Guimaraes Digital Transmission

A Simulation-Aided Introduction with VisSim/Comm
2009
ISBN: 978-3-642-01359-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 863 Seiten

Reihe: Signals and Communication Technology

Digital Transmission - A Simulation-Aided Introduction with VisSim/Comm is a book in which basic principles of digital communication, mainly pertaining to the physical layer, are emphasized. Nevertheless, these principles can serve as the fundamentals that will help the reader to understand more advanced topics and the associated technology. In this book, each topic is addressed in two different and complementary ways: theoretically and by simulation. The theoretical approach encompasses common subjects covering principles of digital transmission, like notions of probability and stochastic processes, signals and systems, baseband and passband signaling, signal-space representation, spread spectrum, multi-carrier and ultra wideband transmission, carrier and symbol-timing recovery, information theory and error-correcting codes. The simulation approach revisits the same subjects, focusing on the capabilities of the communication system simulation software VisSim/Comm on helping the reader to fulfill the gap between the theory and its practical meaning. The presentation of the theory is made easier with the help of 357 illustrations. A total of 101 simulation files supplied in the accompanying CD support the simulation-oriented approach. A full evaluation version and a viewer-only version of VisSim/Comm are also supplied in the CD.

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.

Autoren/Hrsg.

Guimaraes, Dayan Adionel

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;Structure of the Book;19
4;Acknowledgement;21
5;Author Disclaimer;24
6;1 A Review of Probability and Stochastic Processes ;25
6.1;1.1 Set Theory Basics;25
6.1.1;1.1.1 The Venn Diagram and Basic Set Operations;26
6.1.2;1.1.2 Other Set Operations and Properties;27
6.2;1.2 Definitions and Axioms of Probability;27
6.3;1.3 Counting Methods for Determining Probabilities;29
6.3.1;1.3.1 Distinct Ordered k-Tuples;29
6.3.2;1.3.2 Sampling with Replacement and with Ordering;30
6.3.3;1.3.3 Sampling Without Replacement and with Ordering;30
6.3.4;1.3.4 Permutation of Distinct Objects;30
6.3.5;1.3.5 Sampling Without Replacement and Without Ordering;30
6.3.6;1.3.6 Sampling with Replacement and Without Ordering;31
6.4;1.4 Conditional Probability and Bayes Rule;31
6.4.1;Simulation 1.1 -- Conditional Probability;33
6.5;1.5 Random Variables;34
6.5.1;1.5.1 The Cumulative Distribution Function;34
6.5.2;1.5.2 Types of Random Variables;36
6.5.2.1;1.5.2.1 Discrete Random Variables;36
6.5.2.2;1.5.2.2 Continuous Random Variables;36
6.5.2.3;1.5.2.3 Mixed Random Variables;36
6.5.2.4;1.5.2.4 Probability Density Function of a Discrete Random Variable;37
6.5.2.5;1.5.2.5 Properties of the Probability Density Function;37
6.5.2.6;1.5.2.6 The Normalized Histogram as an Approximation for the PDF;38
6.6;1.6 Conditional Probability Densities and Mass Functions;40
6.6.1;1.6.1 The Bayes Rule Revisited;40
6.6.2;1.6.2 The Total Probability Theorem Revisited;41
6.7;1.7 Statistical Averages of Random Variables;41
6.7.1;1.7.1 Mean of Random Variables;41
6.7.2;1.7.2 Moments of Random Variables;43
6.7.3;1.7.3 Joint Moments of Random Variables;44
6.7.3.1;1.7.3.1 Correlation Between Random Variables;45
6.7.3.2;1.7.3.2 Covariance Between Random Variables;45
6.7.4;1.7.4 The Characteristic and the Moment-Generating Functions;45
6.7.5;1.7.5 Conditional Expected Value;47
6.8;1.8 Some Discrete Random Variables;47
6.8.1;1.8.1 Bernoulli Random Variable;47
6.8.2;1.8.2 Binomial Random Variable;48
6.8.3;1.8.3 Geometric Random Variable;48
6.8.4;1.8.4 Poisson Random Variable;49
6.8.5;Simulation 1.2 -- Discrete Random Variables;50
6.9;1.9 Some Continuous Random Variables;51
6.9.1;1.9.1 Uniform Random Variable;51
6.9.2;1.9.2 Exponential Random Variable;52
6.9.3;1.9.3 Gaussian Random Variable;53
6.9.4;1.9.4 Rayleigh Random Variable;55
6.9.5;Simulation 1.3 -- Continuous Random Variables;56
6.9.6;1.9.5 Multivariate Gaussian Random Variables;58
6.10;1.10 Sum of Random Variables and the Central Limit Theorem;59
6.10.1;1.10.1 Mean and Variance for the Sum of Random Variables;59
6.10.2;1.10.2 Moments of the Sum of Random Variables;60
6.10.3;1.10.3 PDF of the Sum of Random Variables;60
6.10.4;1.10.4 The Central Limit Theorem;61
6.11;1.11 Transformations of Random Variables;62
6.11.1;Simulation 1.4 -- A Communication System Analysis;70
6.12;1.12 Parameter Estimation via Sample Mean;71
6.12.1;1.12.1 The Sample Mean;72
6.12.2;1.12.2 The Confidence Interval on the Sample Mean;74
6.12.3;Simulation 1.5 -- Confidence Interval on BER Estimations;77
6.12.4;1.12.3 The Law of Large Numbers;78
6.13;1.13 Generation of Random Numbers;79
6.13.1;1.13.1 Congruential Methods;80
6.13.2;1.13.2 Inverse CDF Method;80
6.13.3;1.13.3 Acceptance/Rejection Methods;81
6.13.4;1.13.4 Box-Muller Method;82
6.13.5;Simulation 1.6 -- Random Numbers Generation;82
6.14;1.14 Random Processes;84
6.14.1;Simulation 1.7 -- The Concept of Random Process;86
6.14.2;1.14.1 Stationarity Classes for Random Processes;87
6.14.3;1.14.2 Averages of Stationary Random Processes;88
6.14.3.1;1.14.2.1 Mean and Variance;88
6.14.3.2;1.14.2.2 Autocovariance and Autocorrelation Functions;89
6.14.3.3;1.14.2.3 Power Spectral Density (PSD);92
6.14.3.4;1.14.2.4 Cross-Covariance and Cross-Correlation Functions;94
6.14.4;Simulation 1.8 -- Estimating Averages of Random Processes;95
6.14.5;1.14.3 Random Processes Through Linear Systems;97
6.14.5.1;1.14.3.1 Mean;98
6.14.5.2;1.14.3.2 Autocorrelation;98
6.14.5.3;1.14.3.3 Power Spectral Density (PSD);99
6.14.5.4;1.14.3.4 Cross-Spectral Density;99
6.14.6;1.14.4 The Gaussian Random Process;100
6.14.7;Simulation 1.9 -- Filtered Complex Gaussian Process;101
6.14.8;1.14.5 Thermal Noise Process;103
6.14.8.1;1.14.5.1 Additive White Gaussian Noise (AWGN);104
6.14.8.2;1.14.5.2 Equivalent Noise Bandwidth;105
6.15;1.15 Summary and Further Reading;106
6.16;1.16 Additional Problems;107
6.17;References;109
7;2 Signals and Systems ;110
7.1;2.1 Signals;110
7.1.1;2.1.1 Classification of Signals;110
7.1.1.1;2.1.1.1 Continuous and Discrete Signals;110
7.1.1.2;2.1.1.2 Periodic and Non-periodic Signals;111
7.1.1.3;2.1.1.3 Even and Odd Signals;112
7.1.1.4;2.1.1.4 Deterministic and Random Signals;112
7.1.1.5;2.1.1.5 Baseband and Passband Signals;112
7.1.1.6;2.1.1.6 Energy and Power Signals;112
7.1.2;2.1.2 Typical Deterministic Signals;113
7.1.2.1;2.1.2.1 Unit-Step Function;113
7.1.2.2;2.1.2.2 Dirac Delta and Kronecker Delta Functions;114
7.1.2.3;2.1.2.3 Rectangular Function;115
7.1.2.4;2.1.2.4 Sinc Function;116
7.2;2.2 Fourier Analysis of Signals;117
7.2.1;2.2.1 Fourier Series;117
7.2.1.1;2.2.1.1 Fourier Series for Continuous-Time Periodic Signals;117
7.2.1.2;2.2.1.2 Convergence of the Fourier Series for Continuous-Time Periodic Signals;118
7.2.2;Simulation 2.1 -- Gibbs Phenomenon;120
7.2.2.1;2.2.1.3 Power of a Continuous-Time Periodic Voltage or Current Signal;121
7.2.2.2;2.2.1.4 Properties of Fourier Series for Continuous-Time Periodic Signals;122
7.2.2.3;2.2.1.5 Fourier Series for Discrete-Time Periodic Signals;122
7.2.2.4;2.2.1.6 Convergence of the Fourier Series for Discrete-Time Periodic Signals;123
7.2.2.5;2.2.1.7 Power of a Discrete-Time Periodic Voltage or Current Signal;123
7.2.2.6;2.2.1.8 Properties of Fourier Series for Discrete-Time Periodic Signals;123
7.2.3;2.2.2 Continuous-Time Fourier Transform;123
7.2.3.1;2.2.2.1 Definition of the Continuous-Time Fourier Transform;125
7.2.3.2;2.2.2.2 Convergence of the Continuous-Time Fourier Transform;126
7.2.3.3;2.2.2.3 Continuous-Time Fourier Transform for Periodic Signals;126
7.2.3.4;2.2.2.4 Energy of a Continuous-Time Aperiodic Voltage or Current Signal;127
7.2.3.5;2.2.2.5 Properties and Pairs of the Continuous-Time Fourier Transform;127
7.2.4;2.2.3 Discrete-Time Fourier Transform;129
7.2.4.1;2.2.3.1 Definition of the Discrete-Time Fourier Transform;129
7.2.4.2;2.2.3.2 Periodicity of the Discrete-Time Fourier Transform;129
7.2.4.3;2.2.3.3 Convergence of the Discrete-Time Fourier Transform;130
7.2.4.4;2.2.3.4 Discrete-Time Fourier Transform for Periodic Signals;130
7.2.4.5;2.2.3.5 Energy of a Discrete-Time Aperiodic Voltage or Current Signal;130
7.2.4.6;2.2.3.6 Properties and Pairs of the Discrete-Time Fourier Transform;131
7.2.5;2.2.4 Discrete Fourier Transform;131
7.2.5.1;2.2.4.1 The DFT and the Discrete-Time Fourier Series;133
7.2.5.2;2.2.4.2 The DFT and the Fourier Transform;133
7.2.5.3;2.2.4.3 Mapping the Discrete-Frequency Index k into the Ordinary Frequency f;133
7.2.5.4;2.2.4.4 Parseval's Relation for the DFT;133
7.2.5.5;2.2.4.5 Direct and Inverse Numerical Fast Fourier Transforms (FFT and IFFT);134
7.2.6;Simulation 2.2 -- The FFT via VisSim/Comm;134
7.2.7;2.2.5 Laplace and Z-Transforms;136
7.3;2.3 Sampling of Deterministic and Random Signals;138
7.3.1;2.3.1 Ideal Sampling of Deterministic Signals;138
7.3.2;2.3.2 Ideal Sampling of Stochastic Processes;140
7.3.3;2.3.3 Practical Sampling;140
7.3.4;Simulation 2.3 -- Sampling;143
7.3.4.1;2.3.3.1 Aliasing as a Desired Effect;144
7.3.4.2;2.3.3.2 Sampling of Discrete-Time Signals;145
7.3.4.3;2.3.3.3 Sampling of Passband Signals;145
7.3.5;2.3.4 Analog-to-Digital Conversion;145
7.3.5.1;2.3.4.1 Uniform Quantization;146
7.3.5.2;2.3.4.2 Non-uniform Quantization;148
7.3.6;Simulation 2.4 -- Uniform and Non-uniform Quantization;150
7.3.6.1;2.3.4.3 Other A/D Conversion Techniques;153
7.4;2.4 Linear Systems;153
7.4.1;2.4.1 Time-Domain Characterization of Linear Systems;153
7.4.2;2.4.2 Frequency-Domain Characterization of Linear Systems;155
7.4.2.1;2.4.2.1 Distortion-Free Linear System;156
7.4.2.2;2.4.2.2 Group Delay;157
7.4.3;2.4.3 Classifications and Properties of Linear Systems;158
7.4.3.1;2.4.3.1 Linear Time-Invariant (LTI) Continuous-Time Systems5;158
7.4.3.2;2.4.3.2 Linear Time-Variant (LTV) Continuous-Time Systems;158
7.4.3.3;2.4.3.3 Causal Continuous-Time LTI Systems;159
7.4.3.4;2.4.3.4 Stable Continuous-Time LTI Systems;159
7.4.3.5;2.4.3.5 Eigenfunctions of Continuous-Time LTI Systems;159
7.4.3.6;2.4.3.6 LTI Systems With and Without Memory;160
7.4.3.7;2.4.3.7 Frequency Response for Systems Characterized by Linear Differential Equations;161
7.4.3.8;2.4.3.8 Frequency Response for Systems Characterized by Linear Difference Equations;161
7.4.4;2.4.4 Mapping a Discrete-Time into a Continuous-Time Frequency;162
7.4.5;Simulation 2.5 -- Moving Average Filter;165
7.4.5.1;2.4.4.1 A Note on Discrete-Time Filtering;166
7.5;2.5 Complex Representation of Signals and Systems;169
7.5.1;Simulation 2.6 -- Real Versus Complex Simulation;171
7.6;2.6 The Power Spectral Density Revisited;173
7.6.1;2.6.1 The PSD of Passband Signals;173
7.6.2;Simulation 2.7 -- Estimating the PSD of Passband Signals;176
7.6.3;2.6.2 Estimation of the PSD via the Periodogram;178
7.6.4;Simulation 2.8 -- Periodogram Estimation of the PSD;179
7.6.5;2.6.3 The PSD of Baseband Digital Communication Signals;182
7.7;2.7 The Bandwidth of Communication Signals;185
7.7.1;2.7.1 Absolute Bandwidth;185
7.7.2;2.7.2 -3 dB (or Half Power) Bandwidth;186
7.7.3;2.7.3 Equivalent Noise Bandwidth;186
7.7.4;2.7.4 Root Mean Square (rms) Bandwidth;186
7.7.5;2.7.5 Null-to-Null or Main Lobe Bandwidth;187
7.7.6;2.7.6 Spectral Mask;188
7.8;2.8 Summary and Further Reading;189
7.9;2.9 Additional Problems;189
7.10;References;191
8;3 Communication Channels ;193
8.1;3.1 Definitions;193
8.1.1;3.1.1 Communication Channel;193
8.1.2;3.1.2 Channel Modeling;196
8.1.3;3.1.3 Channel Sounding;196
8.1.4;3.1.4 Empirical, Deterministic and Stochastic Channel Models;197
8.2;3.2 AWGN Channel Model;197
8.2.1;3.2.1 Vector AWGN Channel;198
8.2.2;Simulation 3.1 -- Waveform and Vector Channel Simulation;200
8.3;3.3 Discrete Memoryless Channels;202
8.3.1;3.3.1 The Binary Symmetric Channel Revisited;203
8.3.2;Simulation 3.2 -- Waveform and BSC Channel Simulation;203
8.4;3.4 Discrete Channels with Memory;205
8.5;3.5 Wireline Channels;206
8.5.1;3.5.1 Twisted Pair;206
8.5.2;3.5.2 Coaxial Cable;209
8.5.3;3.5.3 Waveguide;211
8.5.4;3.5.4 Optical Fiber;212
8.5.5;3.5.5 Low-Voltage Power-Line;216
8.5.5.1;3.5.5.1 Frequency Response of the Indoor PLC Channel;217
8.5.5.2;3.5.5.2 Noise in the Indoor PLC Channel;218
8.5.5.3;3.5.5.3 Generalized Background Noise;219
8.5.5.4;3.5.5.4 Impulse Noise;220
8.6;3.6 Wireless Channels;221
8.6.1;3.6.1 Mobile Outdoor Channel;221
8.6.1.1;3.6.1.1 Large-Scale Propagation;222
8.6.1.2;3.6.1.2 Small-Scale Propagation;228
8.6.2;Simulation 3.3 -- Large-Scale and Small-Scale Propagation;230
8.6.2.1;3.6.1.3 Time-Variant Impulse Response of the Multipath Channel;232
8.6.2.2;3.6.1.4 Flat Fading -- Multiplicative Channel Model;233
8.6.2.3;3.6.1.5 Frequency Selective Fading -- tapped delay line Channel Model;236
8.6.2.4;3.6.1.6 Doppler Shift and Doppler Spread of an Unmodulated Signal;237
8.6.3;Simulation 3.4 -- Mobile Channel Simulator;239
8.6.3.1;3.6.1.7 Channel Correlation Functions and Related Parameters;241
8.6.3.2;3.6.1.8 Overall Classification of the Fading;246
8.6.3.3;3.6.1.9 Level Crossing Rate and Average Duration of a Ricean Fading Envelope;247
8.6.4;Simulation 3.5 -- Exploring the Coherence Bandwidth;248
8.6.5;Simulation 3.6 -- Exploring the Coherence Time;249
8.6.6;Simulation 3.7 -- Flat and Frequency Selective Channel;251
8.6.7;Simulation 3.8 -- A Modulated Signal Under Selective Fading;253
8.6.8;3.6.2 Mobile Indoor Channel;254
8.6.8.1;3.6.2.1 Large-Scale Propagation;255
8.6.8.2;3.6.2.2 Small-Scale Propagation;256
8.6.9;Simulation 3.9 -- Saleh-Valenzuela Indoor Channel Model;259
8.6.10;3.6.3 Terrestrial Microwave Channel;261
8.6.10.1;3.6.3.1 Propagation Losses in a Terrestrial Microwave Channel;262
8.6.10.2;3.6.3.2 Multipath Propagation in the Terrestrial Microwave Channel;266
8.6.10.3;3.6.3.3 Simplified Three-Path Terrestrial Microwave Channel Model;267
8.6.11;Simulation 3.10 -- Rummler Terrestrial Microwave Channel Model;269
8.6.12;3.6.4 Spatial Wireless Channel Models;272
8.6.13;3.6.5 Other Wireless Channels;274
8.6.13.1;3.6.5.1 Underwater Acoustic Channel;274
8.6.13.2;3.6.5.2 Free-Space Optical Channel;276
8.6.13.3;3.6.5.3 Underground Radio Channel;277
8.7;3.7 Summary and Further Reading;278
8.8;3.8 Additional Problems;280
8.9;References;282
9;4 Baseband Digital Transmission ;286
9.1;4.1 Definitions and Typical Baseband Signals;286
9.1.1;4.1.1 Line Codes;287
9.1.1.1;4.1.1.1 Unipolar Non-return-to-Zero (NRZ-u);288
9.1.1.2;4.1.1.2 Unipolar Return-to-Zero (RZ-u);289
9.1.1.3;4.1.1.3 Bipolar Non-return-to-Zero (NRZ-b);290
9.1.1.4;4.1.1.4 Bipolar Return to Zero (RZ-b);290
9.1.1.5;4.1.1.5 Alternate Mark Inversion (AMI);290
9.1.1.6;4.1.1.6 Manchester;291
9.1.1.7;4.1.1.7 Miller;292
9.1.1.8;4.1.1.8 Code Mark Inversion (CMI);292
9.1.1.9;4.1.1.9 High Density Bipolar n(HDBn);292
9.1.2;Simulation 4.1 -- Line Codes;293
9.1.3;4.1.2 M-ary PAM Signaling ;294
9.1.4;Simulation 4.2 -- M-ary PAM Signaling;297
9.2;4.2 Detection of Baseband Pulses in Noise;299
9.2.1;4.2.1 Modeling and Motivation;299
9.2.2;Simulation 4.3 -- Motivation for Baseband Detection Analysis;300
9.2.3;4.2.2 The Matched Filter;305
9.2.4;Simulation 4.4 -- Pulse Signal-to-Noise Ratio Measurement;307
9.2.5;4.2.3 Equivalence Between the Matched Filter and the Correlator ;310
9.2.6;Simulation 4.5 -- Equivalence Matched Filter Correlator;313
9.2.7;4.2.4 Error Probability Analysis;315
9.2.8;Simulation 4.6 -- Equivalence Matched Filter Correlator Revisited;323
9.2.9;4.2.5 MAP and ML Decision Rules for Binary Transmission;325
9.3;4.3 Intersymbol Interference (ISI);328
9.3.1;4.3.1 Distortion-Free Channel and ISI Channel;328
9.3.2;Simulation 4.7 -- Distortion-Free Channel;331
9.3.3;4.3.2 Nyquist Criterion for ISI-Free Transmission;333
9.3.4;Simulation 4.8 -- Vestigial Symmetry;336
9.3.5;4.3.3 The Raised Cosine Spectrum;338
9.3.6;4.3.4 The Root-Raised Cosine Spectrum;340
9.3.7;Simulation 4.9 -- Nyquist Pulses;341
9.3.8;4.3.5 The Eye Diagram and the Bathtub Diagram;344
9.3.8.1;4.3.5.1 The Eye Diagram;344
9.3.9;Simulation 4.10 -- Eye Diagram for M-PAM Signaling;346
9.3.9.1;4.3.5.2 Timing Jitter Considerations;348
9.3.9.2;4.3.5.3 The Bathtub Diagram;349
9.3.10;Simulation 4.11 -- Bathtub Diagram for Binary Signaling;352
9.4;4.4 Correlative Coding;354
9.4.1;Simulation 4.12 -- Polybinary and Polybipolar Signal Generation;355
9.4.2;4.4.1 Duobinary and Modified Duobinary Signaling;356
9.4.3;4.4.2 Generalized Partial Response Signaling;361
9.4.4;Simulation 4.13 -- Duobinary Signaling Using a Matched Filter;362
9.5;4.5 Notions of Channel Equalization;364
9.5.1;4.5.1 Zero Forcing (ZF) Equalization;365
9.5.2;Simulation 4.14 -- ZF Equalization;368
9.5.3;4.5.2 Least Mean Square (LMS) Equalization;370
9.5.4;Simulation 4.15 -- LMS Equalization;375
9.6;4.6 Summary and Further Reading;376
9.7;4.7 Additional Problems;377
9.8;References;378
10;5 Signal-Space Analysis ;381
10.1;5.1 Introduction;381
10.2;5.2 Geometric Representation of Signals;383
10.3;5.3 Dimensionality of a Signal and of a Signal-Space;386
10.4;5.4 Gram-Schmidt Orthogonalization;387
10.5;5.5 Signal Constellation with Symbol Transitions;390
10.6;5.6 Statistics of the Correlator's Outputs;391
10.6.1;Simulation 5.1 -- Signal Space Analysis;396
10.7;5.7 The Vector AWGN Channel Revisited;398
10.7.1;Simulation 5.2 -- The Vector AWGN Channel Revisited;399
10.8;5.8 Generalized Maximum Likelihood Receiver;401
10.8.1;Simulation 5.3 -- Generalized ML Receiver;405
10.9;5.9 Error Probability Analysis;407
10.9.1;5.9.1 Rotation and Translation Invariance of the Error Probability;407
10.9.2;5.9.2 Minimum Energy Constellation;408
10.9.3;Simulation 5.4 -- Constellation Rotation and Translation;409
10.9.4;5.9.3 The Union Bound for Symbol Error Probability Estimation;411
10.9.5;Simulation 5.5 -- Verifying the Validity of the Union Bound;414
10.9.6;5.9.4 Symbol Versus Bit Error Probability;416
10.9.7;Simulation 5.6 -- Symbol Error Rate versus Bit Error Rate;421
10.10;5.10 Symbol-by-Symbol ML Receiver for Channels with ISI;422
10.11;5.11 Summary and Further Reading;425
10.12;5.12 Additional Problems;426
10.13;References;429
11;6 Passband Digital Transmission ;430
11.1;6.1 Definitions and Basic Digital Modulation Schemes;430
11.1.1;6.1.1 Basic Digital Modulations;431
11.1.2;6.1.2 Coherent and Non-coherent Detection;432
11.1.3;6.1.3 Spectral Efficiency and Power Efficiency;432
11.1.4;6.1.4 A Note on a Frequently Used Notation;433
11.2;6.2 M-PSK Modulations with Coherent Detection;434
11.2.1;6.2.1 Binary PSK Modulation;434
11.2.1.1;6.2.1.1 BPSK Waveform;434
11.2.1.2;6.2.1.2 BPSK Base-Function;434
11.2.1.3;6.2.1.3 BPSK Constellation;435
11.2.1.4;6.2.1.4 BPSK Symbol and Bit Error Probability over the AWGN Channel;435
11.2.1.5;6.2.1.5 BPSK Generation and Coherent Detection;436
11.2.1.6;6.2.1.6 Power Spectral Density of a BPSK Modulated Signal;438
11.2.1.7;6.2.1.7 Spectral Efficiency of a BPSK Modulated Signal;438
11.2.2;Simulation 6.1 -- BPSK Generation and Coherent Detection;439
11.2.3;6.2.2 M-ary PSK Modulation;441
11.2.3.1;6.2.2.1 M-PSK Modulated Signal;441
11.2.3.2;6.2.2.2 M-PSK Base-Functions;441
11.2.3.3;6.2.2.3 M-PSK Constellation;442
11.2.3.4;6.2.2.4 M-PSK Symbol and Bit Error Probability over the AWGN Channel;442
11.2.3.5;6.2.2.5 M-PSK Generation and Coherent Detection;445
11.2.3.6;6.2.2.6 The I&Q Modulator;448
11.2.3.7;6.2.2.7 Power Spectral Density of an M-PSK Modulated Signal;449
11.2.3.8;6.2.2.8 Spectral Efficiency of an M-PSK Modulated Signal;451
11.2.4;Simulation 6.2 -- M-PSK Generation and Coherent Detection;451
11.3;6.3 M-QAM Modulations with Coherent Detection;453
11.3.1;6.3.1 M-QAM Modulated Signal;453
11.3.2;6.3.2 M-QAM Base-Functions;454
11.3.3;6.3.3 Square M-QAM Modulations;454
11.3.4;6.3.4 Non-square M-QAM Modulations;456
11.3.5;6.3.5 M-QAM Generation and Coherent Detection;458
11.3.6;Simulation 6.3 -- I&Q Generation of a 32-QAM and a 64-QAM;460
11.3.7;6.3.6 M-QAM Symbol and Bit Error Probability over the AWGN Channel;461
11.3.8;6.3.7 Power Spectral Density of an M-QAM Modulated Signal;465
11.3.9;6.3.8 Spectral Efficiency of an M-QAM Modulated Signal;466
11.3.10;Simulation 6.4 -- M-QAM Generation and Coherent Detection;466
11.3.11;6.3.9 Comparing M-PSK and M-QAM Modulations;468
11.4;6.4 M-FSK Modulations with Coherent Detection;469
11.4.1;6.4.1 Tone Separation and Carrier Frequency for Orthogonality;469
11.4.2;6.4.2 Binary FSK Modulation;470
11.4.2.1;6.4.2.1 BFSK Waveform;471
11.4.2.2;6.4.2.2 BFSK Base-Functions;471
11.4.2.3;6.4.2.3 BFSK Constellation;471
11.4.2.4;6.4.2.4 BFSK Symbol and Bit Error Probability over the AWGN Channel;472
11.4.2.5;6.4.2.5 Continuous-Phase and Non-continuous-phase FSK Modulations;473
11.4.2.6;6.4.2.6 BFSK Generation and Coherent Detection;474
11.4.3;Simulation 6.5 -- Analysis of Tones Used by an FSK Modulation;475
11.4.3.1;6.4.2.7 Power Spectral Density of a BFSK Modulated Signal;477
11.4.3.2;6.4.2.8 Spectral Efficiency of a BFSK Modulated Signal;480
11.4.4;Simulation 6.6 -- BFSK Modulation Methods;480
11.4.5;6.4.3 M-ary FSK Modulation;483
11.4.5.1;6.4.3.1 M-FSK Waveform;483
11.4.5.2;6.4.3.2 M-FSK Base-Functions;483
11.4.5.3;6.4.3.3 M-FSK Constellation;484
11.4.5.4;6.4.3.4 Continuous-Phase and Non-continuous-phase M-FSK Modulations;484
11.4.5.5;6.4.3.5 M-FSK Generation and Coherent Detection;484
11.4.5.6;6.4.3.6 M-FSK Symbol and Bit Error Probability over the AWGN Channel;485
11.4.5.7;6.4.3.7 Power Spectral Density of an M-FSK Modulated Signal;488
11.4.5.8;6.4.3.8 Spectral Efficiency of an M-FSK Modulated Signal;490
11.4.6;Simulation 6.7 -- M-FSK Generation and Coherent Detection;490
11.4.6.1;6.4.3.9 Concluding Remarks About M-ary FSK Modulations;494
11.5;6.5 MSK Modulation with Coherent Detection;494
11.5.1;6.5.1 MSK Signal Generation and Detection;495
11.5.1.1;6.5.1.1 The Reason for the Term ``Minimum'' in the MSK Nomenclature;495
11.5.1.2;6.5.1.2 MSK and Conventional Binary FSK;496
11.5.2;Simulation 6.8 -- BFSK and FFSK Generation via VCO;498
11.5.2.1;6.5.1.3 MSK Signal Generation and Detection from the Complex Representation;499
11.5.3;Simulation 6.9 -- MSK Generation via Complex Representation;502
11.5.4;Simulation 6.10 -- MSK Generation via OQPSK Approach;505
11.5.5;Simulation 6.11 -- MSK Modem via OQPSK Approach;507
11.5.5.1;6.5.1.4 MSK Signal Generation and Detection from the Signal-Space Representation;509
11.5.6;Simulation 6.12 -- MSK Modem via Signal-Space Approach;512
11.5.7;6.5.2 MSK Bit Error Probability;514
11.5.8;Simulation 6.13 -- MSK Modem Performance;515
11.5.9;6.5.3 MSK with Conventional FSK Detection;516
11.5.10;Simulation 6.14 -- MSK with Conventional FSK Detection;521
11.5.11;6.5.4 Power Spectral Density of the MSK Signal;521
11.5.12;Simulation 6.15 -- Power Spectral Density of the MSK Signal;523
11.5.13;6.5.5 Further Attributes and Uses for the MSK Modulation;524
11.5.14;6.5.6 Answering Some Questions About the MSK Modulation;525
11.6;6.6 OQPSK, /4QPSK and GMSK Modulations;526
11.6.1;Simulation 6.16 -- Distortion Caused by Nonlinear Amplification;527
11.6.2;6.6.1 Offset QPSK Modulation;531
11.6.2.1;6.6.1.1 OQPSK Modulator;531
11.6.2.2;6.6.1.2 OQPSK Coherent Demodulator;532
11.6.3;Simulation 6.17 -- OQPSK Signal Generation;533
11.6.4;6.6.2 /4DQPSK Modulation;535
11.6.4.1;6.6.2.1 /4DQPSK Modulator;535
11.6.4.2;6.6.2.2 /4DQPSK Differentially Coherent Demodulator;537
11.6.4.3;6.6.2.3 Power Spectral Density of a /4DQPSK Signal;538
11.6.5;Simulation 6.18 -- /4DQPSK Generation and Detection;539
11.6.6;6.6.3 GMSK Modulation;540
11.6.6.1;6.6.3.1 GMSK Modulator;540
11.6.6.2;6.6.3.2 Power Spectral Density of a GMSK Signal;543
11.6.6.3;6.6.3.3 GMSK Coherent Demodulator;544
11.6.7;Simulation 6.19 -- GMSK Generation and Detection;546
11.6.8;6.6.4 Nonlinear Amplification Distortion Revisited;548
11.6.9;Simulation 6.20 -- Nonlinear Amplification of Modulated Signals;549
11.7;6.7 Non-coherent M-FSK and Differentially Coherent BPSK;553
11.7.1;6.7.1 Non-coherent M-FSK Modulations;553
11.7.1.1;6.7.1.1 Tone Separation for Non-coherent Detection of BFSK Signals;553
11.7.1.2;6.7.1.2 M-FSK Modulated Signal and Non-coherent Demodulation;554
11.7.1.3;6.7.1.3 Symbol and Bit Error Probability for Non-coherent M-FSK;556
11.7.2;Simulation 6.21 -- Non-coherently Detected Binary FSK;557
11.7.3;6.7.2 Differentially-Coherent BPSK Modulation;561
11.7.3.1;6.7.2.1 DBPSK Signal Generation;561
11.7.3.2;6.7.2.2 DBPSK Differential Detection;562
11.7.3.3;6.7.2.3 Bit Error Probability for a Differentially-Coherent BPSK Modulation;563
11.7.4;Simulation 6.22 -- DBPSK Generation and Detection;564
11.7.4.1;6.7.2.4 Power Spectral Density and Spectral Efficiency of a DBPSK Signal;565
11.7.4.2;6.7.2.5 Multiple Symbol Differential Detection;565
11.8;6.8 Carrier and Symbol-Timing Recovery;565
11.8.1;6.8.1 Parameter Estimation;567
11.8.2;6.8.2 Carrier Synchronization;570
11.8.2.1;6.8.2.1 The Costas Loop;571
11.8.2.2;6.8.2.2 Phase Ambiguity;573
11.8.3;Simulation 6.23 -- PLL Response;574
11.8.4;Simulation 6.24 -- BPSK Phase Tracking with Costas Loop;576
11.8.4.1;6.8.2.3 Carrier Synchronization of M-ary Phase-Shift Keying Signals;578
11.8.5;Simulation 6.25 -- M-th Power Loop for QPSK Phase Tracking;580
11.8.5.1;6.8.2.4 Carrier Synchronization for Other Modulations;583
11.8.6;6.8.3 Symbol Synchronization;583
11.8.6.1;6.8.3.1 Early-Late Gate Synchronizer;584
11.8.7;Simulation 6.26 -- Operation of the Early-Late Synchronizer;584
11.8.8;Simulation 6.27 -- Carrier and Symbol Synchronization;587
11.9;6.9 Performance of Digital Modulations over Fading Channels;589
11.9.1;6.9.1 Optimum Receiver Structures for Fading Channels;589
11.9.2;6.9.2 The Effect of Fading on the Error Probability;590
11.9.3;6.9.3 Performance of Digital Modulations over Fading Channels;592
11.9.3.1;6.9.3.1 Performance of Coherent M-ASK;592
11.9.3.2;6.9.3.2 Performance of Coherent Square M-QAM;593
11.9.3.3;6.9.3.3 Performance of Coherent M-PSK;593
11.9.3.4;6.9.3.4 Performance of Coherently Detected DEQPSK and /4-DQPSK;593
11.9.3.5;6.9.3.5 Performance of Coherent M-FSK;594
11.9.3.6;6.9.3.6 Performance of Non-coherent M-FSK;595
11.9.3.7;6.9.3.7 Performance of Differentially Coherent M-DPSK;595
11.10;6.10 Summary and Further Reading;595
11.11;6.11 Additional Problems;597
11.12;References;598
12;7 Wideband Transmission Techniques ;603
12.1;7.1 Spread-Spectrum Transmission;603
12.1.1;7.1.1 Definition;603
12.1.2;7.1.2 A Brief History About the Spread-Spectrum;604
12.1.3;7.1.3 Direct-Sequence Spread-Spectrum;605
12.1.4;7.1.4 Attributes of a Spread-Spectrum Signal;606
12.1.4.1;7.1.4.1 Low Power Spectral Density;606
12.1.4.2;7.1.4.2 Low Probability of Interception;606
12.1.4.3;7.1.4.3 Robustness Against Interference;607
12.1.5;Simulation 7.1 -- DS-SS Signal Under Jamming;609
12.1.5.1;7.1.4.4 Channel Sounding Capability;612
12.1.6;Simulation 7.2 -- Channel Sounding;614
12.1.6.1;7.1.4.5 Multiple Access Capability;617
12.1.6.2;7.1.4.6 Robustness Against Multipath Propagation -- The RAKE Receiver;621
12.1.7;Simulation 7.3 -- RAKE Receiver;626
12.1.8;7.1.5 Spreading Sequences;629
12.1.8.1;7.1.5.1 Maximum-Length Sequences (m-Sequences);630
12.1.9;Simulation 7.4 -- Generation of m-Sequences;635
12.1.10;Simulation 7.5 -- White Noise Generation with m-Sequences;636
12.1.11;Simulation 7.6 -- Exploring Correlation Properties for Synchronism;638
12.1.11.1;7.1.5.2 Gold Sequences;640
12.1.11.2;7.1.5.3 Walsh--Hadamard Sequences;642
12.1.12;Simulation 7.7 -- Exploring Correlation Properties for CDMA;645
12.1.13;7.1.6 Frequency-Hopping Spread-Spectrum;647
12.1.14;Simulation 7.8 -- FH-SS Modem;649
12.1.15;7.1.7 Processing Gain and Jamming Margin for DS-SS and FH-SS;651
12.1.16;7.1.8 Acquisition and Tracking of Spread-Spectrum Signals;652
12.1.16.1;7.1.8.1 Serial-Search Acquisition (SSA);653
12.1.17;Simulation 7.9 -- Serial-Search Acquisition;654
12.1.17.1;7.1.8.2 Rapid Acquisition by Sequential Estimation (RASE);654
12.1.17.2;7.1.8.3 Code Tracking via Delay-Locked Loop (DLL);656
12.1.17.3;7.1.8.4 Code Tracking via Tau-Dither Loop (TDL);657
12.2;7.2 Multi-carrier Transmission;658
12.2.1;7.2.1 Multi-carrier Modulation;659
12.2.2;7.2.2 Multi-carrier CDMA;660
12.2.3;7.2.3 Multi-carrier DS-CDMA;661
12.2.4;7.2.4 Multi-tone CDMA;662
12.2.5;7.2.5 Multi-carrier DS-CDMA using frequency-spread coding;662
12.2.6;7.2.6 Modified Multi-carrier DS-CDMA;663
12.2.7;7.2.7 Implementation Aspects of MC-CDMA Systems;664
12.2.7.1;7.2.7.1 Implementation Aspects of the OFDM Technique;666
12.2.8;Simulation 7.10 -- OFDM Modem;671
12.2.9;7.2.8 Comments on the Performance of MC-CDMA Systems;674
12.2.10;7.2.9 MC-CDMA with Double Spreading Code;675
12.2.11;Simulation 7.11 -- DC-DS-CDMA Modem;681
12.3;7.3 Ultra Wideband Transmission;683
12.3.1;7.3.1 UWB Signaling Techniques;684
12.3.1.1;7.3.1.1 UWB Pulse Shape Design;684
12.3.1.2;7.3.1.2 Generic UWB Transmitted Signal;686
12.3.1.3;7.3.1.3 PPM Signaling;687
12.3.1.4;7.3.1.4 BPSK Signaling;688
12.3.1.5;7.3.1.5 Bi-orthogonal Signaling;688
12.3.1.6;7.3.1.6 PAM Signaling;688
12.3.1.7;7.3.1.7 OOK Signaling;689
12.3.1.8;7.3.1.8 PSM Signaling;689
12.3.2;7.3.2 UWB Channel Models;689
12.3.3;7.3.3 Reception of UWB Signals;690
12.3.4;Simulation 7.12 -- TH-PPM Ultra Wideband Modem;691
12.3.4.1;7.3.3.1 Reception of UWB Signals Using Time Reversal;693
12.3.5;Simulation 7.13 -- Exploring the Time Reversal Technique;695
12.4;7.4 Summary and Further Reading;697
12.5;7.5 Additional Problems;698
12.6;References;700
13;8 Notions of Information Theory and Error-Correcting Codes;706
13.1;8.1 Notions of Information Theory;706
13.1.1;8.1.1 Uncertainty, Information and Entropy;707
13.1.1.1;8.1.1.1 Uncertainty and Information;707
13.1.1.2;8.1.1.2 Entropy of a Discrete Memoryless Source;708
13.1.1.3;8.1.1.3 Gross Bit Rate and Information Bit Rate;709
13.1.2;Simulation 8.1 -- Estimating the Entropy of a Source;710
13.1.3;8.1.2 Source Coding and the Source-Coding Theorem;711
13.1.3.1;8.1.2.1 Source-Coding Theorem;712
13.1.3.2;8.1.2.2 Huffman Coding;712
13.1.4;8.1.3 Discrete Memoryless Channels Revisited;716
13.1.5;8.1.4 Mutual Information and Channel Capacity;717
13.1.6;8.1.5 Channel Coding Theorem;718
13.1.7;8.1.6 Channel Capacity of Some Channels;720
13.1.7.1;8.1.6.1 Capacity of the Binary Symmetric Channel;721
13.1.7.2;8.1.6.2 Capacity of the Binary-Input, Continuous-Output AWGN Channel;721
13.1.7.3;8.1.6.3 Capacity of the Continuous-Time, Band-Limited AWGN Channel;722
13.1.7.4;8.1.6.4 Analyzing the Capacities of a Band-Limited AWGN Channel with Binary Antipodal Signaling and with Unconstrained Input Alphabet;724
13.1.8;8.1.7 Channel Capacity of Other Important Channels;727
13.1.8.1;8.1.7.1 Capacity of the Gaussian Channel with Constrained Constellations;728
13.1.8.2;8.1.7.2 Capacity of Fading Channels;732
13.1.8.3;8.1.7.3 Capacity of a Colored-Noise Gaussian Channel;736
13.1.8.4;8.1.7.4 Capacity of the MIMO Wireless Channel;740
13.2;8.2 Notions of Error-Correcting Codes;746
13.2.1;8.2.1 Terminology and Background;746
13.2.2;8.2.2 Hamming and Reed-Muller Codes;756
13.2.2.1;8.2.2.1 Hamming Codes;756
13.2.2.2;8.2.2.2 Reed-Muller Codes;759
13.2.3;8.2.3 Syndrome Decoding of Binary Linear Block Codes;761
13.2.3.1;8.2.3.1 Standard Array;761
13.2.3.2;8.2.3.2 Syndrome Decoding;762
13.2.4;Simulation 8.2 -- Hard-Decision Versus Soft-Decision ML Decoding;763
13.2.5;Simulation 8.3 -- Coded and Uncoded System Performance;766
13.2.6;8.2.4 Construction of Extension Fields and Polynomial Algebra;768
13.2.7;8.2.5 Cyclic Codes;770
13.2.7.1;8.2.5.1 General Systematic Encoding of Cyclic Codes via LFSR;772
13.2.7.2;8.2.5.2 Syndrome Computation and Error Detection with Cyclic Codes via LFSR;774
13.2.7.3;8.2.5.3 Syndrome Decoding of Cyclic Codes via LFSR;774
13.2.8;Simulation 8.4 -- LFSR Encoding of a Hamming (7, 4) Code;779
13.2.9;Simulation 8.5 -- Meggitt Decoding of a Hamming (7, 4) Code;780
13.2.10;8.2.6 Bose-Chaudhuri-Hocquenghem and Reed-Solomon Codes;781
13.2.10.1;8.2.6.1 Binary BCH Codes;781
13.2.10.2;8.2.6.2 Reed Solomon Codes;783
13.2.10.3;8.2.6.3 Decoding Strategies for BCH and RS Codes;785
13.2.11;Simulation 8.6 -- Reed-Solomon Code Performance;787
13.2.12;8.2.7 Performance of Binary Linear Block Codes;789
13.2.12.1;8.2.7.1 Block Error Probability for Hard-Decision Decoding;789
13.2.12.2;8.2.7.2 Block Error Probability for Unquantized Soft-Decision Decoding;790
13.2.12.3;8.2.7.3 Bit Error Probability;790
13.2.12.4;8.2.7.4 Comments on the Performance of Concatenated codes;793
13.2.13;8.2.8 Convolutional Codes;793
13.2.13.1;8.2.8.1 Convolutional Encoder and Basic Properties of the Code;794
13.2.13.2;8.2.8.2 Viterbi Decoding of Convolutional Codes;797
13.2.13.3;8.2.8.3 Finite Trace-Back Viterbi Algorithm;800
13.2.14;Simulation 8.7 -- Finite Trace-Back Viterbi Decoding;803
13.2.14.1;8.2.8.4 Performance of Convolutional Codes;805
13.2.14.2;8.2.8.5 Convolutional Codes with Good Distance Properties;809
13.2.15;Simulation 8.8 -- Convolutional Code Performance;811
13.2.16;8.2.9 Trellis-Coded Modulation;812
13.2.17;Simulation 8.9 -- Four-State 8PSK Trellis-Coded Modulation;821
13.2.18;8.2.10 Turbo and Low-Density Parity Check Codes;823
13.2.18.1;8.2.10.1 Introduction;823
13.2.18.2;8.2.10.2 A Brief Description of LDPC Codes;825
13.2.18.3;8.2.10.3 General Concepts About Turbo Codes;825
13.2.18.4;8.2.10.4 Single-Parity Check Product Codes;827
13.2.18.5;8.2.10.5 A Key Property of Product Codes;830
13.2.18.6;8.2.10.6 Turbo Decoding of Product Codes;832
13.2.18.7;8.2.10.7 Turbo Decoding of Single-Parity Check Product Codes;834
13.2.18.8;8.2.10.8 An Example of Turbo Decoding of a 2-Dimensional SPC-TPC;837
13.2.18.9;8.2.10.9 General Comments on Multidimensional Product Codes;842
13.2.18.10;8.2.10.10 Simulation Results over the AWGN and Slow Flat Rayleigh Fading Channel;843
13.2.19;8.2.11 Remarks on Coding for Fading Channels;845
13.2.19.1;8.2.11.1 A Synthesizing Phrase;845
13.2.19.2;8.2.11.2 Modern Channel Coding Schemes for Fading Channels;846
13.3;8.3 Summary and Further Reading;847
13.4;8.4 Additional Problems;849
13.5;References;850
14;A Mathematical Tables and Algorithms ;858
14.1;A.1 Trigonometric Relations;858
14.2;A.2 Gaussian Error Function and Gaussian Q-Function;859
14.2.1;A.2.1 Some Tabulated Values of the Complementary Error Function;860
14.3;A.3 Derivatives;861
14.4;A.4 Definite Integrals;861
14.5;A.5 Indefinite Integrals;863
14.6;A.6 Linear Matrix Transformations of Two-Dimensional Spaces;864
14.7;A.7 Mathcad Routine for Converting Decimal to Binary Numbers;865
14.8;A.8 Mathcad Routine for a Binary Counter;865
14.9;A.9 Mathcad Routine for a Gray Counter;866
14.10;A.10 Mathcad Routine for Generating Walsh-Hadamard Sequences;866
14.11;A.11 Mathcad Routine for Generating the IOWEM of a Block Code;866
14.12;A.12 Mathcad Routine for Computing the Euler Function;867
14.13;References;868
15;Abbreviations;869
16;Index;876