Digital Communication (eBook)

Preface 6
Salient Features 7
Acknowledgements 9
Contents 10
Chapter1 Preview and Introduction 15
1.1 Process of Communication 15
1.2 General Definition of Signal 17
1.3 Time-Value Definition of SignalsAnalog and Digital 20
1.3.1 Continuous Time Continuous Valued Signal 21
1.3.2 Discrete Time Continuous Valued Signal 21
1.3.3 Discrete Time Discrete Valued Signal 21
1.4 Analog and Digital Communication Systems 22
1.5 Elements of Digital Communication System 24
1.6 MATLAB Programs 25
1.6.1 Time and Frequency Domain Representation of Signals 25
1.6.2 CTSV, DTCV, DTDV Signals 26
References 27
Chapter2 Waveform Encoding 28
2.1 Introduction 28
2.2 Pulse Code Modulation (PCM) 28
2.2.1 Process of Sampling 29
2.2.1.1 Sampling Theorem 31
Case I 32
Case II 33
Case III 33
2.2.1.2 Aliasing 34
2.2.2 Process of Quantization 35
2.2.3 PCM Transmitter and Receiver 37
2.2.3.1 PCM Transmitter 37
2.2.3.2 PCM Receiver 39
2.2.4 Quantization Error 40
2.2.5 Signal to Noise Ratio (SNR) for Quantized Pulses 42
2.2.6 Non-uniform Quantization: Companding 43
2.2.6.1 -Law 45
2.2.6.2 A-Law 47
2.3 Differential Pulse Code Modulation (DPCM) 48
2.3.1 Cumulative Error in PCM 48
2.3.2 Prevention of Cumulative Error by Applying Feedback 49
2.3.3 How We Can Predict the Future? 51
2.3.4 Analysis of DPCM 53
2.4 Delta Modulation 54
2.4.1 Drawbacks of Delta Modulation 56
2.4.1.1 Slope Overloading 56
2.4.1.2 Granular Noise 57
2.5 Adaptive Delta Modulation 57
2.5.1 Song Algorithm 57
2.5.2 Space-Shuttle Algorithm 59
2.6 Sigma-Delta Modulation (SDM) 60
2.6.1 Noise Performance 61
2.7 Linear Predictive Coder (LPC) 62
2.7.1 Concept 62
2.7.2 Genetic Algorithm Based Approach 63
2.8 MATLAB Programs 66
2.8.1 Aliasing 66
References 67
Chapter3 Digital Baseband Signal Receivers 68
3.1 Introduction 68
3.2 Integrate and Dump Type Filter 69
3.2.1 Noise Power and Variance 72
3.2.2 Figure of Merit 74
3.2.3 Probability of Error 74
3.3 The Optimum Filter 76
3.4 The Matched Filter 80
3.4.1 Impulse Response 80
3.4.2 Probability of Error 80
3.4.3 Properties of Matched Filter 83
3.5 The Correlator 85
3.6 Simulink Communication Block Set Example 87
Integrate and Dump 87
Library 87
Description 87
Dialog Box 87
Examples 88
References 88
Chapter4 Digital Baseband Signal Transmitter 89
4.1 Introduction 89
4.2 Elements of Digital Baseband Communication System 89
4.2.1 Formatting 90
4.2.2 Regenerative Repeater 90
4.3 Properties and Choice of Digital Formats 92
4.4 Line Coding 93
4.5 Power Spectrum Density of Different Digital Formats 95
4.5.1 Unipolar-NRZ 98
4.5.2 Unipolar-RZ 99
4.5.3 Polar-NRZ 100
4.5.4 Polar-RZ 101
4.5.5 Bipolar-NRZ 102
4.5.6 Split-Phase (Manchester) 103
References 105
Chapter5 Equalization 106
5.1 Inter-Symbol Interference (ISI) 106
5.2 Nyquist Criterion for Distortion Less Transmission (Zero ISI) 108
5.2.1 Criteria in Frequency Domain 109
5.2.2 Concept of Ideal Nyquist Channel 111
5.2.3 Limitations of Ideal Solution: Raised Cosine Spectrum 112
5.3 Eye Pattern 114
5.3.1 Information Obtained from Eye Pattern 115
5.4 System Design for Known Channel 115
5.5 Linear Equalizer 117
5.5.1 Linear Transversal Filter 117
5.6 Adaptive Equalizer 119
References 121
Chapter6 Digital Modulation Techniques 122
6.1 Introduction 122
6.2 Amplitude Shift Keying (ASK) 123
6.2.1 Mathematical Model 124
6.2.1.1 On-0Off Keying ( OOK) 125
6.2.2 ASK Modulator 126
6.2.3 Binary ASK Demodulator 128
6.3 Frequency Shift Keying (FSK) 129
6.3.1 Mathematical Model 129
6.3.2 BFSK Modulator 130
6.3.3 FSK Demodulator 132
6.4 Binary Phase Shift Keying (BPSK) 133
6.4.1 Mathematical Model 134
6.4.2 BPSK Modulator 135
6.4.3 BPSK Demodulator 136
6.5 Differential Phase Shift Keying (DPSK) 136
6.5.1 DPSK Modulator 136
6.5.2 DPSK Demodulator 138
6.6 Quadrature Phase Shift Keying (QPSK) 138
6.6.1 Mathematical Model 138
6.6.2 QPSK Modulator 142
6.6.3 QPSK Demodulator 142
6.6.4 Offset QPSK (OQPSK) 143
6.7 Minimum Shift Keying (MSK) 145
6.8 Probability of Error for Different Modulation Schemes 147
6.8.1 Probability of Error in ASK 147
6.8.2 Probability of Error in FSK 148
6.8.3 Probability of Error in PSK 149
6.9 MATLAB Programs 150
6.9.1 QPSK Waveform 150
6.9.2 MSK Waveform 151
References 152
Chapter7 Spread Spectrum Modulation 153
7.1 Introduction 153
7.2 Processing Gain 154
7.3 Pseudo-Noise (PN) Sequence 155
7.3.1 Concept: A Hypothetical Experiment 155
7.3.2 Generation of PN Sequence 156
7.3.3 Properties of PN Sequence 157
7.4 Direct Sequence Spread Spectrum (DSSS) 159
7.4.1 Concept 159
7.4.2 DSSS with Coherent BPSK 161
7.4.3 Probability of Error Calculation 162
7.5 Frequency-Hopped Spread Spectrum 165
7.5.1 Concept 165
7.5.2 FHSS with FSK 167
7.5.3 Rate of Hopping: Fast and Slow 169
7.6 Application of Spread Spectrum 169
7.6.1 GPS (Global Positioning System) 169
7.7 CDMA (Code Division Multiple Access) 173
7.7.1 Orthogonal Chip Sequence 173
7.7.2 Gold Sequence 175
7.7.3 Principle of Operation 176
7.7.3.1 MUX 176
7.7.3.2 DMUX 176
References 176
Chapter8 Information Theory 178
8.1 Introduction 178
8.2 Entropy 180
8.3 Rate of Information 182
8.4 Information Sources 182
8.5 Discrete Memoryless Channel (DMC) 185
8.5.1 Channel Representation 185
8.5.2 The Channel Matrix 185
8.6 Special Channels 186
8.6.1 Lossless Channel 186
8.6.2 Deterministic Channel 187
8.6.3 Noise-Less Channel 188
8.6.4 Binary Symmetric Channel (BSC) 188
8.6.4.1 Saturated or Stable Probability of Error for Cascaded BSC Channel 189
8.6.4.2 Probability Model of Erroneous Detection in Cascaded BSC 189
8.7 Mutual Information 191
8.8 Channel Capacity 192
8.8.1 Gaussian Channel: Shanon-Hartley Theorem 192
8.9 Entropy Coding 194
8.9.1 Shanon-Fano Coding 195
8.9.2 Huffman Coding 196
8.10 MATLAB Code 197
8.10.1 Convergence of Pe in Cascaded BSC 197
References 198
Chapter9 Error Control Coding 199
9.1 Introduction 199
9.2 Scope of Coding 200
Forward Error Correction 200
9.3 Linear Block Code 201
9.3.1 Coding Technique Using Generator Matrix 201
9.3.2 Syndrome Decoding 203
9.4 Convolutional Code 204
9.4.1 Encoder 204
9.4.1.1 Operation 205
9.4.1.2 Code Rate 207
9.4.2 State Diagram 207
9.4.3 Code Tree 208
9.4.4 Trellis Diagram 208
9.4.5 Decoding of Convolutional Code by Viterbi 210
9.4.5.1 Metric 210
9.4.5.2 Surviving Path 210
9.4.5.3 Principle of Decoding 210
9.5 Cyclic Code 212
9.5.1 Concept and Properties 212
9.5.2 Encoder and Decoder 214
9.5.3 Meggitt Decoder 215
9.6 BCH Code 215
9.6.1 Simplified BCH Codes 216
9.6.2 General BCH Codes 218
9.6.3 Properties 218
References 219
AppendixAElementary Probability Theory 220
A.1 Concept of Probability 220
A.1.1 Random Experiments and Sample Space 220
A.1.2 Events 221
A.1.3 Probability-Understanding Approaches 221
A.2 Random Variable 221
A.3 Mean, Variance, Skew-ness and Kurtosis 222
A.4 Cumulative Distribution Function (CDF) 224
A.5 Probability Density Function (PDF) 226
A.5.1 Uniform PDF 226
A.5.2 Frequently Used Probability Distribution 227
A.5.2.1. Bernoulli Distribution 227
A.5.2.2 Gaussian Distribution 228
A.5.2.3. Poisson Distribution 228
A.5.2.4 Rayleigh Distribution 228
References 231
Appendix BConvolution and Correlation – Some CaseStudies 232
B.1 Convolution 232
B.1.1 Basic Properties of Convolution 234
B.1.1.1 Commutative Law 234
B.1.1.2 Associative Law 235
B.1.1.3 Distributive Law 235
B.1.1.4 Transformed Domain Simplicity 236
B.1.2 Case 1: Periodicity of Sampled Spectra 237
B.1.3 Case 2: Transmission of Normally Distributed Information 238
B.1.4 Case 3: Long Multiplication Using Convolution 239
B.2 Correlation 239
B.2.1 Case Study: Pattern (Shape Feature) Matching Between Two Objects Using Cross-Correlation 241
References 243
AppendixC Frequently Used MATLAB Functions 244
plot() 244
Description 244
imshow() 244
Description 245
drawnow() 245
Description 246
Remarks 246
Examples 246
stairs() 246
int2str() 246
Description 247
Examples 247
conv() 247
ginput() 248
Interactive Plotting 248
spline() 248
Description 249
Exceptions 250
Example 250
Reference 251
Index 252