Index

(10, 3, 5) LDPC codes, 669–671

2B1Q code, 331–332

A

Adaptive DM, 308

Adaptive equalization

decision-feedback equalization, 473–474

equalizer operation, 472–473

introduction, 469–470

LMS (least-mean-square) algorithm, 470–472

Additive noise, parameter estimation,124 –125

Alamouti code

receiver considerations, 542–545

space diversity-on-transmit receive systems, fading channels, 540–541

Aliasing, 272–273

Autocorrelation function

bound on the autocorrelation function property, 151

cross-correlation functions, 155–157

mean-square value property, 151

normalization property, 152

overview, 149–157

physical significance of, 152–155

properties of, 151–152

quadrature-modulated processes, 156–157

random binary wave, 154–155

sinusoidal wave with random phase, 152

symmetry property, 151

Autocovariance function, weakly

stationary stochastic processing, 149–157

AWGN channel signaling

BER comparison of signaling schemes, 415–418

capacity, band-limited channels, 477–478

introduction, 323–324

noncoherent orthogonal modulation, 404–410

AWGN channel signaling, coherent detection. See also DPSK (differential phase-shift keying); FSK (frequency-shift keying); PSK (phase-shift keying).

correlation receiver, 341–342

matched filter receiver, 342–343

maximum likelihood decoding, 337–341

AWGN channel signaling, detecting signals of unknown phase

equivalent forms of the quadratic receiver, 402–404

introduction, 400

optimum quadratic receiver, 400–402

AWGN channel signaling, geometric representation of signals

2B1Q code, 331–332

Gram-Schmidt orthogonalization, 329–331

introduction, 324–328

Schwarz inequality, 328–329

AWGN channel signaling, optimum receivers

correlation receiver, 341–342

matched filter receiver, 342–343

maximum likelihood decoding, 337–341

AWGN channel signaling, probability of error

bit versus symbol error probabilities, 351–352

four message points, 348–349

introduction, 344–346

invariance of the probability to translation, 346–347

pairwise error probability, 349–351

rotational invariance, 346

translation of signal constellation, 347–348

AWGN channel synchronization

algorithmic approach, 419

introduction, 418–419

AWGN channel synchronization, recursive maximum likelihood estimation

algorithmic synchronization, 423–424

convergence considerations, 430–431

introduction, 419–420

likelihood functions, 420–423

recursive estimation of group delay, 424–430

AWGN channels, capacity of binary-input, 244–248

AWGN channels, converting to vector

introduction, 332–333

likelihood function, 336–337

statistical characteristics, correlator output, 333–336

B

Band-limited channels

AWGN channel capacity, 477–478

broadband backbone data network, over multiple baseband channels, 474–475

constrained optimization problem, 484–487

distortionless baseband data transmission, 450–454

DSL (digital subscriber lines), 475–477

error rates due to channel noise in matched-filter receivers, 446–447

ideal Nyquist pulse, 450–454

intersymbol interference, 447–449

introduction, 445–446

post-processing techniques, 463–469

RC (raised cosine) spectrum, 454–458

signal design for zero ISI, 450

water-filling solution, 484–487

Band-limited channels, adaptive equalization

decision-feedback equalization, 473–474

equalizer operation, 472–473

introduction, 469–470

LMS (least-mean-square) algorithm, 470–472

Band-limited channels, eye patterns

for binary systems, 467–469

introduction, 463–464

for M-ary transmissions, 466

peak distortion for intersymbol interference, 465–466

for quaternary systems, 467–469

timing features, 464

Band-limited channels, FIR modeling

RC pulse, 456–458

SRRC pulse, 461–463

Band-limited channels, partitioning continuous-time channels. See also DMT system.

geometric SNR, 481–482

introduction, 478–481

loading the DMT system, 482–484

Band-limited channels, SRRC spectrum

introduction, 458–460

pulse shaping compared to RC spectrum, 461

Band-pass signals

amplifiers, nonlinear modeling, A42–A43

canonical representation, 49–52

combining with systems. See Band-pass systems, combining with signals.

complex envelopes, 47–49

Band-pass systems, combining with signals

frequency-domain procedure, 56–58

introduction, 54

simulating communication systems, 58

time-domain procedure, 54–56

Band-pass systems, complex low-pass representations, 52–53

Bayesian inference, hypothesis testing

binary, 130–132

composite, 132–133

introduction, 126–129

Bayesian inference, introduction, 119–122

Bayesian inference, parameter estimation

in additive noise, 124–125

introduction, 122–124

BER comparison of signaling schemes, 415–418

Bernoulli random variable, 101–105, 211–212

Bessel functions, A13–A18

Binary hypothesis testing, 130–132

Binary symmetric channels

channel capacity, 231–232

channel-coding theorem, 234–235

discrete memoryless channels, 225

Binary-input AWGN channel,

capacity of, 244–248

Bipolar RZ signaling, 311

Block interleaving, A30–A32

Bound on the autocorrelation

function property, 151

Boundedness of the distribution, 98

Bounds on the Q-function, A11–A12

Broadband backbone data network,

signaling over multiple

baseband channels, 474–475

C

CAI (coantenna interference), 546–547

Channel capacity. See also MIMO

(multiple input, multiple output)

capacity.

AWGN band-limited channels, 477–478

AWGN binary input channels, 244–248

binary symmetric channels, 231–232

information capacity law, 292–294

introduction, 230–231

NEXT-dominated channel, 252–253

Channel-coding theorem

binary symmetric channels, 234–235

introduction, 232–234

repetition code, 235–236

Characteristic function, 112–113

Chi-square distribution, A1–A3

Clipping-filtering, A37–A38

Coantenna interference (CAI), 546–547

Code division multiple access, fading channels

Gold codes, correlation properties, 563–564

Gold sequences, 562–563

introduction, 560–561

Walsh-Hadamard sequences, 561–562

Coding, history of, 1–2

Coherent detection of AWGN channel signaling

correlation receiver, 341–342

matched filter receiver, 342–343

maximum likelihood decoding, 337–341

Coherent detection of binary FSK

error probability, 378–380

generation and detection, 377–378

power spectra, 380–382

Coherent detection of FSK

bandwidth efficiency, M-ary FSK signals, 396–397

introduction, 375–377

M-ary FSK, introduction, 395–397

M-ary FSK versus M-ary PSK, 398–399

minimum shift keying, 382–383

phase trellis, 383–384

power spectra, M-ary FSK signals, 396

Coherent detection of FSK, MSK

error probability, 390–391

Gaussian filtering, 392–395

generation and detection, 389–390

power spectra, 391–392

signal-space diagram, 384–388

waveforms, 388–389

Coherent detection of optimum AWGN receivers. See also FSK (frequency-shift keying) coherent detection; PSK (phase-shift keying) coherent detection.

correlation receiver, 341–342

matched filter receiver, 342–343

maximum likelihood decoding, 337–341

Colored noise channels, information capacity

capacity of NEXT-dominated channel, 252–253

introduction, 248–252

Communication process

digital communication, 9–11

introduction, 2–4

multiple-access techniques, 4–5

networks, 6–9

Composite hypothesis testing, 132–133

Compound probabilistic codes, introduction, 644–645

Compound probabilistic codes, LDPC codes

(10, 3, 5) codes, 669–671

introduction, 646–669

irregular codes, 674–675

minimum distance, 671–672

probabilistic decoding, 672–674

Constrained optimization problem, 484–487

Convolutional codes. See Error-control coding for convolutional codes.

Convolutional interleaving, A32–A33

Cosine transformation of a random

variable, 109–112

Cross-correlation functions, autocorrelation function, 155–157

Cross-spectral densities property, weakly stationary stochastic processing, 172–174

Cyclic codes, error-control coding

calculating the syndrome, 598–599

cyclic property, 593

encoding, 597–598

generator matrices, 596–597

generator polynomials, 594–595

hamming codes, 599–603

introduction, 593–594

linearity property, 593

maximal-length codes, 603–604

parity-check matrices, 596–597

parity-check polynomials, 595–596

properties, 593

Reed-Solomon codes, 604–605

D

Decision-feedback equalization, 473–474

Delta modulation (DM). See DM (delta modulation).

DFT (discrete Fourier transform). See also IDFT (inverse discrete Fourier transform).

binary sequence for energy calculation, 19–21

Dirac delta function, 28–33

interpreting, 70–72

introduction, 16–19

linear time-invariant systems, 37–41

pairs, 24

periodic signals, 34–36

theorems, 23

time functions, 24

unit Gaussian pulse, 21–22

DFT (discrete Fourier transform), DMT systems

description, 489–491

DFT-based DMT systems, 492–493

DMT-based DSL, practical applications, 493–494

frequency-domain channel descriptions, 491–492

introduction, 487–489

DFT (discrete Fourier transform), numerical computation

computing the IDFT, 77–78

FFT algorithms, 72–77

interpretation of DFT and IDFT, 70–72

introduction, 69–70

DFT-based DMT systems, 492–493

Differential entropy

mutual information, 237–240

uniform distribution, 238–240

Differential phase-shift keying

(DPSK). See DPSK (differential phase-shift keying).

Differential pulse-code modulation (DPCM). See DPCM (differential pulse-code modulation).

Digital communication introduction, 9–11

Digital subscriber lines (DSL). See DSL (digital subscriber lines).

Dirac delta function, 28–33

Discrete Fourier transform (DFT). See DFT (discrete Fourier transform).

Discrete memoryless channels

binary symmetric channel, 225

introduction, 223–225

Discrete memoryless channels, error-control coding

channel coding theorem, 580–581

introduction, 579–580

notation, 582

Discrete multicarrier transmission (DMT). See DMT (discrete multicarrier transmission).

Distortionless baseband data transmission, 450–454

Distribution functions, Bernoulli random variable, 101–105

DM (delta modulation)

adaptive DM, 308

introduction, 305

quantization errors, 307–308

receiver, 307

transmitter, 305–307

DMT (discrete multicarrier transmission) system, DFT

description, 489–491

DFT-based DMT systems, 492–493

DMT-based DSL, practical applications, 493–494

frequency-domain channel descriptions, 491–492

introduction, 487–489

DMT (discrete multicarrier transmission) system, loading, 482–484

DPCM (differential pulse-code modulation)

DPCM receiver, 303

DPCM transmitter, 303

introduction, 301–303

processing gain, 304

DPSK (differential phase-shift keying). See also PSK (phase-shift keying), introduction.

error probability, 412–413

generating DPSK signals, 413

illustration, 412

introduction, 411–412

optimum receiver, 413–415

DSB-SC modulation, 60–61

DSL (digital subscriber lines)

band-limited channels, 475–477

DMT-based, practical applications, 493–494

E

Entropy

Bernoulli random variable, 211–212

differential, 237–240

of extended source, 213–214

extension of a discrete memoryless source, 212–213

introduction, 207–209

properties of, 209–211

relative, 238–239

Envelopes

band-pass signals, complex envelopes, 47–49

low-pass signals, 47

narrowband noise, 191–193

pre-envelopes, 45–47

Equal gain combining, 538

Ergodic processes, weakly stationary

stochastic processing, 157–158

Error rates in band-limited channels due to channel noise in matched-filter receivers, 446–447

Error-control coding. See also Compound probabilistic codes.

forward error correction, 578–579

introduction, 577–578

LDPC codes. See LDPC (low-density parity-check) codes.

Error-control coding, exit charts

approximate Gaussian model, 661–663

developing, 658–661

histogram computation method, 663–666

introduction, 657–658

measuring, 664–666

Error-control coding, turbo coding

extrinsic information, 649–650

introduction, 645–646

mathematical feedback analysis, 651–653

performance, 648–649

serial concatenated codes, 681–687

turbo decoder, 650–651

two-state encoder, 646–648

UMTS turbo decoder, 653–657

UMTS with binary PSK modulation, 653–657

Error-control coding for convolutional codes

code tree, 607–608

convolutional encoder, 606–607

introduction, 605–606

optimum decoding, 613–614

recursive systematic, 611–613

state diagrams, 609–611

trellis graph, 609. See also Trellis-coded modulation.

Error-control coding for convolutional codes, maximum a posteriori probability decoding

algorithmic metrics, 627–628

AWGN channel, branch metric evaluation, 630–634

BCJR algorithm, 623–624, 638

forward-backward recursions, 626–630

introduction, 623–624

lattice-based framework for the derivation, 625–626

log-MAP algorithm, 636–638

MAP decoding algorithm, 624–625, 635–638

max-log-MAP algorithm, 636–638, 639–644

a posteriori L-value, finalizing, 634

Error-control coding for convolutional codes, maximum a posteriori probability max-decoding, 636–638

Error-control coding for convolutional codes, maximum likelihood decoding

asymptotic coding gain, 622–623

correct decoding of received all-zero sequences, 617–618

free distance, 620–621

incorrect decoding of received all-zero sequences, 619

introduction, 614–616

Viterbi algorithm, 616–617, 623

Error-control coding for cyclic codes

calculating the syndrome, 598–599

cyclic property, 593

encoding, 597–598

generator matrices, 596–597

generator polynomials, 594–595

hamming codes, 599–603

introduction, 593–594

linearity property, 593

maximal-length codes, 603–604

parity-check matrices, 596–597

parity-check polynomials, 595–596

properties, 593

Reed-Solomon codes, 604–605

Error-control coding for discrete memoryless channels

channel coding theorem, 580–581

introduction, 579–580

notation, 582

Error-control coding for linear coding blocks

hamming codes, 590–592

introduction, 582–585

minimum distance considerations, 587–589

syndrome decoding, 589–590

syndrome definition and

properties, 585–587

Exit charts

approximate Gaussian model, 661–663

developing, 658–661

histogram computation method, 663–666

introduction, 657–658

measuring, 664–666

Expectation

introduction, 105–106

linearity, 107–108

statistical independence, 108

Exponential distribution, 110–111

Eye patterns

for binary systems, 467–469

introduction, 463–464

for M-ary transmissions, 466

peak distortion for intersymbol interference, 465–466

for quaternary systems, 467–469

timing features, 464

F

Fading channels

comparison of modulation schemes, 525–527

diversity techniques, 525

effects of flat fading, 525–527

introduction, 501–502

propagation effects, 502–505

RAKE receiver and multipath diversity, 564–566

Fading channels, code division multiple access

Gold codes, correlation properties, 563–564

Gold sequences, 562–563

introduction, 560–561

Walsh-Hadamard sequences, 561–562

Fading channels, FIR modeling of doubly spread channels

generating tap coefficients, 523–524

introduction, 520–523

practical matters, 523

Rayleigh processes, 524

Rician-Jakes doppler spectrum model, 524–525

Fading channels, Jakes model

illustrative generation of fading processes, 510–511

implemented as a FIR filter, 509–511

introduction, 506–509

Fading channels, MIMO capacity

channel known at the transmitter, 555–556

ergodic capacity, 551–553

log-det formula capacity, 553–554

outage capacity, 554–555

Fading channels, MIMO systems

basic baseband channel model, 547–551

CAI (coantenna interference), 546–547

introduction, 546

Fading channels, OFDM

introduction, 556

PAPR problem, 556–557

Fading channels, space diversity-on-receive systems

equal gain combining, 538

introduction, 528

maximum-ratio combining, 533–537

outage probability for maximal-ratio combiner, 537

outage probability of selection

combiner, 532

selection combining, 528–532

Fading channels, space diversity-on-transmit receive systems

Alamouti code, 540–541

full-rate complex code, 541

introduction, 538–539

linearity, 542–546

maximum likelihood decoding, 545–546

QPSK (quadriphase-shift keying), 539

receiver considerations, Alamouti code, 542–545

unitarity (complex orthogonality), 541

Fading channels, spread spectrum signals

classification of spread spectrum signals, 557–558

introduction, 557–558

processing gain of the DS/BPSK, 559

Fading channels, statistical characterization of wideband wireless channels

classification of multipath channels, 519–520

Doppler power spectrum, 517–519

introduction, 511–512

multipath correlation function of the channel,512

power-delay profile, 516–517

scattering function of the channel, 514–516

spaced-frequency, spaced-time correlation function of the channel, 514

uncorrelated scattering, 513

wide-sense stationarity, 512–513

FFT (fast Fourier transform) algorithms, 72–77

Filtering two jointly weakly stationary processes, 174

FIR (finite-duration impulse response) modeling, introduction, 456–458

FIR (finite-duration impulse response) modeling of doubly spread fading channels

generating tap coefficients, 523–524

introduction, 520–523

practical matters, 523

Rayleigh processes, 524

Rician-Jakes doppler spectrum model, 524–525

Fourier series, 13–16

Fourier transform. See DFT (discrete Fourier transform); IDFT (inverse discrete Fourier transform).

Frequency-domain

description, 56–58, 268–271

relation to time-domain, 25–28

FSK (frequency-shift keying). See also AWGN channel signaling.

introduction, 375–377

noncoherent detection of binary FSK, 410–411

FSK (frequency-shift keying) coherent detection. See also PSK (phase-shift keying), introduction.

bandwidth efficiency, M-ary FSK signals, 396–397

M-ary FSK, introduction, 395–397

M-ary FSK versus M-ary PSK, 398–399

minimum shift keying, 382–383

phase trellis, 383–384

power spectra, M-ary FSK signals, 396

FSK (frequency-shift keying) coherent detection, binary FSK

error probability, 378–380

generation and detection, 377–378

power spectra, 380–382

FSK (frequency-shift keying) coherent detection, MSK

error probability, 390–391

Gaussian filtering, 392–395

generation and detection, 389–390

power spectra, 391–392

signal-space diagram, 384–388

waveforms, 388–389

Full-rate complex code, 541

G

Gaussian distribution

introduction, 113

jointly Gaussian random variables, 116

linear function of a Gaussian random variable, 114

mean, 114

Gaussian distribution (cont.)

random variables,239–240

standard distribution, table of, 117

sum of independent Gaussian

random variables, 114

variance, 114

Gaussian process

independence, 179

introduction, 176–177

linear filtering, 177–178

multivariate distribution, 178

stationarity, 179

Geometric representation of AWGN channel signals

2B1Q code, 331–332

Gram-Schmidt orthogonalization, 329–331

introduction, 324–328

Schwarz inequality, 328–329

Gold codes, correlation properties, 563–564

Gold sequences, 562–563

Gram-Schmidt orthogonalization, 329–331

Group delays, 66–69

H

Hilbert transform

introduction, 42–44

low-pass signals, 44–45

Huffman coding, lossless data compression, 219–220

Huffman tree, lossless data compression, 220–221

Hypothesis testing

binary, 130–132

composite, 132–133

introduction, 126–129

I

Ideal band-pass filtered white noise, 189–190

Ideal low-pass filtered white noise, 181–182

Ideal Nyquist pulse, band-limited channels, 450–454

IDFT (inverse discrete Fourier transform). See also DFT.

computing, 77–78

interpreting, 70–72

Information capacity, colored noise channels

capacity of NEXT-dominated channel, 252–253

introduction, 248–252

Information capacity law

capacity of binary-input AWGN channels, 244–248

implications of, 244–248

introduction, 240–243

PCM noise, 292–294

sphere packing, 243–244

Information theory, history of, 1–2

Integrals, table of, A57

Interleaving

block, A30–A32

convolutional, A32–A33

introduction, A29–A30

random, A33–A34

Intersymbol interference, band-limited channels, 447–449

Inverse discrete Fourier transform (IDFT). See IDFT (inverse discrete Fourier transform).

J

Jakes model, fading channels

illustrative generation of fading processes, 510–511

implemented as a FIR filter, 509–511

introduction, 506–509

Jointly Gaussian random variables, 116

K

Kraft inequality, lossless data compression, 217–219

L

Lagrange multipliers, A19–A20

LDPC (low-density parity-check) codes

(10, 3, 5) codes, 669–671

history of, 645

introduction, 646–669

irregular codes, 674–675

minimum distance, 671–672

probabilistic decoding, 672–674

Least-mean-square (LMS) algorithm, 470–472

Lempel-Ziv coding, lossless data compression, 221–223

Line codes

bipolar RZ signaling, 311

introduction, 309–310

Manchester code, 311

polar NRZ signaling, 311

split phase, 311

unipolar NRZ signaling, 311

unipolar RZ signaling, 311

Linear coding blocks, error-control coding

hamming codes, 590–592

introduction, 582–585

minimum distance considerations, 587–589

syndrome decoding, 589–590

syndrome definition and properties, 585–587

Linear function of a Gaussian random variable, 114

Linear modulation theory

DSB-SC modulation, 60–61

introduction, 58–60

SSD modulation, 64–66

summary of modulation methods, 66

VSB modulation, 61–64

Linear time-invariant filter, transmitting weakly stationary stochastic processing, 158–160

Linear time-invariant systems, 37–41

Linearity, expectation, 107–108

LMS (least-mean-square) algorithm, 470–472

Log-normal distribution, A3–A6

Lossless data compression algorithms

Huffman coding, 219–220

Huffman tree, 220–221

introduction, 215–216

Kraft inequality, 217–219

Lempel-Ziv coding, 221–223

prefix coding, 216–217

Low-density parity-check (LDPC). See LDPC (low-density parity-check).

Low-pass signals

envelopes, 47

Hilbert transform, 44–45

M

Manchester code, 311

MAP (maximum a posteriori probability) decoding algorithm, 624–625, 635–638

Mathematical tables

integrals, A57

series expansions, A56

trigonometric identities, A55

unit prefixes, A58

useful constants, A58

Maximal-length sequences

choosing, A50–A54

code generation, A51–A54

correlation property, A48–A50

introduction, A47

properties of, A47–A50

Maximum likelihood decoding, 545–546

Maximum-ratio combining, 533–537

Mean functions, weakly stationary stochastic processing, 149–157

Mean-square value property

autocorrelation function, 151

weakly stationary stochastic processing, 164

Method of Lagrange multipliers, A19–A20

MIMO (multiple input, multiple output) capacity, fading channels

channel known at the transmitter, 555–556, A24–A28

ergodic capacity, 551–553

log-det formula capacity, 553–554, A21–A24

outage capacity, 554–555

Mixing random processes with sinusoidal, weakly stationary stochastic processing, 167–169

Monotonicity of the distribution, 99

Monte Carlo integration, A45–A46

m-sequences. See Maximal-length sequences.

MSK (minimum shift keying), FSK coherent detection

error probability, 390–391

Gaussian filtering, 392–395

generation and detection, 389–390

power spectra, 391–392

signal-space diagram, 384–388.

waveforms, 388–389

Mutual information

continuous random ensembles, 237–240

differential entropy, 237–240

expansion, 228–229

introduction, 226–227

nonnegativity, 228

symmetry, 227–228

N

Nakagami distribution, A6–A9

Narrowband noise

envelope, 191–193

ideal band-pass filtered white noise, 189–190

introduction, 183–189

phase components, 191–193

plus sine wave, 193–195

Rayleigh distribution, 192–193

Rician distribution, 194–195

Networks, introduction, 6–9

NEXT-dominated channel, capacity of, 252–253

Noise. See also Narrowband noise; White noise.

definition, 179

shot, 180

thermal, 180

Noise, PCM

error threshold, 291–292

information capacity law, 292–294

introduction, 290–291

Noncoherent detection, binary FSK, 410–411

Noncoherent orthogonal modulation, AWGN channel signaling, 404–410

Nonlinear solid-state power amplifiers, A39–A43

Nonnegativeness property, weakly stationary stochastic processing, 164

Nonnegativity function, 99

Normalization function, 99–100

Normalization property

autocorrelation function, 152

weakly stationary stochastic processing, 165

O

OFDM (orthogonal frequency division multiplexing), PAPR problem

clipping-filtering, PAPR reduction, A37–A38

fading channels, 556–557

introduction, A35

maximum PAPR using M-ary PSK, A36–A37

properties of OFDM signals, A35–A36

Outage probability

for maximal-ratio combiner, 537

of selection combiner, 532

P

PAM (pulse-amplitude modulation), 274–277

PAPR (peak-to-average power ratio) problem

clipping-filtering, PAPR reduction, A37–A38

fading channels, 556–557

introduction, A35

maximum PAPR using M-ary PSK, A36–A37

properties of OFDM signals, A35–A36

Parameter estimation

in additive noise, 124–125

introduction, 122–124

Partitioning continuous-time channels

geometric SNR, 481–482

introduction, 478–481

loading the DMT system, 482–484

PCM (pulse-code modulation)

encoding the transmitter, 288

introduction, 285–286

inverse operations in the receiver, 288–289

quantization of the transmitter, 286–288

regeneration along the transmitter path, 288–290

PCM (pulse-code modulation), noise considerations

error threshold, 291–292

information capacity law, 292–294

introduction, 290–291

Periodic signals, Fourier transform, 34–36

Phase components, narrowband noise, 191–193

Phase delays, 66–69

Phase-shift keying (PSK). See PSK (phase-shift keying).

Poisson process, weakly stationary stochastic processing, 174–176

Polar NRZ signaling, 311

Prediction-error filtering, redundancy reduction

discrete time structure for

predictions, 296–299

introduction, 294–295

Prediction-error filtering, redundancy reduction (cont.)

linear adaptive prediction, 300–301

theoretical considerations, 295–296

Pre-envelopes, 45–47

Prefix coding, lossless data compression, 216–217

Probabilistic compound codes. See Compound probabilistic codes.

Probabilistic model, 90–97

Probability theory

characteristic function, 112–113

introduction, 87–90

probabilistic model, 90–97

random variables, 97–98

set theory, 88–90

Probability theory, central limit theorem

introduction, 118

sum of uniformly distributed random variables, 118–119

Probability theory, distribution functions

Bernoulli random variable, 101–105

boundedness of the distribution, 98

introduction, 98

monotonicity of the distribution, 99

nonnegativity, 99

normalization, 99–100

uniform distribution, 100–101

Probability theory, expectation

introduction, 105–106.

linearity, 107–108

statistical independence, 108

Probability theory, Gaussian distribution

introduction, 113

jointly Gaussian random variables, 116

linear function of a Gaussian random variable, 114

mean, 114

standard distribution, table of, 117

sum of independent Gaussian random variables, 114

variance, 114

Probability theory, second-order statistical averages

cosine transformation of a random variable, 109–112

exponential distribution, 110–111

introduction, 108–109

Processing gain, DPCM, 304

Properties, weakly stationary stochastic processing

cross-spectral densities, 172–174

filtering two jointly weakly stationary processes, 174

introduction, 160–161, 170–172

mean-square value of stationary process, 164

mixing random processes with sinusoidal, 167–169

nonnegativeness, 164

normalization, 165

random binary wave, 166–167

sinusoidal wave with random phase, 165–166

sum of two processes, 173

symmetry, 164

Wiener-Khintchine theorem, 169–170

zero correlation among frequency components, 162–163

zero-frequency value, 164

PSK (phase-shift keying), introduction, 352. See also AWGN channel signaling; DPSK (differential phase-shift keying); FSK frequency-shift keying).

PSK (phase-shift keying), M-ary QAM

average probability of error, 373–375

introduction, 370–371

for M = 4, 371–373

QAM square constellations, 371

square constellations, 371

PSK (phase-shift keying) coherent detection

binary phase-shift keying, 352–357

error probability, binary PSK, 354–356

introduction, 352

M-ary PSK, introduction, 367–370

M-ary PSK versus M-ary FSK, 398–399

PSK (phase-shift keying) coherent detection, power spectra

binary PSK, 356–357

M-ary PSK, 367–370

PSK (phase-shift keying) coherent detection, QPSK

error probability, 362–364

introduction, 357–359

offset QPSK, 365–367

power spectra, 364–365

signal-space diagrams, 358–359

waveforms, 359–365

PSK (phase-shift keying) coherent detection, signal-space diagrams

binary PSK, 353–354

QPSK signals, 358–359

Pulse-amplitude modulation (PAM), 274–277

Pulse-code modulation (PCM). See PCM (pulse-code modulation).

Q

QAM (quadrature amplitude modulation)

average probability of error, 373–375

introduction, 370–371

M-ary QAM for M = 4, 371–373

square constellations, 371

Q-function, bounds on, A11–A12

QPSK (quadriphase-shift keying),

PSK coherent detection

error probability, 362–364

introduction, 357–359

offset QPSK, 365–367

power spectra, 364–365

signal-space diagrams, 358–359

waveforms, 359–365

QPSK (quadriphase-shift keying), space diversity-on-transmit receive systems,539

Quadrature-modulated processes, autocorrelation function, 156–157

Quantization

errors, delta modulation,307–308

introduction, 278–279

noise, 279–281

scalar quantizers, optimality, 282–285

sinusoidal modulating signal, 281–282

R

Raised cosine (RC). See RC (raised cosine).

RAKE receiver and multipath diversity, 564–566

Random binary wave property

autocorrelation function, 154–155

weakly stationary stochastic processing, 166–167

Random interleaving, A33–A34

Random processes, mixing with sinusoidal, 167–169

Random variables

Bernoulli, 101–105

cosine transformation, 109–112

probability theory, 97–98

Random variables, Gaussian

jointly Gaussian, 116

linear function of, 114

sum of independent, 114

Rate distortion theory

Gaussian sources, 255–256

introduction, 253–255

Rayleigh distribution, 192–193

Rayleigh processes, 524

RC (raised cosine) pulse, FIR modeling, 456–458

RC (raised cosine) spectrum

band-limited channels, 454–458

compared to SRRC spectrum, 461

Redundancy reduction, prediction-error filtering

discrete time structure for predictions, 296–299

introduction, 294–295

linear adaptive prediction, 300–301

theoretical considerations, 295–296

Relative entropy, 238–239

Repetition code, 235–236

Rician distribution, 194–195

Rician-Jakes doppler spectrum model, 524–525

S

Sampling theory

aliasing, 272–273

frequency-domain description, 268–271

introduction, 268

sampling theorem, 271

sampling voice signals, 273

Scalar quantizers, optimality, 282–285

Schwarz inequality, 328–329

Second-order statistical averages

cosine transformation of a random variable, 109–112

exponential distribution, 110–111

introduction, 108–109

Selection combining, 528–532

Series expansions, table of, A56

Set theory, 88–90

Shot noise, 180

Signal design for zero ISI, band-limited channels, 450

Simulating communication systems, 58

Sinc function, 30–33

Sine wave, plus narrowband noise, 193–195

Single sideband (SSB) modulation, 64–66

Sinusoidal processes, mixing with random, 167–169

Sinusoidal wave

correlation with white noise, 182–183

with random phase, 165–166

Sinusoidal wave with random phase

autocorrelation function, 152

weakly stationary stochastic processing, 165–166

Source-coding theorem, 214–215

Space diversity-on-receive systems, fading channels

equal gain combining, 538

introduction, 528

maximum-ratio combining, 533–537

outage probability for maximal-ratio combiner, 537

outage probability of selection combiner, 532

selection combining, 528–532

Space diversity-on-transmit receive

systems, fading channels

Alamouti code, 540–541

full-rate complex code, 541

introduction, 538–539

linearity, 542–546

maximum likelihood decoding, 545–546

QPSK (quadriphase-shift keying), 539

receiver considerations, Alamouti code, 542–545

unitarity (complex orthogonality), 541

Sphere packing,243–244

Split phase line codes, 311

SSB (single sideband) modulation, 64–66

Statistical independence, expectation, 108

Stochastic processing

introduction, 145

mathematical definition, 145–147

strictly stationary, 147–149. See also Weakly stationary stochastic processing.

Strictly stationary stochastic

processing, 147–149. See alsoWeakly stationary stochastic

processing.

Sum of independent Gaussian

random variables, 114

Sum of two processes, weakly

stationary stochastic processing, 173

Symmetry property

autocorrelation function, 151

weakly stationary stochastic processing, 164

Synchronization of AWGN channels

algorithmic approach, 419

introduction, 418–419

Synchronization of AWGN channels,

recursive maximum likelihood

estimation

algorithmic synchronization, 423–424

convergence considerations, 430–431

introduction, 419–420

likelihood functions, 420–423

recursive estimation of group delay, 424–430

T

Tables. See Mathematical tables.

TDL (tapped-delay-line) filter. See FIR (finite-duration impulse response) modeling.

(10, 3, 5) LDPC codes, 669–671

Thermal noise, 180

Time functions, Fourier transform, 24

Time-domain

description, 54–56

relation to frequency-domain, 25–28

Trellis-coded modulation

asymptotic coding gain, 678–681

introduction, 675–676

three-level partitioning, QAM constellation, 677–681

two-level partitioning, 8-PSK constellation, 676–677

Ungerboeck 8-PSK code, 678

Trigonometric identities, table of, A55

Turbo coding, error-control coding

extrinsic information, 649–650

introduction, 645–646

mathematical feedback analysis, 651–653

performance, 648–649

serial concatenated codes, 681–687

turbo decoder, 650–651

two-state encoder, 646–648

UMTS turbo decoder, 653–657

UMTS with binary PSK modulation, 653–657

2B1Q code, 331–332

U

UMTS (Universal Mobile Telecommunications Systems), 651–657

Ungerboeck 8-PSK code, 678

Uniform distribution, 100–101

Unipolar NRZ signaling, 311

Unipolar RZ signaling, 311

Unit Gaussian pulse, 21–22

Unit prefixes, table of, A58

Unitarity (complex orthogonality), 541

V

Variance, Gaussian distribution, 114

VSB (vestigial sideband) modulation, 61–64

W

Walsh-Hadamard sequences, 561–562

Water-filling solution, 484–487, A27–A28

Weakly stationary stochastic

processing. See also Strictly

stationary stochastic processing.

autocovariance function, 149–157

ergodic processes, 157–158

introduction, 147–149

mean functions, 149–157

Poisson process, 174–176

transmission through a linear time-invariant filter, 158–160

Weakly stationary stochastic processing, autocorrelation function

bound on the autocorrelation function property, 151

cross-correlation functions, 155–157

mean-square value property, 151

normalization property, 152

overview, 149–157

physical significance of, 152–155

properties of, 151–152

quadrature-modulated processes, 156–157

random binary wave, 154–155

sinusoidal wave with random phase, 152

symmetry property, 151

Weakly stationary stochastic processing, Gaussian process, 176–179

independence, 179

introduction, 176–177

linear filtering, 177–178

multivariate distribution, 178

stationarity, 179

Weakly stationary stochastic processing, power spectral density

introduction, 160–161

physical significance of, 162

Wiener-Khintchine relations, 162–163

Weakly stationary stochastic processing, power spectral density properties

cross-spectral densities, 172–174

filtering two jointly weakly stationary processes, 174

introduction, 160–161, 170–172

mean-square value of stationary process, 164

mixing random processes with sinusoidal, 167–169

nonnegativeness, 164

normalization, 165

random binary wave, 166–167

sinusoidal wave with random phase, 165–166

sum of two processes, 173

symmetry, 164

Wiener-Khintchine theorem, 169–170

zero correlation among frequency

components, 162–163

zero-frequency value, 164

White noise

correlation with sinusoidal wave, 182–183

ideal band-pass filtered, 189–190

ideal low-pass filtered, 181–182

introduction, 180–181

Wiener-Khintchine theorem, 162–163, 169–170

Wireless communication

history of, 2

sinc function, 30–33

Z

Zero correlation among frequency components, 162–163

Zero ISI, signal design for, 450

Zero- frequency value property, 164