DIGITAL COMMUNICATIONS DIGITAL COMMUNICATIONS Mehmet Şafak This edition first published 2017 © 2017 John Wiley & Sons Ltd Registered Office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher Wiley also publishes its books in a variety of electronic formats Some content that 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competent professional should be sought Library of Congress Cataloging-in-Publication Data Names: Şafak, Mehmet, 1948– author Title: Digital communications / Mehmet Şafak Description: Chichester, UK ; Hoboken, NJ : John Wiley & Sons, 2017 | Includes bibliographical references and index Identifiers: LCCN 2016032956 (print) | LCCN 2016046780 (ebook) | ISBN 9781119091257 (cloth) | ISBN 9781119091264 (pdf) | ISBN 9781119091271 (epub) Subjects: LCSH: Digital communications Classification: LCC TK5103.7 S24 2017 (print) | LCC TK5103.7 (ebook) | DDC 621.382–dc23 LC record available at https://lccn.loc.gov/2016032956 A catalogue record for this book is available from the British Library Cover Design: Wiley Cover Image: KTSDESIGN/Gettyimages Set in 10 /12pt Times by SPi Global, Pondicherry, India 10 To my children Emre and Ilgın Contents Preface List of Abbreviations About the Companion Website xiv xviii xxi Signal Analysis 1.1 Relationship Between Time and Frequency Characteristics of Signals 1.1.1 Fourier Series 1.1.2 Fourier Transform 1.1.3 Fourier Transform of Periodic Functions 1.2 Power Spectal Density (PSD) and Energy Spectral Density (ESD) 1.2.1 Energy Signals Versus Power Signals 1.2.2 Autocorrelation Function and Spectral Density 1.3 Random Signals 1.3.1 Random Variables 1.3.2 Random Processes 1.4 Signal Transmission Through Linear Systems References Problems 2 13 15 15 16 18 18 20 27 31 31 Antennas 2.1 Hertz Dipole 2.1.1 Near- and Far-Field Regions 2.2 Linear Dipole Antenna 2.3 Aperture Antennas 2.4 Isotropic and Omnidirectional Antennas 2.5 Antenna Parameters 2.5.1 Polarization 2.5.2 Radiation Pattern 2.5.3 Directivity and Beamwidth 2.5.4 Gain 33 34 37 40 43 47 48 48 51 53 60 viii Contents 2.5.5 Effective Receiving Area 2.5.6 Effective Antenna Height and Polarization Matching 2.5.7 Impedance Matching References Problems 61 68 70 78 78 Channel Modeling 3.1 Wave Propagation in Low- and Medium-Frequency Bands (Surface Waves) 3.2 Wave Propagation in the HF Band (Sky Waves) 3.3 Wave Propagation in VHF and UHF Bands 3.3.1 Free-Space Propagation 3.3.2 Line-Of-Sight (LOS) Propagation 3.3.3 Fresnel Zones 3.3.4 Knife-Edge Diffraction 3.3.5 Propagation Over the Earth Surface 3.4 Wave Propagation in SHF and EHF Bands 3.4.1 Atmospheric Absorption Losses 3.4.2 Rain Attenuation 3.5 Tropospheric Refraction 3.5.1 Ducting 3.5.2 Radio Horizon 3.6 Outdoor Path-Loss Models 3.6.1 Hata Model 3.6.2 COST 231 Extension to Hata Model 3.6.3 Erceg Model 3.7 Indoor Propagation Models 3.7.1 Site-General Indoor Path Loss Models 3.7.2 Signal Penetration Into Buildings 3.8 Propagation in Vegetation References Problems 82 83 84 85 86 86 87 90 95 106 108 110 118 121 123 123 124 125 128 129 130 132 134 137 137 Receiver System Noise 4.1 Thermal Noise 4.2 Equivalent Noise Temperature 4.2.1 Equivalent Noise Temperature of Cascaded Subsystems 4.3 Noise Figure 4.3.1 Noise Figure of a Lossy Device 4.4 External Noise and Antenna Noise Temperature 4.4.1 Point Noise Sources 4.4.2 Extended Noise Sources and Brightness Temperature 4.4.3 Antenna Noise Figure 4.4.4 Effects of Lossy Propagation Medium on the Observed Brightness Temperature 4.4.5 Brightness Temperature of Some Extended Noise Sources 4.4.6 Man-Made Noise 4.5 System Noise Temperature 145 146 147 149 150 152 153 154 154 156 156 160 167 167 Index Note: Page numbers followed by “f” refer to figures, page numbers followed by “t” refer to tables and page numbers in “bold” refer to first comprehensive discussion of the topic absolute quantization, 193, 220 see also quantization adaptive coding and modulation in fading channels, 622 adaptive delta modulation (ADM), 230 adaptive multi-rate (AMR) encoding, 234 Additive White Gaussian Noise (AWGN), 26, 248 autocorrelation, 26, 249 low-pass filtered, 29, 31 pdf, 27, 249 PSD, 26, 146, 249 advanced video coding (AVC), 236 aeronautical channel, 101 AF relaying, 760 AF SRD and direct links (with SC and MRC) with single antennas at source and destination, 765 BEP for BPSK, 766 capacity, 766, 767f cdf, 765, 768f mean SNR, 766 MGF, 765 pdf, 765, 768f AJ and LPI in DSSS, 479, 497 broadband noise jamming, 498, 501, 502f jamming margin, 498 multitone jamming, 498 pulsed-tone jamming, 499, 500f tone jamming, 498 Alamouti scheme, 688 array gain, 689 cdf of SNR, 690 pdf of SNR, 690 transceiver, 689 A-law, 198 aliasing, 188f see also sampling amount of fading (AOF), 590, 599 analog-to-digital conversion (ADC), 184 of video signals, 192 of audio signals, 232 analog repeater, 66, 213 see also regenerative repeater; repeater system noise; satellite relay; bent-pipe (non-regenerative) satellite antenna arrays, 640 angle of arrival (AOA) spread, 649 antenna arrays in fading channels, 650 antenna arrays in non-fading channels, 640 antenna nulling, 644 array factor, 642, 651 array gain, 648, 652 broadside array, 644 current distribution of, 645 end-fire array, 644 input impedance of, 646 mutual impedance between array elements, 646 signal-to-noise power ratio (SNR), 647, 651 transmit power of, 647 uniform linear array (ULA), 641, 643 weighting of array elements, 642 Digital Communications, First Edition Mehmet Şafak © 2017 John Wiley & Sons Ltd Published 2017 by John Wiley & Sons Ltd Companion website: www.wiley.com/go/safak/Digital_Communications 872 antenna current distribution, 41, 70 in array antennas, 642, 645 vs radiation pattern, 42 antenna loss efficiency, 60 antenna noise figure, 156 antenna noise temperature, 153, 155, 158 frequency dependence, 164 antenna radiated power, 36 antennas, 33 see also aperture antennas; Hertz dipole; horn antenna; isotropic antenna; linear dipole antenna; loop antenna; omnidirectional antenna; parasitic dipole antenna; parasitic MIMO; reflector antenna aperture antenna, 43, 45 see also aperture distribution; circular aperture; rectangular aperture gain of, 62 aperture distribution, 46, 57 see also circular aperture; rectangular aperture aperture efficiency, 57, 60t vs beamwidth, 58, 60t vs directivity, 57 nonuniform distribution, 57, 58 vs radiation pattern, 58 sidelobe level, 60t taper, 57f array gain see equal-gain combining (EGC); generalized selection combining (GSC); maximal-ratio combining (MRC); selection combining (SC) Arthur C Clark, 171 ASK see M-ary ASK atmospheric absorption losses, 108 dry-air absorption, 108 specific attenuation, 108, 108f water-vapor absorption, 108 zenith attenuation, 109f atmospheric noise temperature, 156 audio coding, 232 automatic repeat-request (ARQ), 388, 459 acceptance probability, 461 Chase combining, 467 comparison of ARQ techniques, 465f, 467 delay, 466f go-back N (GBN) ARQ, 463 hybrid-ARQ (HARQ), 388, 467 incremental redundancy, 467 probability of correct reception, 460 retransmission probability, 461 selective-repeat (SRe) ARQ, 464 stop-and-wait (SW) ARQ, 463 throughput efficiency, 465 undetected error probability, 460, 461, 462f average fade duration, 602, 603 see also level crossing rate (LCR) effect on transmission rate, 603 for Nakagami-m fading, 602 for Rayleigh fading, 603 for Rician fading, 603 Index vs transmission rate, 603 AWGN channel, 86, 174 bandpass sampling, 191 bandwidth, 28 bandwidth efficiency, 326 baseband bandwidth, 324 coherence bandwidth, 28 half-power bandwidth, 326 noise equivalent bandwidth, 176, 326 null-to-null bandwidth, 326 passband bandwidth, 325 rms bandwidth, 28 transmission bandwidth, 28 baseband signal, base changes in logarithms, 826 Bayes rule, 306 beam scanning, 60 bent-pipe (non-regenerative) satellite, 171 BEP due to ISI, 269, 270f, 569 BEP in AWGN channels 3-ASK, 338 binary coherent FSK, 361 binary DEPSK, 352 binary DPSK, 369 binary noncoherent FSK, 372 binary PSK, 340 binary symmetric channel, 258, 308, 391f, 392, 394f, 412 coherent detection of M-ary signals, 305, 312 duobinary signaling, 281 4-DPSK, 370 effect of correlation between BFSK carriers, 361 effect of symbol timing error, 329, 330f effect of threshold level on, 257 M-ary ASK, 334 M-ary coherent FSK, 363, 363f M-ary noncoherent FSK, 373, 374f M-ary PAM, 265, 266f M-ary PSK, 348 M-ary QAM, 354 matched filter reception of antipodal signals, 258, 261 matched filter reception of orthogonal signals, 261 on-off keying, 337 QPSK, 343 vs symbol error probability, 316 union bound, 313 upper bound on BEP for M-ary PSK, 349 upper bound on BEP for M-ary QAM, 356 BEP in coded channels BCH codes, 427f comparison of Golay and BCH codes, 429f comparison of LDPC with convolutional codes and Shannon’s limit, 436f Golay coding with HDD and SDD, 428f 873 Index Hamming codes, 414f HDD of block codes, 408 ML of convolutional codes, 449 parity check coding, 400 repetition coding, 401 RS codes, 433, 433f SDD of block codes, 411 turbo codes, 459f BEP in cooperative communications AF selection-combined SRD and SD links with relay selection, 772f AF selection-and maximal ratio combined SRD and SD links with relay selection, 773f AF SRD link with relay selection, 741f comparison for SRD and SRD+SD links, 785f comparison for SRD link between AF and DF relaying with multiple antennas, 794f comparison for SRD link between AF and DF relaying with single antennas, 793f effect of outdated CSI for AF relaying, 776f BEP in frequency-nonselective slowly fading channels, 604 BPSK, 605, 606f, 606t, 608 BPSK in combined fading and shadowing channels, 613, 614f BPSK in Nakagami-m channels, 607 coherent BFSK, 605, 606f, 606t, 608 DPSK, 605, 606f, 606t, 608 M-ary coherent FSK, 612, 612f M-ary noncoherent FSK, 613, 613f M-ary PSK, 611, 611f M-ary QAM, 611, 612f noncoherent BFSK, 605, 606f, 606t, 608 BEP in frequency-nonselective slow fading channel with diversity, 621, 657 for BPSK in Nakagami-m fading channel with MRC, 680, 680f for BPSK in Rayleigh fading channel with EGC, 679 for BPSK in Rayleigh fading channel with MRC, 621, 657, 621f, 657f for BPSK in Rayleigh fading channel with SC, 672, 672f for BPSK in Rayleigh fading channel with SC and unequal branch SNR’s, 673, 673f comparison between MRT, Alamouti scheme and TAS, 691f for DPSK in Nakagami-m fading channel with MRC, 609, 610f for DPSK in Rayleigh fading channel with GSC, 682, 682f for DPSK in Rayleigh fading channel with MRC and unequal branch SNR’s, 677, 678f for DPSK in Rayleigh fading channel with SC, 671, 671f for DPSK in Rayleigh fading channel with SSC, 675, 675f for noncoherent BFSK in Rayleigh fading channel with SLC, 685, 686f BEP in frequency selective slowly-fading channel, 621, 621f BEP in MIMO channels × MIMO channel with one-sided correlation, 733 × parasitic MIMO channel, 745f, 746f × MIMO channel with one-sided correlation, 733 × parasitic MIMO channel, 747f BPSK with TAS at transmitter and MRC at receiver, 740 comparison of MRC, × MIMO, TAS-MRC and Alamouti scheme, 741 effect of MIMO size for BPSK, 735 polarization diversity, 752f, 753f BEP vs outage probability, 589 Bessel functions, 827 binary encoding, 206, 317 binary symmetric channel (BSC), 258, 308, 391, 394f, 412 binomial distribution, 868 bivariate distribution, 848 see also multivariate normal distribution Nakagami-m, 695 normal, 848 Rayleigh, 692, 93, 695 block codes, 389 see also linear block codes block fading, 580 block interleaver, 430 Boltzmann’s constant, 146, 155 Bose-Chaudhuri-Hocquenhem (BCH) codes, 389 error probability of, 427f table of, 427t brightness temperature, 154, 160 clear sky, 163f earth, 162f effect of propagation medium, 156 extraterrestrial, 164f burst-error correcting codes, 389 burst error correction, 429 burst error detection, 430 burst length, 430 capacity of MIMO systems, 723 cdf of capacity, 728 mean (ergodic) capacity, 725 outage capacity, 729 capacity of SIMO systems in fading channels, 660 cdf of capacity, 662 correlation effects on, 662–664 ergodic (mean) capacity, 660 multiplexing gain, 664 outage capacity, 664 Cauchy pdf, 854 causal signal, 6, C band (4-8 GHz), 170 CDMA see code division multiple access (CDMA) channel coding, 386 channel coding theorem, 411f channel impulse response (CIR), 245, 560 874 chi-square distribution, 836, 838, 859, 860f cdf, 859, 861 central chi-square distribution, 859 MGF, 859, 860 moments, 859 noncentral chi-square distribution, 860 pdf, 859, 861 circular aperture 46, 47f, 57 Claude Shannon, 411, 472 clear sky noise, 160 codec, 387 coded cooperation, 759, 798 code division multiple access (CDMA), 332, 479, 491 multi-user interference, 479, 493, 495, 496f near-far effect, 493, 494f, 496f transceiver, 492 transmit power control (TPC), 494 code effectiveness, 406 coding gain, 368 coherence bandwidth, 564 see also delay spread effect on data rate, 567 effect on ISI, 568 of GSM signals, 581 of OFDM signals, 581 coherence time, 571 see also Doppler spread effect on data rate, 573 of GSM signals, 581 of OFDM signals, 581 in power control, 574 coherent demodulation in AWGN channels, 302 correlation demodulator, 302f matched-filter demodulator, 304 observation vector, 305 remainder noise, 303 theorem of irrelevance, 303 coherent detection in AWGN channels, 305 likelihood-ratio, 306 log-likelihood ratio, 306 MAP detection, 307 MAP hypothesis testing, 309 ML detection, 307 coin flipping, 845 combining techniques, 666 see also diversity combining; equal-gain combining (EGC); generalized-selection combining (GSC); maximal ratio combining (MRC); optimum combining (OC); post-detection combining; pre-detection combining; selection combining (SC); square-law combining (SLC); switch and stay combining (SSC) compact disc (CD), 189 compander, 197 companding, 197 comparison of passband modulation techniques, 374 coherently detected passband modulations, 332 constant envelope modulations, 324 minimum Euclidean distance comparison of, 367 Index non-coherently detected passband modulations, 367 power-efficiency comparison, 366 power efficiency of modulation techniques, 376 spectral efficiency of modulation techniques, 375 spectrum efficiency comparison of, 377 composite pdf for fading and shadowing, 596 see also probability density function (pdf ) compressing, 197 compressor, 197 concatenated coding, 390, 454, 455 confluent hypergeometric functions, 827 see also hypergeometric functions continuously variable-slope delta modulation (CVSD), 231 convolution, 17, 27, 29 convolutional codes, 368, 389, 436 coding gain, 451 constraint length, 437 decoding, 441 encoding, 440 error probability, 447 error probability for ML HDD, 448 error probability for ML SDD, 449 free distance, 445 generator polynomial representation, 438 hard-decision decoding, 442 impulse response, 438 rate-compatible punctured convolutional (RCPC) codes, 468 recursive systematic convolutional (RSC) encoder, 457 soft-decision decoding, 444 state-diagram, 438 transfer function, 445 trellis diagram, 440 Viterbi algorithm, 442 convolutional interleaver, 432, 433 cooperative communications, 759 see also AF relaying; DF relaying; DF relaying with multiple antennas at the source, relay and destination; DF SRD link, with relay selection, and multiple antennas at source and destination; DF vs AF relaying; equivalent SNR of AF SRD link with relay selection; equivalent SNR of AF SRD link with relay selection and multiple antennas; equivalent SNR of AF SRD link with single antennas at source and destination; outdated CSI in AF SRD links with relay selection; Rayleigh approximation to equivalent SNR with relay selection; RD (relay-destination) link; relay selection for AF relaying; relaying protocols; SD link with multiple antennas; AF SRD and direct links (with SC and MRC) with single antennas at source and destination; selection combined two direct links with single antennas; selection-combined DF SRD and direct links with multiple antennas; selection-combined AF SRD, with relay selection, and direct links with Index multiple antennas; selection-combined AF SRD, with relay selection, and direct link; SR link; SRD link coordinate transformation between Cartesian and polar, 852 between Cartesian and spherical, 810 correlated MIMO channel, 705, 710, 837 see also MIMO channels with double-sided correlation; MIMO channels with single-sided correlation correlated SIMO channel, 654 AOA correlation in cellular radio, 650 BEP for BPSK for correlated receive ULA, 657 cdf of SNR in correlated ULA, 655, 656f correlation between ULA elements, 648, 649f, 651, 652, 654 covariance matrix, 652, 654 eigenvalues of covariance matrix, 654, 655f pdf of SNR in correlated ULA, 652, 653, 654, 656 correlation, 7, 651, 840, 842 see also correlated MIMO channel, correlated SIMO channel, matched filter correlative-level coding, partial response signaling (PRS), 278 bandwidth, 283t duobinary encoding, 279 duobinary filter, 279f duobinary pulse, 279f error probability in duobinary encoding, 280 generalized PRS, 282 modified duobinary signaling, 283 pre-coded duobinary signaling, 279 PSD of duobinary signaling, 281 covariance matrix, 704, 712, 834, 841 cyclic codes, 415 encoder, 418 generator polynomial, 415 generator polynomial vs generator matrix, 420 parity-check polynomial, 418 syndrome decoding of cyclic codes, 419 cyclic-redundancy check (CRC) codes, 389, 428, 429t decision level, 194 delay spread, 559, 562 autocorrelation function of the CIR, 562 vs channel model, 578 coherence bandwidth, 564 discrete MIP model, 562, 567t exponential MIP, 563 ITU-R MIP model, 567 maximum excess delay, 564 MIP model for hilly terrain, 566 MIP model for rural area, 566 MIP model for suburban area, 566 MIP model for urban area, 566 multipath intensity profile (MIP), 562 vs transmission rate, 567 delta modulation (DM), 228 875 delta-sigma modulation, 231 DF relaying, 787 DF relaying with multiple antennas at the source, relay, and destination, 796 cdf, 797 DF SRD link, with relay selection, and multiple antennas at source and destination, 759, 787 BEP for BPSK, 793f, 794f capacity, 786f, 796f cdf, 791 equivalent SNR, 788, 789 mean equivalent SNR, 789, 790f pdf, 791, 792 Rayleigh approximation, 792f DF vs AF relaying, 791–796 differential encoding, 203 differential PCM (DPCM), 226, 227f SNR of, 227 differential phase shift keying (DPSK) see M-ary DPSK differential quantization, 220, 221f diffraction, 90 diffraction loss, 91, 92f double knife-edge diffraction, 94 Fresnel integrals, 91 Fresnel-Kirchhoff diffraction parameter, 90 illuminated region, 90f knife-edge diffraction, 90 reflection boundary, 90f shadow boundary, 90f shadow region, 90f digital-to-analog conversion (DAC), 184 Dirac delta (impulse) function, 6, 13, 14, 819 definition, Fourier transform, 6, 13 multiplication and convolution with a function, relation with unit step function, scaling property of, directivity, 53 aperture antenna, 56 half-wave dipole, 55, 72 Hertz dipole, 55, 73 horn antenna, 56 direct sequence (DS) SS systems, 485 error probability in AWGN, 489 link budget for DSSS Wi-Fi, 489 multipath rejection, 502 output SNR vs input SNR, 488 processing gain, 488 Rake receiver, 503, 617 ranging, 504 spreading, 486 spreading factor, 485 synchronization, 490, 491f transceiver for BPSK/DSSS, 486 transceiver for QPSK/DSSS, 489 discrete-cosine transform (DCT), 235 discrete Fourier transform (DFT), 521 876 discrete memoryless channel (DMC), 391 distortionless transmission in ISI channels, 272, 274f diversity, 664 angle diversity, 665 array gain, 648, 658 diversity gain, 658 diversity gain vs maximum eigenvalue, 659 diversity order, 658 frequency diversity, 665 macroscopic diversity, 665 microscopic diversity, 665 polarization diversity, 665 receive diversity (SIMO), 666 spatial (antenna) diversity, 665 time diversity, 665 diversity combining, 666, 693, 697, 698 see also equal-gain combining (EGC); maximal-ratio combining (MRC); selection combining (SC); square-law combining (SLC) diversity order of MIMO systems, 722, 724f Doppler spread, 559, 569, 571 vs angle-of-arrival (AOA), 570 vs channel model, 578 coherence time, 571 vs data rate, 571 Doppler shift, 560, 570 fast fading, 580 Jake’s Doppler spectrum, 570 slow fading, 580 spaced-time correlation function, 571, 572f time-selective channel, 559 vs transmission rate, 573 vs user velocity, 573 DPSK see differential phase shift keying (DPSK) ducting, 121 elevated ducts, 122 surface-ducts, 122 trapping frequency for ducting, 122 earthquake prediction, 867 effective antenna height, 69 effective antenna receive area, 61 E1 hierarchy, 211t electric vector potential, 44 emissivity, 156 Eb/N0, 260 encoding, 186, 203 energy of a sinusoidal signal, 327 energy signal, 15, 16 equal-gain combining (EGC), 678 array gain, 678, 679 BEP for MRC/EGC for BPSK, 679, 680f equalization, 270, 283 of a deterministic channel, 224 of multi-path channel, 271 equalized channel, 270, 271f equivalent noise temperature, 147, 150f Index cascaded systems, 149 receiver figure-of-merit (G/T), 170 system noise temperature, 167 equivalent SNR of AF SRD link with relay selection, 769 equivalent SNR of AF SRD link with relay selection and multiple antennas, 776, 777 capacity, 781 cdf, 779 mean SNR, 780 MGF, 779 pdf, 778 SNR, 778 equivalent SNR of AF SRD link with single antennas at source and destination, 760, 761t amplification factor, 761 BEP for BPSK, 765 cdf of, 763, 764t mean capacity, 764 mean SNR, 762 MGF, 762 pdf of, 762, 764f Rayleigh approximation, 763 error control coding, 389f error correcting codes, 388 error detecting codes, 388, 399 error probability, 311 see also BEP BEP, 316 geometric interpretation for ML detection, 310 pair-wise error probability, 314, 428 rotational invariance of error probability, 312 symbol error probability, 316 translational invariance of error probability, 312 union bound on error probability, 313 Euclidean distance, 393 exponential integrals, 829 exponential pdf, 859 extended noise sources, 154 external noise, 145, 153 extraterrestrial noise, 145 extremely high-frequency (EHF) (30-300 GHz), 106 extrinsic information, 458 see also turbo codes far-field, 35, 37 fast fading, 580 fast Fourier transform (FFT), 526 feeder line noise, 146, 172 flat fading, 565, 579 flat-top sampling, 189 football game, 867 forward error correction (FEC) codes, 388 Fourier series, of pulse train, 4f of a rectangular pulse train, 3, 4f Fourier transform, 4, 820 see also discrete Fourier transform (DFT); fast Fourier transform (FFT); inverse discrete Fourier transform (IDFT); inverse fast Fourier transform (IFFT) 877 Index conjugation property of, 10 convolution property of, 10, 11 decaying exponential, differentiation property of, 12 duality property of, 10, 10f integration property of, 13 periodic functions, 13 periodic impulse train, 14 sampling, 14, 15f superposition property of, table of, 820 time and frequency scaling property of, 9, 9f time and frequency shift property of, Fraunhofer region, 37 frequency division multiplexing (FDM), 480 frequency-hopping (FH) spread spectrum (FHSS), 479, 508 collision probability, 514 de-hopping, 511 error probability for multi-user FH systems, 514, 515f, 516f fast-frequency hopping, 512, 514f hopping bandwidth, 509 jamming margin, 512 noncoherent combining losses, 513 processing gain, 512 serial-search acquisition, 510 slow-frequency hopping, 510 synchronization, 510 frequency-selective fading, 565, 579 frequency-selective slowly-fading channels, 614 BEP for BPSK, 621 channel model, 616 matched-filter realization of Rake receiver, 618 outage probability, 620 pdf of SNR at matched filter output, 620 frequency translation, 8, 9f Fresnel integral, 830 Fresnel region, 37 Fresnel zone, 87, 89 excess delay, 88 excess path length, 89 Fresnel zone height, 89 Friis transmission formula, 65 FSK (coherent) see M-ary coherent FSK FSK (noncoherent) see M-ary noncoherent FSK gain, 60 aperture antenna, 62 vs directivity, 61 isotropic antenna, 62 galactic noise, 145 Gamma function, 829 Gamma pdf, 861 Gauss hypergeometric functions, 827 see also hypergeometric functions Gaussian noise, 147 see also Additive White Gaussian Noise Gaussian pdf, 857 MGF, 858 moments, 858 Gaussian Q function, 811, 815f, 826 asymptotic approximation to, 815 Craig’s definition of, 811 derivative of, 815 exponential approximation to, 812, 815t inverse Gaussian Q function, 812, 817f properties of, 812 relation to complementary error function, 815 table of Gaussian Q function, 811t, 816t generalized selection combining (GSC), 679 array gain, 683 BEP for GSC of DPSK, 682 cdf of SNR, 682 pdf of SNR, 681 geometric representation of signal space, 300 basis functions, 301, 317 energy of a signal vector, 300 Euclidean distance between signals, 301 norm of a signal vector, 300 orthonormal basis functions, 301 geostationary orbit (GEO), 171 global navigation satellite systems (GNSS), 332 global positioning satellites (GPS), 332, 503, 505 Golay code, 426 error probability, 428f weight distribution, 428t granular noise, 228, 230 Gray encoding, 206, 264, 316 Hamming code, 412 comparison with BCH and Golay codes, 428, 429f encoder, 421f error probability, 414f (7, 4) Hamming code, 412, 416, 420 syndrome calculator, 421f Hamming distance, 393 hard-decision decoding (HDD), 392 health hazard of electromagnetic waves, 66 Hertz dipole, 34, 35, 37 high definition TV (HDTV), 192, 236 high-efficiency video coding (HEVC), 236 high frequencies (HF) (3-30 MHz), 82 horn antenna, 56 Huffman coding, 235 hypergeometric functions, 599, 613, 679, 762, 765, 779, 780, 789, 806, 827 ideal distortionless channel, 246f ideal low-pass channel, 246f impedance matching, 70 impulsive noise, 868, 869f input impedance, 43 instantaneous sampling, 187 integrals involving algebraic functions, 824 878 integrals involving (cont’d) Bessel functions, 825 exponentials, 824 Gaussian Q function, 826 logarithm, 826 trigonometric functions, 824 interarrival time, 866 interleaver delay, 430 interleaving depth, 431 interleaving for burst errors, 430 internal noise, 145 interpolation function, 189 inter-symbol interference (ISI), 268 see also BEP due to ISI; coherence bandwidth; distortionless transmission in ISI channels inverse discrete Fourier transform (IDFT), 521 inverse fast Fourier transform (IFFT), 526 ionospheric channel (sky waves), 84, 85 dispersion, 85 Faraday rotation, 85 ionospheric layers (D-layer, E-layer, F-layer), 85 scintillations, 85 total electron content (TEC), 85 isotropic antenna, 47 gain of, 62 jamming strategies for FHSS systems, 498f, 516 broadband-noise jamming, 498f, 516 downlink jamming of a FH SATCOM link, 518 multiple-tone jamming, 498f partial-band factor, 498f, 517 partial-band noise jamming, 498f, 517 repeat-back jamming, 518 joint photographic expert group (JPEG), 235 Ka band (27-40 GHz), 170 Ku band (12-18 GHz), 170 L band (1-2 GHz), 507 least-mean square (LMS) estimation, 222 level crossing rate (LCR), 600 see also average fade duration effect of diversity on, 673 for Nakagami-m fading, 601 for Rayleigh fading, 601 for Rician fading, 602 likelihood ratio, 259 linear adaptive prediction, 225, 226f linear block codes, 396 see also block codes code rate, 397 coding gain, 409 encoder, 396 erasure decoding, 404 error correction capability, 402, 403f, 404 error detection capability, 402 error probability with HDD, 408, 409f error probability with SDD, 409 generator matrix, 398 Index Hamming bound, 406 length, 396 linearity, 397 minimum Hamming distance, 402 minimum weight, 402 parity-check matrix, 399 parity matrix, 398 perfect codes, 406 standard array, 406 syndrome decoding, 399f, 405 syndrome table, 408 systematic code, 398 undetected error probability, 400 weight, 402 linear dipole antenna, 40, 42, 52 linear low-pass channel, 246 linear prediction, 221 filter, 221f, 222 linear predictive coding, 233f linear system, 27 distortionless transmission, 28 impulse response, 28 input-output relationship, 27 line codes, 206 autocorrelation of, 208, 208t bandwidth of, 208 bipolar NRZ line codes, 207f Manchester code, 207f NRZ, 207f polar NRZ line codes, 207f PSD of, 207, 208t, 209f RZ line codes, 242 unipolar line codes, 207f log-normal shadowing, 591, 858 cdf, 592 handover in cellular radio, 595 moments, 591 useful coverage area in cellular radio, 593, 594f loop antenna, 39 LORAN-C, 332 loss resistance, 60, 73 low-density parity check (LDPC) codes, 389, 435, 436f low earth orbit (LEO), 171 low frequencies (LF) (30-300 kHz), 82 magnetic vector potential, 34, 44 man-made noise, 145, 167f MAP decoding in BSC, 308 MAP detection, 259 Marcum Q-function, 815, 827, 861 approximation to, 815 first order Marcum Q-function, 815 M-ary ASK, 333 average symbol energy, 335 bandwidth, 336 bandwidth efficiency, 336 bit/symbol error probability, 334, 335f Index ML detection, 337 on-off keying (OOK), 325, 336 power-bandwidth tradeoff, 336t PSD, 335 M-ary coherent FSK, 358 bandwidth, 364 bandwidth efficiency, 364, 365t coherent BFSK, 359 coherent BFSK transceiver, 360 coherent M-ary FSK, 362 correlation between carriers in BFSK, 361 orthogonality between carriers, 358, 365f PSD of M-FSK, 364 receiver for coherent M-ary FSK, 362 signal-space diagram for BFSK, 360 symbol error probability for M-FSK, 363, 363f upper bound on symbol error probability for M-FSK, 363 M-ary differential PSK (DPSK), 333, 367 BEP for binary DPSK, 369 binary DPSK, 367 binary DPSK receiver, 368 BEP for binary DPSK, 369 comparison between PSK, DEPSK and DPSK, 370t, 371f differential QPSK, 370 DPSK transceiver, 367 M-ary noncoherent FSK, 371 bandwidth, 376 bandwidth efficiency, 376 bit/symbol error probability, 372, 373 noncoherent BFSK, 371 PSD, 373 receiver for noncoherent binary FSK, 372 M-ary PAM see pulse amplitude modulation (PAM) M-ary PCM see pulse code modulation (PCM) M-ary PSK, 338 bandwidth, 340 bandwidth efficiency, 340 BEP for BPSK, 340 BEP for differentially encoded PSK, 352 bit/symbol error probability for M-PSK, 346, 347f, 348f bit/symbol error probability for QPSK, 315, 343 BPSK, 338 BPSK transceiver, 339 differentially encoded M-ary PSK, 350, 351f M-ary PSK, 344 M-ary PSK receiver, 346 offset QPSK, 344 phase-transitions in offset QPSK, 345 phase-transitions in QPSK, 345 power-bandwidth tradeoff in M-ary PSK, 350 PSD of M-PSK signals, 349, 350f QPSK, 341 QPSK transceiver, 342 upper bound on symbol error probability, 349 M-ary QAM, 352 average symbol energy, 354 879 bit/symbol error probability, 354, 355f bit/symbol error probability for 8-ary QAM, 355 M-ary QAM constellation, 353 M-ary QAM receiver, 354 performance comparison between M-ary QAM and M-ary PSK, 356 spectrum efficiency, 377 matched filter, 249 antipodal signals, 262 bi-orthogonal signals, 263 correlated signals, 260 vs correlation receiver, 252 discrete-time matched filter, 254, 255f error probability, 255 orthogonal signals, 262 maximal-length codes, 422, 481 autocorrelation function, 423, 424f, 482 code length, 423 connection diagram, 424 encoder, 422 PSD of, 423, 424f maximal-ratio combining (MRC), 675 array gain, 676 BEP for BPSK in Nakagami-m fading channels, 676, 677f cdf of SNR, 619, 778 pdf of SNR, 619, 652, 653, 778 vs selection combining (SC), 676t unequal branch SNRs in MRC, 677, 678f maximal-ratio transmission (MRT), 687 see also transmit diversity array gain, 688 maximum likelihood decoding (MLD), 390 medium earth orbit (MEO), 171 medium frequencies (MF) (300-3000 kHz), 82 metrics for decoding, 394 mid-rise quantizer, 194 mid-tread quantizer, 194 MIMO beamforming systems, 730 BEP, 732, 733f, 734f SNR, 732 MIMO channel(s), 702, 703 see also Alamouti scheme; correlated MIMO channel; maximal-ratio transmission (MRT); MIMO channels; MIMO channels with double-sided correlation; MIMO channels with single-sided correlation; transmit antenna selection in MIMO systems; transmit diversity; uncorrelated MIMO channels broadcast channel, 702 cooperative channel, 702 MAC channel, 702 MIMO channel, 702 MIMO channels with double-sided correlation, 706, 711 cdf, 713 eigenvalues of the covariance matrix, 712 mean value of largest eigenvalue, 717, 720 pdf, 713, 715f, 721 880 MIMO channels with single-sided correlation, 706, 713 mean value of largest eigenvalue, 716 pdf of largest eigenvalue, 714, 715f, 717, 840 MIMO systems with polarization diversity, 748 beamforming, 751 BEP, 752f, 753f cross-polar discrimination (XPD), 749 cross-polar isolation (XPI), 749 spatial multiplexing, 750 MISO channels see Alamouti scheme; maximal-ratio transmission; transmit antenna selection in MISO systems; transmit diversity ML detection, 259 modulation techniques see M-ary ASK; M-ary coherent FSK; M-ary differential DPSK; M-ary noncoherent FSK; M-ary PAM; M-ary PSK; M-ary QAM moment generating function (MGF), 607, 849 binomial distribution, 868 characteristic function vs MGF, 849 chi-square distribution central, 859 chi-square distribution noncentral, 860 exponential distribution, 859 Gamma, 862 Gaussian, 858 log-normal, 859 moments of a random variable, 849 Nakagami-m, 589, 864 Poisson, 866 Rayleigh, 584, 859 Rician, 587 uniform, 857 motion compensated predictive coding, 235 motion photographic expert group (MPEG), 235 MPEG-2, 192 μ-law, 198 multidimensional (M-ary) signaling, 263, 299 bit duration vs symbol duration, 264, 298 bit energy vs symbol energy, 298 bit error vs symbol error, 316 bit rate vs symbol rate, 264, 299 bit vs symbol, 264, 299 multipath channel, 86, 559, 561, 562 multiple access in OFDM, 539 distributed mode, 540 downlink design, 539 localized mode, 540 OFDMA, 539 resource allocation in OFDMA, 539 resource blocks, 539 uplink design and single-carrier (SC)-FDMA, 539, 542f multiple-antenna systems, 642 see also MIMO; receive diversity (SIMO); transmit diversity (MISO) multiple random variables, 846 conditional pdf, 20, 848 correlation coefficient, 847, 848 Index covariance, 846 joint cdf, 846 joint moments, 19, 847 joint pdf, 846, 852 joint pdf of two Gaussian random variables, 848 marginal pdf, 20, 847 multiple functions of random variables, 852 orthogonality, 847 statistical independence, 847 uncorrelatedness, 847 multi-user diversity (MUD), 615, 623, 626f multivariate normal distribution, 855 see also bivariate distribution mutual impedance, 74 Nakagami-m fading, 587, 863 average fade duration, 603 cdf, 589, 590f, 863, 864 LCR, 602 moments, 588 MGF, 589, 864 pdf, 587, 589, 863 near field, 37, 38f near-field communications, 38 network coding, 798 noise, 145 see also Additive White Gaussian Noise (AWGN) noise figure, 150, 150f broadband devices, 151 cascaded attenuators, 153 cascaded subsystems, 151 lossy device, 152 non-uniform quantization, 197 Nyquist filter, 273, 274f bandwidth, 274, 283t criterion for distortionless channel, 274 pulse, 274 Nyquist sampling, 188f see also sampling omnidirectional antenna, 52 operating noise figure, 151 ordered statistics, 856, 857f orthogonal frequency division multiplexing (OFDM), 480, 481, 519 adaptive modulation and coding, 544 bit loading, 545 channel estimation, 531 cyclic prefix, 522, 526 ICI, 529, 530f, 549 impulsive noise, 543, 544f OFDM receiver, 523 OFDM system design, 528 OFDM transmitter, 520 orthogonality of subcarriers, 522 scheduling, 545 single-frequency network, 528 SIR, 529, 549 Index SNR, 525 symbol duration, 521 synchronization, 532 orthogonal variable spreading codes, 425, 485 see also Walsh-Hadamard codes outage probability vs BEP, 589 in composite channel, 599 in shadowing channel, 592, 596 outdated CSI in AF SRD links with relay selection, 773 BEP, 775, 778f pdf, 775 oversampling, 188f see also sampling PAL system, 235 PAM see pulse-amplitude modulation (PAM) parasitic dipole antenna, 74 input impedance, 76f mutual impedance, 75 radiation pattern, 76, 77f parasitic MIMO, 740 BEP, 744 impedance, 742 output SNR, 743 × parasitic MIMO, 741 × parasitic MIMO, 746 radiation pattern, 744 parity-check bits, 387, 398 Parseval’s power theorem, partial response signaling see correlative level coding partition cell, 194 passband signal, 2, 324 path-loss models, 123 COST 231 extension to Hata model, 125 dual-slope path loss model, 124 effect of earth constants, 84f Erceg model, 128 excess-loss due to vegetation, 135 free-space propagation, 86 ground-reflected wave, 100 ground wave propagation, 83 Hata model, 123 indoor path-loss models, 129, 131f, 134 ionospheric channel, 85 LOS propagation, 86 median path loss, 125 Okumura model, 125 outdoor path-loss model, 123 path-loss exponent, 124t, 130t plane-Earth path-loss model, 101 propagation in vegetation, 134 rural path loss model, 125 shadowing, 131, 133 signal penetration into buildings, 132 suburban path loss models, 125 urban path loss models, 125 881 peak-to-average-power ratio (PAPR) active constellation extension, 539 in ADC, 195 in ASK, 336t cdf of PAPR, 533 clipping, 538 coding, 534 in OFDM, 532 in PAM, 267 partial transmit sequences, 536 in QAM, 356 selective mapping technique, 535 tone injection technique, 538 tone reservation technique, 538 Phase Shift Keying (PSK) see M-ary PSK Planck’s constant, 146, 155 Planck’s law, 146, 155 pointing loss, 63 see also aperture antennas point noise sources, 154 Poisson distribution, 22, 632, 865 cdf, 866 MGF, 866 moments, 23, 866 pdf, 23, 865 Poisson random process, 22 Poisson’s sum formula, 14, 826 polarization, 48 axial ratio, 50 circular polarization, 49 elliptical polarization, 49 linear polarization, 49 polarization loss efficiency, 51 polarization matching, 69 positioning and navigation in DSSS systems, 504, 505 DGPS (differential GPS), 507 EGNOS, 508 GALILEO, 507 GLONASS, 507 NAVSTAR, 505 PPS (precise positioning system), 507 SA (selective availability), 507 SPS (standard positioning system), 507 power-control rate in mobile radio systems, 574 power signal, 15, 17 power spectral density (PSD), 5, 18 Poynting vector intensity, 36 prediction error, 221 probability density function (pdf), 19 see also binomial distribution; Cauchy pdf; chi-square distribution; composite pdf for fading and shadowing; exponential pdf; Gamma pdf; Gaussian pdf; Nakagami-m fading; Poisson distribution; Rayleigh distribution; Rician distribution; uniform pdf of full-wave rectifier output, Z = X , 851 of ratio of two independent Rayleigh distributed random variables, 862 882 probability density function (pdf) (cont’d) of ratio Z = X/Y of two random variables, 854 relation to MGF, 85, 849 of sinusoidal carrier with random phase, 851 of square-law detector output, 850 sum of multiple independent random variables using MGF, 849, 858, 859, 860, 864 sum of two random variables, 848, 851 of Z = max(X,Y), 854 of Z = min(X,Y), 854 progressive scanning, 235 PSD of passband signals, 324 PSK, see M-ary PSK pseudo-noise (PN) sequences, 481 balance property of, 482 correlation property of, 482, 483 Gold sequences, 483 Kasami sequences, 484 run property of, 482 pulse-amplitude modulation (PAM), 205, 263, 313 PAPR, 267 power efficiency, 266t symbol error probability, 265, 265f, 266f pulse-code modulation (PCM), 212 vs FM, 212 PCM decoder, 214, 217 PCM encoder, 213 receiver noise, 215 SNR, 218, 219f pulse duration modulation (PDM), 205 pulse modulation techniques, 204 see also pulse-amplitude modulation (PAM); pulse duration modulation (PDM); pulse position modulation (PPM) pulse position modulation (PPM), 205 QAM see M-ary QAM Q function see Gaussian Q function; Marcum Q function quantization, 186, 193 quantization error, 195 quantization noise (error), 195 radar, 67 radar cross section, 68 radar equation, 68 radiated-field, 37 radiation hardened components, 869 radiation pattern, 51 see also circular aperture; Hertz dipole; linear dipole antenna; parasitic dipole antenna; parasitic MIMO; rectangular aperture beamwidth, 53 field pattern, 53 half-power beamwidth, 53 main-lobe, 53 power pattern, 53 sidelobe (level), 53 radiation resistance, 36 radio-frequency identification (RFID), 38 Index radio horizon, 123 rain attenuation, 110 co-polar attenuation (CPA), 115, 116f cross-polar discrimination (XPD), 115, 116f depolarization due to rain, 114 frequency-scaling of rain attenuation in terrestrial LOS paths, 111 rain attenuation in Earth-space paths, 116, 118 rain attenuation in terrestrial LOS paths, 110 rain margin, 114, 118 specific attenuation, 110, 112t raised-cosine filter, 276 bandwidth, 277, 283t raised-cosine pulse, 277 roll-off factor, 277 root-raised cosine filter, 277 raised-cosine pulse, 32 random-error correcting codes, 389 random process, 20 autocorrelation and PSD of a random binary process, 22, 26 complex random process, 21, 25 ensemble-averaging, 21f, 24 ergodicity, 24 Poisson process, 22, 23f, 25 PSD of, 25 sample function, 21 stationarity, 24 statistical averages, 21 strict-sense stationarity, 22 time-averaging, 21f, 24 wide-sense stationarity, 22 random signal, 18 random variable, 18, 844 continuous, 19, 844 discrete, 19, 845 function of random variable, 845 median, 846 mixed, 846 moments, 19, 845, 847 variance, 19, 845, 847 Rayleigh approximation to equivalent SNR with relay selection, 763, 802 AF SRD link, 764, 771f, 802 DF SRD link, 792, 793 maximal-ratio combined AF SRD and SD links, 767, 768, 773, 804 selection-combined AF SRD and SD links, 772f, 803 Rayleigh distribution, 582, 862 cdf, 584, 862 MGF, 584, 859 moments, 583, 862 pdf, 583, 862 Rayleigh’s energy theorem, 4, 819 RD (relay-destination) link, 759 reactive field, 37 reconstruction filter, 191 Index reconstruction from signal samples, 188, 189 rectangular aperture, 46, 50 rectangular function (pulse), 5, 8, 819 Fourier transform of, red, green, and blue (RGB), 192 Reed-Solomon (RS) codes, 389 error probability, 433f, 434f reflection over Earth’s surface, 96 array factor, 99 Brewster angle, 98f divergence factor, 103 electrical parameters of Earth, 84t, 96 flat-Earth, 95, 98, 103 rough surface, 104 scattering, 104 skin depth, 84 smooth surface, 104 spherical Earth, 95, 101, 103 surface roughness, 104 surface roughness factor, 105f, 106, 106f reflector antenna, 56, 58 regenerative repeater, 213, 214f, 216 see also analog repeater; repeater system noise; satellite relay regenerative satellite, 171 regular pulse-excited-long term prediction (RPE-LTP), 234 relaying protocols, 759 amplify-and-forward (AF), 759 coded cooperation, 759 decode-and-forward (DF), 759 relay selection for AF relaying, 767 BEP for BPSK of maximal-ratio combined SRD and SD links, 772 BEP for BPSK of selection-combined SRD and SD links, 772 BEP for BPSK of SRD link, 771f cdf of SRD link, 769 mean equivalent SNR of SRD link, 770f pdf of SRD link, 770f relay selection strategies, 769 repeater system noise, 172 see also analog repeater; regenerative repeater repetition coding, 400 representation level, 194 resource allocation in fading channels, 622 Rician distribution, 584, 863 cdf, 587, 863 diffuse component, 584 MGF, 587 moments, 585 pdf, 585, 586, 863 Rice factor, 586 specular component, 584 sampling, 186 see also aliasing; Nyquist sampling; oversampling; undersampling; uniform sampling of color video signals, 193 rate, 187 883 satellite hardening against solar flares, 866 satellite relay, 394 scattering function, 564, 577 scheduling in fading channels, 623 greedy scheduler (GS), 624 proportionally fair scheduler (PFS), 624 round-robin (RR) scheduler, 624 Schwartz’s inequality, 826 scrambler in DVB systems, 434 SD link with multiple antennas, 782 BEP, 782 capacity, 782 selection-combined AF SRD, with relay selection, and direct link, 769 BEP for BPSK, 770, 771f, 772f, 773f capacity, 774 cdf, 769 mean SNR, 770 MGF, 762 pdf, 770f selection-combined AF SRD, with relay selection, and direct links with multiple antennas, 783 BEP, 784, 785f capacity, 785, 786f cdf, 783 mean SNR, 783, 784f pdf, 784 selection-combined DF SRD, with relay selection, and direct links with multiple antennas, 794 selection combined two direct links with single antennas, 766 BEP for BPSK, 766 capacity, 767 cdf, 766 mean SNR, 766 MGF, 766 pdf, 766 selection combining (SC), 667 array gain, 669f, 670 BEP for DPSK, 671f BEP for PSK, 672f cdf of SNR in log-normal shadowing, 668f cdf of SNR in Rayleigh fading, 670f level-crossing rate (LCR), 673 pdf of SNR in Rayleigh fading, 670, 671f switch-and-stay combining (SSC), 674, 675f unequal branch SNRs, 672, 673f shadowing see log-normal shadowing Shannon’s capacity limit, 377, 473 Shannon limit for HDD and HDD, 472 signal-to-quantization noise ratio, 195 for non-uniform quantization, 202 signum function, 8, 819 Fourier transform of, SIMO systems see also correlated SIMO channel; diversity combining; equal-gain combiner (EGC); maximal ratio combining (MRC); selection combining (SC); square-law Combining (SLC) 884 sinc function, 3, 819, 830, 831t Fourier transform of, 5, 10f sine and cosine integrals, 829 SISO (soft-in, soft-out) decoders, 458 slope-overload distortion, 228, 229 slow fading, 580 soft-decision decoding (SDD), 392 solar radiation, 48 source-relay-destination (SRD) link, 759 source-relay (SR) link, 759 spaced-frequency spaced-time correlation function, 563, 574 spread spectrum (SS), 481 see also code division multiple access (CDMA); direct sequence (DS) SS systems; frequency-hopping (FH) spread spectrum (FHSS) square-law combining (SLC), 683 BEP for noncoherent BFSK, 685, 686f pdf of SNR, 685 standard definition TV (SDTV), 192 statistical TDM, 212 step size in DM, 193 Stirling’s approximation, 826 super-high frequency (SHF) (3-30 GHz), 106 surface irregularity, 63 symmetric signal, synchronization, 327 carrier recovery, 327 effect of phase error on BEP, 328, 329t phase-recovery circuit, 327 symbol timing error, 329, 330f thermal noise, 146 T1 hierarchy, 211t time and frequency standards, 330 atomic clocks, 331 cesium clock, 331 optical clock (OC), 331 optical-lattice clock (OLC), 331 rubidium clock, 331 time-division multiplexing (TDM), 209 time-division multiplexing hierarchies, 210, 211f, 211t time-spreading due to band limitation, 247, 248f time-spreading due to multipath, 247, 248f transmit antenna selection in MIMO systems, 734 BEP, 739, 740f cdf of SNR, 737, 737t pdf of SNR, 736 SNR, 738 transceiver, 735 transmit antenna selection (TAS) in MISO systems, 690 BEP for TAS, MRT and Alamouti scheme, 691 transmit diversity (MISO), 666, 686 see also Alamouti scheme; maximal-ratio transmission; transmit antenna selection trellis-coded modulation, 390 Index triangular function, 11, 12, 819 Fourier transform of, 11 tropospheric refraction, 107, 118 effect of Earth’s curvature, 120 refractive index, 118 refractivity, 118 standard-refraction, 121f sub-standard refraction, 121f super-refraction, 121f turbo codes, 456 decoder, 458 encoder, 456 error probability, 459 TV receiver system noise, 172 ultrahigh frequencies (UHF) (300-3000 MHz), 82, 85 uncorrelated MIMO channels, 704, 706 see also correlated MIMO channel; MIMO channel BEP vs MIMO size, 735 cdf of eigenvalues, 710, 711f mean value of eigenvalues, 710t pdf of eigenvalues, 708, 709f, 837t, 838 variances of eigenvalues, 710t under-sampling, 188f uniform pdf, 857 uniform quantization, 193, 195 uniform sampling, 187 unit step function, 7, 13, 819 Fourier transform of, Vandermonde matrix, 837 variable length coding, 235 very-high frequencies (VHF) (30-300 MHz), 82, 85 video coding, 234 video compression, 234 voice encoder (vocoder), 232 Walsh-Hadamard codes, 425, 481, 483 see also orthogonal variable spreading codes; variable length coding water-filling algorithm, 728 Wiener-Hopf equation, 222 Wishart distribution, 835, 837 central Wishart distribution, 837 correlated Wishart distribution, 837 non-central Wishart distribution, 837, 838, 839f properties of Wishart distribution, 835 uncorrelated Wishart distribution, 837 Wishart, John, 834 Wishart matrix, 704, 706, 835 full-rank Wishart matrices, 706, 836 pseudo-Wishart matrix, 77, 841 YUV, 192 zero-order hold circuit, 191 WILEY END USER LICENSE AGREEMENT Go to www.wiley.com/go/eula to access Wiley’s ebook EULA ... DIGITAL COMMUNICATIONS DIGITAL COMMUNICATIONS Mehmet Şafak This edition first published 2017 © 2017 John Wiley... chapters are dedicated to statistical theory of digital communications Chapter Pulse Modulation treats the conversion of analog signals into digital for digital xv communication systems Sampling,... in time The Digital Communications, First Edition Mehmet Şafak © 2017 John Wiley & Sons Ltd Published 2017 by John Wiley & Sons Ltd Companion website: www.wiley.com/go/safak /Digital_ Communications