EBOOK - Introduction to Communication Systems (Upamanyu Madhow)


EBOOK - Giới thiệu về Hệ thống Truyền thông (Upamanyu Madhow) - 470 Trang.

Progress in telecommunications over the past two decades has been nothing short of revolutionary, with communications taken for granted in modern society to the same extent as electricity. There is therefore a persistent need for engineers who are well-versed in the principles of communication systems. These principles apply to communication between points in space, as well as communication between points in time (i.e, storage). Digital systems are fast replacing analog systems in both domains. This book has been written in response to the following core question: what is the basic material that an undergraduate student with an interest in communications should learn, in order to be well prepared for either industry or graduate school? For example, a number of institutions only teach digital communication, assuming that analog communication is dead or dying. Is that the right approach? From a purely pedagogical viewpoint, there are critical questions related to mathematical preparation: how much mathematics must a student learn to become well-versed in system design, what should be assumed as background, and at what point should the mathematics that is not in the background be introduced? Classically, students learn probability and random processes, and then tackle communication.

This does not quite work today: students increasingly (and I believe, rightly) question the applicability of the material they learn, and are less interested in abstraction for its own sake. On the other hand, I have found from my own teaching experience that students get truly excited about abstract concepts when they discover their power in applications, and it is possible to provide the means for such discovery using software packages such as Matlab. Thus, we have the opportunity to get a new generation of students excited about this field: by covering abstractions “just in time” to shed light on engineering design, and by reinforcing concepts immediately using software experiments in addition to conventional pen-and-paper problem solving, we can remove the lag between learning and application, and ensure that the concepts stick. This textbook represents my attempt to act upon the preceding observations, and is an outgrowth of my lectures for a two-course undergraduate elective sequence on communication at UCSB, which is often also taken by some beginning graduate students.

CONTENTS:

1 Introduction 15
1.1 Analog or Digital? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.1.1 Analog communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.1.2 Digital communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.1.3 Why digital? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.1.4 Why analog design remains important . . . . . . . . . . . . . . . . . . . . 21
1.2 A Technology Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3 Scope of this Textbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.4 Why Study Communication Systems? . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.5 Concept Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.6 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Signals and Systems 27
2.1 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 Linear Time Invariant Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.1 Discrete time convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.2 Multi-rate systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4.1 Fourier Series Properties and Applications . . . . . . . . . . . . . . . . . . 49
2.5 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5.1 Fourier Transform Properties . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.5.2 Numerical computation using DFT . . . . . . . . . . . . . . . . . . . . . . 57
2.6 Energy Spectral Density and Bandwidth . . . . . . . . . . . . . . . . . . . . . . . 60
2.7 Baseband and Passband Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.8 The Structure of a Passband Signal . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.8.1 Time Domain Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.8.2 Frequency Domain Relationships . . . . . . . . . . . . . . . . . . . . . . . 69
2.8.3 Complex baseband equivalent of passband filtering . . . . . . . . . . . . . 75
2.8.4 General Comments on Complex Baseband . . . . . . . . . . . . . . . . . . 76
2.9 Wireless Channel Modeling in Complex Baseband . . . . . . . . . . . . . . . . . . 77
2.10 Concept Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
2.11 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3 Analog Communication Techniques 91
3.1 Terminology and notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.2 Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.2.1 Double Sideband (DSB) Suppressed Carrier (SC) . . . . . . . . . . . . . . 93
3.2.2 Conventional AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.2.3 Single Sideband Modulation (SSB) . . . . . . . . . . . . . . . . . . . . . . 102
3.2.4 Vestigial Sideband (VSB) Modulation . . . . . . . . . . . . . . . . . . . . . 108
3.2.5 Quadrature Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . 109
3.2.6 Concept synthesis for AM . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.3 Angle Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.3.1 Limiter-Discriminator Demodulation . . . . . . . . . . . . . . . . . . . . . 114
3.3.2 FM Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.3.3 Concept synthesis for FM . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.4 The Superheterodyne Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.5 The Phase Locked Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.5.1 PLL Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.5.2 Mathematical Model for the PLL . . . . . . . . . . . . . . . . . . . . . . . 126
3.5.3 PLL Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
3.6 Some Analog Communication Systems . . . . . . . . . . . . . . . . . . . . . . . . 132
3.6.1 FM radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
3.6.2 Analog broadcast TV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.7 Concept Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.8 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
3.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4 Digital Modulation 153
4.1 Signal Constellations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.2 Bandwidth Occupancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.2.1 Power Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.2.2 PSD of a linearly modulated signal . . . . . . . . . . . . . . . . . . . . . . 159
4.3 Design for Bandlimited Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
4.3.1 Nyquist’s Sampling Theorem and the Sinc Pulse . . . . . . . . . . . . . . . 162
4.3.2 Nyquist Criterion for ISI Avoidance . . . . . . . . . . . . . . . . . . . . . . 165
4.3.3 Bandwidth efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
4.3.4 Power-bandwidth tradeoffs: a sneak preview . . . . . . . . . . . . . . . . . 170
4.3.5 The Nyquist criterion at the link level . . . . . . . . . . . . . . . . . . . . 172
4.3.6 Linear modulation as a building block . . . . . . . . . . . . . . . . . . . . 173
4.4 Orthogonal and Biorthogonal Modulation . . . . . . . . . . . . . . . . . . . . . . . 173
4.5 Proofs of the Nyquist theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
4.6 Concept Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
4.7 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.A Power spectral density of a linearly modulated signal . . . . . . . . . . . . . . . . 191
4.B Simulation resource: bandlimited pulses and upsampling . . . . . . . . . . . . . . 192
5 Probability and Random Processes 197
5.1 Probability Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
5.2 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
5.3 Multiple Random Variables, or Random Vectors . . . . . . . . . . . . . . . . . . . 208
5.4 Functions of random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
5.5 Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
5.5.1 Expectation for random vectors . . . . . . . . . . . . . . . . . . . . . . . . 222
5.6 Gaussian Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
5.6.1 Joint Gaussianity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
5.7 Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
5.7.1 Running example: sinusoid with random amplitude and phase . . . . . . . 236
5.7.2 Basic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
5.7.3 Second order statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
5.7.4 Wide Sense Stationarity and Stationarity . . . . . . . . . . . . . . . . . . . 240
5.7.5 Power Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
5.7.6 Gaussian random processes . . . . . . . . . . . . . . . . . . . . . . . . . . 246
5.8 Noise Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
5.9 Linear Operations on Random Processes . . . . . . . . . . . . . . . . . . . . . . . 252
5.9.1 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
5.9.2 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
5.10 Concept Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
5.11 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
5.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
5.A Q function bounds and asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . 272
5.B Approximations using Limit Theorems . . . . . . . . . . . . . . . . . . . . . . . . 273
5.C Noise Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
5.D The structure of passband random processes . . . . . . . . . . . . . . . . . . . . . 275
5.D.1 Baseband representation of passband white noise . . . . . . . . . . . . . . 277
5.E SNR Computations for Analog Modulation . . . . . . . . . . . . . . . . . . . . . . 278
5.E.1 Noise Model and SNR Benchmark . . . . . . . . . . . . . . . . . . . . . . . 278
5.E.2 SNR for Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . 278
5.E.3 SNR for Angle Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
6 Optimal Demodulation 289
6.1 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
6.1.1 Error probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
6.1.2 ML and MAP decision rules . . . . . . . . . . . . . . . . . . . . . . . . . . 292
6.1.3 Soft Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
6.2 Signal Space Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
6.2.1 Representing signals as vectors . . . . . . . . . . . . . . . . . . . . . . . . 300
6.2.2 Modeling WGN in signal space . . . . . . . . . . . . . . . . . . . . . . . . 304
6.2.3 Hypothesis testing in signal space . . . . . . . . . . . . . . . . . . . . . . . 306
6.2.4 Optimal Reception in AWGN . . . . . . . . . . . . . . . . . . . . . . . . . 308
6.2.5 Geometry of the ML decision rule . . . . . . . . . . . . . . . . . . . . . . . 311
6.3 Performance Analysis of ML Reception . . . . . . . . . . . . . . . . . . . . . . . . 313
6.3.1 The Geometry of Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
6.3.2 Performance with binary signaling . . . . . . . . . . . . . . . . . . . . . . . 315
6.3.3 M -ary signaling: scale-invariance and SNR . . . . . . . . . . . . . . . . . . 318
6.3.4 Performance analysis for M -ary signaling . . . . . . . . . . . . . . . . . . . 322
6.3.5 Performance analysis for M -ary orthogonal modulation . . . . . . . . . . . 330
6.4 Bit Error Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
6.5 Link Budget Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
6.6 Concept Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
6.7 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
6.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
6.A Irrelevance of component orthogonal to signal space . . . . . . . . . . . . . . . . . 359
7 Channel Coding 361
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
7.2 Model for Channel Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
7.3 Shannon’s Promise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
7.3.1 Design Implications of Shannon Limits . . . . . . . . . . . . . . . . . . . . 372
7.4 Introducing linear codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
7.5 Soft decisions and belief propagation . . . . . . . . . . . . . . . . . . . . . . . . . 382
7.6 Concept Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
7.7 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
7.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
8 Dispersive Channels and MIMO 399
8.1 Singlecarrier System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
8.1.1 Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
8.1.2 Noise Model and SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
8.2 Linear equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
8.2.1 Adaptive MMSE Equalization . . . . . . . . . . . . . . . . . . . . . . . . . 409
8.2.2 Geometric Interpretation and Analytical Computations . . . . . . . . . . . 412
8.3 Orthogonal Frequency Division Multiplexing . . . . . . . . . . . . . . . . . . . . . 418
8.3.1 DSP-centric implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 420
8.4 MIMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
8.4.1 The linear array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
8.4.2 Beamsteering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
8.4.3 Rich Scattering and MIMO-OFDM . . . . . . . . . . . . . . . . . . . . . . 430
8.4.4 Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
8.4.5 Spatial multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
8.5 Concept Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
8.6 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
8.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

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