DIGITALCOMMUNICATIONS

DIGITALCOMMUNICATIONS

Mehmet Şafak

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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–dc23LC record available at https://lccn.loc.gov/2016032956

A catalogue record for this book is available from the British Library.

Cover Design: WileyCover Image: KTSDESIGN/Gettyimages

Set in 10 /12pt Times by SPi Global, Pondicherry, India

10 9 8 7 6 5 4 3 2 1

To my children Emre and Ilgın

Contents

Preface xivList of Abbreviations xviiiAbout the Companion Website xxi

1 Signal Analysis 11.1 Relationship Between Time and Frequency Characteristics of Signals 2

1.1.1 Fourier Series 21.1.2 Fourier Transform 41.1.3 Fourier Transform of Periodic Functions 13

1.2 Power Spectal Density (PSD) and Energy Spectral Density (ESD) 151.2.1 Energy Signals Versus Power Signals 151.2.2 Autocorrelation Function and Spectral Density 16

1.3 Random Signals 181.3.1 Random Variables 181.3.2 Random Processes 20

1.4 Signal Transmission Through Linear Systems 27References 31Problems 31

2 Antennas 332.1 Hertz Dipole 34

2.1.1 Near- and Far-Field Regions 372.2 Linear Dipole Antenna 402.3 Aperture Antennas 432.4 Isotropic and Omnidirectional Antennas 472.5 Antenna Parameters 48

2.5.1 Polarization 482.5.2 Radiation Pattern 512.5.3 Directivity and Beamwidth 532.5.4 Gain 60

2.5.5 Effective Receiving Area 612.5.6 Effective Antenna Height and Polarization Matching 682.5.7 Impedance Matching 70

References 78Problems 78

3 Channel Modeling 823.1 Wave Propagation in Low- and Medium-Frequency Bands (Surface Waves) 833.2 Wave Propagation in the HF Band (Sky Waves) 843.3 Wave Propagation in VHF and UHF Bands 85

3.3.1 Free-Space Propagation 863.3.2 Line-Of-Sight (LOS) Propagation 863.3.3 Fresnel Zones 873.3.4 Knife-Edge Diffraction 903.3.5 Propagation Over the Earth Surface 95

3.4 Wave Propagation in SHF and EHF Bands 1063.4.1 Atmospheric Absorption Losses 1083.4.2 Rain Attenuation 110

3.5 Tropospheric Refraction 1183.5.1 Ducting 1213.5.2 Radio Horizon 123

3.6 Outdoor Path-Loss Models 1233.6.1 Hata Model 1243.6.2 COST 231 Extension to Hata Model 1253.6.3 Erceg Model 128

3.7 Indoor Propagation Models 1293.7.1 Site-General Indoor Path Loss Models 1303.7.2 Signal Penetration Into Buildings 132

3.8 Propagation in Vegetation 134References 137Problems 137

4 Receiver System Noise 1454.1 Thermal Noise 1464.2 Equivalent Noise Temperature 147

4.2.1 Equivalent Noise Temperature of Cascaded Subsystems 1494.3 Noise Figure 150

4.3.1 Noise Figure of a Lossy Device 1524.4 External Noise and Antenna Noise Temperature 153

4.4.1 Point Noise Sources 1544.4.2 Extended Noise Sources and Brightness Temperature 1544.4.3 Antenna Noise Figure 1564.4.4 Effects of Lossy Propagation Medium on the Observed Brightness

Temperature 1564.4.5 Brightness Temperature of Some Extended Noise Sources 1604.4.6 Man-Made Noise 167

4.5 System Noise Temperature 167

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4.6 Additive White Gaussian Noise Channel 174References 175Problems 175

5 Pulse Modulation 1845.1 Analog-to-Digital Conversion 185

5.1.1 Sampling 1865.1.2 Quantization 1935.1.3 Encoding 2035.1.4 Pulse Modulation Schemes 204

5.2 Time-Division Multiplexing 2095.2.1 Time Division Multiplexing 2095.2.2 TDM Hierarchies 2105.2.3 Statistical Time-Division Multiplexing 212

5.3 Pulse-Code Modulation (PCM) Systems 2125.3.1 PCM Transmitter 2135.3.2 Regenerative Repeater 2135.3.3 PCM Receiver 214

5.4 Differential Quantization Techniques 2205.4.1 Fundamentals of Differential Quantization 2205.4.2 Linear Prediction 2215.4.3 Differential PCM (DPCM) 2265.4.4 Delta Modulation 2285.4.5 Audio Coding 2325.4.6 Video Coding 234

References 236Problems 236

6 Baseband Transmission 2456.1 The Channel 245

6.1.1 Additive White Gaussian Noise (AWGN) Channel 2486.2 Matched Filter 249

6.2.1 Matched Filter Versus Correlation Receiver 2526.2.2 Error Probability For Matched-Filtering in AWGN Channel 255

6.3 Baseband M-ary PAM Transmission 2636.4 Intersymbol Interference 268

6.4.1 Optimum Transmit and Receive Filters in an Equalized Channel 2706.5 Nyquist Criterion for Distortionless Baseband Binary Transmission In a

ISI Channel 2726.5.1 Ideal Nyquist Filter 2736.5.2 Raised-Cosine Filter 276

6.6 Correlative-Level Coding (Partial-Response Signalling) 2786.6.1 Probability of Error in Duobinary Signaling 2806.6.2 Generalized Form of Partial Response Signaling (PRS) 282

6.7 Equalization in Digital Transmission Systems 283References 287Problems 287

ixContents

7 Optimum Receiver in AWGN Channel 2987.1 Introduction 2987.2 Geometric Representation of Signals 3007.3 Coherent Demodulation in AWGN Channels 302

7.3.1 Coherent Detection of Signals in AWGN Channels 3057.4 Probability of Error 311

7.4.1 Union Bound on Error Probability 3137.4.2 Bit Error Versus Symbol Error 316

References 319Problems 319

8 Passband Modulation Techniques 3238.1 PSD of Passband Signals 324

8.1.1 Bandwidth 3258.1.2 Bandwidth Efficiency 326

8.2 Synchronization 3278.2.1 Time and Frequency Standards 330

8.3 Coherently Detected Passband Modulations 3328.3.1 Amplitude Shift Keying (ASK) 3338.3.2 Phase Shift Keying (PSK) 3388.3.3 Quadrature Amplitude Modulation (QAM) 3528.3.4 Coherent Orthogonal Frequency Shift Keying (FSK) 358

8.4 Noncoherently Detected Passband Modulations 3678.4.1 Differential Phase Shift Keying (DPSK) 3678.4.2 Noncoherent Orthogonal Frequency Shift Keying (FSK) 370

8.5 Comparison of Modulation Techniques 374References 378Problems 379

9 Error Control Coding 3869.1 Introduction to Channel Coding 3869.2 Maximum Likelihood Decoding (MLD) with Hard and Soft Decisions 3909.3 Linear Block Codes 396

9.3.1 Generator and Parity Check Matrices 3989.3.2 Error Detection and Correction Capability of a Block Code 4029.3.3 Syndrome Decoding of Linear Block Codes 4059.3.4 Bit Error Probability of Block Codes with Hard-Decision Decoding 4089.3.5 Bit Error Probability of Block Codes with Soft-Decision Decoding 4099.3.6 Channel Coding Theorem 4119.3.7 Hamming Codes 412

9.4 Cyclic Codes 4159.4.1 Generator Polynomial and Encoding of Cyclic Codes 4159.4.2 Parity-Check Polynomial 4189.4.3 Syndrome Decoding of Cyclic Codes 4199.4.4 Cyclic Block Codes 422

9.5 Burst Error Correction 4299.5.1 Interleaving 430

x Contents

9.5.2 Reed-Solomon (RS) Codes 4329.5.3 Low-Density Parity Check (LDPC) Codes 435

9.6 Convolutional Coding 4369.6.1 A Rate-½ Convolutional Encoder 4379.6.2 Impulse Response Representation of Convolutional Codes 4389.6.3 Generator Polynomial Representation of Convolutional Codes 4389.6.4 State and Trellis Diagram Representation of a Convolutional Codes 4399.6.5 Decoding of Convolutional Codes 4419.6.6 Transfer Function and Free Distance 4459.6.7 Error Probability of Convolutional Codes 4479.6.8 Coding Gain of Convolutional Codes 451

9.7 Concatenated Coding 4549.8 Turbo Codes 4569.9 Automatic Repeat-Request (ARQ) 459

9.9.1 Undetected Error Probability 4619.9.2 Basic ARQ Protocols 4639.9.3 Hybrid ARQ Protocols 467

Appendix 9A Shannon Limit For Hard-Decision and Soft-Decision Decoding 471References 473Problems 473

10 Broadband Transmission Techniques 47910.1 Spread Spectrum 481

10.1.1 PN Sequences 48110.1.2 Direct Sequence Spread Spectrum 48510.1.3 Frequency Hopping Spread Spectrum 508

10.2 Orthogonal Frequency Division Multiplexing (OFDM) 51910.2.1 OFDM Transmitter 52010.2.2 OFDM Receiver 52310.2.3 Intercarrier Interference (ICI) in OFDM Systems 52910.2.4 Channel Estimation by Pilot Subcarriers 53110.2.5 Synchronization of OFDM Systems 53210.2.6 Peak-to-Average Power Ratio (PAPR) in OFDM 53210.2.7 Multiple Access in OFDM Systems 53910.2.8 Vulnerability of OFDM Systems to Impulsive Channel 54310.2.9 Adaptive Modulation and Coding in OFDM 544

Appendix 10A Frequency Domain Analysis of DSSS Signals 545Appendix 10B Time Domain Analysis of DSSS Signals 547Appendix 10C SIR in OFDM systems 548References 551Problems 552

11 Fading Channels 55711.1 Introduction 55811.2 Characterisation of Multipath Fading Channels 559

11.2.1 Delay Spread 56211.2.2 Doppler Spread 56911.2.3 The Effect of Signal Characteristics on the Choice of a Channel Model 578

xiContents

11.3 Modeling Fading and Shadowing 58211.3.1 Rayleigh Fading 58211.3.2 Rician Fading 58411.3.3 Nakagami-m Fading 58711.3.4 Log-Normal Shadowing 59111.3.5 Composite Fading and Shadowing 59611.3.6 Fade Statistics 600

11.4 Bit Error Probability in Frequency-Nonselective Slowly Fading Channels 60411.4.1 Bit Error Probability for Binary Signaling 60511.4.2 Moment Generating Function 60711.4.3 Bit Error Probability for M-ary Signalling 61011.4.4 Bit Error Probability in Composite Fading and Shadowing Channels 613

11.5 Frequency-Selective Slowly-Fading Channels 61411.5.1 Tapped Delay-Line Channel Model 61511.5.2 Rake Receiver 617

11.6 Resource Allocation in Fading Channels 62211.6.1 Adaptive Coding and Modulation 62211.6.2 Scheduling and Multi-User Diversity 623

References 626Problems 626

12 Diversity and Combining Techniques 63812.1 Antenna Arrays in Non-Fading Channels 640

12.1.1 SNR 64712.2 Antenna Arrays in Fading Channels 65012.3 Correlation Effects in Fading Channels 65412.4 Diversity Order, Diversity Gain and Array Gain 657

12.4.1 Tradeoff Between the Maximum Eigenvalue and the Diversity Gain 65912.5 Ergodic and Outage Capacity in Fading Channels 660

12.5.1 Multiplexing Gain 66312.6 Diversity and Combining 664

12.6.1 Combining Techniques for SIMO Systems 66612.6.2 Transmit Diversity (MISO) 686

References 691Problems 692

13 MIMO Systems 70113.1 Channel Classification 70213.2 MIMO Channels with Arbitrary Number of Transmit and Receive Antennas 70313.3 Eigenvalues of the Random Wishart Matrix HHH 707

13.3.1 Uncorrelated Central Wishart Distribution 70813.3.2 Correlated Central Wishart Distribution 710

13.4 A 2 × 2 MIMO Channel 71813.5 Diversity Order of a MIMO System 72213.6 Capacity of a MIMO System 723

13.6.1 Water-Filling Algorithm 72813.7 MIMO Beamforming Systems 730

xii Contents

13.7.1 Bit Error Probability in MIMO Beamforming Systems 73213.8 Transmit Antenna Selection (TAS) in MIMO Systems 73413.9 Parasitic MIMO Systems 740

13.9.1 Formulation 74113.9.2 Output SNR 74313.9.3 Radiation Pattern 74413.9.4 Bit Error Probability 74413.9.5 5 × 5 Parasitic MIMO-MRC 746

13.10 MIMO Systems with Polarization Diversity 74813.10.1 The Channel Model 74813.10.2 Spatial Multiplexing (SM) with Polarization Diversity 75013.10.3 MIMO Beamforming-MRC System with Polarization Diversity 75113.10.4 Simulation Results 751

References 753Problems 755

14 Cooperative Communications 75814.1 Dual-Hop Amplify-and-Forward Relaying 759

14.1.1 Source-Relay-Destination Link with a Single Relay 76014.1.2 Combined SRD and Direct Links 765

14.2 Relay Selection in Dual-Hop Relaying 76714.2.1 Relay Selection Strategies 76914.2.2 Performance Evaluation of Selection-Combined Best SRD

and SD Links 76914.3 Source and Destination with Multiple Antennas in Dual-Hop AF Relaying 776

14.3.1 Source-Relay-Destination Link 77614.3.2 Source-Destination Link 78214.3.3 Selection-Combined SRD and SD Links 783

14.4 Dual-Hop Detect-and-Forward Relaying 78714.5 Relaying with Multiple Antennas at Source, Relay and Destination 79614.6 Coded Cooperation 798Appendix 14A CDF of γeq and γeq,0 800Appendix 14B Average Capacity of γeq,0 801Appendix 14C Rayleigh Approximation for Equivalent SNR with Relay Selection 802Appendix 14D CDF of γeq,a 804References 806Problems 807

Appendix A: Vector Calculus in Spherical Coordinates 810Appendix B: Gaussian Q Function 811Appendix C: Fourier Transforms 819Appendix D: Mathematical Tools 821Appendix E: The Wishart Distribution 834Appendix F: Probability and Random Variables 844

Index 871

xiiiContents

Preface

Telecommunications is a rapidly evolving areaof electrical engineering, encompassing diverseareas of applications, including RF communi-cations, radar systems, ad-hoc networks, sensornetworks, optical communications, radioastr-onomy, and so on. Therefore, a solid back-ground is needed on numerous topics ofelectrical engineering, including calculus,antennas, wave propagation, signals and sys-tems, random variables and stochastic pro-cesses and digital signal processing. In viewof the above, the success in the telecommunica-tions education depends on the background ofthe student in these topics and how these topicsare covered in the curriculum. For example, theFourier transform may not usually be taught inrelation with time- and frequency-response ofthe systems. Similarly, concepts of probabiliymay not be related to random signals. On theother hand, students studying telecommunica-tions may not be expected to know the detailsof the Maxwell’s equations and wave propaga-tion. However, in view of the fact that wirelesscommunication systems comprise transmit/receive antennas and a propagation medium,it is necessary to have a clear understandingof the radiation by the transmit antenna, propa-gation of electromagnetic waves in the con-sidered channel and the reception of

electromagnetic waves by the receive antenna.Otherwise, the students may face difficulties inunderstanding the telecommunications processin the physical layer.The engineering education requires a careful

tradeoff between the rigour provided by the the-ory and the simple exposure of the correspond-ing physical phenomena and their applicationsin our daily life. Therefore, the book aims to helpthe students to understand the basic principlesand to apply them. Basic principles and analyt-ical tools are provided for the design of commu-nication systems, illustrated with examples, andsupported by graphical illustrations.The book is designed to meet the needs of

electrical engineering students at undergraduateand graduate levels, and those of researchersand practicing engineers. Though the book ison digital communications, many conceptsand approaches presented in the book are alsoapplicable for analog communication systems.The students are assumed to have basic know-ledge of Maxwell’s equations, calculus, matrixtheory, probability and stochastic processes,signals and systems and digital signal process-ing. Mathematical tools required for under-standing some topics are incorporated in therelevant chapters or are presented in theappendices. Each chapter contains graphical

illustrations, figures, examples, references, andproblems for better understanding the exposedconcepts.

Chapter 1 Signal Analysis summarizes thetime-frequency relationship and basic conceptsof Fourier transform for deterministic and ran-dom signals used in the linear systems. Theaim was to provide a handy reference and toavoid repeating the same basic concepts in thesubsequent chapters. Chapter 2 Antennas pre-sents the fundamentals of the antenna theorywith emphasis on the telecommunication aspectsrather thanon theMaxwell’sequations.Chapter3ChannelModeling presents the propagation pro-cesses following the conversion of the electricalsignals in the transmitter into electromagneticwaves by the transmit antenna until they arereconverted into electrical signals by the receiveantenna.Chapter 4 SystemNoise ismainly basedon the standards for determining the receivernoise of internal and external origin and providestools for calculating SNR at the receiver output;the SNR is known to be the figure-of-merit ofcommunication systems since it determines thesystem performance. Chapters 2, 3 and 4 thusrelate the wireless interaction between transmit-ter and receiver in the physical layer. It may beworth mentioning that, unlike many books onwireless communications, covering only VHFand UHF bands, Chapters 2, 3 and 4 extendthe coverage of antennas, receiver noise andchannel modeling to SHF and EHF bands.A thorough understanding of the materials pro-vided in these chapters is believed to be criticalfor deeper understanding of the rest of the book.These three chapters are believed to close the gapbetween the approaches usually followed bybooks on antennas and RF propagation, basedon the Maxwell’s equations, and the books ondigital communications, based on statistical the-ory of communications. One of the aims of thebook is to help the students to fuse these twocomplementary approaches.

The following chapters are dedicated to stat-istical theory of digital communications. Chap-ter 4 Pulse Modulation treats the conversionof analog signals into digital for digital

communication systems. Sampling, quantiza-tion and encoding tradeoffs are presented, linecodes used for pulse transmission are relatedto the transmission bandwidth. Time divisionmultiplexing (TDM) allows multiple digital sig-nals to be transmitted as a single signal. At thereceiver they are reconverted into analog forthe end user. PCM and other pulse modulationsas well as audio and video coding techniques arealso presented.Chapter 5 BasebandModulationfocuses on the optimal reception of pulse modu-lated signals and intersymbol interference (ISI)between pulses, due to filtering so as to limitthe transmission bandwidth or to minimize thereceived noise power. In an AWGN channel,the optimum receiver maximizes the outputSNR by matching the receive filter characteris-tics to those of the transmitter. The optimalchoice of pulse shape, for example, Nyquist,raised-cosine, or correlative-level coding (par-tial-response signaling) is also presented in orderto mitigate the ISI.Chapter 7 Optimum Receiverin AWGN Channels is focused on the geometricrepresentation of the signals so as to be able toidentify the two functionalities (demodulationand detection) of an optimum receiver. Basedon this approach, derivation of the bit error prob-ability (BEP) is presented and upper bounds areprovided when the BEP can not be obtainedexactly. Chapter 8 Passband Modulation Tech-niques starts with the definition of bandwidthand the bandwidth efficiency, followed by thesynchronization (in frequency, phase and sym-bol timing) between transmitted and receivedsymbols. The PSD, bandwidth and power effi-ciencies and bit/symbol error probabilities arederived for M-ary coherent, differentially coher-ent and noncoherent modulations, for example,M-ary PSK, M-ary ASK, M-ary FSK, M-aryQAM and M-ary DPSK. This chapter also pro-vides a comparasion of spectrum and power effi-ciencies of the above-cited passband modulationtechniques. Chapter 9 Error Control Codingpresents the principles of channel coding in orderto control (detect and/or correct) Gaussian (ran-dom) and burst errors occuring in the channeldue to noise, fading, shadowing and other

xvPreface

potential sources of interference. Source codingis not addressed in the book. Channel codingusually comes at the expense of increased trans-mission rate, hence wider transmission band-width, due to the inclusion of additional (paritycheck) bits among the data bits. Use of paritycheck bits reduces energy per channel bits andhence leads to higher channel BEP. However,a good code is expected to correct more errorsthan it creates and the overall coded BEPdecreases at the expense of increased transmis-sion bandwidth. This tradeoff between theBEP and the transmission bandwidth is well-known in the coding theory. As shown by theShannon capacity theorem, one can achieveerror-free communications as the transmissionbandwidth goes to infinity, that is, by using infin-itely many parity check bits, as long as the ratioof the energy per bit to noise PSD (Eb/N0) ishigher than −1.6 dB. This chapter addressesblock and convolutional codeswhich are capableof correcting random and burst-errors. Auto-matic-repeat request (ARQ) techniques basedon error-detection codes and hybrid ARQ(HARQ) techniques exploiting codes whichcan both detect and correct channel bit errorsare also presented. Chapter 10 BroadbandTransmissionTechniques is composed ofmainlytwo sections, namely spread-spectrum (SS) andthe orthogonal frequency division multiplexing(OFDM). SS and OFDM provide alternativeapproaches for transmission of multi-user sig-nals over wide transmission bandwidths. In SS,spread multi-user signals are distinguished fromeach other by orthogonal codes, while, inOFDM, narrowbandmulti-user signals are trans-mitted with different orthogonal subcarriers. Thechapter is focused on two versions of SS, namelythe direct sequence (DS) SS and frequency-hopping (FH) SS. Intercarrier- and intersym-bol-interference, channel estimation and syn-chronization, adaptive modulation and coding,peak-to-average power ratio, andmultiple accessin up- and down-links ofOFDMsystems are alsopresented. Chapter 11 Fading Channelsaccounts for the effects of multipath propagationand shadowing. Fading channels are usually

characterized by delay and Doppler spread ofthe received signals. The fading may be slowor fast, frequency-flat or frequency-selective. Ifthe receiver can not collect coherently all theincoming signal components spread in timeand frequency, then the received signal powerlevel will be decreased drastically, hence leadingto sigificant performance losses. This chapter isfocused on the principal approaches for the chan-nel fading and shadowing, for example, Ray-leigh, Rician, Nakagami, and log-normal. Theeffect of fading and shadowing on the BEP arepresented. Resource allocation and schedulingin fading channels is also treated. Chapter 12Diversity and Combining Techniques addressesthe approaches to alleviate the degradationcaused by fading and shadowing. This isachieved by providing the receiver with mul-tiple, preferably independent, replicas (in time,frequency, space) of the transmitted signal, andcombine these signals in various ways, forexample, selection, equal-gain, maximal-ratio,square-law. The performance improvement pro-vided by diversity and combining techniques ispresented as a function of the correlation andpower balance between the diversity branches.Transmit and receive diversity, pre-detectionand post-detection combining of diversitybranches and channel capacity in fading andshadowing channels are also addressed. In con-trast with telecommunication systems with sin-gle-transmit and single receive antennas (i.e.,the so-called single-input single-output (SISO)systems), Chapter 12 is also concerned withsystems using multiple antennas at the receiveror the transmitter. The receive diversity systemswith multiple receive antennas are also calledas SIMO (single-input multiple-output). Simi-larly, the transmit diversity systems with mul-tiple antennas at the transmitter are referredto as MISO (multiple-input single-output)systems. Chapter 13 MIMO (multiple-inputmultiple-output) Systems is concernedwith tele-communication systems with multiple anten-nas both at the transmit and the receivesides. A MIMO system, equipped with Nt

transmit and Nr receive antennas, can benefit

xvi Preface

an NtNr-fold antenna diversity (NtNr inde-pendent paths between transmitter andreceiver). TheMIMO channels is usually char-acterized by Wishart distribution, presented inAppendix E. The eigenvalues of randomWishart matrices determine the dominantcharacteristics of the MIMO channels, whichmay suffer correlation between the transmittedand/or received signals. This determines thenumber and the relative weights of the eigen-modes; water-filling algorithm can be used toequalize the transmit power or the data ratesupported by each eignmode. Transmitantenna selection (TAS) implies the selectionof one or a few of the multiple transmit anten-nas with highest instantaneous SNRs. TASmakes good use of the transmit diversity bydividing the transmit power only betweenthe transmit antennas with highest instantan-eous SNRs. MIMO systems enjoy full coord-ination between transmit and receive antennas.Consequently, by adjusting the complexantenna weights at the transmit- and receive-sides, the SNR at the output of a MIMO beam-forming system can be maximized, hence min-imizing the BEP. Chapter 14 on CooperativeCommunications is based on dual-hop relayingwith amplify-and-forward, detect-and-forwardand coded cooperation protocols. The source-relay-destination link is modeled as a single linkwith an equivalent SNR, the relay with the high-est equivalent SNR may be selected amongst anumber of relays, and multiple antennas maybe used at the source, at the relay and/or the des-tination. The source-destination link is usuallyselection- or maximal-ratio-combined with thesource-relay-destination link. In coded cooper-ation, relaying and channel coding are simul-taneously used to make better use of thecooperation.

The appendices are believed to provide con-venient references, and useful background for

better understanding of the relevant concepts.AppendixAVectorCalculus in Spherical Coord-inates provides tools for conversion betweenspherical and polar coordinates required forChapter 2 Antennas. Appendix B GaussianQ Function is useful for determining the BEPof majority of modulation schemes. AppendixC presents a list of Fourier Transforms usuallyencountered in telecommunication applications.Appendix DMathematical Tools presents series,integrals and functions used in the book, minim-izing the need to resort to another mathematicalhandbook. Appendix E Wishart Distributionprovides the necessary background for theChapter 13 MIMO Systems. Appendix F Prob-ability and Random Variables aims to help stu-dents with probabilistic concepts, widely usedprobability distributions and random processes.Topics to be taught at undergraduate and

graduate levels may be decided according tothe priority of the instructor and the course con-tents. Some sections and/or chapters may beomitted or covered partially depending on thepreferences of the instructor. However, it maynot be easy to give a unique approach for spe-cifying the curriculum.During my career, I benefited from numer-

ous excellent books, publications and Internetweb pages. I would like to thank the authorsof all sources who contributed for the accumu-lation of the knowledge reflected in this book.I would like to thank all my undergraduate andgraduate students who, with their response tomy teaching approaches, helped enormouslyfor determining the contents and the coverageof the topics of this book. Valuable cooperationand help from Sandra Grayson, Preethi Belkeseand Adalfin Jayasingh from John Wiley andSons is highly appreciated.

Mehmet ŞafakJuly 2016

xviiPreface

List of Abbreviations

ACK acknowledgmentADC analog-to-digital conversionADM adaptive delta modulationAF amplify and forwardAGC automatic gain controlAJ anti jammingAMR adaptive multi rateAOA angle of arrivalAOD angle of departureAOF amount of fadingARQ automatic repeat requestASK amplitude shift keyingAT&T American Telephone &

Telegraph CompanyAWGN additive white Gaussian noiseBCH Bose-Chaudhuri-Hocquenghem

codesBEP bit error probabilityBPSK binary phase shift keyingBS base stationBSC binary symmetric channelC/N carrier-to-noise ratioCCITT International Telegraph and

Telephone ConsultativeCommittee

CD compact discCDF cumulative distribution functionCDMA code division multiple accessCIR channel impulse response

COST European Cooperation forScientific and TechnicalResearch

CP cyclic prefixCPA co-polar attenuationCRC cyclic redundancy checkCSI channel state informationDAC digital to analog conversionDCT discrete cosine transformDF detect and forwardDFT discrete Fourier transformDGPS differential GPSDM delta modulationDMC discrete memoryless channelDPCM differential PCMDPSK differential phase shift keyingDS direct sequenceDSSS direct sequence spread spectrumE1 European telephone multiplex-

ing hierarchyEGC equal gain combiningEGNOS European geostationary

navigation overlay serviceEHF extremely high frequencies

(30-300 GHz)EIRP effective isotropic radiative

powerEP elliptical polarizationESD energy spectral density

ETSI European TelecommunicationsStandards Institute

FDM frequency division multiplexingFEC forward error correctionFFT fast Fourier transformFH frequency hoppingFHSS frequency hopping spread

spectrumFIR finite impulse responseFOM figure of meritFSK frequency shift keyingFT Fourier transformG/T figure of merit of a receiver

(antenna gain to system noisetemperature ratio)

GALILEO European global navigationsatellite system

GBN go-back-N ARQGEO geostationaryGLONASS Russian global navigation

satellite systemGNSS global navigation satellite

systemsGPS global positioning systemGS greedy schedulingGSC generalized selection combiningGSM global system for mobile

communicationsH.264/AVC advanced video codingHARQ hybrid ARQHDD hard decision decodingHDTV high definition TVHEVC high efficiency video codingHF high frequencies (3-30 MHz)HPA high power amplifierICI inter carrier interferenceIDFT inverse discrete Fourier transformIEEE Institute of Electrical and

Electronics EngineersIFFT inverse fast Fourier transformIMT-2000 international mobile telephone

standardIP Internet protocolISI inter symbol interferenceISM industrial, scientific, and

medical frequency band

ISU international system of unitsITU International Telecommunica-

tions UnionJPEG joint photographic experts groupKa-band 26.5-40 GHz bandKu-band 12.4-18 GHz bandL band 1-2 GHz bandLAN local area networkLDPC low-density parity check codesLEO low Earth orbitingLF low frequencies (30-300 kHz)LHCP left hand circular polarizationLMS least mean squareLNA low noise amplifierLORAN-C radio navigation system by land

based beaconsLOS line of sightLP linear polarizationLPF low pass filterLPI low probability of interceptLTI linear time invariantMAC multiple accessMAI multiple access interferenceMAP maximum a posterioriMEO medium Earth orbitMF medium frequencies

(300-3000 kHz)MGF moment generating functionMIMO multiple-input multiple-outputMIP multipath intensity profileMISO multiple-input single-outputML maximum likelihoodMLD maximum likelihood detectionMPEG motion photograpic experts

groupMRC maximal ratio combiningMS mobile stationMUD multiuser detectionMUI multiuser interferenceNACK negative acknowledgmentNAVSTAR NAVigation Satellite Timing

And Ranging (GPS satellitenetwork)

NFC near field communicationsNRZ non return to zeroOC optimum combining

xixList of Abbreviations

OFDM orthogonal frequency divisionmultiplexing

OLC optical lattice clockOOK on-off keyingOVSF orthogonal variable spreading

factorPAL phase alternating linePAM pulse amplitude modulationPAPR peak to average power ratioPCM pulse code modulationPDF probability density functionPDM pulse duration modulationPFS proportionally fair schedulingPLL phase lock loopPN pseudo noisePPM pulse position modulationPPS precise positioning systemPRS partial response signalingPSD power spectral densityPSK phase shift keyingQAM quadrature-amplitude

modulationQPSK quadrature phase shift keyingRCPC rate compatible punctured

convolutionalRD relay destination linkRFID radio frequency identificationRGB red green blueRHCP right hand circular polarizationRPE-LTP regular pulse excited long term

predictionRR round robinRS Reed-SolomonRSC recursive systematic convolu-

tionalRZ return to zeroSA selective availabilitySATCOM satellite communicationsSC selection combiningSC-FDMA single carrier frequency division

multiple accessSDTV standard definition TV

SF spreading factorSGT satellite ground terminalSHF super high frequencies

(3-30 gHz)SIMO single-input multiple-outputSINR signal-to-interference and noise

ratioSIR signal-to-interference ratioSISO single-input single-outputSLC square-law combiningSNR signal-to-noise ratioSPS standard positioning systemSR source-relay linkSRD source-relay-destination linkSRe selective repeat ARQSS spread spectrumSSC switch-and-stay combiningSW stop-and-wait ARQT1 AT&T telephone multiplexing

hierarchyTAS transmit antenna selectionTDM time division multiplexingTEC total electron contentTPC transmit power controlUHF ultra high frequencies

(300-3000 MHz)ULA uniform linear arrayUMTS universal mobile telecommuni-

cations systemUTC universal coordinated timeVHF very-high frequencies

(30-300 MHz)WAN wide area networksWCDMA wideband code division

multiple access (CDMA)WiFi wireless fidelityWiMax worldwide interoperability for

microwave accessX-band 8.2-12.4 GHz bandXPD cross polar discriminationXPI cross polar isolation

xx List of Abbreviations

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1Signal Analysis

In the course of history, human beings commu-nicated with each other using their ears andeyes, by transmitting their messages via voice,sound, light, smoke, signs, paintings, and so on.[1] The invention of writing made written com-munications also possible. Telecommunica-tions refers to the transmission of messages inthe form of voice, image or data by usingelectrical signals and/or electromagneticwaves. As these messages modulate the ampli-tude, the phase or the frequency of a sinusoidalcarrier, electrical signals are characterized bothin time and frequency domains. The behaviorof these signals in time and frequency domainsare closely related to each other. Therefore, thedesign of telecommunication systems takesinto account both the time- and the fre-quency-characteristics of the signals.

In the time-domain, modulating the ampli-tude, the phase and/or the frequency at highrates may become challenging because of thelimitations in the switching capability of elec-tronic circuits, clocks, synchronization andreceiver performance. On the other hand, thefrequency-domain behavior of signals is of crit-ical importance from the viewpoint of the

bandwidth they occupy and the interferencethey cause to signals in the adjacent frequencychannels. Frequency-domain analysis providesvaluable insight for the system design and effi-cient usage of the available frequency spec-trum, which is a scarce and valuable resource.Distribution of the energy or the power of atransmitted signal with frequency, measuredin terms of energy spectral density (ESD) orpower spectral density (PSD), is important forthe efficient use of the available frequencyspectrum. ESD and PSD are determined bythe Fourier transform, which relates time- andfrequency-domain behaviors of a signal, andthe autocorrelation function, which is a meas-ure of the similarity of a signal with a delayedreplica of itself in the time domain. Spectrumefficiency provides a measure of data rate trans-mitted per unit bandwidth at a given transmitpower level. It also determines the interferencecaused to adjacent frequency channels.Signals are classified based on several

parameters. A signal is said to be periodic ifit repeats itself with a period, for example, asinusoidal signal. A signal is said to be aperi-odic if it does not repeat itself 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

signals may also be classified as being analogor discrete (digital). An analog signal varies con-tinuously with time while a digital signal isdefined by a set of discrete values. For example,a digital signalmay be defined as a sequence of 1s and 0 s, which are transmitted by discrete volt-age levels, for example, ±Vvolts.A signal is saidto be deterministic if its behavior is predictable intime- and frequency-domains. However, a ran-dom signal, for example, noise, can not be pre-dicted beforehand and is therefore characterizedstatistically. [2][3][4][5][6][7][8][9]

In this book, we will deal with both basebandand passband signals. The spectrum of abaseband signal is centered around f = 0, whilethe spectrum of a passband signal is locatedaround a sufficiently large carrier frequencyfc, such that the transmission bandwidthremains in the region f > 0. The basebandsignals, though their direct use is limited, facili-tate the analysis and design of the passbandsystems. A baseband signal may be up-converted to become a passband signal by afrequency-shifting operation, that is, multiply-ing the baseband signal with a sinusoidal carrierof sufficiently high carrier frequency fc. Shift-ing the spectrum of a baseband signal, withspectral components for f < 0 and f > 0, toaround a carrier frequency fc, implies that thebandwidth of a passband signal is doubledcompared to a baseband signal. Most telecom-munication systems employ passband signals,that is, the messages to be transmitted modulatecarriers with sufficiently large carrier frequen-cies. Bandpass transmission has numerousadvantages, for example, ease of radiation/reception by antennas, noise and interferencemitigation, frequency-channel assignment bymultiplexing and transmission of multiple mes-sage signals using a single carrier. In addition,passband transmission has the cost advantage,since it usually requires smaller, more cost-effective and power-efficient equipments.

This chapter will deal with analog/digital,periodic/aperiodic, deterministic/random andbaseband/passband signals. Noting that thefundamental concepts can be explained by

analogy to analog systems, this chapter willmostly be focused on analog baseband signalsunless otherwise stated. The conversion of ananalog signal into digital and the characteriza-tion of a digital signal will be treated in the sub-sequent chapters. Since the characteristics ofpassband signals can easily be derived fromthose of the baseband signals, the focus willbe on the baseband signals. Telecommunica-tion systems operate usually with random sig-nals due to the presence of the system noiseand/or fading and shadowing in wireless chan-nels. [4][5][6][7]Assuming that the student is familiar with

probabilistic concepts, a short introduction ispresented on random signals and processes.One may refer to Appendix F, Probabilityand Random Variables, for further details.Diverse applications of these concepts will bepresented in the subsequent chapters.

1.1 Relationship Between Timeand Frequency Characteristicsof Signals

Fourier series and Fourier transform provide use-ful tools for characterizing the relationshipbetween time- and frequency-domain behaviorsof signals. For spectral analysis, we generally usethe Fourier series for periodic signals and theFourier transform for aperiodic signals. Thesetwo will be observed to merge as the period ofa periodic signal approaches infinity. [3][9]

1.1.1 Fourier Series

The Fourier series expansion of a periodic func-tion sT0 t with period T0 = 1/f0 is given by

sT0 t = a0 +∞

n = 1

ancos nw0t + bn sin nw0t

(1.1)

Using the orthogonality between cos(nw0t)and sin(nw0t), the coefficients an and bn arefound as

2 Digital Communications

a0 =E sT0 t =1T0

T0

0sT0 t dt

an =2T0

T0

0sT0 t cos nw0 t dt, n = 1,2,

bn =2T0

T0

0sT0 t sin nw0 t dt, n= 1,2,

(1.2)

where a0 denotes the average value of sT0 t .Using the Euler’s identity e± jx = cosx ± jsinx,the Fourier series expansion given by (1.1)may be rewritten as a complex Fourier seriesexpansion:

sT0 t =∞

n = −∞cn e

jnw0t

cn =1T0

T0

0sT0 t e− jnw0t dt

(1.3)

From the equivalence of (1.1) and (1.3), onemay easily show that

c0 = a0

c ± n =12an ∓ jbn

(1.4)

According to the Parseval’s theorem, thepower of a periodic signal may be expressedin terms of the Fourier series coefficients:

P=1T0

T0

0sT0 t s∗T0 t dt

=1T0

T0

0sT0 t

∞

n= −∞c∗n e

− jnw0t dt

=∞

n= −∞c∗n

1T0

T0

0sT0 t e− jnw0t dt

cn

=∞

n= −∞cn

2 = a20 +12

∞

n = 1

an2 + bn

2

(1.5)

One may also observe from (1.5) that thepower of a periodic signal is equal to the sumof the powers |cn|

2 of its spectral components,located at nf0, and its PSD is discrete withvalues |cn|

2. Hence, the signal power is the sameirrespective of whether it is calculated in time-or frequency-domains.

Example 1.1 Fourier Series of a RectangularPulse Train.Consider the rectangular pulse train shown inFigure 1.1. Using (1.3) we determine the com-plex Fourier series of sT0 t :

cn =1T0

T0 2

−T0 2sT0 t e− jnw0t =

1T0

T 2

−T 2e− jnw0tdt

=T

T0sinc nf0T (1.6)

where f0 = 1/T0. The sinc function is defined by

sinc x = sin πx πx (1.7)

Being a damped sinusoid, the zeros of thesinc function are the same as those of the sinefunction, that is, x = ±1, ±2,..., except for atx = 0 where it is equal to unity:

sinc n = δ n , n= 0, ± 1, ± 2, (1.8)

Figure 1.1(a) shows the variation of cn as afunction of nf0T. Note that as T0 goes to infinityas in Figure 1.1(b), the periodic rectangularpulse train reduces to a single pulse at theorigion. Then, the spectral lines merge, thatis, f0 0, and the discrete spectra shown inFigure 1.1(a) becomes continuous and isdescribed by sinc(fT) whose zeros are givenby k/T, k = 1, 2,…. On the other hand, asT0 T we have sT0 t = 1 (see Figure 1.1(c))and the corresponding Fourier coefficientsbecome

cn = sinc n = δ n , T0 T (1.9)

3Signal Analysis

1.1.2 Fourier Transform

As T0 goes to infinity as shown in Figure 1.1(b),sT0 t tends to become an aperiodic signal,which will be shown hereafter as s(t).Then, f0 = 1/T0 approaches zero, spectral linesat nf0 merge and form a continuous spectrum.The Fourier transform S(f) of an aperiodiccontinuous function s(t) is defined by [2][3][9]

S f =ℑ s t =∞

−∞s t e− jwt dt

s t =ℑ−1 S f =∞

−∞S f ejwt df

(1.10)

This Fourier transform relationship will alsobe denoted as

s t S f (1.11)

Unless otherwise stated, small-case letterswill be used to denote time-functions whilecapital letters will denote their Fourier trans-forms. It is evident from (1.10) that the value

of S(f) at the origin gives the mean value ofthe signal:

S 0 =E s t =∞

−∞s t dt

s 0 =E S f =∞

−∞S f df

(1.12)

while s(0) denotes the average value of S(f).The so-called Rayleigh’s energy theorem

states that the energy of an aperiodic signalfound in time- and frequency-domains are iden-tical to each other:

E =∞

−∞s t 2 dt

=∞

−∞s∗ t dt

∞

−∞S f ejwtdf

=∞

−∞S f df

∞

−∞s∗ t ejwt dt

S∗ f

=∞

−∞S f 2 df

(1.13)

(a) T0≥T

–T0

• •• •

–T/2 0 T/2 T0

t

1

sT0( t )

f0=1/T

0

cn

nf0T4320 1–1–4 –3 –2

nf0T4320 1–1

nf0T

–4 –3 –2

–4 –3 4320 1–1–2

–∞← –T0 –T/2 0 T/2 T

0 →∞ t

1

lim sT0( t )

T0→∞

cn

–T0

–T/2 0 T0

t

1

lim sT0( t )

T→T0

cn

(c) T→T0

T/2

(b) T0→∞

Figure 1.1 Rectangular Pulse Train and the Coefficients of the Complex Fourier Series.

4 Digital Communications

In view of the integration over −∞ < f <∞ in(1.13), the energy of s(t) is equal to the areaunder the energy spectral density Ψs(f) of s(t),that is, the energy per unit bandwidth:

Ψs f = S f 2, J Hz (1.14)

One may observe from (1.10) that theFourier transform, hence the ESD, of a realsignal s(t) with even symetry s(t) = s(−t), hasalso even symmetry with respect to f = 0.

Example 1.2 Fourier Transform of aRectangular Pulse.Let s(t) be defined as

s t =AΠ t T =A1 t <T 2

0 t >T 2(1.15)

where A is a constant. Using (1.10), the Fouriertransform of (1.15) is found as follows:

S f =AT 2

−T 2e− jwt dt

=AT sinc fT

(1.16)

where sinc(x) is defined by (1.7) (see (1.6) andFigure 1.1(b)).

Figure1.2(a) shows theFourier transformrela-tionship between the (1.15) and (1.16). Thefrequency components of the pulse, which istime-limited to ± T/2, extends over (−∞, ∞)in the frequency domain. In the limiting casewhere T ∞, then the pulse extends uniformlyover (−∞,∞) in the time domain, hence a dc sig-nal (band-limited but not time-limited). Then, thepulse can be represented by only a singlefrequency component at f = 0, hence by a deltafunction, in the frequency domain (seeFigure 1.2(b)). On the other hand, if we let A =1/T so that the area under the pulse becomesunity(see Figure 1.2(c)), and let T 0, then the time-limited pulse approaches a delta function and itsFourier transform S(f) tends to be flat in thefrequencydomain.Asonemayalsoobserve fromthe Fourier transform relationship in (1.10), atime-limited signal has frequency componentsover (−∞, ∞), hence not band-limited, while aband-limited signal can not be time-limited. Tohave a better feeling about the time-frequencyrelationship, we observe from Figure 1.2(a) thatthe bandwidth between dc and the first nullof the sinc function is given by W = 1/T. If weuse this bandwidth as a measure of the spectrumoccupancy of the pulse s(t), the product of thepulse duration T and the bandwidth is WT = 1.

s(t)

–T/2 0 T/2 t

A

0 f

1

0 t

A=1/T

0 f

S(f)=A δ(f)

S(f)

–4 –3 –2 –1 0 1 2 3 4 f T

0 t

A

s(t)

s(t)

S(f)=AT sinc(fT)

(a) 0<T<∞

(b) T → ∞

(c) T → 0

Figure 1.2 Fourier Transform of a Rectangular Pulse with Amplitude A.

5Signal Analysis

Ingeneral, the so-called time-bandwidthproduct,which relates time and frequency behaviors of asignal, is a constant and its value depends on theconsidered pulse. This implies that bandwidthand the pulse duration are inversely related toeach other. Hence, faster changing pulses, thatis, pulses with smaller T, occupy wider band-widths. In other words, higher data rate transmis-sions require wider transmission bandwidths.Indeed, high data rate transmissions (with min-imum pulse durations) in minimum possibletransmission bandwidths is one of the challen-ging issues in telecommunications engineering.

1.1.2.1 Impulses and Transforms inthe Limit

Dirac delta function does not exist physically,but is widely used in many areas of engineer-ing. Some functions are used to approximatethe Dirac delta function. For example, the rect-angular pulse shown in Figure 1.2 approxi-mates Dirac delta function in the time domainas T approaches zero. As the area under a Diracdelta function should be equal to unity, theamplitude of the rectangular pulse is chosenas A = 1/T. Figure 1.2(c) also shows that a Diracdelta function in the time domain has a flatspectrum, that is, its PSD is uniform. Similarly,the Fourier transform of a rectangular pulseapproximates a Dirac delta function located atf = 0 as T ∞ (see also Figure 1.2(b)), whichimplies that the Dirac delta function in the fre-quency domain implies a time-invariant signal.

Some alternative definitions of the Diracdelta function are listed below: [2][3][9]

δ t− t0 =∞ t = t0

0 t t0

δ t = limT 0

1TΠ

t

Tδ f = lim

T ∞T sinc fT

δ t− t0 =∞

−∞e± j2π t− t0 λdλ

(1.17)

Some properties of the Dirac delta functionare summarized below:

a. Area under the Dirac delta function is unity:

∞

−∞δ t− t0 dt = 1 (1.18)

b. Sampling of an ordinary function s(t) whichis continuous at t0:

b

as t δ t− t0 dt =

s t0 a < t0 < b

s t0 2 t0 = a, t0 = b

0 otherwise

(1.19)

c. Relation with the unit step function

u t− t0 =t

−∞δ τ− t0 dτ =

1 t > t0

1 2 t = t0

0 t < t0

δ t− t0 =d

dtu t− t0

(1.20)

d. Multiplication and convolution with a con-tinuous function:

s t δ t− t0 = s t0 δ t− t0

s t δ t− t0 = s t− t0(1.21)

e. Scaling

δ at =1aδ t (1.22)

f. Fourier transform

δ t∓ t0 e∓ jwt0

e ± jw0t δ f ∓ f0(1.23)

1.1.2.2 Signals with Even and OddSymmetry and Causality

Assuming that s(t) is a real-valued function, itsFourier transform S(f) may be decomposed intoits even and odd components as follows: [2]

6 Digital Communications