Contents 1 Preview and Introduction... 1 1.1 Process of Communication..... 1 1.2 General Definition of Signal..... 3 1.3 Time-Value Definition of Signals Analog and Digital..... 6 1.3.1 Continuous Time Continuous Valued Signal...... 7 1.3.2 Discrete Time Continuous Valued Signal.... 7 1.3.3 Discrete Time Discrete Valued Signal...... 7 1.4 AnalogandDigitalCommunicationSystems... 8 1.5 ElementsofDigitalCommunicationSystem... 10 1.6 MATLABPrograms... 11 1.6.1 Time and Frequency Domain Representation of Signals. 11 1.6.2 CTSV, DTCV, DTDV Signals..... 12 References... 13 2 Waveform Encoding... 15 2.1 Introduction... 15 2.2 Pulse Code Modulation (PCM)... 15 2.2.1 Process of Sampling..... 16 2.2.2 Process of Quantization... 22 2.2.3 PCM Transmitter and Receiver.... 24 2.2.4 QuantizationError... 27 2.2.5 Signal to Noise Ratio (SNR) for Quantized Pulses... 29 2.2.6 Non-uniform Quantization: Companding.... 30 2.3 Differential Pulse Code Modulation (DPCM)...... 35 2.3.1 CumulativeErrorinPCM... 35 2.3.2 Prevention of Cumulative Error by Applying Feedback.. 36 2.3.3 HowWeCanPredicttheFuture?... 38 2.3.4 AnalysisofDPCM... 40 2.4 Delta Modulation..... 41 2.4.1 Drawbacks of Delta Modulation.... 43 2.5 Adaptive Delta Modulation..... 44 2.5.1 Song Algorithm... 44 2.5.2 Space-Shuttle Algorithm... 46 xiii
xiv Contents 2.6 Sigma-Delta Modulation (SDM)... 47 2.6.1 Noise Performance...... 48 2.7 Linear Predictive Coder (LPC)... 49 2.7.1 Concept...... 49 2.7.2 Genetic Algorithm Based Approach... 50 2.8 MATLABPrograms... 53 2.8.1 Aliasing... 53 References... 54 3 Digital Baseband Signal Receivers... 55 3.1 Introduction... 55 3.2 Integrate and Dump Type Filter... 56 3.2.1 Noise Power and Variance... 59 3.2.2 FigureofMerit... 61 3.2.3 Probability of Error..... 61 3.3 The Optimum Filter.... 63 3.4 The Matched Filter..... 67 3.4.1 Impulse Response...... 67 3.4.2 Probability of Error..... 67 3.4.3 Properties of Matched Filter...... 70 3.5 TheCorrelator... 72 3.6 SimulinkCommunicationBlockSetExample... 74 References... 75 4 Digital Baseband Signal Transmitter... 77 4.1 Introduction... 77 4.2 Elements of Digital Baseband Communication System..... 77 4.2.1 Formatting..... 78 4.2.2 Regenerative Repeater.... 78 4.3 Properties and Choice of Digital Formats... 80 4.4 LineCoding... 81 4.5 Power Spectrum Density of Different Digital Formats..... 83 4.5.1 Unipolar-NRZ... 86 4.5.2 Unipolar-RZ... 87 4.5.3 Polar-NRZ... 88 4.5.4 Polar-RZ... 89 4.5.5 Bipolar-NRZ... 90 4.5.6 Split-Phase (Manchester)... 91 References... 93 5 Equalization... 95 5.1 Inter-Symbol Interference (ISI)... 95 5.2 Nyquist Criterion for Distortion Less Transmission (Zero ISI).. 97 5.2.1 Criteria in Frequency Domain..... 98 5.2.2 Concept of Ideal Nyquist Channel... 100 5.2.3 Limitations of Ideal Solution: Raised Cosine Spectrum.. 101
Contents xv 5.3 EyePattern... 103 5.3.1 InformationObtainedfromEyePattern... 104 5.4 System Design for Known Channel...... 104 5.5 Linear Equalizer...... 106 5.5.1 Linear Transversal Filter... 106 5.6 Adaptive Equalizer..... 108 References... 110 6 Digital Modulation Techniques... 111 6.1 Introduction... 111 6.2 AmplitudeShiftKeying(ASK)... 112 6.2.1 Mathematical Model..... 113 6.2.2 ASK Modulator... 115 6.2.3 Binary ASK Demodulator... 117 6.3 Frequency Shift Keying (FSK)... 118 6.3.1 Mathematical Model..... 118 6.3.2 BFSK Modulator... 119 6.3.3 FSK Demodulator...... 121 6.4 Binary Phase Shift Keying (BPSK)...... 122 6.4.1 Mathematical Model..... 123 6.4.2 BPSK Modulator... 124 6.4.3 BPSK Demodulator..... 125 6.5 Differential Phase Shift Keying (DPSK)... 125 6.5.1 DPSK Modulator...... 125 6.5.2 DPSK Demodulator..... 127 6.6 Quadrature Phase Shift Keying (QPSK).... 127 6.6.1 Mathematical Model..... 127 6.6.2 QPSK Modulator...... 131 6.6.3 QPSK Demodulator..... 131 6.6.4 OffsetQPSK(OQPSK)... 132 6.7 MinimumShiftKeying(MSK)... 134 6.8 Probability of Error for Different Modulation Schemes..... 136 6.8.1 Probability of Error in ASK...... 136 6.8.2 Probability of Error in FSK...... 137 6.8.3 Probability of Error in PSK...... 138 6.9 MATLABPrograms... 139 6.9.1 QPSKWaveform... 139 6.9.2 MSKWaveform... 140 References... 141 7 Spread Spectrum Modulation... 143 7.1 Introduction... 143 7.2 ProcessingGain... 144 7.3 Pseudo-Noise (PN) Sequence.... 145 7.3.1 Concept: A Hypothetical Experiment...... 145 7.3.2 Generation of PN Sequence...... 146
xvi Contents 7.3.3 Properties of PN Sequence... 147 7.4 Direct Sequence Spread Spectrum (DSSS)... 149 7.4.1 Concept...... 149 7.4.2 DSSS with Coherent BPSK...... 151 7.4.3 Probability of Error Calculation.... 152 7.5 Frequency-Hopped Spread Spectrum..... 155 7.5.1 Concept...... 155 7.5.2 FHSSwithFSK... 157 7.5.3 Rate of Hopping: Fast and Slow.... 159 7.6 Application of Spread Spectrum... 159 7.6.1 GPS (Global Positioning System)... 159 7.7 CDMA (Code Division Multiple Access)... 163 7.7.1 Orthogonal Chip Sequence...... 163 7.7.2 Gold Sequence... 165 7.7.3 PrincipleofOperation... 166 References... 166 8 Information Theory... 169 8.1 Introduction... 169 8.2 Entropy... 171 8.3 RateofInformation... 173 8.4 Information Sources.... 173 8.5 Discrete Memoryless Channel (DMC).... 176 8.5.1 Channel Representation... 176 8.5.2 The Channel Matrix..... 176 8.6 Special Channels...... 177 8.6.1 Lossless Channel... 177 8.6.2 Deterministic Channel.... 178 8.6.3 Noise-Less Channel..... 179 8.6.4 Binary Symmetric Channel (BSC)... 179 8.7 MutualInformation... 182 8.8 Channel Capacity..... 183 8.8.1 Gaussian Channel: Shanon-Hartley Theorem...... 183 8.9 EntropyCoding... 185 8.9.1 Shanon-Fano Coding.... 186 8.9.2 HuffmanCoding... 187 8.10MATLABCode... 188 8.10.1 Convergence of P e in Cascaded BSC...... 188 References... 189 9 Error Control Coding... 191 9.1 Introduction... 191 9.2 Scope of Coding...... 192 9.3 Linear Block Code..... 193 9.3.1 Coding Technique Using Generator Matrix... 193 9.3.2 Syndrome Decoding..... 195
Contents xvii 9.4 Convolutional Code.... 196 9.4.1 Encoder...... 196 9.4.2 StateDiagram... 199 9.4.3 CodeTree... 200 9.4.4 Trellis Diagram... 200 9.4.5 Decoding of Convolutional Code by Viterbi...... 202 9.5 CyclicCode... 204 9.5.1 Concept and Properties... 204 9.5.2 Encoder and Decoder.... 206 9.5.3 Meggitt Decoder... 207 9.6 BCHCode... 207 9.6.1 Simplified BCH Codes.... 208 9.6.2 General BCH Codes..... 210 9.6.3 Properties..... 210 References... 211 Appendix A: Elementary Probability Theory... 213 Appendix B: Convolution and Correlation Some Case Studies... 225 Appendix C: Frequently Used MATLAB Functions... 237 Index... 245
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