation 4.8 -- Vestigial Symmetry 336
4.3.3 The Raised Cosine Spectrum 338
4.3.4 The Root-Raised Cosine Spectrum 340
Simulation 4.9 -- Nyquist Pulses 341
4.3.5 The Eye Diagram and the Bathtub Diagram 344
4.3.5.1 The Eye Diagram 344
Simulation 4.10 -- Eye Diagram for M-PAM Signaling 346
4.3.5.2 Timing Jitter Considerations 348
4.3.5.3 The Bathtub Diagram 349
Simulation 4.11 -- Bathtub Diagram for Binary Signaling 352
4.4 Correlative Coding 354
Simulation 4.12 -- Polybinary and Polybipolar Signal Generation 355
4.4.1 Duobinary and Modified Duobinary Signaling 356
4.4.2 Generalized Partial Response Signaling 361
Simulation 4.13 -- Duobinary Signaling Using a Matched Filter 362
4.5 Notions of Channel Equalization 364
4.5.1 Zero Forcing (ZF) Equalization 365
Simulation 4.14 -- ZF Equalization 368
4.5.2 Least Mean Square (LMS) Equalization 370
Simulation 4.15 -- LMS Equalization 375
4.6 Summary and Further Reading 376
4.7 Additional Problems 377
References 378
5 Signal-Space Analysis 381
5.1 Introduction 381
5.2 Geometric Representation of Signals 383
5.3 Dimensionality of a Signal and of a Signal-Space 386
5.4 Gram-Schmidt Orthogonalization 387
5.5 Signal Constellation with Symbol Transitions 390
5.6 Statistics of the Correlator's Outputs 391
Simulation 5.1 -- Signal Space Analysis 396
5.7 The Vector AWGN Channel Revisited 398
Simulation 5.2 -- The Vector AWGN Channel Revisited 399
5.8 Generalized Maximum Likelihood Receiver 401
Simulation 5.3 -- Generalized ML Receiver 405
5.9 Error Probability Analysis 407
5.9.1 Rotation and Translation Invariance of the Error Probability 407
5.9.2 Minimum Energy Constellation 408
Simulation 5.4 -- Constellation Rotation and Translation 409
5.9.3 The Union Bound for Symbol Error Probability Estimation 411
Simulation 5.5 -- Verifying the Validity of the Union Bound 414
5.9.4 Symbol Versus Bit Error Probability 416
Simulation 5.6 -- Symbol Error Rate versus Bit Error Rate 421
5.10 Symbol-by-Symbol ML Receiver for Channels with ISI 422
5.11 Summary and Further Reading 425
5.12 Additional Problems 426
References 429
6 Passband Digital Transmission 430
6.1 Definitions and Basic Digital Modulation Schemes 430
6.1.1 Basic Digital Modulations 431
6.1.2 Coherent and Non-coherent Detection 432
6.1.3 Spectral Efficiency and Power Efficiency 432
6.1.4 A Note on a Frequently Used Notation 433
6.2 M-PSK Modulations with Coherent Detection 434
6.2.1 Binary PSK Modulation 434
6.2.1.1 BPSK Waveform 434
6.2.1.2 BPSK Base-Function 434
6.2.1.3 BPSK Constellation 435
6.2.1.4 BPSK Symbol and Bit Error Probability over the AWGN Channel 435
6.2.1.5 BPSK Generation and Coherent Detection 436
6.2.1.6 Power Spectral Density of a BPSK Modulated Signal 438
6.2.1.7 Spectral Efficiency of a BPSK Modulated Signal 438
Simulation 6.1 -- BPSK Generation and Coherent Detection 439
6.2.2 M-ary PSK Modulation 441
6.2.2.1 M-PSK Modulated Signal 441
6.2.2.2 M-PSK Base-Functions 441
6.2.2.3 M-PSK Constellation 442
6.2.2.4 M-PSK Symbol and Bit Error Probability over the AWGN Channel 442
6.2.2.5 M-PSK Generation and Coherent Detection 445
6.2.2.6 The I& Q Modulator
6.2.2.7 Power Spectral Density of an M-PSK Modulated Signal 449
6.2.2.8 Spectral Efficiency of an M-PSK Modulated Signal 451
Simulation 6.2 -- M-PSK Generation and Coherent Detection 451
6.3 M-QAM Modulations with Coherent Detection 453
6.3.1 M-QAM Modulated Signal 453
6.3.2 M-QAM Base-Functions 454
6.3.3 Square M-QAM Modulations 454
6.3.4 Non-square M-QAM Modulations 456
6.3.5 M-QAM Generation and Coherent Detection 458
Simulation 6.3 -- I& Q Generation of a 32-QAM and a 64-QAM
6.3.6 M-QAM Symbol and Bit Error Probability over the AWGN Channel 461
6.3.7 Power Spectral Density of an M-QAM Modulated Signal 465
6.3.8 Spectral Efficiency of an M-QAM Modulated Signal 466
Simulation 6.4 -- M-QAM Generation and Coherent Detection 466
6.3.9 Comparing M-PSK and M-QAM Modulations 468
6.4 M-FSK Modulations with Coherent Detection 469
6.4.1 Tone Separation and Carrier Frequency for Orthogonality 469
6.4.2 Binary FSK Modulation 470
6.4.2.1 BFSK Waveform 471
6.4.2.2 BFSK Base-Functions 471
6.4.2.3 BFSK Constellation 471
6.4.2.4 BFSK Symbol and Bit Error Probability over the AWGN Channel 472
6.4.2.5 Continuous-Phase and Non-continuous-phase FSK Modulations 473
6.4.2.6 BFSK Generation and Coherent Detection 474
Simulation 6.5 -- Analysis of Tones Used by an FSK Modulation 475
6.4.2.7 Power Spectral Density of a BFSK Modulated Signal 477
6.4.2.8 Spectral Efficiency of a BFSK Modulated Signal 480
Simulation 6.6 -- BFSK Modulation Methods 480
6.4.3 M-ary FSK Modulation 483
6.4.3.1 M-FSK Waveform 483
6.4.3.2 M-FSK Base-Functions 483
6.4.3.3 M-FSK Constellation 484
6.4.3.4 Continuous-Phase and Non-continuous-phase M-FSK Modulations 484
6.4.3.5 M-FSK Generation and Coherent Detection 484
6.4.3.6 M-FSK Symbol and Bit Error Probability over the AWGN Channel 485
6.4.3.7 Power Spectral Density of an M-FSK Modulated Signal 488
6.4.3.8 Spectral Efficiency of an M-FSK Modulated Signal 490
Simulation 6.7 -- M-FSK Generation and Coherent Detection 490
6.4.3.9 Concluding Remarks About M-ary FSK Modulations 494
6.5 MSK Modulation with Coherent Detection 494
6.5.1 MSK Signal Generation and Detection 495
6.5.1.1 The Reason for the Term ``Minimum'' in the MSK Nomenclature 495
6.5.1.2 MSK and Conventional Binary FSK 496
Simulation 6.8 -- BFSK and FFSK Generation via VCO 498
6.5.1.3 MSK Signal Generation and Detection from the Complex Representation 499
Simulation 6.9 -- MSK Generation via Complex Representation 502
Simulation 6.10 -- MSK Generation via OQPSK Approach 505
Simulation 6.11 -- MSK Modem via OQPSK Approach 507
6.5.1.4 MSK Signal Generation and Detection from the Signal-Space Representation 509
Simulation 6.12 -- MSK Modem via Signal-Space Approach 512
6.5.2 MSK Bit Error Probability 514
Simulation 6.13 -- MSK Modem Performance 515
6.5.3 MSK with Conventional FSK Detection 516
Simulation 6.14 -- MSK with Conventional FSK Detection 521
6.5.4 Power Spectral Density of the MSK Signal 521
Simulation 6.15 -- Power Spectral Density of the MSK Signal 523
6.5.5 Further Attributes and Uses for the MSK Modulation 524
6.5.6 Answering Some Questions About the MSK Modulation 525
6.6 OQPSK, /4QPSK and GMSK Modulations 526
Simulation 6.16 -- Distortion Caused by Nonlinear Amplification 527
6.6.1 Offset QPSK Modulation 531
6.6.1.1 OQPSK Modulator 531
6.6.1.2 OQPSK Coherent Demodulator 532
Simulation 6.17 -- OQPSK Signal Generation 533
6.6.2 /4DQPSK Modulation 535
6.6.2.1 /4DQPSK Modulator 535
6.6.2.2 /4DQPSK Differentially Coherent Demodulator 537
6.6.2.3 Power Spectral Density of a /4DQPSK Signal 538
Simulation 6.18 -- /4DQPSK Generation and Detection 539
6.6.3 GMSK Modulation 540
6.6.3.1 GMSK Modulator 540
6.6.3.2 Power Spectral Density of a GMSK Signal 543
6.6.3.3 GMSK Coherent Demodulator 544
Simulation 6.19 -- GMSK Generation and Detection 546
6.6.4 Nonlinear Amplification Distortion Revisited 548
Simulation 6.20 -- Nonlinear Amplification of Modulated Signals 549
6.7 Non-coherent M-FSK and Differentially Coherent BPSK 553
6.7.1 Non-coherent M-FSK Modulations 553
6.7.1.1 Tone Separation for Non-coherent Detection of BFSK Signals 553
6.7.1.2 M-FSK Modulated Signal and Non-coherent Demodulation 554
6.7.1.3 Symbol and Bit Error Probability for Non-coherent M-FSK 556
Simulation 6.21 -- Non-coherently Detected Binary FSK 557
6.7.2 Differentially-Coherent BPSK Modulation 561
6.7.2.1 DBPSK Signal Generation 561
6.7.2.2 DBPSK Differential Detection 562
6.7.2.3 Bit Error Probability for a Differentially-Coherent BPSK Modulation 563
Simulation 6.22 -- DBPSK Generation and Detection 564
6.7.2.4 Power Spectral Density and Spectral Efficiency of a DBPSK Signal 565
6.7.2.5 Multiple Symbol Differential Detection 565
6.8 Carrier and Symbol-Timing Recovery 565
6.8.1 Parameter Estimation 567
6.8.2 Carrier Synchronization 570
6.8.2.1 The Costas Loop 571
6.8.2.2 Phase Ambiguity 573
Simulation 6.23 -- PLL Response 574
Simulation 6.24 -- BPSK Phase Tracking with Costas Loop 576
6.8.2.3 Carrier Synchronization of M-ary Phase-Shift Keying Signals 578
Simulation 6.25 -- M-th Power Loop for QPSK Phase Tracking 580
6.8.2.4 Carrier Synchronization for Other Modulations 583
6.8.3 Symbol Synchronization 583
6.8.3.1 Early-Late Gate Synchronizer 584
Simulation 6.26 -- Operation of the Early-Late Synchronizer 584
Simulation 6.27 -- Carrier and Symbol Synchronization 587
6.9 Performance of Digital Modulations over Fading Channels 589
6.9.1 Optimum Receiver Structures for Fading Channels 589
6.9.2 The Effect of Fading on the Error Probability 590
6.9.3 Performance of Digital Modulations over Fading Channels 592
6.9.3.1 Performance of Coherent M-ASK 592
6.9.3.2 Performance of Coherent Square M-QAM 593
6.9.3.3 Performance of Coherent M-PSK 593
6.9.3.4 Performance of Coherently Detected DEQPSK and /4-DQPSK 593
6.9.3.5 Performance of Coherent M-FSK 594
6.9.3.6 Performance of Non-coherent M-FSK 595
6.9.3.7 Performance of Differentially Coherent M-DPSK 595
6.10 Summary and Further Reading 595
6.11 Additional Problems 597
References 598
7 Wideband Transmission Techniques 603
7.1 Spread-Spectrum Transmission 603
7.1.1 Definition 603
7.1.2 A Brief History About the Spread-Spectrum 604
7.1.3 Direct-Sequence Spread-Spectrum 605
7.1.4 Attributes of a Spread-Spectrum Signal 606
7.1.4.1 Low Power Spectral Density 606
7.1.4.2 Low Probability of Interception 606
7.1.4.3 Robustness Against Interference 607
Simulation 7.1 -- DS-SS Signal Under Jamming 609
7.1.4.4 Channel Sounding Capability 612
Simulation 7.2 -- Channel Sounding 614
7.1.4.5 Multiple Access Capability 617
7.1.4.6 Robustness Against Multipath Propagation -- The RAKE Receiver 621
Simulation 7.3 -- RAKE Receiver 626
7.1.5 Spreading Sequences 629
7.1.5.1 Maximum-Length Sequences (m-Sequences) 630
Simulation 7.4 -- Generation of m-Sequences 635
Simulation 7.5 -- White Noise Generation with m-Sequences 636
Simulation 7.6 -- Exploring Correlation Properties for Synchronism 638
7.1.5.2 Gold Sequences 640
7.1.5.3 Walsh--Hadamard Sequences 642
Simulation 7.7 -- Exploring Correlation Properties for CDMA 645
7.1.6 Frequency-Hopping Spread-Spectrum 647
Simulation 7.8 -- FH-SS Modem 649
7.1.7 Processing Gain and Jamming Margin for DS-SS and FH-SS 651
7.1.8 Acquisition and Tracking of Spread-Spectrum Signals 652
7.1.8.1 Serial-Search Acquisition (SSA) 653
Simulation 7.9 -- Serial-Search Acquisition 654
7.1.8.2 Rapid Acquisition by Sequential Estimation (RASE) 654
7.1.8.3 Code Tracking via Delay-Locked Loop (DLL) 656
7.1.8.4 Code Tracking via Tau-Dither Loop (TDL) 657
7.2 Multi-carrier Transmission 658
7.2.1 Multi-carrier Modulation 659
7.2.2 Multi-carrier CDMA 660
7.2.3 Multi-carrier DS-CDMA 661
7.2.4 Multi-tone CDMA 662
7.2.5 Multi-carrier DS-CDMA using frequency-spread coding 662
7.2.6 Modified Multi-carrier DS-CDMA 663
7.2.7 Implementation Aspects of MC-CDMA Systems 664
7.2.7.1 Implementation Aspects of the OFDM Technique 666
Simulation 7.10 -- OFDM Modem 671
7.2.8 Comments on the Performance of MC-CDMA Systems 674
7.2.9 MC-CDMA with Double Spreading Code 675
Simulation 7.11 -- DC-DS-CDMA Modem 681
7.3 Ultra Wideband Transmission 683
7.3.1 UWB Signaling Techniques 684
7.3.1.1 UWB Pulse Shape Design 684
7.3.1.2 Generic UWB Transmitted Signal 686
7.3.1.3 PPM Signaling 687
7.3.1.4 BPSK Signaling 688
7.3.1.5 Bi-orthogonal Signaling 688
7.3.1.6 PAM Signaling 688
7.3.1.7 OOK Signaling 689
7.3.1.8 PSM Signaling 689
7.3.2 UWB Channel Models 689
7.3.3 Reception of UWB Signals 690
Simulation 7.12 -- TH-PPM Ultra Wideband Modem 691
7.3.3.1 Reception of UWB Signals Using Time Reversal 693
Simulation 7.13 -- Exploring the Time Reversal Technique 695
7.4 Summary and Further Reading 697
7.5 Additional Problems 698
References 700
8 Notions of Information Theory and Error-Correcting Codes 706
8.1 Notions of Information Theory 706
8.1.1 Uncertainty, Information and Entropy 707
8.1.1.1 Uncertainty and Information 707
8.1.1.2 Entropy of a Discrete Memoryless Source 708
8.1.1.3 Gross Bit Rate and Information Bit Rate 709
Simulation 8.1 -- Estimating the Entropy of a Source 710
8.1.2 Source Coding and the Source-Coding Theorem 711
8.1.2.1 Source-Coding Theorem 712
8.1.2.2 Huffman Coding 712
8.1.3 Discrete Memoryless Channels Revisited 716
8.1.4 Mutual Information and Channel Capacity 717
8.1.5 Channel Coding Theorem 718
8.1.6 Channel Capacity of Some Channels 720
8.1.6.1 Capacity of the Binary Symmetric Channel 721
8.1.6.2 Capacity of the Binary-Input, Continuous-Output AWGN Channel 721
8.1.6.3 Capacity of the Continuous-Time, Band-Limited AWGN Channel 722
8.1.6.4 Analyzing the Capacities of a Band-Limited AWGN Channel with Binary Antipodal Signaling and with Unconstrained Input Alphabet 724
8.1.7 Channel Capacity of Other Important Channels 727
8.1.7.1 Capacity of the Gaussian Channel with Constrained Constellations 728
8.1.7.2 Capacity of Fading Channels 732
8.1.7.3 Capacity of a Colored-Noise Gaussian Channel 736
8.1.7.4 Capacity of the MIMO Wireless Channel 740
8.2 Notions of Error-Correcting Codes 746
8.2.1 Terminology and Background 746
8.2.2 Hamming and Reed-Muller Codes 756
8.2.2.1 Hamming Codes 756
8.2.2.2 Reed-Muller Codes 759
8.2.3 Syndrome Decoding of Binary Linear Block Codes 761
8.2.3.1 Standard Array 761
8.2.3.2 Syndrome Decoding 762
Simulation 8.2 -- Hard-Decision Versus Soft-Decision ML Decoding 763
Simulation 8.3 -- Coded and Uncoded System Performance 766
8.2.4 Construction of Extension Fields and Polynomial Algebra 768
8.2.5 Cyclic Codes 770
8.2.5.1 General Systematic Encoding of Cyclic Codes via LFSR 772
8.2.5.2 Syndrome Computation and Error Detection with Cyclic Codes via LFSR 774
8.2.5.3 Syndrome Decoding of Cyclic Codes via LFSR 774
Simulation 8.4 -- LFSR Encoding of a Hamming (7, 4) Code 779
Simulation 8.5 -- Meggitt Decoding of a Hamming (7, 4) Code 780
8.2.6 Bose-Chaudhuri-Hocquenghem and Reed-Solomon Codes 781
8.2.6.1 Binary BCH Codes 781
8.2.6.2 Reed Solomon Codes 783
8.2.6.3 Decoding Strategies for BCH and RS Codes 785
Simulation 8.6 -- Reed-Solomon Code Performance 787
8.2.7 Performance of Binary Linear Block Codes 789
8.2.7.1 Block Error Probability for Hard-Decision Decoding 789
8.2.7.2 Block Error Probability for Unquantized Soft-Decision Decoding 790
8.2.7.3 Bit Error Probability 790
8.2.7.4 Comments on the Performance of Concatenated codes 793
8.2.8 Convolutional Codes 793
8.2.8.1 Convolutional Encoder and Basic Properties of the Code 794
8.2.8.2 Viterbi Decoding of Convolutional Codes 797
8.2.8.3 Finite Trace-Back Viterbi Algorithm 800
Simulation 8.7 -- Finite Trace-Back Viterbi Decoding 803
8.2.8.4 Performance of Convolutional Codes 805
8.2.8.5 Convolutional Codes with Good Distance Properties 809
Simulation 8.8 -- Convolutional Code Performance 811
8.2.9 Trellis-Coded Modulation 812
Simulation 8.9 -- Four-State 8PSK Trellis-Coded Modulation 821
8.2.10 Turbo and Low-Density Parity Check Codes 823
8.2.10.1 Introduction 823
8.2.10.2 A Brief Description of LDPC Codes 825
8.2.10.3 General Concepts About Turbo Codes 825
8.2.10.4 Single-Parity Check Product Codes 827
8.2.10.5 A Key Property of Product Codes 830
8.2.10.6 Turbo Decoding of Product Codes 832
8.2.10.7 Turbo Decoding of Single-Parity Check Product Codes 834
8.2.10.8 An Example of Turbo Decoding of a 2-Dimensional SPC-TPC 837
8.2.10.9 General Comments on Multidimensional Product Codes 842
8.2.10.10 Simulation Results over the AWGN and Slow Flat Rayleigh Fading Channel 843
8.2.11 Remarks on Coding for Fading Channels 845
8.2.11.1 A Synthesizing Phrase 845
8.2.11.2 Modern Channel Coding Schemes for Fading Channels 846
8.3 Summary and Further Reading 847
8.4 Additional Problems 849
References 850
A Mathematical Tables and Algorithms 858
A.1 Trigonometric Relations 858
A.2 Gaussian Error Function and Gaussian Q-Function 859
A.2.1 Some Tabulated Values of the Complementary Error Function 860
A.3 Derivatives 861
A.4 Definite Integrals 861
A.5 Indefinite Integrals 863
A.6 Linear Matrix Transformations of Two-Dimensional Spaces 864
A.7 Mathcad Routine for Converting Decimal to Binary Numbers 865
A.8 Mathcad Routine for a Binary Counter 865
A.9 Mathcad Routine for a Gray Counter 866
A.10 Mathcad Routine for Generating Walsh-Hadamard Sequences 866
A.11 Mathcad Routine for Generating the IOWEM of a Block Code 866
A.12 Mathcad Routine for Computing the Euler Function 867
References 868
Abbreviations 869
Index 876