Fundamentals Of Wireless Communication

558 Index

fast fading channels (Cont.) downlink with multiple transmit

antennas 468 full CSI 468 receiver CSI 468–9

receiver CSI and partial CSI at base-station 469–71

multiuser capacity AWGN uplink 245–7

full channel side information 247–50 multiuser communications with MIMO

systems 436–9 full CSI 438–9

receiver CSI 436–7, 437

uplink with multiple transmit and receive antennas 445

receiver CSI 445–7, 446 flash-OFDM 153–4

flat fading channels 33, 34 Clarke’s model 38–40, 40

foward channel 4, 121 frequency coherence 32 frequency diversity 100–1 basic concept 83–4

direct-sequence (DS) spread-spectrum 91, 92, 101–2

performance analysis 93–5 Rake receiver 91–3, 93

error probability analysis 86–8 extensions 198–9

geometric view 197–8, 198 implementing MLSD 88–91, 88 orthogonal frequency division

multiplexing (OFDM) systems 95–9, 102, 108, 108

block length 99–100

outage performance of parallel channels 195–7

single-carrier with ISI equalization 84–5, 101

frequency-selective channel viewed as MISO channel 85, 85

frequency division duplex (FDD) systems 69, 121

frequency hopping 71 frequency reuse 122, 127–8 frequency-selective channels

fading channels 33, 34 capacity 213

multiuser capacity 252–3

linear time-invariant Gaussian channels coding across sub-carriers 185–6 transformation to parallel channel

181–3, 181

waterfilling power allocation 183–5,

184, 185

Gaussian noise, detection in

complex vector space detection 507–9 scalar detection 503–4, 504

vector space detection 504–7, 505, 506 Gaussian noise, estimation in

complex vector space estimation 511–13

scalar estimation 509–10 vector space estimation 510–11

Gaussian random variables complex Gaussian random

vectors 500–3

real Gaussian random vectors 497–500,

498, 499

scalar real Gaussian random variables 496–7, 497

Global System for Mobile (GSM) communication systems 4 narrowband allocations 124–5

performance 125

signal characteristics and receiver design 125–6

time diversity 69–71, 70

Hadamard sequences 146 handoff 121

see also soft handoff Hermitian matrices 75 hopping patterns 150–2, 151

i.i.d. Gaussian code 170 ideal interweaving 533–4

imperfect power control averaging 141 impulse response

baseband equivalent 25 fading multipath channel 21

information theory 166, 167, 516 capacity of fast fading channels

MIMO channels 534–6 scalar channels 533–4

discrete memoryless channels 516–18,

517, 518

entropy, conditional entropy and mutual information 518–21

formal derivation of AWGN capacity 526, 527–9

analog memoryless channels 526–7 multiple access channels

capacity region 537–9, 539 capacity region corner points

539–40, 540

fast fading uplink 540–1

noisy channel coding theorem 521 achieving upper bound 523–5 operational interpretation 525–6 reliable communication and conditional

entropy 521–2 outage formulation 536–7

559

Index

receiver optimality fading channels 364

MMSE is information lossless 362–3 time-invariant channel 363–4

sphere-packing interpretation 529 achievability 530–2, 531 converse 529–30, 530

time-invariant parallel channel 532–3 inner codes 194

inter-cell interference 145–6 interference 1

interference averaging 141 interference avoidance 271 interference diversity 141 interference nuller 81, 350 interference-limited rate 235 interference-limited systems 129

capacity 142 interleaving 59, 60, 61

inter-symbol interference (ISI) 83 equalization and CDMA multiuser

detection 364–5, 365

IS-856

downlink 209–10, 210 prediction uncertainty 211–13 rate control 210–11

rate versus power control 210 IS-95 link

CDMA downlink 146, 146 CDMA uplink 136–7, 136

power control 138–9, 139

Jensen inequality 202–3, 245, 295, 338

Kuhn–Tucker condition 183

large-scale fading 10, 11, 40 Latin squares 150

orthogonal 151 linear decorrelator 434

geometric derivation 349–52, 350, 351 performance for deterministic H

matrix 352

performance in fading channels 352–4,

353, 354 linear equalizers 90

linear time-invariant (LTI) channel 13 linear time-varying system model for

wireless channels 20–2 local area networks (LANs)

ad hoc network 5 wireless systems 5 log-likelihood ratio 51

low-complexity detection 80–1, 82

macrodiversity 59, 130 matched filter 61

maximal ratio combining 61, 140 maximum length shift register (MLSR)

132–3

maximum likelihood (ML) rule 51, 503, 504 maximum likelihood sequence detection

(MLSD) 86

Viterbi algorithm 88–91, 88 memoryless channels 526–7 minimum Hamming distance 69 minimum mean square error (MMSE)

equalizers 90, 333 information theoretic optimality

fading channels 364

MMSE is information lossless 362–3 time-invariant channel 363–4

linear MMSE receiver

decorrelator limitations 356–7, 357 derivation 357–60, 358 MMSE–SIC 361–2, 361, 362 performance 360, 361

performance enhancement by MMSE decoding 459–61, 460

mobile switching center (MSC) see mobile telephone switching office (MTSO)

mobile telephone switching office (MTSO) 3–4

multipath fading 11, 16

multiple input multiple output (MIMO) channels 290–1, 328–9

see also multiuser communications with MIMO systems

antenna diversity

degrees of freedom 77–8, 78 low-complexity detection 80–1, 82 spacial multiplexing 79–80 summary of 2 × 2 schemes 82

capacity 332–3, 345, 373 CSI at receiver 336–8 performance gainss 338–46

D-BLAST archicture 368

coding across transmit antennas 371–2, 371

suboptimality 368–70 diversity-multiplexing tradeoffs 383, 384

2 × 2 MIMO Rayleigh channel 392–5 formulation 384–6

MIMO Rayleigh channel 392, 393, 393 MISO Rayleigh channel 391–2

n × n MIMO i.i.d. Rayleigh channel 395–8, 396, 397

parallel Rayleigh channel 390–1, 391 scalar Rayleigh channel 386–90,

388, 389 full CSI 346

capacity 346

performance analysis 347–8 transceiver architecture 347

560

Index

multiple input multiple output (MIMO) channels (Cont.)

modeling fading channels 309 angular domain transformation

315–16, 316

basic approach 309–10, 310 dependency on antenna spacing 323–7,

324, 325, 326, 327

i.i.d. Rayleigh fading model 327–8 multipath channels 311

multiplexing architectures 332–3, 373 fast fading channels 335–6 V-BLAST 333–5

multiplexing capability 291, 309 capacity via singular value

decomposition 291–4, 293 rank and condition number 294–5

physical modeling 295–6

antenna arrays with only a line-of-sight path 299–300

geographically separated antennas 300–6, 300, 303, 304, 305 line-of-sight MISO channels 298–9 line-of-sight plus one reflected path

306–9, 307, 308 line-of-sight SIMO channels

296–8, 296

receiver architectures 348–9

information theoretic optimality 362–4 linear decorrelator 349–54, 350, 351,

353, 354

linear MMSE receiver 356–62, 357,

358, 361, 362

successive cancellation 355–6, 355 slow fading channels 366–8

high SNR 368

universal space-time codes 383, 398, 411, 415–16

design criterion 412–13

properties of approximately universal codes 413–15

QAM is approximately universal for scalar channels 398–400

universality of D-BLAST 411–12 multiple input single output (MISO)

channels 73

frequency-selective channels 85, 85 large transmit antenna arrays 344, 345 linear time-invariant Gaussian channels

179–80 modeling 298–9

Rayleigh fading 391–2 universal code design 407, 410

conversion to parallel channels 408–9

design criterion 409–10

viewed as parallel channels 407–8,

multiplexing

D-BLAST architecture 368 coding across transmit antennas

371–2, 371 suboptimality 368–70

MIMO architectures 332–3, 373 fast fading channels 335–6 V-BLAST 333–5

receiver architectures 348–9

information theoretic optimality 362–4 linear decorrelator 349–54, 350, 351,

353, 354

linear MMSE receiver 356–62, 357,

358, 361, 362

successive cancellation 355–6, 355 slow fading MIMO channels 366–8

high SNR 368 multiuser capacity 228–9

see also capacity of wireless channels AWGN downlink 235–6, 236, 241

general case of superposition coding achieves capacity 238–40, 239

symmetric case of two capacity-achieving schemes 236–8

AWGN fading downlink 250

channel side information at receiver only 250–1

full channel side information 251–2 AWGN fading uplink 243, 250

fast fading 245–7

slow fading 243–4, 245 AWGN uplink 240–1

capacity via successive interference cancellation (SIC) 229–32,

229, 230

compared with conventional CDMA 232, 233

compared with orthogonal multiple access 232–4, 234

general K-user uplink capacity 234–5 frequency-selective fading channels 252–3

multiuser communications with MIMO systems 425–6

downlink with multiple receive and transmit antennas 471–3, 471, 472, 481

downlink with multiple transmit antennas 448, 448

degrees of freedom 448–9 fast fading 468–71

precoding for downlink 465–8 precoding for interference known at

transmitter 454–65, 455, 456, 457 uplink-downlink duality and transmit

beamforming 449–53 multiple antennas in cellular networks

uplink 478–9

561

Index

uplink with multiple receive antennas 426, 426

fast fading 436–9 multiuser diversity 439–42

slow fading 433–6, 435, 436 space-division multiple access (SDMA)

426–7

space-division multiple access (SDMA) capacity region 428–30, 429

system implications 431–2, 432 uplink with multiple transmit and receive

antennas 442 fast fading 445–7

SDMA 442–4, 443, 444 system implications 444–5, 445

multiuser diversity 228, 229, 276–7 channel prediction and feedback 262–3 fair scheduling 258

multiuser diversity gain in practice 261–2, 261, 262

proportional fair scheduling 258–60, 259

superposition coding 260–1, 261 multicell systems 270–2

multiuser communications with MIMO systems 439

one user at a time policy 439–40 optimal power allocation policy

440–2, 441

multiuser diversity gain 253–6, 254 multiuser versus classical diversity 256 system aspects 256–8

system view 272–5 mutual information 520–1

chain rule 521

narrowband systems 122, 123–4, 124, 128 allocation in GSM system 124–5

performance 125

signal characteristics and receiver design 125–6

nearest neighbor rule 504, 505 near-far problem 129, 232 nested lattice codes 463, 463 noise spheres 169, 529, 530 non-coherent detection

direct-sequence (DS) spread-spectrum 103–5, 104, 105

Rayleigh fading channels 50–2, 51, 54

one-ring model 39

opportunistic beamforming 229, 275–6, 469, 469

dumb antennas 263–6, 264, 265 dumb, smart and smarter 268–70,

269, 270 fast fading 266–8 slow fading 266

opportunistic communications 166, 228–9, 442

opportunistic nulling 271 opportunistic orthogonal coding 464–5 optimality principle of dynamic

programming 90, 90 orthogonal codes 175

orthogonal frequency division multiplexing (OFDM) systems 84, 95–9, 102, 108, 108, 122, 148

allocations design principles 148–50 block length 99–100

flash-OFDM 153–4 hopping pattern 150–2

signal characteristics and receiver design 152

transmission and reception schemes 99 orthogonal Latin squares 151

orthogonal multiple access

compared with AWGN uplink channel capacity 232–4, 234

uplink with multiple receive antennas 476, 481

orthogonality principle 510 orthonormal set of waveforms 29 outage 138, 187, 190

formulation 536–7 parallel channels 199 Rayleigh fading 188

time and frequency diversity 195–7 outer codes 194

out-of-cell interference averaging 141

pairwise error probability 75 parallel channels

linear time-invariant Gaussian channels 181–3, 181

outage 199

time and frequency diversity 195–7 time-invariant parallel channel 532–3 universal space-time codes 400–6, 402,

403, 405, 406–7

waterfilling power allocation 204–5, 206, 207–9

Parseval theorem for DFTs 182 passband spectrum 23

peak to average power ratio (PAPR) 126 peak transmit power 126

performance gains in MIMO fading channels 338, 348

high SNR regime 338–40

large antenna array regime 341–3,

342, 343

low SNR regime 340, 341 periodic hopping patterns 150, 151 phased-array antenna 298

power decay 18–19

562

Index

power gain 72, 179 power-limited systems 174, 174 processing gain 91, 135

pseudo-covariance matrix 500, 501 pseudonoise (PN) 91

Q function 496, 497

quadrature amplitude modulation (QAM) 23–4

approximately universal for scalar channels 398–400

quadrature phase-shift-keying (QPSK) 60 degrees of freedom 56–9

differential QPSK 60 quarter circle law 342, 342 quasi-static scenario 187

radio broadcast systems (AM, FM, etc.) 5 Rake receiver 91–3, 93

performance analysis 93–5 rate-splitting 231

ray tracing 14 Rayleigh fading 36–7

2 × 2 MIMO Rayleigh channel

four schemes 392–4, 392, 393, 393 optimal tradeoff 394–5

channel detection

coherent detection 52–6, 54 non-coherent detection 50–2, 51, 54

dumb antennas for opportunistic beamforming 267, 268

MIMO capacity 338–9, 339, 392–4 MISO channels 391–2

multiuser diversity gain 253–4, 253 n × n MIMO i.i.d. Rayleigh channel

geometric interpretation 397–8, 397 optimal tradeoff 395–6, 396

outage probability 188 parallel channels 390–1, 391 scalar channels

optimal tradeoff 389–90

PAM and QAM 386–9, 388, 389 Rayleigh random variables 501

receive beamforming 179, 273, 358, 449 receive diversity 189–90, 195

receiver architectures 348–9 information theoretic optimality

fading channels 364

MMSE is information lossless 362–3 time-invariant channel 363–4

linear decorrelator

geometric derivation 349–52,

350, 351

performance for deterministic H matrix 352

performance in fading channels 352–4,

353, 354

linear MMSE receiver

decorrelator limitations 356–7, 357 derivation 357–60, 358 MMSE–SIC 361–2, 361, 362, 427,

429–30 performance 360, 361

successive cancellation 355–6, 355 reliability of air interface 2 repetition coding 49, 59, 60–4, 65

AWGN channel capacity 167–8 packing spheres 168, 169

transmit diversity 194–5 reverse channel 4, 121

richly scattered environment 328 Rician fading 37

dumb antennas for opportunistic beamforming 267–8, 268

multiuser diversity gain 253–4, 253 rotation coding 64–6, 65

scattering reflections 20 scheduler 258, 259 sectorization 121–2, 122 selection combining 140 separation of time-scales 145 shadowing 19

signal-to-interference plus noise ratio (SINR) 122

CDMA uplink 135 signal-to-noise ratio (SNR)

binary phase-shift-keying (BPSK) 56 quadrature phase-shift-keying (QPSK) 56 Rayleigh fading channels 109

coherent detection 53, 54, 55 non-coherent detection 52

sinc(t) function 25

single input multiple output (SIMO) channels

large receive antenna arrays 344, 345 linear time-invariant Gaussian

channels 179 modeling 296–8, 296

singular value decomposition (SVD) 291–4, 293

slow fading channels 31, 34 capacity 187–9, 187, 215–16

transmitter side information 204 dumb antennas for opportunistic

beamforming 266 multiplexing architecture for MIMO

366–8

high SNR 368 multiuser capacity

AWGN uplink 243–4, 245 multiuser communications with MIMO

systems 433–6, 435, 436 small-scale fading 10, 41

soft capacity limit 130

563

Index

soft handoff 130 see also handoff

CDMA downlink 146 CDMA uplink 139–41, 139

softer handoff 140

space-division multiple access (SDMA) 426–7

ArrayComm systems 479–81 capacity region 428–30, 429 orthogonal multiple access 432–3 uplink with multiple receive antennas

476–8, 481

uplink with multiple transmit antennas 442–4, 443, 444

space-time codes 73 determinant criterion 74–7

spatial multiplexing 79–80, 290–1, 308 see also V-BLAST multiplexing

spatial signature 297

spectral efficiency 2, 143–4, 144, 172, 173 specular path 37

sphere covering 458 sphere hardening effect 169

sphere packing 168–72, 168, 169, 458, 529 upper bound 529–30, 530

squared product distance 66 square-law detectors 51 stationary ergodic fading 534 statistical multiplexing 130, 144 successive cancellation 228

successive interference cancellation (SIC) 228, 275, 333

AWGN uplink channel 229–32, 229, 230 implementation issues 241–2 MMSE–SIC receivers 361–2, 361, 362,

427, 429–30

receiver architectures 355–6, 355 sum capacity 230

superposition coding 228, 275 general case 238–40, 239 multiuser diversity 260–1, 261 symmetric case 237–8, 238

symbol-by-symbol precoding 454–7, 455,

456, 457, 461 decoding 462 performance 458–9

transmitter knowledge of interference 461–3, 462

symmetric capacity 230, 235 system capacity 141

system view 2

tap gain auto-correlation function 37–8 time diversity 60, 61

code design criterion 68 extensions 198–9 geometric view 197–8, 198

Global System for Mobile (GSM) systems 69–71, 70

other coding systems 64–7, 65

outage performance of parallel channels 195–7

repetition coding 60–4, 65 time division duplex (TDD) 121

time-division multiple access (TDMA) 4 Global System for Mobile (GSM)

systems 69 transition probabilities 516

transmit beamforming 180, 340, 452–3 transmit diversity 191, 195

Alamouti scheme 191–4, 192 repetition coding 194–5

transmit power control 137 transmitter-centric scheme 466 trellis representation 89, 89

ultra-wideband (UWB) 5, 32 uncertainty sphere 531, 531 underspread channels 22, 34 uniform linear antenna arrays 296 universal frequency reuse 129–30

universal space-time codes 383–4, 398, 400, 406–7

bit-reversal scheme 405–6 design criterion 400–2, 402, 403 high SNR 403–4

MIMO channels 411, 415–16 design criterion 412–13 downlink 415

properties of approximately universal codes 413–15

universality of D-BLAST 411–12 MISO channels 407, 410

conversion to parallel channels 408–9 design criterion 409–10

viewed as parallel channels 407–8, 408 properties of approximately universal

codes 404–5, 405

QAM is approximately universal for scalar channels 398–400

universal frequency reuse 122 upconversion 22, 24

uplink 4, 121

uplink-downlink duality 450–2, 451

V-BLAST multiplexing 332, 333 see also spatial multiplexing MIMO architecture 333–5

virtual channels 150, 151

Viterbi algorithm 83–4, 88–91, 88 voice communications 4

waterfilling power allocation 183–5, 184, 185, 204–6, 206, 207–9

compared with channel inversion 209

564 Index

well-conditioned matrices 295

white Gaussian noise (WGN) 29–30, 35 wideband systems 122, 128–31

CDMA downlink 145–6, 146 CDMA uplink 131–45, 132

system issues 147 OFDM 148–52 sectorization 153

wireless channels 10 input/output modeling 20, 41

additive white noise 29–30

baseband equivalent model 22–5, 23, 24 discrete-time baseband equivalent

model 25–8, 27, 28, 29

linear time-varying system model 20–2 physical modeling 10–11

channel quality variation 11

free space, fixed transmit and receive antennas 12–13

free space, moving antenna 13–14 moving antenna, multiple reflectors

19–20

power decay with distance and shadowing 18–19

reflecting ground plate 17–18, 18 reflecting wall, fixed antenna 14–15,

14, 15

reflecting wall, moving antenna 15–17,

16, 17

statistical modeling 41–2

Clarke’s model for flat fading channels 38–40, 40

modeling philosophy 34–5 Rayleigh and Rician fading 36–7

tap gain auto-correlation function 37–8 summary of defining characteristics 34 summary of physical parameters 34

time and frequency coherence

delay spread and coherence bandwidth 31–3

Doppler spread and coherence time 30–1

wireless LANs (local area networks) 5 wireless systems, historical perspective 2–5

zero cross-correlation property 103 zero-forcing equalizers 90 zero-forcing receiver 81, 350–1