PREFACE
1 SIGNALS AND SPECTRA 1
1.1 Digital Communication Signal Processing, 3
1.1.1 Why Digital?, 3
1.1.2 Typical Block Diagram and Transformations, 4
1.1.3 Basic Digital Communication Nomenclature, 11
1.1.4 Digital versus Analog Performance Criteria, 13
1.2 Classification of Signals, 14
1.2.1 Deterministic and Random Signals, 14
1.2.2 Periodic and Nonperiodic Signals, 14
1.2.3 Analog and Discrete Signals, 14
1.2.4 Energy and Power Signals, 14
1.2.5 The Unit Impulse Function, 16
1.3 Spectral Density, 16
1.3.1 Energy Spectral Density, 17
1.3.2 Power Spectral Density, 17
1.4 Autocorrelation, 19
1.4.1 Autocorrelation of an Energy Signal, 19
1.4.2 Autocorrelation of a Periodic (Power) Signal, 20
1.5 Random Signals, 20
1.5.1 Random Variables, 20
1.5.2 Random Processes, 22
1.5.3 Time Averaging and Ergodicity, 25
1.5.4 Power Spectral Density of a Random Process, 26
1.5.5 Noise in Communication Systems, 30
1.6 Signal Transmission through Linear Systems, 33
1.6.1 Impulse Response, 34
1.6.2 Frequency Transfer Function, 35
1.6.3 Distortionless Transmission, 36
1.6.4 Signals, Circuits, and Spectra, 42
1.7 Bandwidth of Digital Data, 45
1.7.1 Baseband versus Bandpass, 45
1.7.2 The Bandwidth Dilemma, 47
1.8 Conclusion, 51
2 FORMATTING AND BASEBAND MODULATION 55
2.1 Baseband Systems, 56
2.2 Formatting Textual Data (Character Coding), 58
2.3 Messages, Characters, and Symbols, 61
2.3.1 Example of Messages, Characters, and Symbols, 61
2.4 Formatting Analog Information, 62
2.4.1 The Sampling Theorem, 63
2.4.2 Aliasing, 69
2.4.3 Why Oversample? 72
2.4.4 Signal Interface for a Digital System, 75
2.5 Sources of Corruption, 76
2.5.1 Sampling and Quantizing Effects, 76
2.5.2 Channel Effects, 77
2.5.3 Signal-to-Noise Ratio for Quantized Pulses, 78
2.6 Pulse Code Modulation, 79
2.7 Uniform and Nonuniform Quantization, 81
2.7.1 Statistics of Speech Amplitudes, 81
2.7.2 Nonuniform Quantization, 83
2.7.3 Companding Characteristics, 84
2.8 Baseband Modulation, 85
2.8.1 Waveform Representation of Binary Digits, 85
2.8.2 PCM Waveform Types, 85
2.8.3 Spectral Attributes of PCM Waveforms, 89
2.8.4 Bits per PCM Word and Bits per Symbol, 90
2.8.5 M-ary Pulse Modulation Waveforms, 91
2.9 Correlative Coding, 94
2.9.1 Duobinary Signaling, 94
2.9.2 Duobinary Decoding, 95
2.9.3 Precoding, 96
2.9.4 Duobinary Equivalent Transfer Function, 97
2.9.5 Comparison of Binary with Duobinary Signaling, 98
2.9.6 Polybinary Signaling, 99
2.10 Conclusion, 100
3 BASEBAND DEMODULATION/DETECTION 104
3.1 Signals and Noise, 106
3.1.1 Error-Performance Degradation in Communication Systems, 106
3.1.2 Demodulation and Detection, 107
3.1.3 A Vectorial View of Signals and Noise, 110
3.1.4 The Basic SNR Parameter for Digital Communication Systems, 117
3.1.5 Why Eb/N0 Is a Natural Figure of Merit, 118
3.2 Detection of Binary Signals in Gaussian Noise, 119
3.2.1 Maximum Likelihood Receiver Structure, 119
3.2.2 The Matched Filter, 122
3.2.3 Correlation Realization of the Matched Filter, 124
3.2.4 Optimizing Error Performance, 127
3.2.5 Error Probability Performance of Binary Signaling, 131
3.3 Intersymbol Interference, 136
3.3.1 Pulse Shaping to Reduce ISI, 138
3.3.2 Two Types of Error-Performance Degradation, 142
3.3.3 Demodulation/Detection of Shaped Pulses, 145
3.4 Equalization, 149
3.4.1 Channel Characterization, 149
3.4.2 Eye Pattern, 151
3.4.3 Equalizer Filter Types, 152
3.4.4 Preset and Adaptive Equalization, 158
3.4.5 Filter Update Rate, 160
3.5 Conclusion, 161
4 BANDPASS MODULATION AND DEMODULATION/
DETECTION 167
4.1 Why Modulate? 168
4.2 Digital Bandpass Modulation Techniques, 169
4.2.1 Phasor Representation of a Sinusoid, 171
4.2.2 Phase Shift Keying, 173
4.2.3 Frequency Shift Keying, 175
4.2.4 Amplitude Shift Keying, 175
4.2.5 Amplitude Phase Keying, 176
4.2.6 Waveform Amplitude Coefficient, 176
4.3 Detection of Signals in Gaussian Noise, 177
4.3.1 Decision Regions, 177
4.3.2 Correlation Receiver, 178
4.4 Coherent Detection, 183
4.4.1 Coherent Detection of PSK, 183
4.4.2 Sampled Matched Filter, 184
4.4.3 Coherent Detection of Multiple Phase Shift Keying, 188
4.4.4 Coherent Detection of FSK, 191
4.5 Noncoherent Detection, 194
4.5.1 Detection of Differential PSK, 194
4.5.2 Binary Differential PSK Example, 196
4.5.3 Noncoherent Detection of FSK, 198
4.5.4 Required Tone Spacing for Noncoherent Orthogonal FSK, 200
4.6 Complex Envelope, 204
4.6.1 Quadrature Implementation of a Modulator, 205
4.6.2 D8PSK Modulator Example, 206
4.6.3 D8PSK Demodulator Example, 208
4.7 Error Performance for Binary Systems, 209
4.7.1 Probability of Bit Error for Coherently Detected BPSK, 209
4.7.2 Probability of Bit Error for Coherently Detected
Differentially Encoded Binary PSK, 211
4.7.3 Probability of Bit Error for Coherently Detected
Binary Orthogonal FSK, 213
4.7.4 Probability of Bit Error for Noncoherently Detected
Binary Orthogonal FSK, 213
4.7.5 Probability of Bit Error for Binary DPSK, 216
4.7.6 Comparison of Bit Error Performance for Various
Modulation Types, 218
4.8 M-ary Signaling and Performance, 219
4.8.1 Ideal Probability of Bit Error Performance, 219
4.8.2 M-ary Signaling, 220
4.8.3 Vectorial View of MPSK Signaling, 222
4.8.4 BPSK and QPSK Have the Same Bit Error Probability, 223
4.8.5 Vectorial View of MFSK Signaling, 225
4.9 Symbol Error Performance for M-ary Systems (M > 2), 229
4.9.1 Probability of Symbol Error for MPSK, 229
4.9.2 Probability of Symbol Error for MFSK, 230
4.9.3 Bit Error Probability versus Symbol Error Probability
for Orthogonal Signals, 232
4.9.4 Bit Error Probability versus Symbol Error Probability
for Multiple Phase Signaling, 234
4.9.5 Effects of Intersymbol Interference, 235
4.10 Conclusion, 236
5 COMMUNICATIONS LINK ANALYSIS 242
5.1 What the System Link Budget Tells the System Engineer, 243
5.2 The Channel, 244
5.2.1 The Concept of Free Space, 244
5.2.2 Error-Performance Degradation, 245
5.2.3 Sources of Signal Loss and Noise, 245
5.3 Received Signal Power and Noise Power, 250
5.3.1 The Range Equation, 250
5.3.2 Received Signal Power as a Function of Frequency, 254
5.3.3 Path Loss is Frequency Dependent, 256
5.3.4 Thermal Noise Power, 258
5.4 Link Budget Analysis, 259
5.4.1 Two Eb/N0 Values of Interest, 262
5.4.2 Link Budgets are Typically Calculated in Decibels, 263
5.4.3 How Much Link Margin is Enough? 264
5.4.4 Link Availability, 266
5.5 Noise Figure, Noise Temperature, and System Temperature, 270
5.5.1 Noise Figure, 270
5.5.2 Noise Temperature, 273
5.5.3 Line Loss, 274
5.5.4 Composite Noise Figure and Composite Noise Temperature, 276
5.5.5 System Effective Temperature, 277
5.5.6 Sky Noise Temperature, 282
5.6 Sample Link Analysis, 286
5.6.1 Link Budget Details, 287
5.6.2 Receiver Figure of Merit, 289
5.6.3 Received Isotropic Power, 289
5.7 Satellite Repeaters, 290
5.7.1 Nonregenerative Repeaters, 291
5.7.2 Nonlinear Repeater Amplifiers, 295
5.8 System Trade-Offs, 296
5.9 Conclusion, 297
6 CHANNEL CODING: PART 1 304
6.1 Waveform Coding and Structured Sequences, 305
6.1.1 Antipodal and Orthogonal Signals, 307
6.1.2 M-ary Signaling, 308
6.1.3 Waveform Coding, 309
6.1.4 Waveform-Coding System Example, 313
6.2 Types of Error Control, 315
6.2.1 Terminal Connectivity, 315
6.2.2 Automatic Repeat Request, 316
6.3 Structured Sequences, 317
6.3.1 Channel Models, 318
6.3.2 Code Rate and Redundancy, 320
6.3.3 Parity Check Codes, 321
6.3.4 Why Use Error-Correction Coding? 323
6.4 Linear Block Codes, 328
6.4.1 Vector Spaces, 329
6.4.2 Vector Subspaces, 329
6.4.3 A (6, 3) Linear Block Code Example, 330
6.4.4 Generator Matrix, 331
6.4.5 Systematic Linear Block Codes, 333
6.4.6 Parity-Check Matrix, 334
6.4.7 Syndrome Testing, 335
6.4.8 Error Correction, 336
6.4.9 Decoder Implementation, 340
6.5 Error-Detecting and Correcting Capability, 342
6.5.1 Weight and Distance of Binary Vectors, 342
6.5.2 Minimum Distance of a Linear Code, 343
6.5.3 Error Detection and Correction, 343
6.5.4 Visualization of a 6-Tuple Space, 347
6.5.5 Erasure Correction, 348
6.6 Usefulness of the Standard Array, 349
6.6.1 Estimating Code Capability, 349
6.6.2 An (n, k) Example, 351
6.6.3 Designing the (8, 2) Code, 352
6.6.4 Error Detection versus Error Correction Trade-Offs, 352
6.6.5 The Standard Array Provides Insight, 356
6.7 Cyclic Codes, 356
6.7.1 Algebraic Structure of Cyclic Codes, 357
6.7.2 Binary Cyclic Code Properties, 358
6.7.3 Encoding in Systematic Form, 359
6.7.4 Circuit for Dividing Polynomials, 360
6.7.5 Systematic Encoding with an (n - k)-Stage Shift Register, 363
6.7.6 Error Detection with an (n - k)-Stage Shift Register, 365
6.8 Well-Known Block Codes, 366
6.8.1 Hamming Codes, 366
6.8.2 Extended Golay Code, 369
6.8.3 BCH Codes, 370
6.9 Conclusion, 374
7 CHANNEL CODING: PART 2 381
7.1 Convolutional Encoding, 382
7.2 Convolutional Encoder Representation, 384
7.2.1 Connection Representation, 385
7.2.2 State Representation and the State Diagram, 389
7.2.3 The Tree Diagram, 391
7.2.4 The Trellis Diagram, 393
7.3 Formulation of the Convolutional Decoding Problem, 395
7.3.1 Maximum Likelihood Decoding, 395
7.3.2 Channel Models: Hard versus Soft Decisions, 396
7.3.3 The Viterbi Convolutional Decoding Algorithm, 401
7.3.4 An Example of Viterbi Convolutional Decoding, 401
7.3.5 Decoder Implementation, 405
7.3.6 Path Memory and Synchronization, 408
7.4 Properties of Convolutional Codes, 408
7.4.1 Distance Properties of Convolutional Codes, 408
7.4.2 Systematic and Nonsystematic Convolutional Codes, 413
7.4.3 Catastrophic Error Propagation in Convolutional Codes, 414
7.4.4 Performance Bounds for Convolutional Codes, 415
7.4.5 Coding Gain, 416
7.4.6 Best Known Convolutional Codes, 418
7.4.7 Convolutional Code Rate Trade-Off, 420
7.4.8 Soft-Decision Viterbi Decoding, 420
7.5 Other Convolutional Decoding Algorithms, 422
7.5.1 Sequential Decoding, 422
7.5.2 Comparisons and Limitations of Viterbi and Sequential Decoding, 425
7.5.3 Feedback Decoding, 427
7.6 Conclusion, 429
8 CHANNEL CODING: PART 3 436
8.1 ReedDSolomon Codes, 437
8.1.1 ReedDSolomon Error Probability, 438
8.1.2 Why RDS Codes Perform Well Against Burst Noise, 441
8.1.3 RDS Performance as a Function of Size,
Redundancy, and Code Rate, 441
8.1.4 Finite Fields, 445
8.1.5 ReedDSolomon Encoding, 450
8.1.6 ReedDSolomon Decoding, 454
8.2 Interleaving and Concatenated Codes, 461
8.2.1 Block Interleaving, 463
8.2.2 Convolutional Interleaving, 466
8.2.3 Concatenated Codes, 468
8.3 Coding and Interleaving Applied to the Compact Disc
Digital Audio System, 469
8.3.1 CIRC Encoding, 470
8.3.2 CIRC Decoding, 472
8.3.3 Interpolation and Muting, 474
8.4 Turbo Codes, 475
8.4.1 Turbo Code Concepts, 477
8.4.2 Log-Likelihood Algebra, 481
8.4.3 Product Code Example, 482
8.4.4 Encoding with Recursive Systematic Codes, 488
8.4.5 A Feedback Decoder, 493
8.4.6 The MAP Decoding Algorithm, 498
8.4.7 MAP Decoding Example, 504
8.5 Conclusion, 509
Appendix 8A The Sum of Log-Likelihood Ratios, 510
9 MODULATION AND CODING TRADE-OFFS 520
9.1 Goals of the Communications System Designer, 521
9.2 Error Probability Plane, 522
9.3 Nyquist Minimum Bandwidth, 524
9.4 ShannonDHartley Capacity Theorem, 525
9.4.1 Shannon Limit, 528
9.4.2 Entropy, 529
9.4.3 Equivocation and Effective Transmission Rate, 532
9.5 Bandwidth Efficiency Plane, 534
9.5.1 Bandwidth Efficiency of MPSK and MFSK Modulation, 535
9.5.2 Analogies Between Bandwidth-Efficiency
and Error Probability Planes, 536
9.6 Modulation and Coding Trade-Offs, 537
9.7 Defining, Designing, and Evaluating Digital
Communication Systems, 538
9.7.1 M-ary Signaling, 539
9.7.2 Bandwidth-Limited Systems, 540
9.7.3 Power-Limited Systems, 541
9.7.4 Requirements for MPSK and MFSK Signaling, 542
9.7.5 Bandwidth-Limited Uncoded System Example, 543
9.7.6 Power-Limited Uncoded System Example, 545
9.7.7 Bandwidth-Limited and Power-Limited
Coded System Example, 547
9.8 Bandwidth-Efficient Modulation, 555
9.8.1 QPSK and Offset QPSK Signaling, 555
9.8.2 Minimum Shift Keying, 559
9.8.3 Quadrature Amplitude Modulation, 563
9.9 Modulation and Coding for Bandlimited Channels, 566
9.9.1 Commercial Telephone Modems, 567
9.9.2 Signal Constellation Boundaries, 568
9.9.3 Higher Dimensional Signal Constellations, 569
9.9.4 Higher-Density Lattice Structures, 572
9.9.5 Combined Gain: N-Sphere Mapping and Dense Lattice, 573
9.10 Trellis-Coded Modulation, 573
9.10.1 The Idea Behind Trellis-Coded Modulation (TCM), 574
9.10.2 TCM Encoding, 576
9.10.3 TCM Decoding, 580
9.10.4 Other Trellis Codes, 583
9.10.5 Trellis-Coded Modulation Example, 585
9.10.6 Multi-Dimensional Trellis-Coded Modulation, 589
9.11 Conclusion, 590
10 SYNCHRONIZATION 598
10.1 Introduction, 599
10.1.1 Synchronization Defined, 599
10.1.2 Costs versus Benefits, 601
10.1.3 Approach and Assumptions, 602
10.2 Receiver Synchronization, 603
10.2.1 Frequency and Phase Synchronization, 603
10.2.2 Symbol Synchronization?aDiscrete Symbol Modulations, 625
10.2.3 Synchronization with Continuous-Phase Modulations (CPM), 631
10.2.4 Frame Synchronization, 639
10.3 Network Synchronization, 643
10.3.1 Open-Loop Transmitter Synchronization, 644
10.3.2 Closed-Loop Transmitter Synchronization, 647
10.4 Conclusion, 649
11 MULTIPLEXING AND MULTIPLE ACCESS 656
11.1 Allocation of the Communications Resource, 657
11.1.1 Frequency-Division Multiplexing/Multiple Access, 660
11.1.2 Time-Division Multiplexing/Multiple Access, 665
11.1.3 Communications Resource Channelization, 668
11.1.4 Performance Comparison of FDMA and TDMA, 668
11.1.5 Code-Division Multiple Access, 672
11.1.6 Space-Division and Polarization-Division Multiple Access, 674
11.2 Multiple Access Communications System and Architecture, 676
11.2.1 Multiple Access Information Flow, 677
11.2.2 Demand Assignment Multiple Access, 678
11.3 Access Algorithms, 678
11.3.1 ALOHA, 678
11.3.2 Slotted ALOHA, 682
11.3.3 Reservation-ALOHA, 683
11.3.4 Performance Comparison of S-ALOHA and R-ALOHA, 684
11.3.5 Polling Techniques, 686
11.4 Multiple Access Techniques Employed with INTELSAT, 689
11.4.1 Preassigned FDM/FM/FDMA or MCPC Operation, 690
11.4.2 MCPC Modes of Accessing an INTELSAT Satellite, 690
11.4.3 SPADE Operation, 693
11.4.4 TDMA in INTELSAT, 698
11.4.5 Satellite-Switched TDMA in INTELSAT, 704
11.5 Multiple Access Techniques for Local Area Networks, 708
11.5.1 Carrier-Sense Multiple Access Networks, 708
11.5.2 Token-Ring Networks, 710
11.5.3 Performance Comparison of CSMA/CD and Token-Ring Networks, 711
11.6 Conclusion, 713
12 SPREAD-SPECTRUM TECHNIQUES 718
12.1 Spread-Spectrum Overview, 719
12.1.1 The Beneficial Attributes of Spread-Spectrum Systems, 720
12.1.2 A Catalog of Spreading Techniques, 724
12.1.3 Model for Direct-Sequence Spread-Spectrum
Interference Rejection, 726
12.1.4 Historical Background, 727
12.2 Pseudonoise Sequences, 728
12.2.1 Randomness Properties, 729
12.2.2 Shift Register Sequences, 729
12.2.3 PN Autocorrelation Function, 730
12.3 Direct-Sequence Spread-Spectrum Systems, 732
12.3.1 Example of Direct Sequencing, 734
12.3.2 Processing Gain and Performance, 735
12.4 Frequency Hopping Systems, 738
12.4.1 Frequency Hopping Example, 740
12.4.2 Robustness, 741
12.4.3 Frequency Hopping with Diversity, 741
12.4.4 Fast Hopping versus Slow Hopping, 742
12.4.5 FFH/MFSK Demodulator, 744
12.4.6 Processing Gain, 745
12.5 Synchronization, 745
12.5.1 Acquisition, 746
12.5.2 Tracking, 751
12.6 Jamming Considerations, 754
12.6.1 The Jamming Game, 754
12.6.2 Broadband Noise Jamming, 759
12.6.3 Partial-Band Noise Jamming, 760
12.6.4 Multiple-Tone Jamming, 763
12.6.5 Pulse Jamming, 763
12.6.6 Repeat-Back Jamming, 765
12.6.7 BLADES System, 768
12.7 Commercial Applications, 769
12.7.1 Code-Division Multiple Access, 769
12.7.2 Multipath Channels, 771
12.7.3 The FCC Part 15 Rules for Spread-Spectrum Systems, 772
12.7.4 Direct Sequence versus Frequency Hopping, 773
12.8 Cellular Systems, 775
12.8.1 Direct Sequence CDMA, 776
12.8.2 Analog FM versus TDMA versus CDMA, 779
12.8.3 Interference-Limited versus Dimension-Limited Systems, 781
12.8.4 IS-95 CDMA Digital Cellular System, 782
12.9 Conclusion, 795
13 SOURCE CODING 803
13.1 Sources, 804
13.1.1 Discrete Sources, 804
13.1.2 Waveform Sources, 809
13.2 Amplitude Quantizing, 811
13.2.1 Quantizing Noise, 813
13.2.2 Uniform Quantizing, 816
13.2.3 Saturation, 820
13.2.4 Dithering, 823
13.2.5 Nonuniform Quantizing, 826
13.3 Differential Pulse-Code Modulation, 835
13.3.1 One-Tap Prediction, 838
13.3.2 N-Tap Prediction, 839
13.3.3 Delta Modulation, 841
13.3.4 Sigma-Delta Modulation, 842
13.3.5 Sigma-Delta A-to-D Converter (ADC), 847
13.3.6 Sigma-Delta D-to-A Converter (DAC), 848
13.4 Adaptive Prediction, 850
13.4.1 Forward Prediction, 851
13.4.2 Synthesis/Analysis Coding, 852
13.5 Block Coding, 853
13.5.1 Vector Quantizing, 854
13.6 Transform Coding, 856
13.6.1 Quantization for Transform Coding, 857
13.6.2 Subband Coding, 857
13.7 Source Coding for Digital Data, 859
13.7.1 Properties of Codes, 860
13.7.2 Huffman Codes, 862
13.7.3 Run-Length Codes, 866
13.8 Examples of Source Coding, 870
13.8.1 Audio Compression, 870
13.8.2 Image Compression, 875
13.9 Conclusion, 884
14 ENCRYPTION AND DECRYPTION 890
14.1 Models, Goals, and Early Cipher Systems, 891
14.1.1 A Model of the Encryption and Decryption Process, 893
14.1.2 System Goals, 893
14.1.3 Classic Threats, 893
14.1.4 Classic Ciphers, 894
14.2 The Secrecy of a Cipher System, 897
14.2.1 Perfect Secrecy, 897
14.2.2 Entropy and Equivocation, 900
14.2.3 Rate of a Language and Redundancy, 902
14.2.4 Unicity Distance and Ideal Secrecy, 902
14.3 Practical Security, 905
14.3.1 Confusion and Diffusion, 905
14.3.2 Substitution, 905
14.3.3 Permutation, 907
14.3.4 Product Cipher Systems, 908
14.3.5 The Data Encryption Standard, 909
14.4 Stream Encryption, 915
14.4.1 Example of Key Generation Using a Linear
Feedback Shift Register, 916
14.4.2 Vulnerabilities of Linear Feedback Shift Registers, 917
14.4.3 Synchronous and Self-Synchronous Stream
Encryption Systems, 919
14.5 Public Key Cryptosystems, 920
14.5.1 Signature Authentication using a Public Key Cryptosystem, 921
14.5.2 A Trapdoor One-Way Function, 922
14.5.3 The RivestDShamirDAdelman Scheme, 923
14.5.4 The Knapsack Problem, 925
14.5.5 A Public Key Cryptosystem based on a Trapdoor Knapsack, 927
14.6 Pretty Good Privacy, 929
14.6.1 Triple-DES, CAST, and IDEA, 931
14.6.2 Diffie-Hellman (Elgamal Variation) and RSA, 935
14.6.3 PGP Message Encryption, 936
14.6.4 PGP Authentication and Signature, 937
14.7 Conclusion, 940
15 FADING CHANNELS 944
15.1 The Challenge of Communicating over Fading Channels, 945
15.2 Characterizing Mobile-Radio Propagation, 947
15.2.1 Large-Scale Fading, 951
15.2.2 Small-Scale Fading, 953
15.3 Signal Time-Spreading, 958
15.3.1 Signal Time-Spreading Viewed in the Time-Delay Domain, 958
15.3.2 Signal Time-Spreading Viewed in the Frequency Domain, 960
15.3.3 Examples of Flat Fading and Frequency-Selective Fading, 965
15.4 Time Variance of the Channel Caused by Motion, 966
15.4.1 Time Variance Viewed in the Time Domain, 966
15.4.2 Time Variance Viewed in the Doppler-Shift Domain, 969
15.4.3 Performance over a Slow- and Flat-Fading Rayleigh Channel, 975
15.5 Mitigating the Degradation Effects of Fading, 978
15.5.1 Mitigation to Combat Frequency-Selective Distortion, 980
15.5.2 Mitigation to Combat Fast-Fading Distortion, 982
15.5.3 Mitigation to Combat Loss in SNR, 983
15.5.4 Diversity Techniques, 984
15.5.5 Modulation Types for Fading Channels, 987
15.5.6 The Role of an Interleaver, 988
15.6 Summary of the Key Parameters Characterizing Fading Channels, 992
15.6.1 Fast Fading Distortion: Case 1, 992
15.6.2 Frequency-Selective Fading Distortion: Case 2, 993
15.6.3 Fast-Fading and Frequency-Selective Fading Distortion: Case 3, 993
15.7 Applications: Mitigating the Effects of Frequency-Selective Fading, 996
15.7.1 The Viterbi Equalizer as Applied to GSM, 996
15.7.2 The Rake Receiver as Applied to Direct-Sequence
Spread-Spectrum (DS/SS) Systems, 999
15.8 Conclusion, 1001
A A REVIEW OF FOURIER TECHNIQUES 1012
A.1 Signals, Spectra, and Linear Systems, 1012
A.2 Fourier Techniques for Linear System Analysis, 1012
A.2.1 Fourier Series Transform, 1014
A.2.2 Spectrum of a Pulse Train, 1018
A.2.3 Fourier Integral Transform, 1020
A.3 Fourier Transform Properties, 1021
A.3.1 Time Shifting Property, 1022
A.3.2 Frequency Shifting Property, 1022
A.4 Useful Functions, 1023
A.4.1 Unit Impulse Function, 1023
A.4.2 Spectrum of a Sinusoid, 1023
A.5 Convolution, 1025
A.5.1 Graphical Example of Convolution, 1027
A.5.2 Time Convolution Property, 1028
A.5.3 Frequency Convolution Property, 1030
A.5.4 Convolution of a Function with a Unit Impulse, 1030
A.5.5 Demodulation Application of Convolution, 1031
A.6 Tables of Fourier Transforms and Operations, 1033
B FUNDAMENTALS OF STATISTICAL DECISION THEORY 1035
B.1 Bayes?ˉ Theorem, 1035
B.1.1 Discrete Form of Bayes?ˉ Theorem, 1036
B.1.2 Mixed Form of Bayes?ˉ Theorem, 1038
B.2 Decision Theory, 1040
B.2.1 Components of the Decision Theory Problem, 1040
B.2.2 The Likelihood Ratio Test and the Maximum
A Posteriori Criterion, 1041
B.2.3 The Maximum Likelihood Criterion, 1042
B.3 Signal Detection Example, 1042
B.3.1 The Maximum Likelihood Binary Decision, 1042
B.3.2 Probability of Bit Error, 1044
C RESPONSE OF A CORRELATOR TO WHITE NOISE 1047
D OFTEN-USED IDENTITIES 1049
E s-DOMAIN, z-DOMAIN AND DIGITAL FILTERING 1051
E.1 The Laplace Transform, 1051
E.1.1 Standard Laplace Transforms, 1052
E.1.2 Laplace Transform Properties, 1053
E.1.3 Using the Laplace Transform, 1054
E.1.4 Transfer Function, 1055
E.1.5 RC Circuit Low Pass Filtering, 1056
E.1.6 Poles and Zeroes, 1056
E.1.7 Linear System Stability, 1057
E.2 The z-Transform, 1058
E.2.1 Calculating the z-Transform, 1058
E.2.2 The Inverse z-Transform, 1059
E.3 Digital Filtering, 1060
E.3.1 Digital Filter Transfer Function, 1061
E.3.2 Single Pole Filter Stability, 1062
E.3.3 General Digital Filter Stability, 1063
E.3.4 z-Plane Pole-Zero Diagram and the Unit Circle, 1063
E.3.5 Discrete Fourier Transform of Digital Filter Impulse Response, 1064
E.4 Finite Impulse Response Filter Design, 1065
E.4.1 FIR Filter Design, 1065
E.4.2 The FIR Differentiator, 1067
E.5 Infinite Impulse Response Filter Design, 1069
E.5.1 Backward Difference Operator, 1069
E.5.2 IIR Filter Design using the Bilinear Transform, 1070
E.5.3 The IIR Integrator, 1071
F LIST OF SYMBOLS 1072
INDEX 1075
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