Principles of Communication Systems Simulation with ... · Principles of Communication Systems Simulation with Wireless Applications William H. Tranter K. Sam Shanmugan Theodore S

Principlesof Communication Systems Simulation

with Wireless Applications

William H. TranterK. Sam Shanmugan

Theodore S. RappaportKurt L. Kosbar

PRENTICE HALLProfessional Technical ReferenceUpper Saddle River, New Jersey 07458www.phptr.com

Tranter FM revised 11-18.fm Page 1 Wednesday, November 19, 2003 10:34 AM

Ao longo do livro, as marcações come esta se referem aos tópicos de TP547 ministrados nas primeiras 40 horas do curso. Como elaspoderão ser atualizadas à medida que as aulas progredirem, recomenda-se refazer o download do correspondente arquivo PDF a cadasemana, por meio do link https://www.inatel.br/docentes/dayan/material-de-aula/27-easyfolder/42-tp547.

Muitas das marcações supracitadas são apenas observações, outras são correções. Espera-se que a interpretação das versões incorretas(ou parcialmente corretas) e corretas possa contribuir ainda mais para o entendimento dos conceitos, já que as incorreções sãoexemplos de falhas de interpretação comuns por parte dos alunos.

Os assuntos cobertos pelo curso têm como pré-requisito as disciplinas TP537 (Transmissão Digital) e TP501 (Probabilidade,Estatística e Processes Estocásticos), e como co-requisito a disciplina TP519 (Análise de Desempenho de Redes deTelecomunicações). Pressupõe-se também o conhecimento sobre fundamentos de Sinais e Sistemas Lineares e de MATLAB.

Este livro, embora não vá ser utilizado em sua totalidade, tem um conteúdo bastante abrangente e direcionado para sistemas decomunicação, sendo portanto muito útil como fonte de consulta para a modelagem, o desenvolvimento e a implementação desimulações. Como complemento, principalmente no que se refere à simulação de sistemas contínuos, o livro Digital Transmission - ASimulation-Aided Introduction with VisSim/Comm, de autoria do Prof. Dayan Adionel Guimarães, também poderá ser útil. Nasanotações aqui registradas tal livro é referido como Digital Transmission.

Por fim, os códigos em MATLAB apresentados no livro, alguns com versões complementadas ou corrigidas na pasta de TP547 napágina https://www.inatel.br/docentes/dayan/, não serão alvo de explicações detalhadas por parte do professor, pois vale lembrar queo curso é sobre princípios de simulação, não sobre MATLAB.

NOTAS IMPORTANTES

Library of Congress Cataloging-in-Publication DataPrinciples of communication systems simulation with wireless applications / William H. Tranter ...[et al.]

p. cm. – (Prentice Hall communications engineering and emerging technologies series ; 16)Includes bibliographical references and index.ISBN 0-13-494790-81. Telecommunication systems–Computer simulation. I. Tranter, William H. II. Series.

TK\5102.5.P673 2003621.382'01'1–dc22

2003063403Editorial/production supervision: Kerry ReardonComposition: Lori Hughes and TIPS Technical Publishing, Inc.Cover design director: Jerry VottaCover design: Nina ScuderiArt director: Gail Cocker-BoguszManufacturing manager: Alexis Heydt-LongManufacturing buyer: Maura ZaldivarPublisher: Bernard GoodwinEditorial assistant: Michelle VincentiMarketing manager: Dan DePasqualeFull-service production manager: Anne R. Garcia

Prentice Hall PTR offers excellent discounts on this book when ordered in quantity for bulk purchases of special sales. For more information, please contact: U.S. Corporate and Government Sales, 1-800-382-3419, [email protected]. For sales outside of the U.S., please contact: International Sales, 1-317-581-3793, [email protected]

Company and product names mentioned herein are the trademarks of their respective owners.

MATLAB is a registered trademark of The MathWorks, Inc. for MATLAB product information, please contact:

The Mathworks, Inc.3 Apple Hill DriveNatick, MA 01760-2098 USATel: 508-647-7000Fax: 508-647-7101Email: [email protected]: www.mathworks.com

All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher.

Printed in the United States of America

First printing

ISBN 0-13-494790-8

Pearson Education LTD.Pearson Education Australia PTY, LimitedPearson Education Singapore, Pte. Ltd.Pearson Education North Asia Ltd.Pearson Education Canada, Ltd.Pearson Education de Mexico, S.A. de C.V.Pearson Education-JapanPearson Education Malaysia, Pte. Ltd.

Copyright © 2004 Pearson Education, Inc.

Prentice Hall Professional Technical Reference

Upper Saddle River, NJ 07458


Dedications

To my loving and supportive wife Judy.William H. Tranter

To my loving wife Radha.K. Sam Shanmugan

To my loving wife, our children, and my former students.Theodore S. Rappaport

To my wife and children.Kurt L. Kosbar


“TranterBook” — 2003/11/18 — 14:44 — page v — #1�

�

�

�

�

�

�

�

CONTENTS

PREFACE xvii

Part I Introduction 1

1 THE ROLE OF SIMULATION 11.1 Examples of Complexity 2

1.1.1 The Analytically Tractable System 31.1.2 The Analytically Tedious System 51.1.3 The Analytically Intractable System 7

1.2 Multidisciplinary Aspects of Simulation 81.3 Models 111.4 Deterministic and Stochastic Simulations 14

1.4.1 An Example of a Deterministic Simulation 161.4.2 An Example of a Stochastic Simulation 17

1.5 The Role of Simulation 191.5.1 Link Budget and System-Level Specification Process 201.5.2 Implementation and Testing of Key Components 221.5.3 Completion of the Hardware Prototype and Validation

of the Simulation Model 221.5.4 End-of-Life Predictions 22

1.6 Software Packages for Simulation 231.7 A Word of Warning 261.8 The Use of MATLAB 271.9 Outline of the Book 271.10 Further Reading 28

v

THE ROLE OF SIMULATIONIntrodução

Tópico doplano de ensino

“TranterBook” — 2003/11/18 — 14:44 — page vi — #2�

�

�

�

�

�

�

�

vi Contents

2 SIMULATION METHODOLOGY 312.1 Introduction 322.2 Aspects of Methodology 34

2.2.1 Mapping a Problem into a Simulation Model 342.2.2 Modeling of Individual Blocks 412.2.3 Random Process Modeling and Simulation 47

2.3 Performance Estimation 492.4 Summary 522.5 Further Reading 522.6 Problems 52

Part II Fundamental Concepts and Techniques 55

3 SAMPLING AND QUANTIZING 553.1 Sampling 56

3.1.1 The Lowpass Sampling Theorem 563.1.2 Sampling Lowpass Random Signals 613.1.3 Bandpass Sampling 61

3.2 Quantizing 653.3 Reconstruction and Interpolation 71

3.3.1 Ideal Reconstruction 713.3.2 Upsampling and Downsampling 72

3.4 The Simulation Sampling Frequency 783.4.1 General Development 793.4.2 Independent Data Symbols 813.4.3 Simulation Sampling Frequency 83

3.5 Summary 873.6 Further Reading 893.7 References 903.8 Problems 90

4 LOWPASS SIMULATION MODELS FOR BANDPASSSIGNALS AND SYSTEMS 954.1 The Lowpass Complex Envelope for Bandpass Signals 95

4.1.1 The Complex Envelope: The Time-Domain View 964.1.2 The Complex Envelope: The Frequency-Domain View 1084.1.3 Derivation of Xd(f) and Xq(f) from X̃(f) 1104.1.4 Energy and Power 111

SAMPLING AND QUANTIZINGFundamentos

LOWPASS SIMULATION MODELS FOR BANDPASSSIGNALS AND SYSTEMS

Fundamentos

The Complex Envelope: The Time-Domain View4.1.1

“TranterBook” — 2003/11/18 — 14:44 — page vii — #3�

�

�

�

�

�

�

�

Contents vii

4.1.5 Quadrature Models for Random Bandpass Signals 1124.1.6 Signal-to-Noise Ratios 115

4.2 Linear Bandpass Systems 1184.2.1 Linear Time-Invariant Systems 1184.2.2 Derivation of hd(t) and hq(t) from H(f) 122

4.3 Multicarrier Signals 1254.4 Nonlinear and Time-Varying Systems 128

4.4.1 Nonlinear Systems 1284.4.2 Time-Varying Systems 130

4.5 Summary 1324.6 Further Reading 1334.7 References 1344.8 Problems 1344.9 Appendix A: MATLAB Program QAMDEMO 139

4.9.1 Main Program: c4 qamdemo.m 1394.9.2 Supporting Routines 140

4.10 Appendix B: Proof of Input-Output Relationship 141

5 FILTER MODELS AND SIMULATION TECHNIQUES 1435.1 Introduction 1445.2 IIR and FIR Filters 146

5.2.1 IIR Filters 1465.2.2 FIR Filters 1475.2.3 Synthesis and Simulation 147

5.3 IIR and FIR Filter Implementations 1485.3.1 Direct Form II and Transposed Direct

Form II Implementations 1485.3.2 FIR Filter Implementation 154

5.4 IIR Filters: Synthesis Techniques and Filter Characteristics 1555.4.1 Impulse-Invariant Filters 1555.4.2 Step-Invariant Filters 1565.4.3 Bilinear z-Transform Filters 1575.4.4 Computer-Aided Design of IIR Digital Filters 1655.4.5 Error Sources in IIR Filters 167

5.5 FIR Filters: Synthesis Techniques and Filter Characteristics 1675.5.1 Design from the Amplitude Response 1705.5.2 Design from the Impulse Response 1775.5.3 Implementation of FIR Filter Simulation Models 1805.5.4 Computer-Aided Design of FIR Digital Filters 184

“TranterBook” — 2003/11/18 — 14:44 — page viii — #4�

�

�

�

�

�

�

�

viii Contents

5.5.5 Comments on FIR Design 1865.6 Summary 1865.7 Further Reading 1895.8 References 1895.9 Problems 1905.10 Appendix A: Raised Cosine Pulse Example 192

5.10.1 Main program c5 rcosdemo.m 1925.10.2 Function file c5 rcos.m 192

5.11 Appendix B: Square Root Raised Cosine Pulse Example 1935.11.1 Main Program c5 sqrcdemo.m 1935.11.2 Function file c5 sqrc.m 193

5.12 Appendix C: MATLAB Code and Data for Example 5.11 1945.12.1 c5 FIRFilterExample.m 1955.12.2 FIR Filter AMP Delay.m 1965.12.3 shift ifft.m 1985.12.4 log psd.m 198

6 CASE STUDY: PHASE-LOCKED LOOPSAND DIFFERENTIAL EQUATION METHODS 2016.1 Basic Phase-Locked Loop Concepts 202

6.1.1 PLL Models 2046.1.2 The Nonlinear Phase Model 2066.1.3 Nonlinear Model with Complex Input 2086.1.4 The Linear Model and the Loop Transfer Function 208

6.2 First-Order and Second-Order Loops 2106.2.1 The First-Order PLL 2106.2.2 The Second-Order PLL 214

6.3 Case Study: Simulating the PLL 2156.3.1 The Simulation Architecture 2156.3.2 The Simulation 2166.3.3 Simulation Results 2196.3.4 Error Sources in the Simulation 220

6.4 Solving Differential Equations Using Simulation 2236.4.1 Simulation Diagrams 2246.4.2 The PLL Revisited 225


“TranterBook” — 2003/11/18 — 14:44 — page ix — #5�

�

�

�

�

�

�

�

Contents ix

6.9 Appendix A: PLL Simulation Program 2366.10 Appendix B: Preprocessor for PLL Example Simulation 2376.11 Appendix C: PLL Postprocessor 238

6.11.1 Main Program 2386.11.2 Called Routines 239

6.12 Appendix D: MATLAB Code for Example 6.3 241

7 GENERATING AND PROCESSING RANDOM SIGNALS 2437.1 Stationary and Ergodic Processes 2447.2 Uniform Random Number Generators 248

7.2.1 Linear Congruence 2487.2.2 Testing Random Number Generators 2527.2.3 Minimum Standards 2567.2.4 MATLAB Implementation 2577.2.5 Seed Numbers and Vectors 258

7.3 Mapping Uniform RVs to an Arbitrary pdf 2587.3.1 The Inverse Transform Method 2597.3.2 The Histogram Method 2647.3.3 Rejection Methods 266

7.4 Generating Uncorrelated Gaussian Random Numbers 2697.4.1 The Sum of Uniforms Method 2707.4.2 Mapping a Rayleigh RV to a Gaussian RV 2737.4.3 The Polar Method 2757.4.4 MATLAB Implementation 276

7.5 Generating Correlated Gaussian Random Numbers 2777.5.1 Establishing a Given Correlation Coefficient 2777.5.2 Establishing an Arbitrary PSD

or Autocorrelation Function 2787.6 Establishing a pdf and a PSD 2827.7 PN Sequence Generators 2837.8 Signal Processing 290

7.8.1 Input/Output Means 2917.8.2 Input/Output Cross-Correlation 2917.8.3 Output Autocorrelation Function 2927.8.4 Input/Output Variances 293


GENERATING AND PROCESSING RANDOM SIGNALSGeração de números aleatórios

“TranterBook” — 2003/11/18 — 14:44 — page x — #6�

�

�

�

�

�

�

�

x Contents

7.13 Appendix A: MATLAB Code for Example 7.11 2997.14 Main Program: c7 Jakes.m 299

7.14.1 Supporting Routines 300

8 POSTPROCESSING 3038.1 Basic Graphical Techniques 304

8.1.1 A System Example—π/4 DQPSK Transmission 3048.1.2 Waveforms, Eye Diagrams, and Scatter Plots 307

8.2 Estimation 3098.2.1 Histograms 3098.2.2 Power Spectral Density Estimation 3168.2.3 Gain, Delay, and Signal-to-Noise Ratios 323

8.3 Coding 3298.3.1 Analytic Approach to Block Coding 3308.3.2 Analytic Approach to Convolutional Coding 333

8.4 Summary 3368.5 Further Reading 3368.6 References 3388.7 Problems 3398.8 Appendix A: MATLAB Code for Example 8.1 342

8.8.1 Main Program: c8 pi4demo.m 3428.8.2 Supporting Routines 344

9 INTRODUCTION TO MONTE CARLO METHODS 3479.1 Fundamental Concepts 347

9.1.1 Relative Frequency 3489.1.2 Unbiased and Consistent Estimators 3499.1.3 Monte Carlo Estimation 3499.1.4 The Estimation of π 351

9.2 Application to Communications Systems—The AWGN Channel 3549.2.1 The Binomial Distribution 3559.2.2 Two Simple Monte Carlo Simulations 359

9.3 Monte Carlo Integration 3669.3.1 Basic Concepts 3689.3.2 Convergence 3709.3.3 Confidence Intervals 371


INTRODUCTION TO MONTE CARLO METHODSMétodos de Monte Carlo

Estudo eletivo:processamento desinais aleatórios,

somente Seção 8.2

POSTPROCESSING

8.2 Estimation

“TranterBook” — 2003/11/18 — 14:44 — page xi — #7�

�

�

�

�

�

�

�

Contents xi

10 MONTE CARLO SIMULATIONOF COMMUNICATION SYSTEMS 37910.1 Two Monte Carlo Examples 38010.2 Semianalytic Techniques 393

10.2.1 Basic Considerations 39410.2.2 Equivalent Noise Sources 39710.2.3 Semianalytic BER Estimation for PSK 39810.2.4 Semianalytic BER Estimation for QPSK 40010.2.5 Choice of Data Sequence 404

10.3 Summary 40510.4 References 40610.5 Problems 40610.6 Appendix A: Simulation Code for Example 10.1 408

10.6.1 Main Program 40810.6.2 Supporting Program: random binary.m 409

10.7 Appendix B: Simulation Code for Example 10.2 41010.7.1 Main Program 41010.7.2 Supporting Programs 41410.7.3 vxcorr.m 414

10.8 Appendix C: Simulation Code for Example 10.3 41510.8.1 Main Program: c10 PSKSA.m 41510.8.2 Supporting Programs 416

10.9 Appendix D: Simulation Code for Example 10.4 41810.9.1 Supporting Programs 419

11 METHODOLOGY FOR SIMULATINGA WIRELESS SYSTEM 42111.1 System-Level Simplifications and Sampling Rate Considerations 42311.2 Overall Methodology 424

11.2.1 Methodology for Simulation of the Analog Portionof the System 429

11.2.2 Summary of Methodology for Simulatingthe Analog Portion of the System 441

11.2.3 Estimation of the Coded BER 44111.2.4 Estimation of Voice-Quality Metric 44111.2.5 Summary of Overall Methodology 442


Estudo eletivo:exemplos adicionais de

aplicação do métodode Monte Carlo

MONTE CARLO SIMULATIONOF COMMUNICATION SYSTEMS

“TranterBook” — 2003/11/18 — 14:44 — page xii — #8�

�

�

�

�

�

�

�

xii Contents

Part III Advanced Models and Simulation Techniques 447

12 MODELING AND SIMULATION OF NONLINEARITIES 44712.1 Introduction 448

12.1.1 Types of Nonlinearities and Models 44812.1.2 Simulation of Nonlinearities—Factors to Consider 449

12.2 Modeling and Simulation of Memoryless Nonlinearities 45112.2.1 Baseband Nonlinearities 45212.2.2 Bandpass Nonlinearities—Zonal Bandpass Model 45312.2.3 Lowpass Complex Envelope

(AM-to-AM and AM-to-PM) Models 45512.2.4 Simulation of Complex Envelope Models 46112.2.5 The Multicarrier Case 462

12.3 Modeling and Simulation of Nonlinearities with Memory 46812.3.1 Empirical Models Based on Swept Tone Measurements 47012.3.2 Other Models 472

12.4 Techniques for Solving Nonlinear Differential Equations 47512.4.1 State Vector Form of the NLDE 47612.4.2 Recursive Solutions of NLDE-Scalar Case 47912.4.3 General Form of Multistep Methods 48312.4.4 Accuracy and Stability of Numerical Integration Methods 48312.4.5 Solution of Higher-Order NLDE-Vector Case 485

12.5 PLL Example 48612.5.1 Integration Methods 486

12.6 Summary 48812.7 Further Reading 48812.8 References 48912.9 Problems 49012.10 Appendix A: Saleh’s Model 49312.11 Appendix B: MATLAB Code for Example 12.2 494


13 MODELING AND SIMULATIONOF TIME-VARYING SYSTEMS 49713.1 Introduction 497

13.1.1 Examples of Time-Varying Systems 49813.1.2 Modeling and Simulation Approach 499

13.2 Models for LTV Systems 50013.2.1 Time-Domain Description for LTV System 500

MODELING AND SIMULATION OF NONLINEARITIESModelagem esimulação de

não-linearidades.

Tópico eletivo:Seção 12.3

“TranterBook” — 2003/11/18 — 14:44 — page xiii — #9�

�

�

�

�

�

�

�

Contents xiii

13.2.2 Frequency Domain Description of LTV Systems 50313.2.3 Properties of LTV Systems 505

13.3 Random Process Models 51113.4 Simulation Models for LTV Systems 515

13.4.1 Tapped Delay Line Model 51513.5 MATLAB Examples 518

13.5.1 MATLAB Example 1 51813.5.2 MATLAB Example 2 520

13.6 Summary 52213.7 Further Reading 52313.8 References 52313.9 Problems 52313.10 Appendix A: Code for MATLAB Example 1 525

13.10.1 Supporting Program 52613.11 Appendix B: Code for MATLAB Example 2 527

13.11.1 Supporting Routines 52813.11.2 mpsk pulses.m 528

14 MODELING AND SIMULATIONOF WAVEFORM CHANNELS 52914.1 Introduction 529

14.1.1 Models of Communication Channels 53014.1.2 Simulation of Communication Channels 53114.1.3 Discrete Channel Models 53214.1.4 Methodology for Simulating Communication

System Performance 53214.1.5 Outline of Chapter 533

14.2 Wired and Guided Wave Channels 53314.3 Radio Channels 534

14.3.1 Tropospheric Channel 53614.3.2 Rain Effects on Radio Channels 537

14.4 Multipath Fading Channels 53814.4.1 Introduction 53814.4.2 Example of a Multipath Fading Channel 53814.4.3 Discrete Versus Diffused Multipath 545

14.5 Modeling Multipath Fading Channels 54614.6 Random Process Models 547

14.6.1 Models for Temporal Variationsin the Channel Response (Fading) 549

MODELING AND SIMULATIONOF WAVEFORM CHANNELS

Estudo eletivo: aplicações de simulação de

sistemas contínuos

“TranterBook” — 2003/11/18 — 14:44 — page xiv — #10�

�

�

�

�

�

�

�

xiv Contents

14.6.2 Important Parameters 55014.7 Simulation Methodology 552

14.7.1 Simulation of Diffused Multipath Fading Channels 55314.7.2 Simulation of Discrete Multipath Fading Channels 55814.7.3 Examples of Discrete Multipath Fading Channel Models 56514.7.4 Models for Indoor Wireless Channels 571


14.12.1 Main Program 57714.12.2 Supporting Functions 578

14.13 Appendix B: MATLAB Code for Example 14.2 58014.13.1 Main Program 58014.13.2 Supporting Functions 581

15 DISCRETE CHANNEL MODELS 58315.1 Introduction 58415.2 Discrete Memoryless Channel Models 58615.3 Markov Models for Discrete Channels with Memory 589

15.3.1 Two-State Model 58915.3.2 N -state Markov Model 59615.3.3 First-Order Markov Process 59715.3.4 Stationarity 59715.3.5 Simulation of the Markov Model 598

15.4 Example HMMs—Gilbert and Fritchman Models 60115.5 Estimation of Markov Model Parameters 604

15.5.1 Scaling 61115.5.2 Convergence and Stopping Criteria 61215.5.3 Block Equivalent Markov Models 613

15.6 Two Examples 61515.7 Summary 62115.8 Further Reading 62215.9 References 62215.10 Problems 62315.11 Appendix A: Error Vector Generation 627

15.11.1 Program: c15 errvector.m 62715.11.2 Program: c15 hmmtest.m 628

“TranterBook” — 2003/11/18 — 14:44 — page xv — #11�

�

�

�

�

�

�

�

Contents xv

15.12 Appendix B: The Baum-Welch Algorithm 62915.13 Appendix C: The Semi-Hidden Markov Model 63215.14 Appendix D: Run-Length Code Generation 63615.15 Appendix E: Determination of Error-Free Distribution 637

15.15.1 c15 intervals1.m 63715.15.2 c15 intervals2.m 637

16 EFFICIENT SIMULATION TECHNIQUES 63916.1 Tail Extrapolation 64016.2 pdf Estimators 64216.3 Importance Sampling 645

16.3.1 Area of an Ellipse 64616.3.2 Sensitivity to the pdf 65516.3.3 A Final Twist 65616.3.4 The Communication Problem 65716.3.5 Conventional and Improved Importance Sampling 659



17 CASE STUDY: SIMULATIONOF A CELLULAR RADIO SYSTEM 67117.1 Introduction 67117.2 Cellular Radio System 673

17.2.1 System-Level Description 67317.2.2 Modeling a Cellular Communication System 676

17.3 Simulation Methodology 68817.3.1 The Simulation 68817.3.2 Processing the Simulation Results 700

17.4 Summary 70617.5 Further Reading 70617.6 References 70717.7 Problems 70817.8 Appendix A: Program for Generating the Erlang B Chart 71017.9 Appendix B: Initialization Code for Simulation 71217.10 Appendix C: Modeling Co-Channel Interference 714

“TranterBook” — 2003/11/18 — 14:44 — page xvi — #12�

�

�

�

�

�

�

�

xvi Contents

17.10.1 Wilkinson’s Method 71517.10.2 Schwartz and Yeh’s Method 717

17.11 Appendix D: MATLAB Code for Wilkinson’s Method 718

18 TWO EXAMPLE SIMULATIONS 71918.1 A Code-Division Multiple Access System 720

18.1.1 The System 72018.1.2 The Simulation Program 72418.1.3 Example Simulations 72618.1.4 Development of Markov Models 729

18.2 FDM System with a Nonlinear Satellite Transponder 73418.2.1 System Description and Simulation Objectives 73418.2.2 The Overall Simulation Model 73718.2.3 Uplink FDM Signal Generation 73818.2.4 Satellite Transponder Model 74018.2.5 Receiver Model and Semianalytic BER Estimator 74118.2.6 Simulation Results 74218.2.7 Summary and Conclusions 744

18.3 References 74618.4 Appendix A: MATLAB Code for CDMA Example 747

18.4.1 Supporting Functions 75018.5 Appendix B: Preprocessors for CDMA Application 753

18.5.1 Validation Run 75318.5.2 Study Illustrating the Effect of the Ricean K-Factor 753

18.6 Appendix C: MATLAB Function c18 errvector.m 75518.7 Appendix D: MATLAB Code for Satellite FDM Example 756

18.7.1 Supporting Functions 760

INDEX 767

ABOUT THE AUTHORS 775

“TranterBook” — 2003/11/19 — 15:38 — page xvii — #13�

�

�

�

�

�

�

�

PREFACE

This book is a result of the recent rapid advances in two related technologies: com-munications and computers. Over the past few decades, communication systemshave increased in complexity to the point where system design and performanceanalysis can no longer be conducted without a significant level of computer sup-port. Many of the communication systems of fifty years ago were either power ornoise limited. A significant degrading effect in many of these systems was thermalnoise, which was modeled using the additive Gaussian noise channel. Many moderncommunication systems, however, such as the wireless cellular system, operate inenvironments that are interference and bandwidth limited. In addition, the desirefor wideband channels and miniature components pushes transmission frequenciesinto the gigahertz range, where propagation characteristics are more complicatedand multipath-induced fading is a common problem. In order to combat these ef-fects, complex receiver structures, such as those using complicated synchronizationstructures, demodulators and symbol estimators, and RAKE processors, are oftenused. Many of these systems are not analytically tractable using non-computerbased techniques, and simulation is often necessary for the design and analysis ofthese systems.

The same advances in technology that made modern communication systemspossible, namely microprocessors and DSP techniques, also provided us with high-speed digital computers. The modern workstation and personal computer (PC)have computational capabilities greatly exceeding the mainframe computers usedjust a few years ago. In addition, modern workstations and PCs are inexpensiveand therefore available at the desktop of design engineers. As a result, simulation-based design and analysis techniques are practical tools widely used throughout thecommunications industry.

As a result, graduate-level courses dealing with simulation-based design andanalysis of communication systems are becoming more common. Students derivea number of benefits from these courses. Through the use of simulation, studentsin communications courses can study the operating characteristics of systems thatare more complex and more real world than those studied in traditional commu-nications courses since, in traditional courses, complexity must be constrained toensure that analyses can be conducted. Simulation allows system parameters tobe easily changed, and the impact of these changes can be rapidly evaluated by

xvii

“TranterBook” — 2003/11/19 — 15:38 — page xviii — #14�

�

�

�

�

�

�

�

xviii Preface

using interactive and visual displays of simulation results. In addition, an under-standing of simulation techniques supports the research programs of many graduatestudents working in the communications area. Finally, students going into the com-munications industry upon graduation have skills needed by industry. This book isintended to support these courses.

A number of the applications and examples discussed in this book are targetedto wireless communication systems. This was done for several reasons. First, manystudents studying communications will eventually work in the wireless industry.Also, a significant number of graduate students pursuing university-based researchare working on problems related to wireless communications. Finally, as a resultof the high level of interest in wireless communications, many graduate programscontain courses in wireless communications. This book is designed to support, atleast in part, these courses, as well as the self-study needs of the working engineer.

This book is divided into three major sections. The first section, Introduction,consists of two chapters. The first of these introductory chapters discusses the moti-vation for using simulation in both the analysis and the design process. The theoryof simulation is shown to draw on several classic fields of study such as number the-ory, probability theory, stochastic processes, and digital signal processing, to nameonly a few. We hope that students will appreciate that the study of simulation tiestogether, or unifies, material from a number of separate areas of study. Differenttypes of simulations are discussed, as well as software packages used for simulation.The development of appropriate simulation models and simulation methodology isa basic theme of this book, and the basic concepts of model development are intro-duced in Chapters 1 and 2. Chapter 2 focuses on methodology at a very high level.Many of the basic concepts used throughout the book are introduced here. Studentsare encouraged to revisit this material frequently as the remainder of the book isstudied. Revisiting this material will help ensure that the big picture remains infocus as specific concepts are explored in detail.

The second section, Fundamental Techniques, consists of nine chapters (Chap-ters 3-11). These nine chapters present basic material encountered in almost allsimulations of communication systems. The sampling theorem, and the role ofthe sampling theorem in simulation, is the subject of Chapter 3. Also covered arequantization, pulse shaping, and the effect of pulse shaping on the required samplingfrequency. The representation of bandpass signals by quadrature lowpass signals,which is a fundamental tool of simulation methodology, is the subject of Chapter 4.This is a key chapter, in that the techniques presented here will be used repeatedlythroughout the book. Filter models and simulation techniques for digital filtersare the subject of Chapter 5. Filters, of course, have memory, and more computa-tion is required to simulate filters than most other functional blocks in a system.As a result, filters must be efficiently simulated if reasonable run times are to beachieved. The simulation of a phase-locked loop is presented as a case study inChapter 6. The student should realize that, even though this material is presentedearly in the study of simulation, important problems can be investigated with thetools developed to this point. This case study focuses on the acquisition behavior ofthe phase-locked loop. Acquisition studies require the use of nonlinear models and,

“TranterBook” — 2003/11/19 — 15:38 — page xix — #15�

�

�

�

�

�

�

�

Preface xix

as a result, analysis is very difficult using traditional techniques. The methodologyused to develop the simulation is presented in detail, and serves as a guide to thesimulations developed later in the book. The simulation techniques for generatingrandom numbers are the subject of Chapter 7. Initially, the focus is on the generationof a pseudo-random sequence having a uniform probability density function (pdf).Both linear conguential methods and techniques based on pseudo-noise (PN)sequences are included. A number of methods for shaping the pdf and PSD of arandom sequence are presented. Postprocessing, which is the manipulation of thedata generated by a simulation into desired forms for visualization and analysis,is the subject of Chapter 8. Monte Carlo simulation techniques are introduced inChapter 9 as a general tool for estimating the value of a parameter. The conceptof unbiased and consistent estimators is introduced, and the convergence proper-ties of estimators is investigated. The concepts developed in Chapter 9 are appliedto communications systems in Chapter 10, which is devoted to Monte Carlo andsemianalytic simulation of communication systems. Several simple examples arepresented in this chapter. Chapter 11 discusses in detail the methodology used forsimulating a wireless communications system in a slowly-varying environment. Thecalculation of the outage probability is emphasized, and a number of semianalytictechniques are presented for reducing the simulation run time.

The third section of this book, Advanced Models and Simulation Techniques, isdevoted to a number of specialized topics encountered when developing more ad-vanced simulations. Chapter 12 is devoted to the simulation of nonlinear systems.Model development based on measurements is emphasized, and a number of modelsthat have found widespread use are presented. Chapter 13 deals with time-varyingsystems. The important subject of modeling time-varying channels is introduced.Chapter 14 presents a number of models for waveform channels. Drawing on thematerial presented in the preceding chapter, models for multipath fading channelsare developed. Chapter 15 continues the study of channel models, and presentstechniques for replacing waveform channel models with discrete channel models atthe symbol level. The motivation is a significant reduction in the required simu-lation run time. The principal tools used are the Baum-Welch algorithm and thehidden Markov model. System models based on the hidden Markov model arepresented. Chapter 16 deals with various strategies for reducing the variance of abit error rate estimator. Several strategies are presented, but the emphasis is onimportance sampling. Chapter 17 is devoted to the simulation of wireless cellularcommunication systems. It is shown that cellular systems tend to be interferencelimited rather than noise limited. In many systems, co-channel interference is a ma-jor degrading effect. Chapter 18 concludes the book with two example simulations.The first of these considers a CDMA system, and presents a simulation in which thebit error rate is computed as a function of the spread-spectrum processing gain, thenumber of interferers, the power-delay profile, and the signal-to-noise ratio at thereceiver input. The data collected by the simulation is used to construct a discretechannel model based on the hidden Markov model. The hidden Markov model isthen used to statistically reconstruct the error events on the channel. The BER isthen computed using the discrete channel model, and the results are compared with

“TranterBook” — 2003/11/19 — 15:38 — page xx — #16�

�

�

�

�

�

�

�

xx Preface

the results obtained using a waveform-level channel model. The second example isan FDM system operating over a nonlinear channel. The effect of intermodulationdistortion on bit error rate is investigated using semianalytic techniques.

From the preceding discussion, it is clear that this book covers a very widerange of topics. A completely rigorous treatment of all of the topics consideredhere would require a volume many times the size of this book, and the result wouldnot be suitable as a course textbook. A compromise between completeness andrigor must always be made in developing a textbook. We have, in developing thisbook, attempted to provide sufficient rigor to make the results both understandable andbelievable. A large number of references are given for those wishing additional study.

Although this book is targeted to a one-semester course in communications,there is more material included here than is typically covered in a one-semestercourse. In the view of the authors, all courses using this book should cover the firsttwo sections (Chapters 1-11). The instructor can then complete the course withselected material from the third section (Chapters 12-18), assuming that time isavailable.

A number of computer programs, written in MATLAB, are included in the text.The decision to include computer code within the body of the book was made for anumber of reasons. First, the programs illustrate the methodology used to developsimulations, and illustrate the algorithms used to perform a number of importantDSP operations. In addition, many code segments included in the MATLAB exam-ples can be used by the student to aid the development of their own simulations.In order not to break the flow of the material, only short programs, those requiringno more than a single page of text, are included within the body of the chapters.Programs that are too long to fit on a single page are placed in appendices at theend of the chapter. The MATLAB code included here is designed to be easily fol-lowed by the student. For that reason, a number of the MATLAB programs arenot written in the most efficient manner possible, in that for-loops are often usedwhen the loop could be replaced by a matrix operation. It is not suggested thatthe student type the computer code from the text. A web page is maintained byPrentice Hall containing all of the computer code included in the text, and codecan be downloaded from this site. The URL is

http://authors.phptr.com/tranter/

The MATLAB code on this site will be updated periodically in order to ensure thaterrors and omissions are corrected.

The choice of MATLAB requires some explanation. There are a number ofreasons for this choice, and these are discussed in detail in Chapter 1. The mainmotivations are compactness (complex algorithms can be expressed with a very fewlines of code), graphics support, and the installed base. Since MATLAB is usedextensively in engineering curricula, most students will already have the resourcesrequired to execute the MATLAB programs contained herein. Many simulationprograms involve extensive computational burden, and reasonable execution runtimes require the use of a compiled language such as C or C++. This is especially

http://authors.phptr.com/tranter/

Os códigos não estão mais disponíveis nesteendereço. Alguns deles estão disponíveis em:https://www.inatel.br/docentes/dayan/material-de-aula/27-easyfolder/42-tp547/

“TranterBook” — 2003/11/19 — 15:38 — page xxi — #17�

�

�

�

�

�

�

�

Preface xxi

true of Monte Carlo simulations used to estimate the bit error rate when the signal-to-noise ratio is high. Many symbols must be processed through the channel in orderto achieve a quality (low variance) estimator. MATLAB, however, is a powerful tooleven in this situation, since a prototype simulation can be developed in MATLABto design and test the individual signal-processing algorithms, as well as the entiresimulation. The resulting MATLAB code can then be mapped to C or C++ codefor more efficient execution, and the results obtained can be compared against theresults achieved with the prototype MATLAB simulation. Using MATLAB forprototyping allows conceptual errors to be quickly identified, which often speedsthe development of the final software product. SIMULINK, although designed forsimulation, was not used in this book, so that the details of the algorithms usedin simulation programs, and the methodology used to develop the simulation code,would be clear to the students.

ACKNOWLEDGMENTS

A number of colleagues, research sponsors, and organizations have contributed sig-nificantly to this book. Early in this project a CRCD (Combined Research Cur-riculum Development) grant was awarded to Virginia Tech by the National ScienceFoundation. Much of the material in Chapters 3-10 and Chapter 17 was developedas a part of this effort. The NSF program manager Mary Poats, encouraged us todevelop simulation-based courses within the communications curriculum, and wethank her for the encouragement and support. The authors thank Cyndy Grahamof Virginia Tech for her LaTeX skills, and for managing the development of sucha large manuscript. In addition, the individual authors have the following specificacknowledgements:

William H. Tranter thanks the many students who took the simulation of com-munications systems course at the University of Missouri–Rolla, Canterbury Uni-versity (Christchurch, New Zealand), and at Virginia Tech from the notes thatformed the basis of much of this book. These students provided many valuable sug-gestions. Specific thanks are due to Jing Jiang, who helped with the semianalyticestimators in Chapter 10; Ihsan Akbar, who did much of the coding of the Markovand semi-Markov model estimators in Chapter 15 (especially the code containedin Appendices B, C, and D); and Bob Boyle, who developed the CDMA estima-tor upon which the CDMA case study in Chapter 18 is based. He also thanksSam Shanmugan, who provided friendship, support, encouragement, and above allpatience, through the years that it took to bring this material together. Also tobe thanked are Des Taylor and Richard Duke, who provided support through anErskine Fellowship at Canterbury University, and Theodore Rappaport at VirginiaTech, who provided support during a sabbatical year. It was during this sabbaticalthat much of the material in the early chapters of this book were originally drafted.

Sam Shanmugan would like to thank his colleagues and students at the Uni-versity of Kansas, who have in many ways contributed to this book, and also theUniversity of Canterbury, Christchurch, New Zealand for the Erskine Professorshipduring his sabbatical when much of this book was written. He would also like tothank his wife for her patience, understanding, and support while he was working

“TranterBook” — 2003/11/19 — 15:38 — page xxii — #18�

�

�

�

�

�

�

�

xxii Preface

on this and on many other writing projects. Dr. Shanmugan would like to add aspecial note of thanks to his co-author Professor William Tranter, for his friendshipand the extra effort he put in towards pulling together all the material for this book.

Ted Rappaport wishes to thank his many graduate students who provided in-sights and support through their teaching and research activites in wireless com-munications simulation and analysis. In particular, Prof. Paulo Cardieri, Univer-sity of Campinas—UNICAMP, Brazil; Hao Xu of QUALCOMM Incorporated; andProf. Gregory Durgin of the Georgia Institute of Technology, all contributed sugges-tions for the text. In particular, Dr. Cardieri’s experiences as a graduate studentresearcher formed the basis of Chapter 17.

Kurt Kosbar thanks the students who screened early versions of this material,and the reviewers who provided valuable comments, including Douglas Bell, HarryNichols, and David Cunningham.

William H. TranterK. Sam Shanmugan

Theodore S. RappaportKurt L. Kosbar

“TranterBook” — 2003/11/18 — 16:12 — page 1 — #19�

�

�

�

�

�

�

�

PART I

Introduction

Chapter 1

THE ROLE OF SIMULATION

The complexity of modern communication systems is a driving force behind thewidespread use of simulation. This complexity results both from the architecture ofmodern communication systems and from the environments in which these systemsare deployed. Modern communication systems are required to operate at high datarates with constrained power and bandwidth. These conflicting requirements leadto complex modulation and pulse shaping along with error control coding and anincreased level of signal processing at the receiver. Synchronization requirementsalso become more stringent at high data rates and, as a result, receivers becomemore complex. While the analysis of linear communication systems operating inthe presence of additive, white, Gaussian noise is usually quite simple, most modernsystems operate in much more hostile environments. Multihop systems often requirenonlinear amplifiers for efficiency. Wireless cellular systems often operate in thepresence of heavy interference along with multipath and shadowing that leads tosignal fading at the receiver site. This combination of complex systems and hostileenvironments leads to design and analysis problems that are no longer analyticallytractable using traditional (nonsimulation-based) techniques.

Fortunately, the past two decades have seen the development of digital comput-ers that are both powerful and inexpensive. Thus, modern computers are suitablefor use at the desktop and can therefore be dedicated to the solution of problemstaking many hours of computer time without interfering with the work of others.Computers have become easy to use, and the cost of computer resources is no longer

1

THE ROLE OF SIMULATION

This combination of complex systems and hostileenvironments leads to design and analysis problems that are no longer analyticallytractable using traditional (nonsimulation-based) techniques.

complexity of modern communication systems


�

�

�

�

�

�

�

2 The Role of Simulation Chapter 1

a significant factor in many efforts. As a result, computer-aided design and analysistechniques are available to almost all who need them. The development of powerfulsoftware packages targeted to communication systems has accelerated the use ofsimulation in the communications area. Thus, the increase in system complexityhas been accompanied by an increase in computing power. In many cases, the avail-ability of appropriate computational power has directly led to many of the complexsignal-processing structures that constitute the building blocks of modern commu-nication systems. Thus, it is not just good luck that computational tools appearedat the time they were needed. Rather, practical computational power, in the form ofthe microprocessor, is the enabling technology for modern communication systemsand is also the enabling technology for powerful simulation engines.

The growth in computer technology has also been accompanied by a rapidgrowth in what we loosely refer to as simulation theory. As a result, the toolsand methodologies required for the successful application of simulation to designand analysis problems are more accessible and better understood than was the casea few decades ago. A large number of technical papers and several books are nowavailable that illustrate the application of these tools to the design and analysis ofcommunication systems.

An important motivation for the use of simulation is that simulation is a valuabletool for gaining insight into system behavior. A properly developed simulation ismuch like a laboratory implementation of a system. Measurements can easily bemade at various points in the system under study. Parametric studies are easilyconducted, since parameter values, such as filter bandwidths and signal-to-noiseratios (SNRs), can be changed at will and the effects of these changes on systemperformance can quickly be observed. Time-domain waveforms, signal spectra,eye diagrams, signal constellations, histograms, and many other graphical displayscan easily be generated and, if desired, a comparison can be made between thesegraphical products and the equivalent displays generated by system hardware. Wewill see that the process of comparing simulation results with hardware-generatedresults is an important part of the design process. Most importantly, perhaps, onecan perform “what if” studies more easily and economically using a simulation thanwith actual system hardware. Although we often perform a simulation to obtain anumber, such as a bit error rate (BER), the main role of simulation, as noted by R.W. Hamming, is not to obtain numbers but to gain insight.

1.1 Examples of Complexity

The complexity of communication systems varies widely. We now consider threecommunications systems of increasing complexity. We will see that for the firstsystem, simulation is not necessary. For the second system, simulation, while notnecessary, may be useful. For the third system, simulation is necessary in orderto conduct detailed performance studies. Even the most complicated of the threesystems considered here is still simple by today’s standard.

An important motivation for the use of simulation is that simulation is a valuabletool for into system behavior.

Most importantly, perhaps, onecan perform “what if” studies more easily and economically using a simulation thanwith actual system hardware. Although we often perform a simulation to obtain anumber, such as a bit error rate (BER), the main role of simulation, as noted by R.W. Hamming, is not to obtain numbers but to gain insight.

Examples of Complexity

A properly developed simulation ismuch like a laboratory implementation of a system.

the increase in system complexityhas been accompanied by an increase in computing power. In many cases, the avail-ability of appropriate computational power has directly led to many of the complexsignal-processing structures that constitute the building blocks of modern commu-nication systems.

gaining insight

“what if”


�

�

�

�

�

�

�

Section 1.1. Examples of Complexity 3

^

^

Figure 1.1 Analytically tractable communications system.

1.1.1 The Analytically Tractable System

A very simple communications system is shown in Figure 1.1. This system shouldremind us of the basic communications system studied in a first course on communi-cations theory. The data source generates a sequence of symbols, dk. The symbolsare assumed to be discrete. The source symbols are assumed to be elements froma finite symbol library. For a binary communication system, the source alphabetconsists of two symbols, which are usually denoted {0, 1}. In addition, the sourceis assumed to be memoryless, which means that the kth symbol generated by thesource is independent from all other symbols generated by the source. A data sourcesatisfying these properties is referred to as a discrete memoryless source (DMS). Therole of the modulator is to map the source symbols onto waveforms, with a differentwaveform representing each of the source symbols. For a binary system, we havetwo possible waveforms generated by the modulator. This set of waveforms may bedenoted {s1(t), s2(t)}. The transmitter, in this case, is simply assumed to amplifythe modulator output so that the signals generated by the modulator are radiatedwith the desired energy per bit.

The next part of the system is the channel. In general, the channel is the mostdifficult part of the system to model accurately. Here, however, we will assume thatthe channel simply adds noise to the transmitted signal. This noise is assumed tohave a power spectral density (PSD) that is constant for all frequency. Noise satis-fying this constant PSD property is referred to as white noise. The noise amplitudeis also assumed to have a Gaussian probability density function. Channels in whichthe noise is additive, white, and Gaussian are referred to as AWGN channels.

The function of the receiver is to observe the signal at the receiver input andfrom this observation form an estimate, denoted d̂k, of the original data signal,

Analytically tractable communications system.

1.1.1 The Analytically Tractable System

AWGN channel model


�

�

�

�

�

�

�


dk. The receiver illustrated in Figure 1.1 is referred to as an optimum receiverbecause the estimate of the data symbol is made so that the probability of error,PE , is minimized. We know from basic digital communication theory that theoptimum receiver for the system described in the preceding paragraphs (binarysignaling in an AWGN environment) consists of a matched filter (or, equivalently, acorrelation receiver), which observes the signal over a symbol period. The output ofthe matched filter is sampled at the end of a symbol period to generate a statistic,Vk, which is a random variable because of the addition of noise to the transmittedsignal in the channel. The statistic, Vk, is compared to a threshold, T . If Vk > Tthe decision, d̂k, is made in favor in one of the data symbols. If Vk < T the decisionis made in favor of the other data signal.

We refer to this system as an analytically tractable because, with a knowledgeof basic communication theory, analysis of the system is carried out with ease. Forexample, the probability of error is found to be

PE = Q

(√k

EsN0

)(1.1)

where Es represents the average energy, calculated over a symbol period, associatedwith the set of waveforms {s1(t), s2(t)}, and N0 represents the single-sided powerspectral density of the additive channel noise. The parameter, k, is determined bythe correlation of the waveforms {s1(t), s2(t)}. As an example, for FSK (frequency-shift keying) transmission, the waveforms {s1(t), s2(t)} are sinusoids having differentfrequencies and equal power. Assuming that the frequencies are chosen correctly,the signals are uncorrelated and k = 1. For the PSK case (phase-shift keying),the signals used for data transmission are assumed to be sinusoids having the samefrequencies and equal power but different initial phases. If the phase difference is πradians, so that s2(t) = −s1(t), the signals are anticorrelated and k = 2.

The performance of the system illustrated in Figure 1.1 is easily determined usingtraditional analysis techniques, and we are therefore able to classify the system asanalytically tractable. Why is this system analytically tractable? The first andmost obvious reason deals with the AWGN channel and the fact that the receiveris linear. Since the noise is Gaussian and the matched filter is a linear system,the decision statistic, Vk, is a Gaussian random variable. We are therefore ableto calculate the bit error rate (BER) analytically as a function of the parametersof the receiver filter and determine the values of those parameters that result in aminimum BER.

There are a number of other factors leading to the fact that the system shownin Figure 1.1 is analytically tractable. These relate to the simplicity of the systemmodel, which results from a number of assumptions. The data source was assumedmemoryless, which may or may not be true in practice. In addition, perfect symbolsynchronization was assumed, so that we have exact knowledge of the beginning andending times of the data symbols. This assumption allows the decision statistic, Vk,to be correctly extracted.

Would simulation ever play a role in an analytically tractable system? Theanswer is yes, since the system shown in Figure 1.1 may well be the basic building


�

�

�

�

�

�

�


block of a more complex system. The simulation code can be developed for thesystem. The resulting simulation can be validated with ease, since analysis of thesystem is straightforward. At this point the data source, modulator, channel, orreceiver can be modified as required to model the system under study. In addition,other subsystems as needed can be added to the simulation model. As we proceedwith the task of developing a simulation model of the system of interest, we can beconfident that the starting point was correct.

1.1.2 The Analytically Tedious System

We now turn attention to a somewhat more complex system. The system illustratedin Figure 1.2, which is identical to the previously investigated system except for theaddition of the nonlinear high-power amplifier (HPA) and filter in the transmitter.Consider first the nonlinear amplifier. Nonlinear amplifiers exhibit much higherpower efficiency than linear amplifiers and, as a result, are often preferred over lin-ear amplifiers for use in environments where power is limited. Examples includespace applications and mobile cellular systems, where battery power must be con-served. Unlike linear amplifiers, which preserve the spectrum of the input signal,the nonlinear amplifier will generate harmonic and intermodulation distortion. Asa result, the spectrum of the amplifier output will be spread over a much largerbandwidth than that occupied by the spectrum of the modulator output. The filterfollowing the amplifier will in most cases be a bandpass filter with a center fre-quency equal to the desired carrier frequency. The role of the filter is to attenuatethe harmonic and intermodulation distortion resulting from the nonlinearity.

The filter following the modulator and HPA leads to time dispersion of the datasignal so that the filtered signals are no longer time limited to the symbol period.

^

^

Figure 1.2 Analytically tedious communications system.Analytically tedious communications system.

1.1.2 The Analytically Tedious System

intermodulation distortion

O filtro atenua somenteaquela distorção que estivernas vizinhanças da bandadesejada, já que aqueladentro desta banda não podeser atenuada por filtragem.

AWGN channel model


�

�

�

�

�

�

�


This leads to intersymbol interference (ISI). As a result of ISI, the probability oferror of the ith symbol is dependent upon one or more of the symbols previous tothe symbol upon which the decision is being made. The number of previous symbolsthat must be considered in the demodulation of the ith symbol depends upon thememory associated with the signal at the filter output. If the probability of errorfor the ith symbol depends on the k previous symbols we compute the quantity

Pr {Ei|di−1di−2 · · ·di−k}For the binary case there are 2k different sequences of length k. Assuming that eachdata symbol is equally likely to be a binary 0 or 1, the error probability of the ith

symbol is given by

PE =12k

1∑di−1=0

1∑di−2=0

· · ·1∑

di−k=0

Pr {Ei|di−1di−2 · · · di−k} (1.2)

In other words, one must compute 2k different error probabilities, with each errorprobability dependent upon one of the 2k preceding sequences of length k, andaverage the k results. Since the channel is assumed AWGN, each of the 2k errorprobabilities is a Gaussian Q-function. It is a straightforward, but tedious procedureto calculate the argument of each Q-function and, therefore, simulation is often used.

The system illustrated in Figure 1.2 has an important property that makesanalysis straightforward. Note that the system is linear from the point at whichthe noise is injected to the point at which the statistic Vk appears. The statistic Vkoften takes the form

Vk = Sk + Ik + Nk (1.3)

where Sk and Ik are the components of Vk due to signal and intersymbol interference,respectively, and Nk is the component of Vk due to the channel noise. Thus, if thechannel noise is Gaussian, Nk will be a Gaussian random variable, since it is a lineartransformation of a Gaussian random variable. In addition, the decision statisticVk will be a Gaussian random variable having the same variance as Nk but withmean Sk + Ik, both of which are deterministic. The mean of Vk can be computedin a straightforward manner. The variance of Vk is determined from knowledge ofthe power spectral density of the channel noise and the equivalent noise bandwidththe system from the channel to the point where Vk appears. The pdf of Vk istherefore known and the error probability is easily determined. To summarize, thereason that we can easily determine the pdf of Vk, even though the system has anonlinearity, is because the noise does not pass through the system nonlinearity.

The fact that the noise passes only through the linear portion of the systemhas a significant impact on the simulation methodology. Because the noise doesnot pass through a nonlinearity, the mean of Vk can quickly be determined using anoise-free simulation. The variance of Vk can be determined analytically and, as aresult, the pdf of Vk is known and the error probably is easily determined. Theseconcepts are combined in a simulation technique that is both simple and fast. The

Pode-se ter dispersãotemporal controlada eponto de não haver ISI.

may leadThis leads to intersymbol interference (ISI).

O filtro casado é linear,mas a amostragem não é.Ainda assim, a análise ésimples porque aamostragem não altera adistribuição do sinal desaída do filtro (no casoela continua sendoGaussiana).

both of which are deterministic.

Ik pode serextremamente complexade calcular devido àextensão temporal da ISIe à quantidade decombinações desímbolos e amplitudesdas interferências.


�

�

�

�

�

�

�


result is the semi-analytic method in which analysis and simulation is combined ina way that leads to very fast simulations. Semi-analytic simulation is an importanttool and will be the subject of a later chapter.

1.1.3 The Analytically Intractable System

The system illustrated in Figure 1.3 is referred to as an analytically intractablesystem and is a simple model of a two-hop satellite communications system. Thesatellite transponder is modeled as a nonlinear HPA and a filter to remove the out-of-band harmonic distortion caused by the nonlinearity. Comparison of Figure 1.3with Figure 1.2 shows that they are quite similar. A satellite channel model has beenadded and consists of two noise sources rather than one. One noise source representsthe uplink (transmitter-to-satellite) noise, and the other noise source represents thedownlink (satellite-to-receiver) noise. The problem lies in the fact that the noise atthe receiver consists of two components; the downlink noise and the uplink noisethat was passed through the nonlinear HPA. Even assuming that both the uplinkand the downlink noise are Gaussian, the pdf of the noise at the receiver is very

^

^

Figure 1.3 Analytically intractable communications system.Analytically intractable communications system.

1.1.3 The Analytically Intractable System


�

�

�

�

�

�

�


difficult to determine. The downlink noise is easy to model, since the downlink noisepasses only through the linear portion of the system. The uplink noise, however,leads to difficulties. The reason for the difficulty lies in the fact that the uplinknoise passes through the nonlinear HPA. Even if the uplink noise is Gaussian, thepdf of the uplink noise at receiver input is no longer Gaussian. Determination of thepdf of the decision statistic, Vk, is a very difficult, if not impossible, undertaking.Without exact knowledge of the pdf of the decision statistic, the probability of errorcannot be determined. Simulation is an essential tool for these types of systems.

The range of communication systems considered in this section has been verynarrow. The systems were chosen simply to illustrate how increasing complexitygives rise to the need for simulation. Many systems of current interest fall into theanalytically intractable category. Consider, for example, a wireless cellular radiolink operating in a high interference and multipath environment. Simulation isalmost always necessary for the detailed analysis of such systems.

1.2 Multidisciplinary Aspects of Simulation

Prior to the 1970s simulation problems were often solved in a somewhat ad hoc man-ner. The methodologies for developing simulations, and the error sources presentin all simulation programs, were not understood by many. Over the past 20 years,the research community has produced a body of knowledge that provides a method-ology for simulation development and a theoretical framework for solving many ofthe problems that arise in the development of simulation programs. This body ofknowledge provides those using simulation as an analytical tool the insights andunderstanding necessary to develop reliable simulations that execute in reasonablecomputer run times. Building this body of knowledge has required the integrationof material from a variety of fields. Although not exhaustive, nine important areasof study that impact our study of simulation are depicted in Figure 1.4. We willnow briefly look at these nine areas in order to better understand their relationshipto the art and science of simulation.

The concepts of linear system theory give us the techniques for determining theinput-output relationships of linear systems. This body of knowledge allows us torepresent system models in both the time domain (the system impulse response)and in the frequency domain (the system transfer function). The basic concepts oflinear system theory builds the foundation for much of what follows.

An understanding of communication theory is obviously important to our study.The architecture of systems, the operational characteristics of various subsystemssuch as modulators and equalizers, and the details of channel models must be un-derstood prior to the development of a simulation. While simulation can be used todetermine appropriate values for system parameters, the practical range of param-eter values must usually be known before the simulation is developed. Some insightinto proper system behavior is necessary in order to ensure that the simulation isworking properly and that the results are reasonable.

The tools of digital signal processing (DSP) are used to develop the algorithmsthat constitute the simulation model of a communication system. This simulation

Multidisciplinary Aspects of Simulation

The reason for the difficulty lies in the fact that the uplinknoise passes through the nonlinear HPA. Even if the uplink noise is Gaussian, thepdf of the uplink noise at receiver input is no longer Gaussian. Determination of thepdf of the decision statistic, is a very difficult, if not impossible, undertaking.VkVV ,

The range of communication systems considered in this section has been verynarrow. The systems were chosen simply to illustrate how increasing complexitygives rise to the need for simulation. Many systems of current interest fall into theanalytically intractable category. Consider, for example, a wireless cellular radiolink operating in a high interference and multipath environment. Simulation isalmost always necessary for the detailed analysis of such systems.


�

�

�

�

�

�

�

Section 1.2. Multidisciplinary Aspects of Simulation 9

Simulation ofCommunication

Systems

NumericalAnalysis Stochastic

ProcessTheory

CommunicationTheory

NumberTheory

DigitalSignal

Processing

LinearSystemTheory

ProbabilityTheory

ComputerScience

EstimationTheory

Figure 1.4 Areas impacting the study of the simulation of communication systems.

model usually consists of several discrete-time approximations of continuous-timesystem components, such as filters, and a knowledge of DSP techniques is necessaryto understand and appreciate the nature of these approximations. As a matter offact, each functional block in a simulation model is a DSP operation and, there-fore, the tools of digital signal processing provide the techniques for implementingsimulations.

Numerical analysis is closely related to DSP but is mentioned separately, sinceit is an older discipline. Many classical techniques, such as the suite of tools fornumerical integration, polynomial interpolation, and curve fitting have their originsin numerical analysis.

The concepts of probability are also fundamental to our study. The performancemeasures of communication systems are often expressed in probabilistic terms. Asexamples, we often have interest in the probability of bit error or symbol errorin a digital communication system. In synchronization systems we have interestin the probability that a phase error will exceed a given level. Basic probabilitytheory provides us with the concept of random variables and the probability densityfunction. Knowledge of the underlying probability density function allows us tocompute the quantities previously discussed. We will see later that the result ofmany simulations (called stochastic simulations) is typically a random variable,and the variance of that random variable is often a measure of the usefulness andstatistical accuracy of the simulation.

The signal and noise waveforms that are processed by our simulations will, inmany cases, be assumed to be sample functions of a stochastic process. Developmentof the algorithms to produce waveforms having the appropriate statistical properties

Areas impacting the study of the simulation of communication systems.

DigitalSignal

Processing

NumericalAnalysis

NumberTheory

ComputerScience

EstimationTheory

CommunicationTheory

LinearSystemTheory

StochasticProcessTheory

TheoryyProbabilityy

Ferramentas,algoritmos,análise de complexidadee de precisão.

Geração denúmeros aleatórios, sequências.

Cálculo numérico,interpolação, encaixe

Processamento de sinais discretos

Estimação deparâmetrosTópicos

maisimportantespara TP547


�

�

�

�

�

�

�


will require knowledge of the underlying stochastic process. This is especially truefor developing simulation models for channels. Stochastic process theory gives us thetools to describe these processes in the time domain (the autocorrelation function)and in the frequency domain (the power spectral density). Many other applicationsof stochastic process theory will appear in the course of our work.

A few of the very basic concepts of number theory provide us with the toolsused to develop random number generators. These random number generatorsare the basic building blocks of the waveform generators used to represent digitalsequences, noise waveforms, signal fading, and random interference, to name onlya few applications.

Some of the basic concepts of computer science will be useful in the course of ourstudy. As examples, the word length, and the format of words, used to representsamples of signals will impact simulation accuracy, although this is often of minimalimportance in floating-point processors. The choice of language is important in thedevelopment of commercial simulators. Available memory, and the organization ofthat memory, will impact the manner in which data and instructions are passedfrom one part of the simulation to another. Graphics requirements and capabilitieswill determine how waveforms are displayed and will impact the transportability ofthe simulation code from one computer platform to another.

The tools and concepts of estimation theory will allow us to evaluate the effec-tiveness of a given simulation result. As mentioned earlier, the result of a stochasticsimulation is a random variable. Each execution of the simulation will produce avalue of that random variable, and this random variable will constitute an estimatorof a desired quantity. Typically, all values produced by replications of the simula-tion will be different. Simulations are most useful when the estimator produced bya simulation is unbiased and consistent. Unbiased estimators are those for whichthe average value of the estimate is the quantity being measured. This is anotherway of saying that on the average the estimates produced by the simulation arecorrect. This is clearly a desired attribute. A consistent estimate is one for whichthe variance of the estimate decreases as the simulation run length increases. Inother words, if 100 independent measurements of the height of a person are made,and the results averaged, we would expect a more accurate estimate of the heightthan would result from a single measurement. Estimation theory provides us withthe analytical tools necessary to explore questions of this type and, in general, toaccess the reliability of simulation results.

The previous paragraphs are not intended to make a study of simulation appearto be a daunting task. The goal is simply to point out that simulation is a fieldof study in its own right. It draws from many other fields just as electrical engi-neering draws from physics, mathematics, and chemistry, to name only a few. It isexpected that those embarking on this study have a grasp of linear system theory,communications, and probability theory. Much of the remaining material will betreated in the following chapters of this text.


�

�

�

�

�

�

�

Section 1.3. Models 11

1.3 Models

The first step in developing a simulation of a communication system is the devel-opment of a simulation model for the system of interest. We are all familiar withmodels and should understand that models describe the input-out relationship ofphysical systems or devices. These models are typically expressed in mathematicalform. The art of modeling is to develop behavioral models (we use this term sincethe model captures the input-output behavior of the device under specific condi-tions) that are sufficiently detailed to maintain the essential features of the systembeing modeled and yet are not overly complex so that the models can be used withreasonable expenditures of computational resources. Tradeoffs between accuracy,complexity, and computational requirements are therefore usually required.

It is useful to consider two different types of models in the work to follow:analytical models and simulation models. Both analytical models and simulationmodels are abstractions of a physical device or system as illustrated in Figure 1.5.The physical device illustrated in Figure 1.5 may be a single circuit element suchas a resistor or a subsystem such as a single chip implementation of a phase-lockedloop (PLL) used as a bit synchronizer. It may be a complete communications sys-tem. The first and most important step in the modeling process is to identify thoseattributes and operational characteristics of the physical device that are to be rep-resented in the model. The identification of these essential features often requiresconsiderable engineering judgment and always requires a thorough understandingof the application for which the model is being developed. The accuracy requiredof any mathematical analysis or any computer simulation based on the model islimited by the accuracy of the model. Once these questions have been answered,an analytical model is developed that captures the essential features of the phys-ical device. Analytical models typically take the form of equations, or systems ofequations, that define the input-output relationship of the physical device. These

PhysicalDevice

AnalyticalModel

SimulationModel

Hardware

Equations

Computer Code

Increasing Level ofAbstraction

Figure 1.5 Devices and models.

Models

The first step in developing a simulation of a communication system is the devel-opment of a simulation model for the system of interest.

models describe the input-out relationship ofphysical systems or devices. These models are typically expressed in mathematicalform.

Tradeoffs between accuracy,complexity, and computational requirements are therefore usually required.

Devices and models.

always requires a thorough understandingof the application for which the model is being developed.

No caso, requerentendimento

sobre sistemas decomunicação.

( )The first and most important step in the modeling process is to identify those

attributes and operational characteristics of the physical device that are to be rep-resented in the model.

device, system or subsystem

Physicaldevice, systemor subsystem


�

�

�

�

�

�

�


equations are, at best, only a partial description of the device being modeled, sinceonly certain aspects of the device are modeled. In addition, the equations that de-fine the device are typically accurate only over a limited range of voltages, currents,and frequencies. The simulation model is usually a collection of algorithms thatimplement a numerical solution of the equations defining the analytical model. Thetechniques of numerical analysis and digital signal processing are the tools used inthe development of these algorithms.

We also see from Figure 1.5 that the level of abstraction increases as one movesfrom the physical device to the analytical model and finally to the simulation model.The increase in abstraction results, in part, from the assumptions and approxi-mations made in moving from the physical device to the analytical model to thesimulation model. Every assumption and approximation moves us farther from thephysical device and its operating characteristics. In addition, the level of abstractionpresent at any step in the process is due, in large part, to the representation used forthe analytical model. As an example, assume that the physical device being consid-ered is a phase-locked loop. The analytical model for a PLL can take many forms,with each form corresponding to a different level of abstraction. An analytical modelhaving a low level of abstraction could consist of a system of equations, with eachequation corresponding a single functional operation within the PLL. Each of thesefunctional, or signal-processing, operations within the PLL (phase detector, loopfilter, and voltage-controlled oscillator) is represented by a separately identifiableequation within the system of equations defining the overall PLL. The process andassumptions used in moving from the hardware device to the analytical model areoften clear from observation of these equations. In addition, simulations developedfrom such a system of equations may allow individual signals of interest within thePLL to be observed and compared to corresponding signals in the hardware device.We will see that such comparisons are often an essential part of the design process.On the other hand, the individual equations representing separate signal-processingoperations may be combined into a single nonlinear (and perhaps time-varying)differential equation relating the input-output relationship of the PLL, which leadsto a much more abstract model. The individual signal-processing operations thattake place within the PLL, and the waveforms associated with these operations, areno longer separately identifiable. It might seem logical to consider only analyticalmodels having a low level of abstraction. This, however, is not the case.

Models having different levels of abstraction will be frequently encounteredthroughout our studies. As another example, we will see that channels may bemodeled using a waveform-level approach, in which sample values of waveforms areprocessed by the model. On the other hand, channels may be represented by adiscrete Markov process based on symbols rather than on samples of waveforms. Inaddition, Markov channel models usually absorb the modulator, transmitter, andreceiver into the channel. These models are highly abstract and are difficult toparameterize accurately but, once found, result in numerically efficient simulationsthat execute rapidly. This efficiency is a principal reason for having interest in themore abstract modeling approaches.

.

Models having different levels of abstraction will be frequently encounteredthroughout our studies. As another example, we will see that channels may bemodeled using a waveform-level approach, in which sample values of waveforms areprocessed by the model. On the other hand, channels may be represented by adiscrete Markov process based on symbols rather than on samples of waveforms. Inaddition, Markov channel models usually absorb the modulator, transmitter, andreceiver into the channel. These models are highly abstract and are difficult toparameterize accurately but, once found, result in numerically efficient simulationsthat execute rapidly. This efficiency is a principal reason for having interest in the

.more abstract modeling approaches.

equations are, at best, only a partial description of the device being modeled, sinceonly certain aspects of the device are modeled.


�

�

�

�

�

�

�

Section 1.3. Models 13

Model ComplexityLow High

Run Time vs. ComplexityError vs. Complexity

Long

ShortLow

High Practical Region ofOperation

Mod

elin

gE

rror

sSim

ulation Run T

ime

Figure 1.6 Effects of model complexity.

Figure 1.6 also tells us much about the modeling process. It is intuitively ob-vious that a desirable attribute of a simulation is fast execution of the simulationcode. Simple models will execute faster than more complex models, since fewerlines of computer code need to be processed each time the model is invoked bythe simulation. Simple models may not, however, fully characterize the importantattributes of a device, and therefore the simulation may yield inaccurate results. Insuch a case, more complex models are necessary. While more complex models mayyield more accurate simulation results, the increased accuracy usually comes at thecost of increased simulation run time.

Figure 1.6 makes it clear that the desirable attributes of simulation accuracy andexecution speed are in competition. A well-designed simulation is one that providesreasonable accuracy along with reasonable execution speeds. Of course, when thespecifications for a simulation demand a high level of accuracy, the ability to tradeoff accuracy and execution speed becomes severely constrained. In this case themodel complexity must be sufficient to guarantee the required accuracy, and longsimulation run times become, perhaps, unavoidable.

Figure 1.6 tells only part of the story. More complex models often requirethat extensive measurements be made before accurate simulation models can bedeveloped. The development of simulation models for a nonlinear amplifier is oneexample. Another, and even more complex example is the development of a simula-tion model of a wireless communication channel when multiple interference sourcesand severe frequency selective fading is present. There are many other cases wecould mention in which extensive measurements are required. It should be kept inmind that these measurements require resources (both equipment and engineeringtime) and therefore a relationship exists between the cost of model developmentand model complexity. It should also be kept in mind that complex models aremore error prone than simple models.

Effects of model complexity.

Error vs. Complexity Run Time vs. Complexity

Desirable

complex models often requirethat extensive measurements be made before accurate simulation models can bedeveloped. The development of simulation models for a nonlinear amplifier is oneexample. Another, and even more complex example is the development of a simula-tion model of a wireless communication channel when multiple interference sourcesand severe frequency selective fading is present.


�

�

�

�

�

�

�


When we move from an analytical model to a discrete-time (digital) simulationmodel, additional assumptions and approximations are involved. At this point wemention only a few of the most obvious. The voltages and currents present in boththe physical device and in the analytical model are usually considered to be continu-ous functions of the continuous variable time. In moving from the analytical modelto the simulation model, we move from the continuous domain to the discrete do-main. This process involves quantizing the amplitudes of the voltages and currentsand time sampling these quantities. The process of time sampling leads to alias-ing errors, and quantizing amplitudes leads to quantizing errors. While quantizingerrors are often negligible in simulations performed on floating-point processors,aliasing errors require our attention if the sampling frequency for the simulation isto be selected appropriately. Aliasing errors are reduced by increasing the samplingfrequency, but an increased sampling frequency results in more samples being re-quired to represent a given segment of data. The result is that more samples mustbe processed in order to execute the simulation, and the time necessary to exe-cute the simulation is thereby increased. Hence, a tradeoff therefore exists betweensampling frequency and simulation run time. One therefore should not attempt toeliminate aliasing errors, or most other errors for that matter, but rather shouldseek a simulation having the required accuracy with reasonable run times.

The modeling concepts briefly touched on here will be revisited in more detailin the following chapter and will be encountered many times throughout this book.The purpose of this brief introduction is simply to remind the reader that we dealnot with physical devices but with models in performing any engineering analy-sis. Analytical models (equations) are abstractions of physical devices and involvemany assumptions and approximations. Simulation models are based on analyticalmodels and involve additional assumptions and approximations. Great care mustbe exercised at each step in this process to ensure a valid simulation model and toensure that the simulation results reflect reality.

1.4 Deterministic and Stochastic Simulations

There are basically two types of simulation: deterministic simulation and stochasticsimulation. Deterministic simulation is probably familiar to most of us from pre-vious experiences. An example might be a SPICE simulation of a fixed electricalcircuit in which the response to certain deterministic input signals are of interest. Asoftware program is developed that represents the components of the circuit and theinput applied to the circuit. The simulation generates the currents present in eachbranch of the network and, consequently, generates the voltage across each circuitelement. The voltages and currents are typically expressed as waveforms. The de-sired time duration of these waveforms is specified prior to executing the simulationprogram. Since the circuit is fixed and the input signal is deterministic, identicalresults will be obtained each time the simulation is executed. In addition, thesesame waveforms will be obtained if the network is solved using traditional (penciland paper) techniques. Simulation is used in order to save time and to avoid themathematical errors that result from performing long and tedious calculations.

Deterministic and Stochastic Simulations

(Simulation is used in order to save time and to avoid the)

mathematical errors that result from performing long and tedious calculations.

An example might be a SPICE simulation of a fixed electricalcircuit in which the response to certain deterministic input signals are of interest.

quantizingerrors are often negligible in simulations performed on floating-point processors,aliasing errors require our attention if the sampling frequency for the simulation isto be selected appropriately.

SPICE é umsimulador decircuitos.

É muito mais comum otermo quantization error.

quantizing errors.

Deterministic simulation

��

When we move from an analytical model to a discrete-time (digital) simulation(model, additional assumptions and approximations are involved.


�

�

�

�

�

�

�

Section 1.4. Deterministic and Stochastic Simulations 15

Now assume that the input to the network is a random waveform. (In moreprecise terminology we would say that the input to the network is a sample functionof a stochastic process.) Equivalently the system model might require that theresistance of a resistor is a random variable defined by a certain probability densityfunction. The result of this simulation will no longer be a deterministic waveform,and samples of this waveform will yield a set of random variables. Simulations inwhich random quantit

Documents

Principles of Communication Systems Simulation with ... · Principles of Communication Systems Simulation with Wireless Applications William H. Tranter K. Sam Shanmugan Theodore S