Chapter 1: Fourier Analysis 1 1.1 CONTINUOUS-TIME FOURIER SERIES (CTFS)................................................................... 2 1.2 PROPERTIES OF CTFS............................................................................................................... 6 1.2.1 Time-Shifting Property....................................................................................................... 6 1.2.2 Frequency-Shifting Property ............................................................................................ 6 1.2.3 Modulation Property......................................................................................................... 6 1.3 CONTINUOUS-TIME FOURIER TRANSFORM (CTFT)....................................................... 7 1.4 PROPERTIES OF CTFT............................................................................................................. 13 1.4.1 Linearity............................................................................................................................ 13 1.4.2 Conjugate Symmetry........................................................................................................ 13 1.4.3 Real Translation (Time Shifting) and Complex Translation (Frequency Shifting)..... 14 1.4.4 Real Convolution and Correlation................................................................................... 14 1.4.5 Complex Convolution – Modulation/Windowing.......................................................... 14 1.4.6 Duality............................................................................................................................... 17 1.4.7 Parseval Relation - Power Theorem................................................................................ 18 1.5 DISCRETE-TIME FOURIER TRANSFORM (DTFT)............................................................ 18 1.6 DISCRETE-TIME FOURIER SERIES - DFS/DFT.................................................................. 19 1.7 SAMPLING THEOREM............................................................................................................. 21 1.7.1 Relationship between CTFS and DFS ........................................................................... 21 1.7.2 Relationship between CTFT and DTFT.......................................................................... 27 1.7.3 Sampling Theorem............................................................................................................ 27 1.8 POWER, ENERGY, AND CORRELATION............................................................................ 29 1.9 LOWPASS EQUIVALENT OF BANDPASS SIGNALS........................................................ 30 Chapter 2: PROBABILITY AND RANDOM PROCESSES 39 2.1 PROBABILITY........................................................................................................................... 39 2.1.1 Definition of Probability................................................................................................. 39 2.1.2 Joint Probability and Conditional Probability............................................................... 40 2.1.3 Probability Distribution/Density Function..................................................................... 41 2.1.4 Joint Probability Density Function................................................................................. 41 2.1.5 Condtional Probability Density Function...................................................................... 41 2.1.6 Independence................................................................................................................... 41 2.1.7 Function of a Random Variable...................................................................................... 42 2.1.8 Expectation, Covariance, and Correlation..................................................................... 43 2.1.9 Conditional Expectation.................................................................................................. 47 2.1.10 Central Limit Theorem - Normal Convergence Theorem............................................. 47 2.1.11 Random Processes............................................................................................................ 49 2.1.12 Stationary Processes and Ergodic Processes.................................................................. 51 2.1.13 Power Spectral Density (PSD)......................................................................................... 53 2.1.14 White Noise and Colored Noise...................................................................................... 53 2.2 LINEAR FILTERING OF A RANDOM PROCESS................................................................ 57 2.3 PSD OF A RANDOM PROCESS.............................................................................................. 58 2.4 FADING EFFECT OF A MULTIPATH CHANNEL............................................................... 58 Chapter 3: ANALOG MODULATION 71 3.1 AMPLITUDE MODULATION (AM)....................................................................................... 71 3.1.1 DSB (Double Sideband)-AM (Amplitude Modulation)............................................... 71 3.1.2 Conventional AM (Amplitude Modulation)................................................................ 75 3.1.3 SSB (Single Sideband)-AM(Amplitude Modulation)................................................. 78 3.2 ANGLE MODULATION (AGM) - FREQUENCY/PHASE MODULATIONS .................. 82 Chapter 4: ANALOG-TO-DIGITAL CONVERSION 87 4.1 QUANTIZATION........................................................................................................................ 87 4.1.1 Uniform Quantization..................................................................................................... 88 4.1.2 Non-uniform Quantization.............................................................................................. 89 4.1.3 Non-uniform Quantization Considering the Absolute Errors .................................... 91 4.2 Pulse Code Modulation (PCM)................................................................................................... 95 4.3 Differential Pulse Code Modulation (DPCM)........................................................................... 97 4.4 Delta Modulation (DM)............................................................................................................. 100 Chapter 5: BASEBAND TRANSMISSION 107 5.1 RECEIVER (RCVR) and SNR ............................................................................................... 107 5.1.1 Receiver of RC Filter Type.......................................................................................... 109 5.1.2 Receiver of Matched Filter Type................................................................................. 110 5.1.3 Signal Correlator........................................................................................................... 112 5.2 PROBABILITY OF ERROR WITH SIGNALING................................................................ 114 5.2.1 Antipodal (Bipolar) Signaling...................................................................................... 114 5.2.2 On-Off Keying (OOK)/Unipolar Signaling................................................................. 118 5.2.3 Orthogonal Signaling.................................................................................................... 119 5.2.4 Signal Constellation Diagram...................................................................................... 121 5.2.5 Simulation of Binary Communication......................................................................... 123 5.2.6 Multi-Level(amplitude) PAM Signaling..................................................................... 127 5.2.7 Multi-Dimensional Signaling....................................................................................... 129 5.2.8 Bi-Orthogonal Signaling............................................................................................... 133 Chapter 6: BANDLIMITED CHANNEL AND EQUALIZER 139 6.1 BANDLIMITED CHANNEL................................................................................................... 139 6.1.1 Nyquist Bandwidth........................................................................................................ 139 6.1.2 Raised-Cosine Frequency Response............................................................................ 141 6.1.3 Partial Respone Signaling - Duobinary Signaling...................................................... 143 6.2 EQUALIZER............................................................................................................................. 148 6.2.1 Zero-Forcing Equalizer (ZFE)...................................................................................... 148 6.2.2 MMSE Equalizer (MMSEE)........................................................................................ 151 6.2.3 Adaptive Equalizer (ADE)........................................................................................... 154 6.2.4 Decision Feedback Equalizer (DFE)............................................................................ 155 Chapter 7: BANDPASS TRANSMISSION 169 7.1 AMPLITUDE SHIFT KEYING (ASK)................................................................................... 169 7.2 FREQUENCY SHIFT KEYING (FSK)................................................................................... 178 7.3 PHASE SHIFT KEYING (PSK)............................................................................................... 187 7.4 DIFFERENTIAL PHASE SHIFT KEYING (DPSK)............................................................. 190 7.5 QUADRATURE AMPLITUDE MODULATION (QAM).................................................... 195 7.6 COMPARISON OF VARIOUS SIGNALINGS...................................................................... 200 Chapter 8: CARRIER RECOVERY AND SYMBOL SYNCHRONIZATION 227 8.1 INTRODUCTION..................................................................................................................... 227 8.2 PLL (PHSE-LOCKED LOOP)................................................................................................. 228 8.3 ESTIMATION OF CARRIER PHASE USING PLL............................................................. 233 8.4 CARRIER PHASE RECOVERY............................................................................................. 235 8.4.1 Carrier Phase Recovery Using a Squaring Loop for BPSK Signals.......................... 235 8.4.2 Carrier Phase Recovery Using Costas Loop for PSK Signals.................................... 237 8.4.3 Carrier Phase Recovery for QAM Signals.................................................................. 240 8.5 SYMBOL SYNCHRONIZATION (TIMING RECOVERY)................................................ 243 8.5.1 Early-Late Gate Timing Recovery for BPSK Signals................................................ 243 8.5.2 NDA-ELD Synchronizer for PSK Signals.................................................................. 246 Chapter 9: INFORMATION AND CODING 257 9.1 MEASURE OF INFORMATION - ENTROPY...................................................................... 257 9.2 SOURCE CODING................................................................................................................... 259 9.2.1 Huffman Coding............................................................................................................ 259 9.2.2 Lempel-Zip-Welch Coding........................................................................................... 262 9.2.3 Source Coding vs. Channel Coding............................................................................. 265 9.3 CHANNEL MODEL AND CHANNEL CAPACITY............................................................ 266 9.4 CHANNEL CODING................................................................................................................ 271 9.4.1 Waveform Coding......................................................................................................... 272 9.4.2 Linear Block Coding..................................................................................................... 273 9.4.3 Cyclic Coding................................................................................................................ 282 9.4.4 Convolutional Coding and Viterbi Decoding.............................................................. 287 9.4.5 Trellis-Coded Modulation (TCM)................................................................................ 296 9.4.6 Turbo Coding................................................................................................................. 300 9.4.7 Low-Density Parity-Check (LDPC) Coding............................................................... 311 9.4.8 Differential Space-Time Block Coding (DSTBC)...................................................... 316 9.5 CODING GAIN ....................................................................................................................... 319 Chapter 10: SPREAD-SPECTRUM SYSTEM 339 10.1 PN (Pseudo Noise) Sequence..................................................................................................... 339 10.2 DS-SS (Direct Sequence Spread Spectrum)............................................................................. 347 10.3 FH-SS (Frequency Hopping Spread Spectrum)........................................................................ 352 Chapter 11: OFDM SYSTEM 359 11.1 OVERVIEW OF OFDM......................................................................................................... 359 11.2 FREQUENCY BAND AND BANDWIDTH EFFICIENCY OF OFDM............................ 363 11.3 CARRIER RECOVERY AND SYMBOL SYNCHRONIZATION.......................................... 364 11.4 CHANNEL ESTIMATION AND EQUALIZATION.......................................................... 381 11.5 INTERLEAVING AND DEINTERLEAVING..................................................................... 384 11.6 PUNCTURING AND DEPUNCTURING............................................................................ 386 11.7 IEEE STANDARD 802.11A - 1999....................................................................................... 388