Index A American Digital Cellular and Japanese Digital Cellular systems, 243 Amount of fading (AF) cascaded fading channels, 340, 342 Gaussian pdf, 575 lognormal shadowing channel, 574, 576 MRC diversity, 572 Nakagami fading, 317 Nakagami parameter, 575, 576 Rayleigh fading, 305, 308 Rician fading, 309, 310 shadowing models, 323 short term faded Nakagami channel, 572 SSC, 573 two channel selection combining diversity, 573 Amplitude shift keying (ASK), 225, 226 Arnold and Strauss s bivariate gamma distribution, 81 B Bayes theorem, 89 BER. See Bit error rate Bessel function, 327, 508 Beta Distribution, 14 16 Binary phase shift keying (BPSK) digital signal spectra, 231 gray encoding, 234 M-ary signals, 232 233 MQAM, 243, 244 null-to-null criterion, 231 QPSK modulator, 236 offset-qpsk scheme, 237, 238 phase constellation, 235 π/4-qpsk, 237 240 time domain waveforms, 236, 237 waveforms, 237 signal space, 233 symbol error coherent MPSK, 242, 243 equivalent bit error rate, 242 generic MPSK constellation, 241 k bits encoding/mapping, 241 spectral efficiencies and SNR, 242, 243 Binomial distribution, 16 17 Bit error rate (BER) BPSK, 364 367 CDF, 366 fading channel, 366 moderately shadowed channel, 368 MRC, 706, 708 Nakagami channels average error probability, 700, 703, 705 hypergeometric function, 702 MeijerG function, 702 pdf, 707 Rayleigh channels, 698, 701 severely shadowed channel, 368, 369 shadowed fading channels average error rates, 705, 706 CCI effect, 705 cochannels, 707 N Nakagami interferers, 704 BPSK. See Binary phase shift keying Springer International Publishing AG 2017 P.M. Shankar, Fading and Shadowing in Wireless Systems, DOI 10.1007/978-3-319-53198-4 807
808 Index C Cascaded channels, 511 512 Cascaded fading channels AF, 340, 342 average SNR, 340 CDF, 342, 343 density function, 340, 341 gamma-distribution, 339 MeijerG function, 339, 340 Nakagami-gamma model, 342 Cascaded Nakagami channels AF, 605, 610 average error probabilities, 615, 616 BER, 610, 612 CDFs, 606, 607, 610, 613, 614 density function, SNR, 617 Matlab, 606 M-fold convolution, 613 MGF, 613, 614 MRC diversity, AF, 613, 614 multihop relayed communication system, 605 order statistics, 607 outage probability, 612, 613, 616 pdfs, SNR, 605, 607 609, 611 received signal power, 605 threshold SNR, 614 Cauchy distribution, 18 CDFs. See Cumulative distribution functions Central limit theorem (CLT), 48 50 Characteristic function (CHF), 13, 60 Chebyshev inequality, 97 99, 531 Chi-squared distribution, 18, 20 Cochannel interference, 4 Cognitive radio diversity techniques, 765, 766, 773 energy detection, ideal channels (see Energy detection) random number simulation generalized K channel, 781 ideal channel and Nakagami channel, 777, 780 integral(.), 777 integral2(.), 777 Nakagami channel, 789, 796 Nakagami-lognormal channel, 785 performance comparison, 798, 802 polyarea(.), 777 Coherent binary phase shift keying (CBPSK), 576 Cumulative distribution functions (CDFs), 10 13, 419, 421, 422, 538, 540 D Decision theory and error rates channel noise Gaussian case Bayes theorem, 89, 92 binary channel, 90 conditional density functions, 91 conditional probability, 89 error probability, 91, 93 false alarm probability, 92 hypothesis testing, 89, 91 likelihood ratio, 92 probability of miss, 93 non-gaussian case false alarm probability, 95 hypothesis testing, 94, 96 probability of miss, 95 Q function, 96 Rayleigh densities, 93 Rician densities, 93 Differential phase shift keying (DPSK), 258 Digital frequency modulation (DFM) block diagram, 247 CPFSK, 248 frequency deviation, 248 pulse shape, 247 Diversity techniques, 1 AF Gaussian pdf, 575 lognormal shadowing channel, 574, 576 MRC diversity, 572 Nakagami parameter, 575, 576 short term faded Nakagami channel, 572 SSC, 573 two channel selection combining diversity, 573 average error probability average error rate, 576, 577 CBPSK, 576 CDF, 579 density functions, 544, 582, 584 586 dual branch correlated MRC, 581 dual branch MRC, 587, 588 dual branch SC, 580, 588 four-branch diversity, 582 four channel MRC, 586, 587 GSC algorithm, 582, 583 hybrid diversity approach, 586 Laplace transform, 577 MGF, 577 MRC algorithm, 578 Nakagami channel, 578, 582
Index 809 Nakagami-lognormal model, 584 Nakagami-m channel, MRC, 579 Q function, 578 shadowed fading channels, 586, 589, 592, 593 branch correlation effects correlated SC and SSC receiver, 546 exponential correlation, 543 joint CDF, 548 Marcum s Q function, 546 modified Bessel function, 547, 548 MRC algorithm (see Maximal ratio combining algorithm) Nakagami parameter, 541, 580 pdf, SC algorithm, 548 cascaded Nakagami channels (see Cascaded Nakagami channels) CDF, 533 diversity receivers, 530 EGC algorithm, 533 frequency diversity, 572 gamma shadowing, 571 generalized gamma and Weibull channels AF, 596 average error probability, 600, 601 BER, dual diversity, 602 CDFs, 561, 597 599 coherent BPSK modem, 598 complementary incomplete gamma function, 601 detection scheme, 599 dual MRC, 602 dual SC, BER, 604 keyhole scattering, 605 MGF, 617 modulation type, 599 Nakagami-m distribution, 595 Nakagami pdf, 595 SNR, pdfs, 595, 597, 600 GSC algorithm, 570 average error probabilities, 618, 619 average SNR, 566 CDFs, 567, 568, 570, 607, 619 CDMA system, 563 densities and distributions, 570 gamma random variables, 570 joint pdf, 564, 565 M c signals, 564 Nakagami channels, 568, 569 Nakagami-m faded channels, 570, 595 normalized peak values, 570 outage probabilities, 617, 620 output SNR, pdfs, 618 RAKE reception, 563 Rayleigh channel, 563, 565 three-branch diversity receiver, pdfs, 568, 618 macrodiversity (see Macrodiversity techniques) MRC algorithm (see Maximal ratio combining algorithm) multipath diversity, 528 Nakagami-m distribution (see Nakagami-m distribution) noise power, 524 outage probability CDF, 591 MRC algorithm, 591, 593 Nakagami fading channels, 592 SC algorithm, 617 sensitivity, 591 shadowed fading channel, 592, 593 short-term faded channel, 591 pdf, 523 polarization diversity, 527 Rayleigh faded channel, 523 received signal power, 523 SC algorithm, 525 CDFs, 530 SNR expression, 529, 530 SSC algorithm (see Switched and stay combining algorithm) signal processing methods, 521 SNR, 522 space diversity, 525 526 time diversity, 527 528 types, 524 525 E Energy detection AUC gamma density, 723 performance index, 720, 721 polyarea(.), 727 ROC curve, 722 SNR, 719, 728 hypothesis testing, 714 ideal channel, 715 Matlab command marcumq(.), 717 polyarea(.), 718 Nakagami fading channel, 728, 729, 732, 736, 741 N*Nakagami channels, 759, 760, 765 partial AUC, 753, 756, 757
810 Index Energy detection (cont.) shadowed fading channels, 744, 748 signal-to-noise ratio, 714 Equal gain combining (EGC) algorithm, 648 Ergodic channel capacity additive white Gaussian noise, 393 cascaded short-term fading channel, 397 channel bandwidth, 393 density function, generalized K distribution, 327 double Nakagami cascaded channels, 397 MeijerG function, 394 Nakagami faded channel, 394 Nakagami-Hoyt channels, 395, 396 normalized average channel capacity, 394 quadruple cascaded channels, 397, 398 Rayleigh fading, 394 Rician faded channel, 394, 396 shadowed fading channels, 399 triple cascaded channels, 397, 398 Erlang distribution, 21 Exponential distribution, 21, 22 F F (Fisher-Snedecor) distribution, 22 23 Frequency diversity, 526 Frequency shift keying (FSK), 228, 229, 245 247 G Gamma distribution, 24 26 Gaussian distribution, 36 37 Gaussian function, 507 Gaussian minimum shift keying (GMSK), 251 Generalized Bessel K (GBK) distribution, 68 Generalized gamma distribution definition, 26 generalized gamma pdf, 27 normalization factor, 81 random variable, 26 scaling factor, 28 Stacy distribution, 26 two-sided generalized gamma pdf, 29 Generalized K (GK) distribution, 553, 554 Generalized selection combining (GSC) algorithm, 618 641 average error probabilities, 618, 619 average SNR, 566 CDFs, 568, 570, 607, 619 CDMA system, 563 densities and distributions, 570 gamma random variables, 570 joint pdf, 564, 565 M c signals, 564 Nakagami channels, 568, 569 Nakagami-m faded channels, 570, 595 normalized peak values, 570 outage probabilities, 617, 620 output SNR, pdfs, 618 RAKE reception, 563 Rayleigh channel, 563, 565 three-branch diversity receiver, pdfs, 568, 618 GK distribution. See Generalized K distribution GMSK. See Gaussian minimum shift keying K Kibble s bivariate gamma distribution, 79 Kurtosis coefficient, 12 L Laplace distribution, 29 Laplace transforms, 13 14, 512 8-Level phase shift keying (8PSK) demodulator, 263 modulator, 263 phase constellation, 235 phase encoding, 261, 262 waveform, 264 Lognormal distribution, 31, 32 M Macrodiversity techniques microdiversity systems CDFs, 561 density functions, 557, 558 gamma pdf, 553 GK distribution, 554 joint pdf, 554, 555 MeijerG functions, 560 MRC diversity, 557, 559 MRC SC, 554 556 pdfs, 561, 562 shadowed fading channel, 560 short-term fading effects, 549 SNR, SC, 558, 560 shadowing mitigation CDF, SC algorithm, 549 dual correlated Nakagami channels, 551 multiple base stations, 548
Index 811 normalized Gaussian variable, 550 SNR, 549, 551, 552 three-base station arrangement, 548 Marcum s Q functions, 3, 285, 287, 288 M-ary phase shift keying (MPSK). See Binary phase shift keying M-ary quadrature amplitude modulation (MQAM), 243, 245 Matlab and Maple, 5 Maximal ratio combining (MRC) algorithm, 543 545, 709 Chebyshev inequality, 531 correlation coefficient correlated branch expression, 543 density functions, 544 SNR, fractional decline, 545 noise power, 531 processing algorithm, 531 signal power, 531 McKay s bivariate gamma distribution, 80 Meijer G function, 105, 136, 357, 503, 505 507, 509 MGF. See Moment generating function Minimum shift keying (MSK) modulator, 249, 250 power spectrum, 249 waveform, 249 Modems bandwidth requirement, 279 bit energy, 268 carrier regeneration and synchronization, 271, 272 channel capacity, 281 complementary error function, 282, 284, 285, 287, 288 correlator, 218 cos() and sine() functions, 222 differentially encoded signals, 256 coherent vs. noncoherent modems, 261 DPSK, 258 error probability, 256 8-level PSK (see 8-Level phase shift keying) modified Bessel function, 258 noise variance, 257 noncoherent detection, 257 noncoherent receiver, 258, 259 non-gaussian statistics, 256 phase encoding, 260 Rician statistics, 257 digital communication system, 214 digital modulation techniques, 221 digital signal bandwidth, 268, 269 digital transmission, 215 error function, 282 Euclidian distance, 224 gamma functions, 283 Gaussian Q function, 217, 252, 255 general nonlinear modulation schemes DFM (see Digital frequency modulation)) error rates, 255 256 FSK, 245, 246 GMSK, 251, 252 MSK (see Minimum shift keying) orthogonal M-ary FSK, 252, 254, 255 gray coding, 214 inter symbol interference cosine pulse shape, 289, 290 eye pattern, 291, 292 impulse response, 288 roll-off factor, 290 Kroenecker delta function, 222 Marcum s Q functions, 285, 287, 288 M-ary signaling, 214 M-ary transmission system, 222 matched filter, 218 modulation techniques, 226 228 ASK, 225, 226 BPSK (see Binary phase shift keying) FSK, 228 230 PSK, 226 228 QAM, 245 N-dimensional orthogonal space, 222 noise power, 268 noise variance, 216 Nyquist criteria, 219, 221 OFDM digital Fourier transforms principle, 265, 266 fast Fourier transform algorithm, 266 frequency domain representations, 265 inter channel interference, 264, 266 inverse fast Fourier transform approach, 266 subcarrier frequencies, 265, 266 transmitter and receiver, 266 optimum filter, impulse response, 218 phase mismatch angular mismatch, 274, 275 coherent QPSK, 278 correlation function, 276 fixed phase mismatch, 274 jitter, 276 matched filter, 276 normalized timing offset, 277
812 Index Modems (cont.) random phase mismatch, 274, 275 timing offset, 276 power spectral density, 217 probability of error, 223 225 probability density function, 216 pulse shapes, 218 220 Q functions, 282, 285 Shannon s channel capacity theorem, 280 signal-to-noise ratio, 217 sin c pulse, 220 spectral and power efficiencies, 280 symbol energy, 268 zero mean Gaussian white noise, 215 Moment generating function (MGF), 13 14, 577 MQAM. See M-ary quadrature amplitude modulation MRC algorithm. See Maximal ratio combining algorithm MSK. See Minimum shift keying Multipath diversity, 528, 529 Multipath propagation phenomenon, 3 N Nakagami channels, 684 685, 700, 702, 703, 705 bit error rates average error probability, 700, 703, 705 hypergeometric function, 702 MeijerG function, 702 pdf, 694 N*Nakagami channels, 759 762 Nakagami distribution, 32 35 Nakagami fading AF, 317 CDF, 351, 352 channel, 508 510 chi-square density function, 315 clustering/bunching concept, 314 density moments, 312 Gaussian densities, 315 Nakagami-m pdf moments, 314, 315 received signal envelope, 312, 313 Rician envelope densities, 316 Nakagami fading channel, 728 743 Nakagami-gamma/generalized K models, 326, 327, 329 Nakagami-inverse Gaussian distribution, 332 Nakagami-m distribution CDF, 536 540 density functions, 536 537 EGC algorithm, 533 Matlab, 536 MRC algorithm, 534, 535, 543 received signal power, 605 SC algorithm, 530, 534 SNR improvement, 541 statistical model, 522 Nakagami-N-gamma channels, 4 Natural logarithm, 508 Non-central chi-squared distribution, 35 Nyquist criteria, 219, 221 O Orthogonal frequency division multiplexing (OFDM), 3 digital Fourier transforms principle, 265, 266 fast Fourier transform algorithm, 266 frequency domain representations, 265 inter channel interference, 264, 267 inverse fast Fourier transform approach, 266 subcarrier frequencies, 265, 266 transmitter and receiver, 266 P Pdf. See Probability density function Phase shift keying (PSK), 226 228 Poisson distribution, 37 38 Polarization diversity, 527 Probability and statistics concepts bivariate correlated distributions gamma pdf, 79 81 generalized gamma pdf, 81 82 Nakagami pdf, 78 79 normal pdf Rician distribution, 82 Weibull pdf, 82 CDF, 10 12 Chebyshev inequality, 97 99 Chernoff bound, 99 100 CHF, 13, 60 CLT, 49 conditional densities, 46 47 correlation coefficient, 48 covariance, 47 decision theory and error rates (see Decision theory and error rates) expected value, random variables, 46, 47 independent random variables, 48 joint densities, 46 47
Index 813 joint pdf, multiple random variable CDF differentiation, 59 diversity combining algorithm, 60 Jacobian, 54, 55 Leibniz s rule, 58 probability volume calculation, 58 region of interest, 58, 151 two-scaled random variables, 55 Laplace transforms, 13 marginal densities, 46, 47 moment generating functions, 13 14 normal pdf, 77 order statistics bivariate correlated pdf, 86 bivariate lognormal densities, 87 bivariate Nakagami pdf, 86 bivariate Rayleigh pdf, 79, 86 exponential pdf, 85 generalized Bernoulli trial, 16 joint CDF, 83 lognormal random variables, 89 Marcum Q function, 87 selection combining algorithm, 83 short-term fading, indoor wireless channels, 87 orthogonality, 47 48 pdf, 12, 26, 43 beta distribution, 14, 16 binomial distribution, 16, 17 Cauchy distribution, 18 chi-squared distribution, 18 20 Erlang distribution, 21 exponential distribution, 21 22 F distribution, 22 23 gamma distribution, 24, 25 Gaussian distribution, 29 generalized gamma distribution (see Generalized gamma distribution) Laplace distribution, 29 30 lognormal distribution, 31 32 Nakagami distribution, 32, 34, 35 non-central chi-squared distribution, 35 36 Poisson distribution, 37, 38 Rayleigh distribution, 38 41 rectangular/uniform distribution, 41 42 student s t distribution (see Student s t distribution) Weibull distribution, 45 46 random variable transformations Bessel function, 62, 66 doubling formula, 65 gamma random variable sum, 65, 68 Gaussian, chi-squared and student t distributions relationship, 75, 76 GBK distribution, 69 K distribution, 68 lognormal fading conditions, 71 marginal density function, 61 Meijer s G function, 70, 71 monotonic transformation property, 66 Nakagami-m distributed envelope values, 72 phase statistics, 62 Rician factor, 63 SNR, 74 stochastic processes, 100 105 autocovariance, 102 ergodicity concept, 104 first order density function, 102 higher-order density functions, 102 power spectral density, 104 second order density function, 102 spectral density, 104 thermal noise, 104 time domain function, 100 wide stationary sense process, 103 Y ¼ g(x), pdf and CDF derivation filter, input-output relationship, 50, 51 many-to-one transformation, 52 monotonic transformation, 50, 51 non-monotonic transformation, 51, 52 Z ¼ X + Y, pdf, 53 54 Probability density function (pdf), 13, 29, 304, 401, 405, 694 699 beta distribution, 14, 16 binomial distribution, 16, 17 Cauchy distribution, 18 chi-squared distribution, 18 20 Erlang distribution, 21 exponential distribution, 21 22 F distribution, 22 gamma distribution, 24, 25 Gaussian distribution, 29 Gaussian pdf, 322 generalized gamma distribution (see Generalized gamma distribution) Laplace distribution, 29 lognormal distribution, 31 32 Nakagami channels, 694 Nakagami distribution, 32 34 Nakagami-Hoyt pdf, 391 Nakagami-m pdf, 307 non-central chi-squared distribution, 35 36 Poisson distribution, 37 Rayleigh channels, 698, 701
814 Index Probability density function (pdf) (cont.) Rayleigh distribution, 38 41 rectangular/uniform distribution, 41, 42 Rician fading, 313 second order statistics conditional pdf, 401 envelope pdf, 405 SNR, joint pdf, 401 shadowed fading channels N interfering channels, 697 probability density functions, 696, 698, 699 signal-to-cci ratio, 696 SNR, density function, 694 696 student s t distribution (see Student s t distribution) Weibull distribution, 45 46 PSK. See Phase shift keying Q Quadrature amplitude modulation (QAM), 231 Quaternary phase shift keying (QPSK) modulator, 236 offset-qpsk scheme, 237 phase constellation, 235 π/4-qpsk, 237 240 time domain waveforms, 236, 237 waveforms, 237 R RAKE receiver, 528 Random number simulation generalized K channel, 781 ideal channel and Nakagami channel, 777 779, 781 integral(.), 777 integral2(.), 777 Nakagami channel, 789, 799 Nakagami-lognormal channel, 785, 789 performance comparison, 798, 801 polyarea(.), 777 Rayleigh channels, 680 684 bit error rates, 698, 701 N cochannels, 677 outage probability, 680 CCI channels, 683, 684 desired signal power, 682, 683 multiple cochannels, 682 SIR/q, 680 Z 0 /ZT, 681 pdf, 693 Poisson random variable, 683 protection ratio, 678 signal-to-interference, 693 threshold and protection factor, 679 Rayleigh distribution, 38, 39, 41 Rayleigh fading AF, 307 amplitude, 303 exponential densities, 305 Gaussian random variables, 304 histogram, 305, 306 inphase and quadrature notation, 303 multipath phenomenon, 303 Nakagami-m pdf, 307 pdf, 305 Rayleigh density function, 305 Rayleigh-lognormal channel, 328 Rectangular/uniform distribution, 41, 42 Rician factor, 63, 83 Rician fading AF, 332 average power, 310, 394 density function, 308, 309, 312 error function, 312 Gaussian statistics, 310 Marcum Q function, 309 mean and second moments, 309 phase, pdf, 311 received power, 308 Rician factor, 308, 311 S Selection combining (SC) algorithm, 529, 530 Shadowed fading channels AF, 332, 333 BER, 362, 363 average error rates, 705, 706 BPSK, 364 366 CCI effect, 705 CDF, 366 cochannels, 707 fading channel, 366 moderately shadowed channel, 368 Nakagami interferers, 704 severely shadowed channel, 369 cascaded approach AF, 349 351 CDF, 352, 419 central limit theorem, 344 density function, 345, 348 digamma and trigamma function, 346
Index 815 gamma parameter, 346 gamma random variables, 347 GK distribution, 397 inverse Gaussian distribution, 344 MeijerG function and Bessel function, 347 Nakagami-N-gamma distribution, 344 outage probabilities and error rates, 349 shadowing, higher level, 347, 349 conditional density function, 687 equivalent gamma model, 687 generalized gamma model, 330, 331 N interfering channels, 697 Nakagami-gamma/generalized K models Nakagami-inverse-Gaussian model, 328 330 Nakagami-lognormal models average power, 325 density functions, 325 vs. short term fading, 326 outage probability CDF, 378, 381 density function, 378, 381 multiple interfering shadowed fading channels, 690, 691 Nakagami-cascaded gamma channel, 377, 379 Nakagami inverse Gaussian channel, 379 Nakagami-lognormal channel, 375, 377 379 Nakagami-m distributed cochannel, 687, 688 Nakagami parameter, 377 single interfering channel, 690 pdf, 696 N interfering channels signal-to-cci ratio, 696, 697 SNR, density function, 694, 704 shadowing density, 687 Shannon s channel capacity theorem, 280 Short-term fading attenuation, 302 average power, gamma pdf moments, 318 CDF, 319 gamma fading channel, 318, 320, 321 generalized gamma channel, 319 321 Nakagami fading AF, 317 CDF, 314 chi-square density function, 315 clustering/bunching concept, 314 density moments, 312 Gaussian densities, 315 Nakagami-m pdf moments, 315 received signal envelope, 312 Rician envelope densities, 316 Rayleigh fading AF, 307 amplitude, 303 exponential densities, 305 Gaussian random variables, 304 histogram, 305, 306 inphase and quadrature notation, 303 multipath phenomenon, 303 Nakagami-m pdf, 307 pdf, 305 Rayleigh density function, 305 Rician fading AF, 332 average power, 310, 394 density function, 308, 309, 312 error function, 312 Gaussian statistics, 310 Marcum Q function, 309 mean and second moments, 309 phase, pdf, 311 received power, 308 Rician factor, 308, 311 statistical characteristics, 303 Weibull fading model, 320, 321 Signal transmission and deterioration, 1 Skewness coefficient, 12 Space Diversity, 525, 526 SSC algorithm. See Switched and stay combining algorithm Stacy distribution, 26 Statistical decision theory, 3 Statistical distributions, 2 Stochastic processes, 100 autocovariance, 102 ergodicity concept, 104 first order density function, 101 higher-order density functions, 102 power spectral density, 104 second order density function, 102 spectral density, 104 thermal noise, 104 time domain function, 100 wide stationary sense process, 103 Student s t distribution, 43 cumulative distributions functions, 43, 44 Gaussian and Cauchy distributions, 43 moments of, 43 random variable, 43
816 Index Switched and stay combining (SSC) algorithm CDFs, 537, 538 logic and switching circuits, 538 Nakagami parameter, SNR improvement, 541, 542 vs. SC dual branch, density functions, 540 vs. SC SNR enhancement, 538, 542 T Thermal noise, 104 Time diversity, 527 Time domain function, 100 W Weibull distribution, 45, 46 Weibull fading model, 320, 321 Wireless channels, 1, 2, 300 attenuation, 302 average probability of error bit error rate (see Bit error rate) coherent BPSK modem, 692 probability density function (see Probability density function) cascaded models, 300, 353 cascaded fading channels (see Cascaded fading channels) cooperative diversity, 338 double Rician channels, 353 multiple scattering, 338 N*Weibull channels, 353 shadowed fading channels (see Shadowed fading channels) composite model cluster power, 334 double Nakagami fading and Nakagami-m fading, 336 double Rayleigh and Rayleigh densities, 338 gamma Weibull/Weibull Weibull channel, 337 miniclusters, 334 received signal power, 333 scaling factors, 334 signal-to-noise ratio, 338 Doppler fading, 302 ergodic channel capacity additive white Gaussian noise, 393 cascaded short-term fading channel, 397 channel bandwidth, 393 density function, generalized K distribution, 327 double Nakagami cascaded channels, 397 MeijerG function, 394 Nakagami faded channel, 394 Nakagami-Hoyt channels, 395, 396 normalized average channel capacity, 394 quadruple cascaded channels, 397, 398 Rayleigh fading, 394 Rician faded channel, 394, 396 shadowed fading channels, 399 triple cascaded channels, 397, 398 error rates, 364 cascaded channels, 361 363 complimentary error function, 355 generalized gamma channel, 359, 362 ideal Gaussian channel, 439 lognormal channel, 359 lognormal random variable, 359, 360 lognormal shadowing, 359 Nakagami channels, 358, 375 Nakagami-Hoyt channels, 392, 424 power penalty, 355, 357 Rayleigh fading channel, 355 Rician channel, 358 shadowed fading channels (see Shadowed fading channels) signal-to-noise ratio, 357 SNR correction factor, 360 Weibull channels, 361 fading channel, 509 frequency selective fading channels, 302 general fading models AF, 392 central limit theorem, 382 cluster based scattering model, 383 Gaussian random variables, 388 generalized Nakagami pdf, 391 η μ density, 384 α η μ distributions, 382 Hoyt fading channel, 387 κ μ density, 389 α λ μ distributions, 391 modified Bessel function, 385 Nakagami-Hoyt distribution, 384 Nakagami-Hoyt pdf, 384 Nakagami parameter, 385, 386 Rice distribution, 388 total power, 388 unified model, 382 long-term fading, 301 multipath transmission, 301 multiple scattering, 301
Index 817 outage probability cascaded N*Nakagami channel, 342 CDF, 372 generalized gamma fading channel, 372 Nakagami channels, 684 685 Nakagami-Hoyt channels, 392 Nakagami-m faded channel, 371 Rayleigh channels (see Rayleigh channels) shadowed fading channels (see Shadowed fading channels) SNR, 370 Weibull channels, 372, 374 second order statistics average fade duration, 401, 403, 405 conditional pdf, 407 envelope pdf, 405 level crossing rates, 401 maximum Doppler frequency shift, 402 Nakagami fading channel, 406 Rayleigh faded channel, 401 Rician channel, LCR, 404 shadowed fading channels, 406 SNR, joint pdf, 401 temporal characteristics, 401 transmitter and receiver effects, 307, 409 Weibull fading, 404, 405 shadowed fading channels, 301 (see also Shadowed fading channels) shadowing models AF, 323 definition, 322 gamma distribution, 324 Gaussian pdf, 322 lognormal density function, 323 shadowing parameter vs. gamma parameter, 324 short-term fading (see Short-term fading) variance ratio, inphase and quadrature component, 383, 386