Fundamentals of Communication Systems 2nd Edition John G. Proakis

Answer manual for Principles of Communication Infrastructure 2nd Variation John G. Proakis

ISBN-13: 9780137848706

For one- or two-semester, senior-level undergraduate programs in Communication Infrastructure for Electrical and Computer Engineering majors.

This textual document introduces the essential techniques used in contemporary communication infrastructure and provides elementary instruments and methodologies used in the analysis and design of these systems. The authors emphasize digital communication infrastructure, including new generations of wireless communication infrastructure, satellite communication, and data transmission networks. A background in calculus, linear algebra, basic digital circuits, linear system theory, and likelihood and random variables is assumed.

Table of contents

PREFACE xvii

1 INTRODUCTION 1

1.1 Historical Analysis 1

1.2 Elements of an Electrical Communication Infrastructure 4

1.2.1 Digital Communication Infrastructure, 7

1.2.2 Early Work in Digital Communications, 10

1.3 Communication Channels and Their Characteristics 12

1.4 Mathematical Models for Communication Channels 18

1.5 Abstract and Additional Study 20

2 SIGNALS AND LINEAR SYSTEMS 21

2.1 Fundamental Concepts 21

2.1.1 Fundamental Operations on Signals, 21

2.1.2 Categorization of Signals, 23

2.1.3 Some Essential Signals and Their Properties, 31

2.1.4 Categorization of Systems, 38

2.1.5 Analysis of LTI Systems in the Time Domain, 41

2.2 Fourier Series 43

2.2.1 Fourier Series and Its Properties, 44

2.2.2 Response of LTI Systems to Periodic Signals, 54

2.2.3 Parseval’s Relation, 56

2.3 Fourier Transform 58

2.3.1 From Fourier Series to Fourier Transforms, 58

2.3.2 Fundamental Properties of the Fourier Transform, 64

2.3.3 Fourier Transform for Periodic Signals, 78

2.3.4 Transmission over LTI Systems, 81

2.4 Filter Design 85

2.5 Power and Energy 89

2.5.1 Energy-Type Signals, 89

2.5.2 Power-Type Signals, 92

2.6 Hilbert Transform and Its Properties 95

2.7 Lowpass and Bandpass Signals 98

2.8 Abstract and Additional Study 100

Exercises 101

3 AMPLITUDE MODULATION 117

3.1 Introduction to Modulation 118

3.2 Amplitude Modulation 119

3.2.1 Double-Sideband Suppressed-Carrier AM, 119

3.2.2 Conventional Amplitude Modulation, 126

3.2.3 Single-Sideband AM, 132

3.2.4 Vestigial-Sideband AM, 134

3.3 Implementation of Amplitude Modulators and Demodulators 137

3.4 Signal Multiplexing 144

3.4.1 Frequency-Division Multiplexing, 144

3.4.2 Quadrature-Carrier Multiplexing, 145

3.5 AM Radio Broadcasting 146

3.6 Abstract and Additional Study 149

Appendix 3A: Derivation of the Expression for SSB-AM Signals 149

Exercises 151

4 ANGLE MODULATION 161

4.1 Representation of FM and PM Signals 161

4.2 Spectral Characteristics of Angle-Modulated Signals 166

4.2.1 Angle Modulation by a Sinusoidal Signal, 166

4.2.2 Angle Modulation by an Arbitrary Message Signal, 170

4.3 Implementation of Angle Modulators and Demodulators 171

4.4 FM Radio Broadcasting 179

4.5 Abstract and Additional Study 181

Exercises 182

5 PROBABILITY AND RANDOM PROCESSES 190

5.1 Analysis of Probability and Random Variables 190

5.1.1 Sample Space, Events, and Probability, 190

5.1.2 Conditional Probability, 191

5.1.3 Random Variables, 194

5.1.4 Functions of a Random Variable, 201

5.1.5 Several Random Variables, 203

5.1.6 Sums of Random Variables, 208

5.2 Random Processes: Fundamental Concepts 209

5.2.1 Statistical Averages, 212

5.2.2 Wide-Sense Stationary Processes, 215

5.2.3 Several Random Processes, 217

5.2.4 Random Processes and Linear Systems, 218

5.2.5 Power Spectral Density of Stationary Processes, 220

5.2.6 Power Spectral Density of a Sum Process, 225

5.3 Gaussian and White Processes 226

5.3.1 Gaussian Processes, 226

5.3.2 White Processes, 228

5.3.3 Filtered Noise Processes, 230

5.4 Abstract and Additional Study 235

Exercises 236

6 EFFECT OF NOISE ON ANALOG COMMUNICATION INFRASTRUCTURE 255

6.1 Impact of Noise on Amplitude Modulation Systems 255

6.1.1 Impact of Noise on a Baseband System, 256

6.1.2 Impact of Noise on DSB-SC AM, 256

6.1.3 Impact of Noise on SSB AM, 258

6.1.4 Impact of Noise on Conventional AM, 259

6.2 Impact of Noise on Angle Modulation 263

6.2.1 Threshold Impact in Angle Modulation, 271

6.2.2 Preemphasis and Deemphasis Filtering for FM, 274

6.3 Comparison of Analog-Modulation Systems 277

6.4 Effects of Transmission Losses and Noise in Analog Communication

Systems 278

6.4.1 Characterization of Thermal Noise Sources, 279

6.4.2 Effective Noise Temperature and Noise Figure, 280

6.4.3 Transmission Losses, 283

6.4.4 Repeaters for Signal Transmission, 284

6.5 Abstract and Additional Study 287

Exercises 288

7 ANALOG-TO-DIGITAL CONVERSION 296

7.1 Sampling of Signals and Signal Reconstruction from Samples 297

7.1.1 The Sampling Theorem, 297

7.2 Quantization 301

7.2.1 Scalar Quantization, 302

7.2.2 Vector Quantization, 309

7.3 Encoding 311

7.4 Waveform Coding 312

7.4.1 Pulse Code Modulation, 313

7.4.2 Differential Pulse Code Modulation, 317

7.4.3 Delta Modulation, 318

7.5 Analysis—Synthesis Techniques 321

7.6 Digital Audio Transmission and Digital Audio Recording 325

7.6.1 Digital Audio in Phone Transmission Systems, 325

7.6.2 Digital Audio Recording, 327

7.7 The JPEG Image-Coding Standard 332

7.8 Abstract and Additional Study 335

Exercises 336

8 DIGITAL MODULATION METHODS IN AN ADDITIVE WHITE GAUSSIAN NOISE CHANNEL 347

8.1 Geometric Representation of Signal Waveforms 348

8.2 Binary Modulation Schemes 352

8.2.1 Binary Antipodal Signaling, 352

8.2.2 Binary Orthogonal Signaling, 356

8.3 Optimum Receiver for Binary Modulated Signals in Additive White Gaussian Noise 361

8.3.1 Correlation-Type Demodulator, 362

8.3.2 Matched-Filter-Type Demodulator, 371

8.3.3 The Efficiency of the Optimum Detector for Binary Signals, 379

8.4 M-ary Digital Modulation 384

8.4.1 The Optimum Receiver for M-ary Signals in AWGN, 384

8.4.2 A Union Bound on the Probability of Error, 396

8.5 M-ary Pulse Amplitude Modulation 398

8.5.1 Carrier-Modulated PAM for Bandpass Channels (M-ary ASK), 400

8.5.2 Demodulation and Detection of Amplitude-Modulated PAM Signals, 403

8.5.3 Probability of Error for M-ary PAM, 403

8.6 Phase-Shift Keying 406

8.6.1 Geometric Representation of PSK Signals, 408

8.6.2 Demodulation and Detection of PSK Signals, 410

8.6.3 Probability of Error for Phase-Coherent PSK Modulation, 411

8.6.4 Differential Phase Encoding and Differential Phase Modulation

and Demodulation, 416

8.6.5 Probability of Error for DPSK, 418

8.7 Quadrature Amplitude-Modulated Digital Signals 419

8.7.1 Geometric Representation of QAM Signals, 421

8.7.2 Demodulation and Detection of QAM Signals, 423

8.7.3 Probability of Error for QAM, 424

8.8 Carrier-Phase Estimation 429

8.8.1 The Phase-Locked Loop, 429

8.8.2 The Costas Loop, 437

8.8.3 Carrier-Phase Estimation for PAM, 439

8.8.4 Carrier-Phase Estimation for PSK, 440

8.8.5 Carrier-Phase Estimation for QAM, 444

8.9 Image Synchronization 446

8.9.1 Early—Late Gate Synchronizers, 447

8.9.2 Minimum Mean Square Error Method, 450

8.9.3 Maximum-Likelihood Method, 451

8.9.4 Spectral-Line Method, 452

8.9.5 Image Synchronization for Carrier-Modulated Signals, 455

8.10 Regenerative Repeaters 456

8.11 Abstract and Additional Study 457

Exercises 459

9 MULTIDIMENSIONAL DIGITAL MODULATION 485

9.1 M-ary Orthogonal Signals 485

9.1.1 Probability of Error for M-ary Orthogonal Signals, 488

9.1.2 A Union Bound on the Error Probability of M-ary Orthogonal Signals, 491

9.2 Biorthogonal Signals 492

9.2.1 Probability of Error for M-ary Biorthogonal Signals, 495

9.3 Simplex Signals 497

9.3.1 Probability of Error for M-ary Simplex Signals, 498

9.4 Binary-Coded Signals 499

9.4.1 Probability of Error for Binary-Coded Signals, 501

9.5 Frequency-Shift Keying 501

9.5.1 Demodulation of M-ary FSK, 503

9.5.2 Optimum Detector for Noncoherent Binary FSK, 507

9.5.3 Probability of Error for Noncoherent Detection of M-ary FSK, 510

9.6 Modulation Systems with Memory 513

9.6.1 Regular-Phase FSK, 513

9.6.2 Spectral Characteristics of CPFSK Signals, 524

9.7 Comparison of Modulation Methods 525

9.8 Abstract and Additional Study 532

Exercises 533

10 DIGITAL TRANSMISSION THROUGH BANDLIMITED AWGN CHANNELS 543

10.1 Characterization of Bandlimited Channels and Signal Distortion 543

10.1.1 Intersymbol Interference in Signal Transmission, 547

10.1.2 Digital Transmission via Bandlimited Bandpass Channels, 549

10.2 The Power Spectrum of Digitally Modulated Signals 552

10.3 Signal Design for Bandlimited Channels 556

10.3.1 Design of Bandlimited Signals for Zero ISI–The Nyquist

Criterion, 558

10.3.2 Design of Bandlimited Signals with Controlled ISI–Partial Response Signals, 564

10.4 Detection of Partial-Response Signals 566

10.4.1 Picture-by-Picture Detection, 567

10.4.2 Probability of Error for Picture-by-Picture Detection, 570

10.4.3 Maximum-Likelihood Sequence Detection of Partial-Response

Signals, 573

10.4.4 Error Probability of the Maximum-Likelihood Sequence

Detector, 576

10.5 System Design in the Presence of Channel Distortion 577

10.5.1 Design of Transmitting and Receiving Filters for a Known

Channel, 578

10.5.2 Channel Equalization, 582

10.6 Abstract and Additional Study 599

Appendix 10A: Power Spectrum of Modulated Signals 601

10A.1 The Power Spectrum of the Baseband Signal, 601

10A.2 The Power Spectrum of the Carrier Modulated Signals, 603

Exercises 604

11 MULTICARRIER MODULATION AND OFDM 621

11.1 Orthogonal Frequency-Division Multiplexing 621

11.2 Modulation and Demodulation in an OFDM System 622

11.3 An OFDM System Utilized via the FFT Algorithm 626

11.4 Spectral Characteristics of OFDM Signals 629

11.5 Peak-to-Average Power Ratio in OFDM Systems 631

11.6 Applications of OFDM 633

11.6.1 Digital Subscriber Lines, 633

11.6.2 Wireless LANs, 635

11.6.3 Digital Audio Broadcasting, 636

11.7 Abstract and Additional Study 636

Exercises 637

12 AN INTRODUCTION TO INFORMATION THEORY 641

12.1 Modeling Data Sources 642

12.1.1 Measure of Information, 644

12.1.2 Joint and Conditional Entropy, 647

12.1.3 Mutual Information, 650

12.1.4 Differential Entropy, 650

12.2 The Source Coding Theorem 652

12.3 Source Coding Algorithms 655

12.3.1 The Huffman Source Coding Algorithm, 655

12.3.2 The Lempel—Ziv Source Coding Algorithm, 659

12.4 Modeling of Communication Channels 661

12.5 Channel Capacity 664

12.5.1 Gaussian Channel Capacity, 669

12.6 Bounds on Communication 671

12.7 Abstract and Additional Study 674

Exercises 675

13 CODING FOR RELIABLE COMMUNICATIONS 689

13.1 The Role of Coding 689

13.2 Linear Block Codes 694

13.2.1 Decoding and Efficiency of Linear Block Codes, 700

13.2.2 Some Important Linear Block Codes, 707

13.2.3 Error Detection versus Error Correction, 708

13.2.4 Burst-Error-Correcting Codes, 709

13.3 Convolutional Codes 711

13.3.1 Fundamental Properties of Convolutional Codes, 712

13.3.2 Maximum Likelihood Decoding of Convolutional Codes–The Viterbi

Algorithm, 717

13.3.3 Alternative Decoding Algorithms for Convolutional Codes, 722

13.3.4 Bounds on the Error Probability of Convolutional Codes, 722

13.4 Good Codes Based on Combination of Simple Codes 725

13.4.1 Product Codes, 727

13.4.2 Concatenated Codes, 728

13.5 Turbo Codes and Iterative Decoding 728

13.5.1 MAP Decoding of Convolutional Codes–The BCJR Algorithm, 731

13.5.2 Iterative Decoding for Turbo Codes, 737

13.5.3 Efficiency of Turbo Codes, 739

13.6 Low-Density Parity-Check Codes 741

13.6.1 Decoding LDPC Codes, 745

13.7 Coding for Bandwidth-Constrained Channels 747

13.7.1 Hybrid Coding and Modulation, 748

13.7.2 Trellis-Coded Modulation, 749

13.8 Practical Applications of Coding 756

13.8.1 Coding for Deep-Space Communications, 756

13.8.2 Coding for Phone-Line Modems, 758

13.9 Summary and Additional Study 759

Exercises 760

14 DATA TRANSMISSION IN FADING MULTIPATH CHANNELS 769

14.1 Characterization of Physical Wireless Channels 769

14.2 Channel Models for Time-Variant Multipath Channels 771

14.2.1 Frequency Nonselective Fading Channel, 774

14.2.2 Frequency Selective Fading Channel, 777

14.2.3 Models for the Doppler Power Spectrum, 778

14.2.4 Propagation Models for Cell Radio Channels, 781

14.3 Performance of BinaryModulation in Rayleigh Fading Channels 783

14.3.1 Probability of Error in Frequency Nonselective Channels, 783

14.3.2 Performance Improvement via Signal Range, 786

14.3.3 The RAKE Demodulator and Its Performance in Frequency Selective

Channels, 792

14.3.4 OFDM Signals in Frequency Selective Channels, 794

14.4 Multiple Antenna Systems 795

14.4.1 Channel Models for Multiple Antenna Systems, 796

14.4.2 Signal Transmission in a Slow Fading Frequency Nonselective MIMO

Channel, 797

14.4.3 Detection of Data Symbols in a MIMO System, 799

14.4.4 Error Rate Performance of the Detectors, 800

14.4.5 Space—Time Codes for MIMO Systems, 802

14.5 Budget Analysis for Radio Channels 810

14.6 Summary and Additional Study 813

Exercises 815

15 SPREAD-SPECTRUM COMMUNICATION INFRASTRUCTURES 825

15.1 Model of a Spread-Spectrum Digital Communication Infrastructure 826

15.2 Direct Sequence Spread-Spectrum Systems 827

15.2.1 Impact of Despreading on a Narrowband Interference, 830

15.2.2 Probability of Error at the Detector, 831

15.2.3 Performance of Coded Spread-Spectrum Signals, 836

15.3 Some Applications of DS Spread-Spectrum Signals 836

15.3.1 Low-Detectability Signal Transmission, 836

15.3.2 Code Division Multiple Access, 837

15.3.3 Communication over Channels with Multipath, 838

15.4 Technology of PN Sequences 840

15.5 Frequency-Hopped Spread Spectrum 843

15.5.1 Slow Frequency-Hopping Systems and Partial-Band Interference, 844

15