Digital Communications

Dr. Bernard Sklar has over 40 years of experience in technical design and management positions at Republic Aviation, Hughes Aircraft, Litton Industries, and The Aerospace Corporation, where he helped develop the MILSTAR satellite system. He is now head of advanced systems at Communications Engineering Services, a consulting company he founded in 1984. He has taught engineering courses at several universities, including UCLA and USC, and has trained professional engineers worldwide. Dr. Fredric J. Harris is a professor of electrical engineering and the CUBIC signal processing chair at San Diego State University and an internationally renowned expert on DSP and communication systems. He is also the co-inventor of the Blackman–Harris filter. He has extensively published many technical papers, the most famous being the seminal 1978 paper “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform.” He is also the author of the textbook Multi-Rate Signal Processing for Communication Systems and the source coding chapter in the previous edition of this book.

• Preface     xxiii Chapter 1  SIGNALS AND SPECTRA     1 1.1 Digital Communication Signal Processing     2 1.1.1 Why Digital?     2 1.1.2 Typical Block Diagram and Transformations     4 1.1.3 Basic Digital Communication Nomenclature     7 1.1.4 Digital Versus Analog Performance Criteria     9 1.2 Classification of Signals     10 1.2.1 Deterministic and Random Signals     10 1.2.2 Periodic and Nonperiodic Signals     10 1.2.3 Analog and Discrete Signals     10 1.2.4 Energy and Power Signals     11 1.2.5 The Unit Impulse Function     12 1.3 Spectral Density     13 1.3.1 Energy Spectral Density     13 1.3.2 Power Spectral Density     14 1.4 Autocorrelation     15 1.4.1 Autocorrelation of an Energy Signal     10 1.4.2 Autocorrelation of a Periodic (Power) Signal     16 1.5 Random Signals     17 1.5.1 Random Variables     17 1.5.2 Random Processes     19 1.5.3 Time Averaging and Ergodicity     21 1.5.4 Power Spectral Density and Autocorrelation of a Random Process     22 1.5.5 Noise in Communication Systems     27 1.6 Signal Transmission Through Linear Systems     30 1.6.1 Impulse Response     30 1.6.2 Frequency Transfer Function     31 1.6.3 Distortionless Transmission     32 1.6.4 Signals, Circuits, and Spectra     39 1.7 Bandwidth of Digital Data     41 1.7.1 Baseband Versus Bandpass     41` 1.7.2 The Bandwidth Dilemma     44 1.8 Conclusion     47 Chapter 2  FORMATTING AND BASEBAND MODULATION     53 2.1 Baseband Systems     54 2.2 Formatting Textual Data (Character Coding)     55 2.3 Messages, Characters, and Symbols     55 2.3.1 Example of Messages, Characters, and Symbols     56 2.4 Formatting Analog Information     57 2.4.1 The Sampling Theorem     57 2.4.2 Aliasing     64 2.4.3 Why Oversample?     67 2.4.4 Signal Interface for a Digital System     69 2.5 Sources of Corruption     70 2.5.1 Sampling and Quantizing Effects     71 2.5.2 Channel Effects     71 2.5.3 Signal-to-Noise Ratio for Quantized Pulses     72 2.6 Pulse Code Modulation     73 2.7 Uniform and Nonuniform Quantization     75 2.7.1 Statistics of Speech Amplitudes     75 2.7.2 Nonuniform Quantization     77 2.7.3 Companding Characteristics     77 2.8 Baseband Transmission     79 2.8.1 Waveform Representation of Binary Digits     79 2.8.2 PCM Waveform Types     80 2.8.3 Spectral Attributes of PCM Waveforms     83 2.8.4 Bits per PCM Word and Bits per Symbol     84 2.8.5 M-ary Pulse-Modulation Waveforms     86 2.9 Correlative Coding     88 2.9.1 Duobinary Signaling     88 2.9.2 Duobinary Decoding     89 2.9.3 Precoding     90 2.9.4 Duobinary Equivalent Transfer Function     91 2.9.5 Comparison of Binary and Duobinary Signaling     93 2.9.6 Polybinary Signaling     94 2.10 Conclusion     94 Chapter 3  BASEBAND DEMODULATION/DETECTION     99 3.1 Signals and Noise     100 3.1.1 Error-Performance Degradation in Communication Systems     100 3.1.2 Demodulation and Detection     101 3.1.3 A Vectorial View of Signals and Noise     105 3.1.4 The Basic SNR Parameter for Digital Communication Systems     112 3.1.5 Why Eb /N0 Is a Natural Figure of Merit     113 3.2 Detection of Binary Signals in Gaussian Noise     114 3.2.1 Maximum Likelihood Receiver Structure     114 3.2.2 The Matched Filter     117 3.2.3 Correlation Realization of the Matched Filter     119 3.2.4 Optimizing Error Performance     122 3.2.5 Error Probability Performance of Binary Signaling     126 3.3 Intersymbol Interference     130 3.3.1 Pulse Shaping to Reduce ISI     133 3.3.2 Two Types of Error-Performance Degradation     136 3.3.3 Demodulation/Detection of Shaped Pulses     140 3.4 Equalization     144 3.4.1 Channel Characterization     144 3.4.2 Eye Pattern     145 3.4.3 Equalizer Filter Types     146 3.4.4 Preset and Adaptive Equalization     152 3.4.5 Filter Update Rate     155 3.5 Conclusion     156 Chapter 4  BANDPASS MODULATION AND DEMODULATION/DETECTION     161 4.1 Why Modulate?     162 4.2 Digital Bandpass Modulation Techniques     162 4.2.1 Phasor Representation of a Sinusoid     163 4.2.2 Phase-Shift Keying     166 4.2.3 Frequency-Shift Keying     167 4.2.4 Amplitude Shift Keying     167 4.2.5 Amplitude-Phase Keying     168 4.2.6 Waveform Amplitude Coefficient     168 4.3 Detection of Signals in Gaussian Noise     169 4.3.1 Decision Regions     169 4.3.2 Correlation Receiver     170 4.4 Coherent Detection     175 4.4.1 Coherent Detection of PSK     175 4.4.2 Sampled Matched Filter     176 4.4.3 Coherent Detection of Multiple Phase-Shift Keying     181 4.4.4 Coherent Detection of FSK     184 4.5 Noncoherent Detection     187 4.5.1 Detection of Differential PSK     187 4.5.2 Binary Differential PSK Example     188 4.5.3 Noncoherent Detection of FSK     190 4.5.4 Required Tone Spacing for Noncoherent Orthogonal FSK Signaling     192 4.6 Complex Envelope     196 4.6.1 Quadrature Implementation of a Modulator     197 4.6.2 D8PSK Modulator Example     198 4.6.3 D8PSK Demodulator Example     200 4.7 Error Performance for Binary Systems     202 4.7.1 Probability of Bit Error for Coherently Detected BPSK     202 4.7.2 Probability of Bit Error for Coherently Detected, Differentially Encoded Binary PSK     204 4.7.3 Probability of Bit Error for Coherently Detected Binary Orthogonal FSK     204 4.7.4 Probability of Bit Error for Noncoherently Detected Binary Orthogonal FSK     206 4.7.5 Probability of Bit Error for Binary DPSK     208 4.7.6 Comparison of Bit-Error Performance for Various Modulation Types     210 4.8 M-ary Signaling and Performance     211 4.8.1 Ideal Probability of Bit-Error Performance     211 4.8.2 M-ary Signaling     212 4.8.3 Vectorial View of MPSK Signaling     214 4.8.4 BPSK and QPSK Have the Same Bit-Error Probability     216 4.8.5 Vectorial View of MFSK Signaling     217 4.9 Symbol Error Performance for M-ary Systems (M > 2)     221 4.9.1 Probability of Symbol Error for MPSK     221 4.9.2 Probability of Symbol Error for MFSK     222 4.9.3 Bit-Error Probability Versus Symbol Error Probability for Orthogonal Signals     223 4.9.4 Bit-Error Probability Versus Symbol Error Probability for Multiple-Phase Signaling     226 4.9.5 Effects of Intersymbol Interference     228 4.10 Conclusion     228 Chapter 5  COMMUNICATIONS LINK ANALYSIS     235 5.1 What the System Link Budget Tells the System Engineer     236 5.2 The Channel     236 5.2.1 The Concept of Free Space     237 5.2.2 Error-Performance Degradation     237 5.2.3 Sources of Signal Loss and Noise     238 5.3 Received Signal Power and Noise Power     243 5.3.1 The Range Equation     243 5.3.2 Received Signal Power as a Function of Frequency     247 5.3.3 Path Loss Is Frequency Dependent     248 5.3.4 Thermal Noise Power     250 5.4 Link Budget Analysis     252 5.4.1 Two Eb /N0 Values of Interest     254 5.4.2 Link Budgets Are Typically Calculated in Decibels     256 5.4.3 How Much Link Margin Is Enough?     257 5.4.4 Link Availability     258 5.5 Noise Figure, Noise Temperature, and System Temperature     263 5.5.1 Noise Figure     263 5.5.2 Noise Temperature     265 5.5.3 Line Loss     266 5.5.4 Composite Noise Figure and Composite Noise Temperature     269 5.5.5 System Effective Temperature     270 5.5.6 Sky Noise Temperature     275 5.6 Sample Link Analysis     279 5.6.1 Link Budget Details     279 5.6.2 Receiver Figure of Merit     282 5.6.3 Received Isotropic Power     282 5.7 Satellite Repeaters     283 5.7.1 Nonregenerative Repeaters     283 5.7.2 Nonlinear Repeater Amplifiers     288 5.8 System Trade-Offs     289 5.9 Conclusion     290 Chapter 6  CHANNEL CODING: PART 1: WAVEFORM CODES AND BLOCK CODES     297 6.1 Waveform Coding and Structured Sequences     298 6.1.1 Antipodal and Orthogonal Signals     298 6.1.2 M-ary Signaling     300 6.1.3 Waveform Coding     300 6.1.4 Waveform-Coding System Example     304 6.2 Types of Error Control     307 6.2.1 Terminal Connectivity     307 6.2.2 Automatic Repeat Request     307 6.3 Structured Sequences     309 6.3.1 Channel Models     309 6.3.2 Code Rate and Redundancy     311 6.3.3 Parity-Check Codes     312 6.3.4 Why Use Error-Correction Coding?     315 6.4 Linear Block Codes     320 6.4.1 Vector Spaces     320 6.4.2 Vector Subspaces     321 6.4.3 A (6, 3) Linear Block Code Example     322 6.4.4 Generator Matrix     323 6.4.5 Systematic Linear Block Codes     325 6.4.6 Parity-Check Matrix     326 6.4.7 Syndrome Testing     327 6.4.8 Error Correction     329 6.4.9 Decoder Implementation     332 6.5 Error-Detecting and Error-Correcting Capability     334 6.5.1 Weight and Distance of Binary Vectors     334 6.5.2 Minimum Distance of a Linear Code     335 6.5.3 Error Detection and Correction     335 6.5.4 Visualization of a 6-Tuple Space     339 6.5.5 Erasure Correction     341 6.6 Usefulness of the Standard Array     342 6.6.1 Estimating Code Capability     342 6.6.2 An (n, k) Example     343 6.6.3 Designing the (8, 2) Code     344 6.6.4 Error Detection Versus Error Correction Trade-Offs     345 6.6.5 The Standard Array Provides Insight     347 6.7 Cyclic Codes     349 6.7.1 Algebraic Structure of Cyclic Codes     349 6.7.2 Binary Cyclic Code Properties     351 6.7.3 Encoding in Systematic Form     352 6.7.4 Circuit for Dividing Polynomials     353 6.7.5 Systematic Encoding with an (n ? k)-Stage Shift Register     356 6.7.6 Error Detection with an (n ? k)-Stage Shift Register     358 6.8 Well-Known Block Codes     359 6.8.1 Hamming Codes     359 6.8.2 Extended Golay Code     361 6.8.3 BCH Codes     363 6.9 Conclusion     367 Chapter 7  CHANNEL CODING: PART 2: CONVOLUTIONAL CODES AND REED–SOLOMON CODES     375 7.1 Convolutional Encoding     376 7.2 Convolutional Encoder Representation     378 7.2.1 Connection Representation     378 7.2.2 State Representation and the State Diagram     382 7.2.3 The Tree Diagram     385 7.2.4 The Trellis Diagram     385 7.3 Formulation of the Convolutional Decoding Problem     388 7.3.1 Maximum Likelihood Decoding     388 7.3.2 Channel Models: Hard Versus Soft Decisions     390 7.3.3 The Viterbi Convolutional Decoding Algorithm     394 7.3.4 An Example of Viterbi Convolutional Decoding     394 7.3.5 Decoder Implementation     398 7.3.6 Path Memory and Synchronization     401 7.4 Properties of Convolutional Codes     402 7.4.1 Distance Properties of Convolutional Codes     402 7.4.2 Systematic and Nonsystematic Convolutional Codes     406 7.4.3 Catastrophic Error Propagation in Convolutional Codes     407 7.4.4 Performance Bounds for Convolutional Codes     408 7.4.5 Coding Gain     409 7.4.6 Best-Known Convolutional Codes     411 7.4.7 Convolutional Code Rate Trade-Off     413 7.4.8 Soft-Decision Viterbi Decoding     413 7.5 Other Convolutional Decoding Algorithms     415 7.5.1 Sequential Decoding     415 7.5.2 Comparisons and Limitations of Viterbi and Sequential Decoding     418 7.5.3 Feedback Decoding     419 7.6 Reed–Solomon Codes     421 7.6.1 Reed–Solomon Error Probability     423 7.6.2 Why R–S Codes Perform Well Against Burst Noise     426 7.6.3 R–S Performance as a Function of Size, Redundancy, and Code Rate     426 7.6.4 Finite Fields     429 7.6.5 Reed–Solomon Encoding     435 7.6.6 Reed–Solomon Decoding     439 7.7 Interleaving and Concatenated Codes     446 7.7.1 Block Interleaving     449 7.7.2 Convolutional Interleaving     452 7.7.3 Concatenated Codes     453 7.8 Coding and Interleaving Applied to the Compact Disc Digital Audio System     454 7.8.1 CIRC Encoding     456 7.8.2 CIRC Decoding     458 7.8.3 Interpolation and Muting     460 7.9 Conclusion     462 Chapter 8  CHANNEL CODING: PART 3: TURBO CODES AND LOW-DENSITY PARITY CHECK (LDPC) CODES     471 8.1 Turbo Codes     472 8.1.1 Turbo Code Concepts     472 8.1.2 Log-Likelihood Algebra     476 8.1.3 Product Code Example     477 8.1.4 Encoding with Recursive Systematic Codes     484 8.1.5 A Feedback Decoder     489 8.1.6 The MAP Algorithm     493 8.1.7 MAP Decoding Example     499 8.2 Low-Density Parity Check (LDPC) Codes     504 8.2.1 Background and Overview     504 8.2.2 The Parity-Check Matrix     505 8.2.3 Finding the Best-Performing Codes     507 8.2.4 Decoding: An Overview     509 8.2.5 Mathematical Foundations     514 8.2.6 Decoding in the Probability Domain     518 8.2.7 Decoding in the Logarithmic Domain     526 8.2.8 Reduced-Complexity Decoders     531 8.2.9 LDPC Performance     532 8.2.10 Conclusion     535 Appendix 8A: The Sum of Log-Likelihood Ratios     535 Appendix 8B: Using Bayes' Theorem to Simplify the Bit Conditional Probability     537 Appendix 8C: Probability that a Binary Sequence Contains an Even Number of Ones     537 Appendix 8D: Simplified Expression for the Hyperbolic Tangent of the Natural Log of a Ratio of Binary Probabilities     538 Appendix 8E: Proof that phi(x) = phi^-1(x)     538 Appendix 8F: Bit Probability Initialization     539 Chapter 9  MODULATION AND CODING TRADE-OFFS     549 9.1 Goals of the Communication System Designer     550 9.2 Error-Probability Plane     550 9.3 Nyquist Minimum Bandwidth     552 9.4 Shannon–Hartley Capacity Theorem     554 9.4.1 Shannon Limit     556 9.4.2 Entropy     557 9.4.3 Equivocation and Effective Transmission Rate     560 9.5 Bandwidth-Efficiency Plane     562 9.5.1 Bandwidth Efficiency of MPSK and MFSK Modulation     563 9.5.2 Analogies Between the Bandwidth-Efficiency and Error-Probability Planes     564 9.6 Modulation and Coding Trade-Offs     565 9.7 Defining, Designing, and Evaluating Digital Communication Systems     566 9.7.1 M-ary Signaling     567 9.7.2 Bandwidth-Limited Systems     568 9.7.3 Power-Limited Systems     569 9.7.4 Requirements for MPSK and MFSK Signaling     570 9.7.5 Bandwidth-Limited Uncoded System Example     571 9.7.6 Power-Limited Uncoded System Example     573 9.7.7 Bandwidth-Limited and Power-Limited Coded System Example     575 9.8 Bandwidth-Efficient Modulation     583 9.8.1 QPSK and Offset QPSK Signaling     583 9.8.2 Minimum-Shift Keying     587 9.8.3 Quadrature Amplitude Modulation     591 9.9 Trellis-Coded Modulation     594 9.9.1 The Idea Behind Trellis-Coded Modulation     595 9.9.2 TCM Encoding     597 9.9.3 TCM Decoding     601 9.9.4 Other Trellis Codes     604 9.9.5 Trellis-Coded Modulation Example     606 9.9.6 Multidimensional Trellis-Coded Modulation     610 9.10 Conclusion     610 Chapter 10  SYNCHRONIZATION     619 10.1 Receiver Synchronization     620 10.1.1 Why We Must Synchronize     620 10.1.2 Alignment at the Waveform Level and Bit Stream Level     620 10.1.3 Carrier-Wave Modulation     620 10.1.4 Carrier Synchronization     621 10.1.5 Symbol Synchronization     624 10.1.6 Eye Diagrams and Constellations     625 10.2 Synchronous Demodulation     626 10.2.1 Minimizing Energy in the Difference Signal     628 10.2.2 Finding the Peak of the Correlation Function     629 10.2.3 The Basic Analog Phase-Locked Loop (PLL)     631 10.2.4 Phase-Locking Remote Oscillators     631 10.2.5 Estimating Phase Slope (Frequency)     633 10.3 Loop Filters, Control Circuits, and Acquisition     634 10.3.1 How Many Loop Filters Are There in a System?     634 10.3.2 The Key Loop Filters     634 10.3.3 Why We Want R Times R-dot     634 10.3.4 The Phase Error S-Curve     636 10.4 Phase-Locked Loop Timing Recovery     637 10.4.1 Recovering Carrier Timing from a Modulated Waveform     637 10.4.2 Classical Timing Recovery Architectures     638 10.4.3 Timing-Error Detection: Insight from the Correlation Function     641 10.4.4 Maximum-Likelihood Timing-Error Detection     642 10.4.5 Polyphase Matched Filter and Derivative Matched Filter     643 10.4.6 Approximate ML Timing Recovery PLL for a 32-Path PLL     647 10.5 Frequency Recovery Using a Frequency-Locked Loop (FLL)     652 10.5.1 Band-Edge Filters     654 10.5.2 Band-Edge Filter Non-Data-Aided Timing Synchronization     660 10.6 Effects of Phase and Frequency Offsets     664 10.6.1 Phase Offset and No Spinning: Effect on Constellation     665 10.6.2 Slow Spinning Effect on Constellation     667 10.6.3 Fast Spinning Effect on Constellation     670 10.7 Conclusion     672 Chapter 11  MULTIPLEXING AND MULTIPLE ACCESS     681 11.1 Allocation of the Communications Resource     682 11.1.1 Frequency-Division Multiplexing/Multiple Access     683 11.1.2 Time-Division Multiplexing/Multiple Access     688 11.1.3 Communications Resource Channelization     691 11.1.4 Performance Comparison of FDMA and TDMA     692 11.1.5 Code-Division Multiple Access     695 11.1.6 Space-Division and Polarization-Division Multiple Access     698 11.2 Multiple-Access Communications System and Architecture     700 11.2.1 Multiple-Access Information Flow     701 11.2.2 Demand-Assignment Multiple Access     702 11.3 Access Algorithms     702 11.3.1 ALOHA     702 11.3.2 Slotted ALOHA     705 11.3.3 Reservation ALOHA     706 11.3.4 Performance Comparison of S-ALOHA and R-ALOHA     708 11.3.5 Polling Techniques     710 11.4 Multiple-Access Techniques Employed with INTELSAT     712 11.4.1 Preassigned FDM/FM/FDMA or MCPC Operation     713 11.4.2 MCPC Modes of Accessing an INTELSAT Satellite     713 11.4.3 SPADE Operation     716 11.4.4 TDMA in INTELSAT     721 11.4.5 Satellite-Switched TDMA in INTELSAT     727 11.5 Multiple-Access Techniques for Local Area Networks     731 11.5.1 Carrier-Sense Multiple-Access Networks     731 11.5.2 Token-Ring Networks     733 11.5.3 Performance Comparison of CSMA/CD and Token-Ring Networks     734 11.6 Conclusion     736 Chapter 12  SPREAD-SPECTRUM TECHNIQUES     741 12.1 Spread-Spectrum Overview     742 12.1.1 The Beneficial Attributes of Spread-Spectrum Systems     742 12.1.2 A Catalog of Spreading Techniques     746 12.1.3 Model for Direct-Sequence Spread-Spectrum Interference Rejection     747 12.1.4 Historical Background     748 12.2 Pseudonoise Sequences     750 12.2.1 Randomness Properties     750 12.2.2 Shift Register Sequences     750 12.2.3 PN Autocorrelation Function     752 12.3 Direct-Sequence Spread-Spectrum Systems     753 12.3.1 Example of Direct Sequencing     755 12.3.2 Processing Gain and Performance     756 12.4 Frequency-Hopping Systems     759 12.4.1 Frequency-Hopping Example     761 12.4.2 Robustness     762 12.4.3 Frequency Hopping with Diversity     762 12.4.4 Fast Hopping Versus Slow Hopping     763 12.4.5 FFH/MFSK Demodulator     765 12.4.6 Processing Gain     766 12.5 Synchronization     766 12.5.1 Acquisition     767 12.5.2 Tracking     772 12.6 Jamming Considerations     775 12.6.1 The Jamming Game     775 12.6.2 Broadband Noise Jamming     780 12.6.3 Partial-Band Noise Jamming     781 12.6.4 Multiple-Tone Jamming     783 12.6.5 Pulse Jamming     785 12.6.6 Repeat-Back Jamming     787 12.6.7 BLADES System     788 12.7 Commercial Applications     789 12.7.1 Code-Division Multiple Access     789 12.7.2 Multipath Channels     792 12.7.3 The FCC Part     15 Rules for Spread-Spectrum Systems     793 12.7.4 Direct Sequence Versus Frequency Hopping     794 12.8 Cellular Systems     796 12.8.1 Direct-Sequence CDMA     796 12.8.2 Analog FM Versus TDMA Versus CDMA     799 12.8.3 Interference-Limited Versus Dimension-Limited Systems     801 12.8.4 IS-95 CDMA Digital Cellular System     803 12.9 Conclusion     814 Chapter 13  SOURCE CODING     823 13.1 Sources     824 13.1.1 Discrete Sources     824 13.1.2 Waveform Sources     829 13.2 Amplitude Quantizing     830 13.2.1 Quantizing Noise     833 13.2.2 Uniform Quantizing     836 13.2.3 Saturation     840 13.2.4 Dithering     842 13.2.5 Nonuniform Quantizing     845 13.3 Pulse Code Modulation     849 13.3.1 Differential Pulse Code Modulation     850 13.3.2 One-Tap Prediction     853 13.3.3 N-Tap Prediction     854 13.3.4 Delta Modulation     856 13.3.5 S-D Modulation     858 13.3.6 S-D A-to-D Converter (ADC)     862 13.3.7 S-D D-to-A Converter (DAC)     863 13.4 Adaptive Prediction     865 13.4.1 Forward Adaptation     865 13.4.2 Synthesis/Analysis Coding     866 13.5 Block Coding     868 13.5.1 Vector Quantizing     868 13.6 Transform Coding     870 13.6.1 Quantization for Transform Coding     872 13.6.2 Subband Coding     872 13.7 Source Coding for Digital Data     873 13.7.1 Properties of Codes     875 13.7.2 Huffman Code     877 13.7.3 Run-Length Codes     880 13.8 Examples of Source Coding     884 13.8.1 Audio Compression     884 13.8.2 Image Compression     889 13.9 Conclusion     898 Chapter 14  FADING CHANNELS     905 14.1 The Challenge of Communicating over Fading Channels     906 14.2 Characterizing Mobile-Radio Propagation     907 14.2.1 Large-Scale Fading     912 14.2.2 Small-Scale Fading     914 14.3 Signal Time Spreading     918 14.3.1 Signal Time Spreading Viewed in the Time-Delay Domain     918 14.3.2 Signal Time Spreading Viewed in the Frequency Domain     920 14.3.3 Examples of Flat Fading and Frequency-Selective Fading     924 14.4 Time Variance of the Channel Caused by Motion     926 14.4.1 Time Variance Viewed in the Time Domain     926 14.4.2 Time Variance Viewed in the Doppler-Shift Domain     929 14.4.3 Performance over a Slow- and Flat-Fading Rayleigh Channel     935 14.5 Mitigating the Degradation Effects of Fading     937 14.5.1 Mitigation to Combat Frequency-Selective Distortion     939 14.5.2 Mitigation to Combat Fast-Fading Distortion     942 14.5.3 Mitigation to Combat Loss in SNR     942 14.5.4 Diversity Techniques     944 14.5.5 Modulation Types for Fading Channels     946 14.5.6 The Role of an Interleaver     947 14.6 Summary of the Key Parameters Characterizing Fading Channels     951 14.6.1 Fast-Fading Distortion: Case 1     951 14.6.2 Frequency-Selective Fading Distortion: Case 2     952 14.6.3 Fast-Fading and Frequency-Selective Fading Distortion: Case 3     953 14.7 Applications: Mitigating the Effects of Frequency-Selective Fading     955 14.7.1 The Viterbi Equalizer as Applied to GSM     955 14.7.2 The Rake Receiver Applied to Direct-Sequence Spread-Spectrum (DS/SS) Systems     958 14.8 Conclusion     960 Chapter 15  THE ABCs OF OFDM (ORTHOGONAL FREQUENCY- DIVISION MULTIPLEXING)     971 15.1 What Is OFDM?     972 15.2 Why OFDM?     972 15.3 Getting Started with OFDM     973 15.4 Our Wish List (Preference for Flat Fading and Slow Fading)     974 15.4.1 OFDM's Most Important Contribution to Communications over Multipath Channels     975 15.5 Conventional Multi-Channel FDM versus Multi-Channel OFDM     976 15.6 The History of the Cyclic Prefix (CP)     977 15.6.1 Examining the Lengthened Symbol in OFDM     978 15.6.2 The Length of the CP     979 15.7 OFDM System Block Diagram     979 15.8 Zooming in on the IDFT     981 15.9 An Example of OFDM Waveform Synthesis     981 15.10 Summarizing OFDM Waveform Synthesis     983 15.11 Data Constellation Points Distributed over the Subcarrier Indexes     984 15.11.1 Signal Processing in the OFDM Receiver     986 15.11.2 OFDM Symbol-Time Duration     986 15.11.3 Why DC Is Not Used as a Subcarrier in Real Systems     987 15.12 Hermitian Symmetry     987 15.13 How Many Subcarriers Are Needed?     989 15.14 The Importance of the Cyclic Prefix (CP) in OFDM     989 15.14.1 Properties of Continuous and Discrete Fourier Transforms     990 15.14.2 Reconstructing the OFDM Subcarriers     991 15.14.3 A Property of the Discrete Fourier Transform (DFT)     992 15.14.4 Using Circular Convolution for Reconstructing an OFDM Subcarrier     993 15.14.5 The Trick That Makes Linear Convolution Appear Circular     994 15.15 An Early OFDM Application: Wi-Fi Standard 802.11a     997 15.15.1 Why the Transform Size N Needs to Be Larger Than the Number of Subcarriers     999 15.16 Cyclic Prefix (CP) and Tone Spacing     1000 15.17 Long-Term Evolution (LTE) Use of OFDM     1001 15.17.1 LTE Resources: Grid, Block, and Element     1002 15.17.2 OFDM Frame in LTE     1003 15.18 Drawbacks of OFDM     1006 15.18.1 Sensitivity to Doppler     1006 15.18.2 Peak-to-Average Power Ratio (PAPR) and SC-OFDM     1006 15.18.3 Motivation for Reducing PAPR     1007 15.19 Single-Carrier OFDM (SC-OFDM) for Improved PAPR Over Standard OFDM     1007 15.19.1 SC-OFDM Signals Have Short Mainlobe Durations     1010 15.19.2 Is There an Easier Way to Implement SC-OFDM?     1011 15.20 Conclusion     1012 Chapter 16  THE MAGIC OF MIMO (MULTIPLE INPUT/MULTIPLE OUTPUT)     1017 16.1 What is MIMO?     1018 16.1.1 MIMO Historical Perspective     1019 16.1.2 Vectors and Phasors     1019 16.1.3 MIMO Channel Model     1020 16.2 Various Benefits of Multiple Antennas     1023 16.2.1 Array Gain     1023 16.2.2 Diversity Gain     1023 16.2.3 SIMO Receive Diversity Example     1026 16.2.4 MISO Transmit Diversity Example     1027 16.2.5 Two-Time Interval MISO Diversity Example     1028 16.2.6 Coding Gain     1029 16.2.7 Visualization of Array Gain, Diversity Gain, and Coding Gain     1029 16.3 Spatial Multiplexing     1031 16.3.1 Basic Idea of MIMO-Spatial Multiplexing (MIMO-SM)     1031 16.3.2 Analogy Between MIMO-SM and CDMA     1033 16.3.3 When Only the Receiver Has Channel-State Information (CSI)     1033 16.3.4 Impact of the Channel Model     1034 16.3.5 MIMO and OFDM Form a Natural Coupling     1036 16.4 Capacity Performance     1037 16.4.1 Deterministic Channel Modeling     1038 16.4.2 Random Channel Models     1040 16.5 Transmitter Channel-State Information (CSI)     1042 16.5.1 Optimum Power Distribution     1044 16.6 Space-Time Coding     1047 16.6.1 Block Codes in MIMO Systems     1047 16.6.2 Trellis Codes in MIMO Systems     1050 16.7 MIMO Trade-Offs     1051 16.7.1 Fundamental Trade-Off     1051 16.7.2 Trade-Off Yielding Greater Robustness for PAM and QAM     1052 16.7.3 Trade-Off Yielding Greater Capacity for PAM and QAM     1053 16.7.4 Tools for Trading Off Multiplexing Gain and Diversity Gain     1054 16.8 Multi-User MIMO (MU-MIMO)     1058 16.8.1 What Is MU-MIMO?     1059 16.8.2 SU-MIMO and MU-MIMO Notation     1059 16.8.3 A Real Shift in MIMO Thinking     1061 16.8.4 MU-MIMO Capacity     1067 16.8.5 Sum-Rate Capacity Comparison for Various Precoding Strategies     1081 16.8.6 MU-MIMO Versus SU-MIMO Performance     1082 16.9 Conclusion     1083 Index     1089 ONLINE ONLY: Chapter 17  Encryption and Decryption Appendix A  A Review of Fourier Techniques Appendix B  Fundamentals of Statistical Decision Theory Appendix C  Response of a Correlator to White Noise Appendix D  Often-Used Identities Appendix E  S-Domain, Z-Domain, and Digital Filtering Appendix F  OFDM Symbol Formation with an N-Point Inverse Discrete Fourier Transform (IDFT) Appendix G  List of Symbols