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(AF) Cascaded Fading Channels, 233 Index A p/4-QPSK, 133–136 American Digital Cellular and Japanese time domain waveforms, 131, 132 Digital Cellular systems, 138 waveforms, 130 Amount of fading (AF) signal space, 129 cascaded fading channels, 233, 235 symbol error Gaussian pdf, 366 coherent MPSK, 137, 138 lognormal shadowing channel, 364, 366 equivalent bit error rate, 137 MRC diversity, 362 generic MPSK constellation, 136, 137 Nakagami fading, 211 k bits encoding/mapping, 136 Nakagami parameter, 364, 366 spectral efficiencies and SNR, 138, 139 Rayleigh fading, 200–201 Binomial distribution, 13–15 Rician fading, 203, 204 Bit error rate (BER), 255, 256, 307 shadowing models, 216 BPSK, 256–259 short term faded Nakagami channel, 362 CDF, 259 SSC, 363 fading channel, 259 two channel selection combining moderately shadowed channel, 260, 262 diversity, 363 MRC, 448–450 Amplitude shift keying (ASK), 121–122 Nakagami channels Arnold and Strauss’s bivariate gamma average error probability, 442, 444, 445 distribution, 76 hypergeometric function, 443 MeijerG function, 443 pdf, 449 B Rayleigh channels, 441–442 Bayes theorem, 86–87 severely shadowed channel, 260, 261 BER. See Bit error rate shadowed fading channels Bessel function, 221, 303 average error rates, 446, 447 Beta distribution, 11–13 CCI effect, 446 Binary phase shift keying (BPSK) cochannels, 448 digital signal spectra, 127 N Nakagami interferers, 445 gray encoding, 129, 130 BPSK. See Binary phase shift keying M-ary signals, 128–129 MQAM, 139–141 null-to-null criterion, 127 C QPSK Cascaded channels, 306 modulator, 131, 132 Cascaded fading channels offset-QPSK scheme, 133, 134 AF, 233, 235 phase constellation, 131 average SNR, 233 P.M. Shankar, Fading and Shadowing in Wireless Systems, 455 DOI 10.1007/978-1-4614-0367-8, # Springer Science+Business Media, LLC 2012 456 Index Cascaded fading channels (cont.) probability of miss, 91, 92 CDF, 235, 236 Q function, 92 density function, 233, 234 Rayleigh densities, 90 gamma-distribution, 232 Rician densities, 90 MeijerG function, 232–233 Differential phase shift keying (DPSK), 154 Nakagami-gamma model, 234 Digital frequency modulation (DFM) Cascaded Nakagami channels block diagram, 142, 143 AF, 395, 400, 401 CPFSK, 144 average error probabilities, 405, 406 frequency deviation, 143 BER, 401, 402 pulse shape, 143 CDFs, 396–401, 404, 405 Diversity techniques, 1 density function, SNR, 395 AF Matlab, 396 Gaussian pdf, 366 M-fold convolution, 403, 404 lognormal shadowing channel, 364, 365 MGF, 404, 405 MRC diversity, 363 MRC diversity, AF, 403–404 Nakagami parameter, 364, 366 multihop relayed communication short term faded Nakagami channel, 362 system, 395 SSC, 364 order statistics, 400 two channel selection combining outage probability, 401, 403, diversity, 363 405, 407 average error probability pdfs, SNR, 396, 398–400, 402 average error rate, 366–367 received signal power, 395 CBPSK, 367 threshold SNR, 404 CDF, 369 Cauchy distribution, 15–16 density functions, 373–377 CDFs. See Cumulative distribution functions dual branch correlated MRC, 372 Central limit theorem (CLT), 46–47 dual branch MRC, 375, 377–379 Characteristic function (CHF), 10–11, 57 dual branch SC, 371, 372, 378, 379 Chebyshev inequality, 94–95, 323 four-branch diversity, 371 Chi-squared distribution, 16–18 four channel MRC, 375, 378 Cochannel interference, 5 GSC algorithm, 371, 373 Coherent binary phase shift keying hybrid diversity approach, 375 (CBPSK), 367 Laplace transform, 367 Cumulative distribution functions (CDFs), 8–9, MGF, 367–368 207–208, 322, 330–331 MRC algorithm, 369 Nakagami channel, 368, 373 Nakagami-lognormal model, 373 D Nakagami-m channel, MRC, 370, 371 Decision theory and error rates Q function, 368 channel noise, 85–86 shadowed fading channels, 375, 377, Gaussian case 378, 379 Bayes theorem, 86–87 branch correlation effects binary channel, 86 correlated SC and SSC receiver, 337 conditional density functions, 87 exponential correlation, 334 conditional probability, 87 joint CDF, 339 error probability, 87, 89, 90 Marcum’s Q function, 337 false alarm probability, 89 modified Bessel function, 337, 339 hypothesis testing, 86, 88 MRC algorithm (see Maximal ratio likelihood ratio, 89 combining algorithm) probability of miss, 89 Nakagami parameter, 337, 338 non-Gaussian case pdf, SC algorithm, 339 false alarm probability, 91 cascaded Nakagami channels (see hypothesis testing, 91, 93 Cascaded Nakagami channels) Index 457 CDF, 325 short-term faded channel, 381 diversity receivers, 321 pdf, 314 EGC algorithm, 324 polarization diversity, 318–319 frequency diversity, 318 Rayleigh faded channel, 315 gamma shadowing, 362 received signal power, 315 generalized gamma and Weibull channels SC algorithm AF, 386 CDFs, 322 average error probability, 391, 392 SNR expression, 321–322 BER, dual diversity, 393, 394 SSC algorithm (see Switched and stay CDFs, 387–389, 391 combining algorithm) coherent BPSK modem, 389 signal processing methods, 313 complementary incomplete SNR, 316 gamma function, 390 space diversity, 317–318 detection scheme, 390 time diversity, 319 dual MRC, 392 types, 316 dual SC, BER, 394 “keyhole” scattering, 395 MGF, 392 E modulation type, 389 Equal gain combining (EGC) algorithm, 324 Nakagami-m distribution, 385 Ergodic channel capacity Nakagami pdf, 385 additive white Gaussian noise, 284, 285 SNR, pdfs, 385, 387, 388, 391 cascaded short-term fading channel, 287 GSC algorithm, 361 channel bandwidth, 285 average error probabilities, 408, 409 density function, generalized K average SNR, 357 distribution, 289–290 CDFs, 357–359, 408, 409 double Nakagami cascaded channels, 288 CDMA system, 353 MeijerG function, 285 densities and distributions, 359–360 Nakagami faded channel, 285, 286 gamma random variables, 359 Nakagami-Hoyt channels, 287, 288 joint pdf, 354–356 normalized average channel capacity, 285 Mc signals, 354 quadruple cascaded channels, 287, 289 Nakagami channels, 358, 360 Rayleigh fading, 286 Nakagami-m faded channels, 360, 361 Rician faded channel, 286, 287 normalized peak values, 360 shadowed fading channels, 290, 291 outage probabilities, 407, 410 triple cascaded channels, 287, 289 output SNR, pdfs, 408 Erlang distribution, 18 RAKE reception, 353 Exponential distribution, 18–20 Rayleigh channel, 354–356 three-branch diversity receiver, pdfs, 358, 359 F macrodiversity (see Macrodiversity F (Fisher-Snedecor) distribution, 20–21 techniques) Frequency diversity, 318 MRC algorithm (see Maximal ratio Frequency shift keying (FSK), 124–126, combining algorithm) 141–142 multipath diversity, 320 Nakagami-m distribution (see Nakagami-m distribution) G noise power, 315 Gamma distribution, 21–23 outage probability Gaussian distribution, 33–35 CDF, 381 Gaussian function, 301 MRC algorithm, 382, 384 Gaussian minimum shift keying (GMSK), Nakagami fading channels, 382 146–149 SC algorithm, 382 Generalized Bessel K (GBK) distribution, 65 sensitivity, 381 Generalized gamma distribution, 25 shadowed fading channel, 383–385 definition, 22 458 Index Generalized gamma distribution (cont.) gamma pdf, 344 generalized gamma pdf, 24 GK distribution, 344, 345 normalization factor, 25 joint pdf, 345–346 random variable, 24 MeijerG functions, 351 scaling factor, 25 MRC diversity, 348, 349 Stacy distribution, 24 MRC–SC, 345–347, 350–351 two-sided generalized gamma pdf, 26 pdfs, 352, 353 Generalized K (GK) distribution, 344, 345 shadowed fading channel, 349 Generalized selection combining (GSC) short-term fading effects, 343 algorithm, 361 SNR, SC, 349–350 average error probabilities, 408, 409 shadowing mitigation average SNR, 357 CDF, SC algorithm, 341 CDFs, 357–359, 408, 409 dual correlated Nakagami channels, CDMA system, 353 342 densities and distributions, 359–360 multiple base stations, 340 gamma random variables, 359 normalized Gaussian variable, 341 joint pdf, 354–356 SNR, 340, 342, 343 Mc signals, 354 three-base station arrangement, Nakagami channels, 358, 360 340, 341 Nakagami-m faded channels, 360, 361 Marcum’s Q functions, 3, 179–182 normalized peak values, 360 M-ary phase shift keying (MPSK). See Binary outage probabilities, 407, 410 phase shift keying output SNR, pdfs, 408 M-ary quadrature amplitude modulation RAKE reception, 353 (MQAM), 139–141 Rayleigh channel, 354–356 Matlab and Maple, 5 three-branch diversity receiver, pdfs, 358, 359 Maximal ratio combining (MRC) algorithm, GK distribution. See Generalized K 448–450 distribution Chebyshev inequality, 323 GMSK. See Gaussian minimum shift keying correlation coefficient correlated branch expression, 334 density functions, 335, 336 K SNR, fractional decline, 337 Kibble’s bivariate gamma distribution, 76 noise power, 323 Kurtosis coefficient, 10 processing algorithm, 322 signal power, 323 McKay’s bivariate gamma distribution, 76 L Meijer G function, 67, 68, 299–301, 304 Laplace distribution, 27–28 MGF. See Moment generating function Laplace transforms, 11, 307 Minimum shift keying (MSK) 8-Level phase shift keying (8PSK) modulator, 144, 145 demodulator, 158 power spectrum, 144 modulator, 158 waveform, 144–146 phase constellation, 156, 157 Modems phase encoding, 156, 157 bandwidth requirement, 174 waveform, 159 bit energy, 163 Lognormal distribution, 28–29 carrier regeneration and synchronization, 166–168 channel capacity, 175 M complementary error function, 176–179 Macrodiversity techniques correlator, 114 microdiversity systems cos() and sine() functions, 119 CDFs, 352 differentially encoded signals density functions, 348, 349 coherent vs. noncoherent modems, 156 Index 459 DPSK, 154 inter channel interference, 160, 162 error probability, 152 inverse fast
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