Simulation of Communication Systems

Simulation of Communication Systems Modeling, Methodology and Techniques Second Edition Michel C.Jeruchim, Philip Balaban, and K.Sam Shanmugan

Communication Systems Second Edition

Series Editor: Jack Keil Wolf

University of California at San Diego

La Jolla, California

Editorial Board: James E Mazo

Bell Laboratories, Lucent Technologies Murray Hill, New Jersey

John Proakis

Northeastern University Boston, Massachusetts

Principles of Digital Transmission: With Wireless Applications

Sergio Benedetto and Ezio Biglieri

Simulation of Communication Systems, Second Edition: Methodology,

Modeling, and Techniques

Michel C Jeruchim, Philip Balaban, and K Sam Shanmugan

A Continuation Order Plan is available for this series A continuation order will bring delivery of each new volume immediately upon publication Volumes are billed only upon actual shipment For further information please contact the publisher.

Simulation of

Modeling, Methodology, and Techniques

Michel C Jeruchim

Lockheed Martin Management & Data Systems

Valley Forge, Pennsylvania

KLUWER ACADEMIC PUBLISHERS

NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

9LVLW.OXZHU2QOLQHDW KWWSNOXZHURQOLQHFRP

KWWSHERRNVNOXZHURQOLQHFRP

Joan, Claude, and Kenny

and to the memory of my parents, Sonia and Samuel

—MCJ Anna, to Victor and Nona and their families

and to the memory of my parents, Shifra and Israel

—PBRadha, Kannon, and Ravi

and to the memory of my parents

—KSS

Since the first edition of the book was published, the field of modeling and simulation ofcommunication systems has grown and matured in many ways, and the use of simulation as aday-to-day tool is now even more common practice Many new modeling and simulationapproaches have been developed in the recent years, many more commercial simulationpackages are available, and the evolution of powerful general mathematical applicationspackages has provided still more options for computer-aided design and analysis With thecurrent interest in digital mobile communications, a primary area of application of modelingand simulation is now to wireless systems of a different flavor than the traditional ones.Since the objective of modeling and simulation is to study and evaluate the behavior andperformance of systems of current interest, the practice of simulation has naturally evolvedalong with the types of systems that have emerged or are being designed for the future.Nevertheless, to the extent that simulation is an embodiment of fundamental principles ofseveral disciplines, communication theory in particular, the practice of modeling and simu-lation is still very much grounded in those basics It is these principles, along with the manytricks of the trade that accompany their application, that still form the main focus of thissecond edition

This edition represents a substantial revision of the first, partly to accommodate the newapplications that have arisen The text has been extensively reorganized and expanded It nowcontains 13 chapters instead of the previous 7 Some of the former chapters have been dividedinto more logical units, edited for greater clarity where needed, and extended in coverage forselected topics This division was made in part to facilitate the use of this book as a teachingtext Two new chapters were added on material only lightly covered in the first edition Onenew chapter, on modeling and simulation of nonlinear systems, provides a fairly extensivediscussion of “black-box” modeling of nonlinear systems with memory, and a comple-mentary section on related measurement techniques As hinted above, perhaps the most

dramatic change in the communications/telecommunications industry since the first edition

has been the explosion of wireless services In consequence, we have included a new chapter

on channel modeling, the bulk of which deals with multipath and fading channels, the usualenvironment for wireless systems As in the first edition, one chapter provides several casestudies as a means of illustrating different ways of approaching a problem and applyingspecific modeling and computational techniques from the arsenal of possibilities available tothe simulation practitioner The first case study is a thoroughly reworked version of a previous

vii

one, and three new case studies are given A consolidated set of problems can be foundfollowing Chapter 12.

By their nature, simulation and modeling embrace the whole of the fields to which they

are applied To cover such a breadth of material, even larger now than in the first edition, wehave had again to rely on the generosity of friends and colleagues to provide us with adviceand material on various topics First, we would like to reacknowledge the contributors to thefirst edition, whose contributions by and large still live in these pages

For the second edition, the list has grown longer To our good friend and colleague at

Lockheed Martin M&DS, Dr Robert J Wolfe, mathematician and statistician par excellence,

we extend our gratitude for innumerable pieces of advice, proofs, and inputs on coding,nonlinear differential equations, random number generation, and interpolation, among others

Dr Wolfe also reviewed several chapters and provided the basic material for the section onlarge-deviations theory (Section 11.2.5.3.2) Numerous contributions were also made by othermembers of the Communications Analysis and Simulation Group at Lockheed MartinM&DS Aside from Bob Wolfe’s work just mentioned, Douglas Castor and Dr GregoryMaskarinec kindly made available their previously published work on minimum-shift-keying,which was edited into Case Study III in Chapter 12 In addition, Doug generated all thefigures and carefully reviewed the final manuscript for that case study We also benefited from

many discussions with Dr Maskarinec about nonlinear modeling, based on his extensive

survey of the literature; Greg also reviewed Chapter 5 and contributed the model in Section

5.3.4.2 We appreciate the efforts of Gregory Sternberg, who used his expertise in matica to compute Table 11.1 and to generate Figures 11.23 and 11.24 We thank Paul

Mathe-Beauvilliers for using his experience in simulating phase-locked loops to produce the materialfor Example 8.12.2 and the associated figures We also express our appreciation to DanielMcGahey, who supplied the block diagram, its details, and the timing information that formthe basis for the discussion in Section 11.2.1

The team of Dr Christopher Silva, Christopher Clark, Dr Andrew Moulthrop, and

Michael Muha at Aerospace Corporation were most generous in lending us the benefit of their

experience and knowledge in nonlinear system modeling and measurement The team

supplied Section 5.5 on measurement techniques for nonlinear components Dr Silva wentbeyond the call of duty by providing the material on generalized Volterra models and poly-

spectral models in Section 5.3.3, as well as the material in Section 5.2.4.3, supplying several

of the related problems, and thoroughly reviewing Chapter 5 Chris Clark is also to bethanked individually for writing Section 5.3.4.2 on nonlinear parametric discrete-timemodels We have also benefited from numerous discussions with Harvey Berger of TRW onhis published and unpublished work in nonlinear amplifier modeling

Several individuals presently or formerly at AT&T Laboratories, or formerly with BellLaboratories, made contributions that we would like to acknowledge Our appreciation is

extended to Dr William Turin, who codeveloped and coauthored Case Study IV in Chapter

12; Bill also kindly reviewed sections of the book dealing with Markov models We also thank

Dr Don Li for his contributions as a codeveloper of the material in Case Study IV We aremost grateful to Dr Thomas M Willis III for contributing the material on shadow fading inChapter 9 We also express our gratitude to Dr Seong (Sam) Kim for providing the materialand the figures on indoor channel modeling in Chapter 9 We also acknowledge manydiscussions with Dr Zoran Kostic on the workings of code division multiple-access (CDMA)systems; his advice helped shape Case Study IV

We are indebted to Prof Irving Kalet of the Technion, Haifa, Israel, for providing thematerial (and its iterations) on orthogonal frequency division multiplexing (OFDM) that

appears in Section 8.7.2.2 We much appreciate the efforts of Prof J Keith Townsend ofNorth Carolina State University for many discussions on importance sampling, for inputs intoSection 11.2.5.4 on stochastic importance sampling, and for the whole of Section 11.2.6 on

importance splitting Keith also made other materials available that could not be modated for space reasons We thank Dr Faroukh Abrishamkar of Qualcomm for his advice

accom-on CDMA system modeling and for providing some of the reference channel models in theAppendix to Chapter 9 Professor Vasant Prabhu of the University of Texas at Arlington was

most kind to provide us with several problems that he uses for his course in simulation, andlikewise we are pleased to acknowledge Prof Brian Woerner of Virginia Polytechnic Institutefor providing us with a number of projects following Chapter 12

Finally, we renew our acknowledgment to our families for bearing with us—a secondtime—through this long process

Michel C JeruchimPhilip Balaban

K Sam Shanmugan

Chapter 1 Introduction

1.1

1.2

1.3.

1.4.

1.5.

Methods of Performance Evaluation

1.1.1 1.1.2 Introduction

Hierarchical View

Simulation Approach: Waveform-Level Simulation of Communication Systems

The Application of Simulation to the Design of Communication Systems

Historical Perspective

Outline of the Book

References

Chapter 2 Simulation and Modeling Methodology 2.1 2.2 2.3. Some General Remarks on Methodology

Methodology of Problem Solving for Simulation

Basic Concepts of Modeling

2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 System Modeling

Device Modeling

Random Process Modeling

Modeling Hypothetical Systems

Simulation with Hardware in the Loop

2.4 2.5. Performance Evaluation Techniques

Error Sources in Simulation

2.5.1 2.5.2 2.5.3 2.5.4 Errors in System Modeling

Errors in Device Modeling

Errors in Random Process Modeling

Processing Errors

2.6. Validation

2.6.1 2.6.2 2.6.3 Validating Models of Devices or Subsystems

Validating Random Process Models

Validating the System Model

2.7. Simulation Environment and Software Issues

2.7.1 2.7.2 2.7.3 2.7.4 Features of the Software Environment

Components of the Software Environment

Hardware Environment

Miscellaneous

xi

1 1

2 3 5 6 8 12

14 16 17 21 21 22 23 25 26 28 30 31 32 35 36 37 38 39 41 42 43 45 45

2.9.

The Role of Simulation in Communication System Engineering

Summary .

References

Chapter 3 Representation of Signals and Systems in Simulation: Analytic Fundamentals 3.1 3.2 3.3 3.4 3.5. Introduction to Deterministic Signals and Systems

3.1.1 3.1.2 3.1.3 Continuous Signals

Discrete-Time Signals

Systems

3.1.3.1 3.1.3.2 Properties of Systems .

Block Diagram Representation of Systems

Linear Time-Invariant Systems

3.2.1 Continuous Linear Time-Invariant Systems

3.2.1.1 3.2.1.2 The Impulse Response

The Convolution Integral,

3.2.2. Discrete Linear Time-Invariant Systems

3.2.2.1 3.2.2.2 The Impulse Response

Convolution Sum (Discrete Convolution)

Frequency-Domain Representation

3.3.1 The Fourier Transform

3.3.1.1 3.3.1.2 The Impulse Response

The Convolution Integral

3.3.2 Frequency-Domain Representation of Periodic Continuous Signals .

3.3.2.1 3.3.2.2. The Fourier Series

Parseval’s Theorem for Periodic Signals

3.3.3 The Fourier Transform

3.3.3.1 3.3.3.2 Convergence

Properties of the Fourier Transform

3.3.4 The Frequency Response

3.3.4.1 3.3.4.2 Interconnection of Systems in the Frequency Domain

Parseval’s Theorem for Continuous Signals .

3.3.5 3.3.6 3.3.7 The Gibbs Phenomenon

Relationship between the Fourier Transform and the Fourier Series

3.3.6.1 3.3.6.2. Introduction

Fourier Series Coefficients .

The Fourier Transform of a Periodic Signal

3.3.7.1 3.3.7.2 Periodic Convolution

The Poisson Sum Formula .

Lowpass-Equivalent Signals and Systems

3.4.1 3.4.2 3.4.3 3.4.4 3.4.5. The Hilbert Transform

Properties of the Hilbert Transform

Lowpass-Equivalent Modulated Signals

Hilbert Transform in System Analysis .

3.4.4.1 3.4.4.2 Introduction .

Lowpass Equivalent of a Bandpass Filter

Practical Considerations in Modeling of Lowpass Equivalents for Simulation .

3.4.5.1 3.4.5.2 Signals

Filters

Sampling and Interpolation

49 52 54

56 56 57 59 59 60 61 62 62 62 62 62 63 63 63 62 62 65 65 66 66 67 67 70 70 70 71 72 72 72 72 73 74 74 75 77 78 79 79 79 82 82 83 83

3.5.2.

3.5.3.

3.5.4.

Impulse Sampling

Sampling Theorem

Multirate Sampling and Sampling Conversion

Interpolation

3.5.4.1 3.5.4.2 3.5.4.3 3.5.4.4 3.5.4.5 Introduction .

Interpolator Structures for Integer Upconversion .

Bandlimited and Windowed Bandlimited Interpolation

Linear Interpolation .

Spline Interpolation

3.6 3.7 3.8 3.9 3.10. Characterization of Linear Time-Invariant Systems Using the Laplace Transform

3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 The Laplace Transform

3.6.1.1 3.6.1.2 Introduction .

Convergence and Stability

Inverse Laplace Transform

Properties of the Laplace Transform

Transfer or System Function .

Interconnections of LTI Systems (Block Diagrams)

Systems Characterized by Linear Constant-Coefficient Differential Equations

3.6.6.1 3.6.6.2. Properties of the Transfer Function for Linear Constant-Coefficient Differential Equations

Realizations of Rational Transfer Functions Using Biquadratic Expansion .

3.6.7. Frequency Response

Representation of Continuous Systems by Discrete Transfer Functions

3.7.1. The z-Transform .

3.7.1.1 3.7.1.2 3.7.1.3 3.7.1.4 Convergence and Stability

Table of Simple z-Transforms

Properties of the z-Transform

Discrete Transfer or System Function

Fourier Analysis for Discrete-Time Systems

3.8.1 3.8.2 3.8.3 3.8.4. Introduction

The Discrete Fourier Transform

The Fast Fourier Transform

Properties of the Discrete Fourier Transform

3.8.4.1 3.8.4.2 3.8.4.3 3.8.4.4 3.8.4.5 3.8.4.6 3.8.4.7 3.8.4.8. Periodic or Circular Properties

The Periodic Time-Shift Property

The Periodic or Circular Convolution

The Discrete Periodic Convolution Theorem

The Discrete Frequency Response

Relationship between the Bandwidth and the Duration of the Impulse Response .

Relationship between the Discrete Fourier Transform and the z-Transform

Increasing the Frequency Resolution of the Discrete Fourier Transform

Summary .

Appendix: A Brief Summary of Some Transforms and Theorems Useful in Simulation .

References

83 86 87 89 90 93 96 98 100 106 106 106 106 107 107 108 108 110 111 112 114 115 115 116 117 117 117 118 118 119 120 121 121 122 123 124 124 124 125 125 126 127 131

Chapter 4 Modeling and Simulation of Linear Time-Invariant and

Time-Varying Systems

4.1 Modeling and Simulation of Linear Time-Invariant Systems

4.1.1 4.1.2 4.1.3 4.1.4 LTI Filters: Description, Specification, and Approximation

4.1.1.1 4.1.1.2 4.1.1.3 4.1.1.4 4.1.1.5 4.1.1.6 Filter Descriptions .

Continuous Classical Filters

Frequency Transformations

Lowpass Equivalents of Bandpass Filters Represented by Rational Functions

Filter Specifications .

Approximating Continuous Structures in Discrete Time for Simulation

Simulation of Filtering with Finite Impulse Response Filters

4.1.2.1 4.1.2.2 4.1.2.3 4.1.2.4 Simulation of FIR Filtering in the Time Domain

4.1.2.1.1 4.1.2.1.2. Introduction

Windowing

Simulation of FIR Filtering in the Frequency Domain

4.1.2.2.1 4.1.2.2.2 4.1.2.2.3 4.1.2.2.4 4.1.2.2.5 4.1.2.2.6 Difference between Periodic and Linear Convolution

Linear Convolution for a Signal of Arbitrary Duration via the FFT

The Overlap-and-Add (OA) Method

The Overlap-and-Save (OS) Method .

Efficiency of the Linear Convolution via the FFT .

Implications of Frequency-Domain FIR Filtering

Mapping of Continuous Filters into Discrete FIR Filters

4.1.2.3.1 4.1.2.3.2. FIR Filters Defined in the Time Domain

FIR Filters Defined in the Frequency Domain

Comparison of Time-Domain (Impulse Response) and Frequency-Domain (FFT) Implementations for FIR Filtering

Simulation of Filtering with IIR Filters

4.1.3.1 4.1.3.2 Systems Characterized by Linear Constant-Coefficient Difference Equations

Structures of Recursive Discrete Filters Implemented in Simulation Models

4.1.3.2.1 4.1.3.2.2 4.1.3.2.3 Direct-Form (Canonic) Realization .

The Cascade Interconnections of Biquadratic Canonic Sections .

The Parallel Realization

4.1.3.3 Transformations between Continuous-Time and Discrete-Time Systems Represented by Rational Functions

4.1.3.3.1 4.1.3.3.2 4.1.3.3.3 4.1.3.3.4 Impulse-Invariant Transformation .

The Bilinear Transformation .

Effect of Mapping on Lowpass-Equivalent Filters Represented by Rational Functions .

Guide for Mapping Recursive Filters Specified in Frequency Domain

Effects of Finite Word Length in Simulation of Digital Filters

4.1.4.1 4.1.4.2 4.1.4.3 Roundoff Noise in Simulations of IIR Filters .

Roundoff Noise in Simulations of FIR Filters

Effects of Quantization in Computation of the Fast Fourier Transform .

133

134 135 136 141 142 145 145 149 149 149 150 152 153 154 155 156 158 158 159 159 159 162 165 165 166 166 168 169 169 170 173 178 178 181 181 182 182

4.1.5. Summary of the Process of Mapping Continuous Signals and Systems

into Discrete Signals and Systems for Simulation

4.1.5.1 4.1.5.2. Introduction

A Guide to the Selection of the Proper Method of Filter Simulation 4.2 4.3 4.4 Time-Varying Linear Systems .

4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 Examples of Time-Varying Systems

Time-Domain Description for Linear Time-Varying Systems

4.2.2.1 4.2.2.2 The Impulse Response

The Superposition Integral .

Frequency-Domain Representations of Time-Varying Systems

4.2.3.1 4.2.3.2 4.2.3.3. Two-Dimensional Frequency Response

Bandwidth Relations in Time-Varying Systems

Sampling Rate

Properties of Linear Time-Varying Systems

4.2.4.1 4.2.4.2. Introduction

Interconnections of Linear Time-Varying Systems

Models for LTV Systems

4.2.5.1 4.2.5.2 4.2.5.3. Linear Differential Equation with Time-Varying Coefficients

Separable Models

Tapped Delay-Line Channel Models

Summary

Appendix: Biquadratic Factors for Classical Filters

References

Chapter 5 Modeling and Simulation of Nonlinear Systems 5.1 5.2 5.3. Modeling Considerations for Nonlinear Systems

Memoryless Nonlinearities .

5.2.1 5.2.2 5.2.3 5.2.4. Memoryless Baseband Nonlinearities

Estimating the Sampling Rate for Nonlinear Systems

Memoryless Bandpass Nonlinearities: Analytically Based Models

5.2.3.1 5.2.3.2. The Limiter Family

Power Series Model

Memoryless Bandpass Amplifiers: Empirically Based Models

5.2.4.1 5.2.4.2 5.2.4.3 5.2.4.4 5.2.4.5. Description and Interpretation of AM/AM and AM/PM Characteristics for Simulation

Lowpass Equivalent of a Bandpass Amplifier

Alternative Approaches to Defining AM/AM and AM/PM Characteristics

Multiple Carriers and Intel-modulation Products

Setting the Operating Point of a Memoryless Nonlinearity

Nonlinearities with Memory (NLWM)

5.3.1 5.3.2. NLWM Modeling I: Fitting Swept-Tone AM/AM and AM/PM Measurements

5.3.1.1 5.3.1.2 5.3.1.3. The Poza–Sarokozy–Berger (PSB) Model

5.3.1.1.1. 5.3.1.1.2 5.3.1.1.3. AM/AM Characteristics

AM/PM Characteristics

Combined Model

The Saleh Model

The Abuelma’atti Model .

NLWM Modeling II: Fitting Preset Structures

182 182 183 184 185 186 186 187 188 189 189 190 190 190 190 192 192 193 195 196 198 201

204 206 206 207 209 212 214 215 218 219 220 221 223 224 227 227 227 229 229 229 232 234

5.3.2.2.

One Filter–One Nonlinearity (Two-Box) Models .

5.3.2.1.1 5.3.2.1.2 5.3.2.1.3 5.3.2.1.4 Filter–Nonlinearity with Least-Squares Fit

Filter–Nonlinearity ARMA Model .

Filter–Nonlinearity with Small-Signal Transfer Function .

Nonlinearity–Filter with Least-Squares Fit

Filter–Nonlinearity–Filter (Three-Box) Models

5.3.2.2.1 5.3.2.2.2 Three-Box Model with Least-Squares Fit

Three-Box Model with Specified Characteristics .

5.3.3 5.3.4 5.3.5 NLWM Modeling III: Analytical Models

5.3.3.1 5.3.3.2 Volterra Series Modeling .

Polyspectral Models .

5.3.3.2.1 5.3.3.2.2 Nonlinearity–Filter Polyspectral Model

Filter–Nonlinearity Polyspectral Model

NLWM Modeling IV: Miscellaneous Models .

5.3.4.1 5.3.4.2 5.3.4.3 Power-Dependent Transfer Function Model .

Nonlinear Parametric Discrete-Time Models

Instantaneous Frequency Model .

Setting the Operating Point for a Nonlinearity with Memory

5.4 5.5 5.6 Nonlinear Differential Equations

5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 Outline of Numerical Methods

Families of Numerical Methods .

5.4.2.1 5.4.2.2 Solution Using Explicit Methods

Solution Using Implicit Methods

5.4.2.2.1 5.4.2.2.2 Iterated Predictor–Corrector Method .

Root Finding Using Newton–Raphson Method

Properties of Numerical Methods: Accuracy and Stability

5.4.3.1 5.4.3.2 Order of a Method: Computation of Local or Truncation Error .

Absolute Stability

Computational Considerations: Methods of Quality Control

Application of Numerical Methods .

5.4.5.1 5.4.5.2. Introduction

Stand-Alone Model for a Traveling-Wave Semiconductor Amplifier

Measurement Technique for Nonlinear Components

5.5.1 5.5.2 5.5.3 The Vector Network Analyzer Single-Tone Measurement

Dynamic AM/AM and AM/PM Measurement Techniques Using a Periodically Modulated Signal .

Time-Domain Measurement Techniques .

Summary

References

234 234 235 235 236 236 236 237 237 237 245 246 249 252 252 253 255 256 257 257 261 263 263 263 264 266 268 269 270 271 271 272 275 275 277 280 284 285 289 291 291 291 293 294 297 297 Chapter 6 Fundamentals of Random Variables and Random Processes for Simulation 6.1 6.2 6.3 Introduction

Random Variables .

6.2.1 6.2.2 6.2.3 Basic Concepts, Definitions, and Notations

6.2.1.1 6.2.1.2 Introduction .

Statistical Averages or Expected Values

Multidimensional Random Variables (Random Vectors)

Complex Random Variables

Univariate Models

6.3.1. Univariate Models–Discrete

6.3.1.1 6.3.1.2 6.3.1.3 6.3.1.4 Uniform .

Binomial .

Negative Binomial

Poisson .

6.3.2 Univariate Models—Continuous .

6.3.2.1 6.3.2.2 6.3.2.3 6.3.2.4 6.3.2.5 6.3.2.6 6.3.2.7 6.3.2.8 6.3.2.9 Uniform .

Gaussian (Normal) .

Exponential

Gamma .

Rayleigh .

Chi-Square

Student’s t .

F Distribution .

Generalized Exponential

6.4 Multivariate Models

6.4.1 6.4.2. Multinomial

Multivariate Gaussian .

6.4.2.1 6.4.2.2 Properties of the Multivariate Gaussian Distribution

Moments of Multivariate Gaussian pdf .

6.5 Transformations (Functions) of Random Variables .

6.5.1 6.5.2 6.5.3 Scalar-Valued Function of One Random Variable

6.5.1.1 6.5.1.2 Discrete Case .

Continuous Case .

Functions of Several Random Variables

6.5.2.1 6.5.2.2 6.5.2.3 Special Case—Linear Transformation .

Sum of Random Variables

Order Statistics .

Nonlinear Transformations

6.5.3.1 6.5.3.2 Moment-Based Techniques .

Monte Carlo Simulation Techniques

6.6 Bounds and Approximations .

6.6.1 6.6.2 6.6.3 6.6.4 6.6.5 Chebyshev’s Inequality .

Chernoff Bound .

Union Bound

Central Limit Theorem

Approximate Computation of Expected Values

6.6.5.1 6.6.5.2 6.6.5.3. Series Expansion Technique

Moments of Finite Sums of Random Variables

Quadrature Approximations

6.7. Random Processes

6.7.1 6.7.2 Basic Definitions and Notations

Methods of Description

6.7.2.1 6.7.2.2 6.7.2.3 6.7.2.4 Joint Distribution .

Analytical Description Using Random Variables

Average Values

Two or More Random Processes .

6.7.3 Stationarity, Time Averaging, and Ergodicity .

6.7.3.1 6.7.3.2 Time Averages .

Ergodicity .

6.7.4. Correlation and Power Spectral Density Function of Stationary Random Processes

298 298 298 299 299 300 300 301 301 302 302 303 303 304 304 304 304 305 305 308 308 310 310 310 313 313 314 315 316 316 316 317 317 318 318 320 321 321 322 323 326 326 328 328 328 329 330 331 332 333 334

6.7.4.2.

6.7.4.3.

6.7.4.4.

6.7.4.5.

Autocorrelation Function and Its Properties .

Cross-Correlation Function and Its Properties

Power Spectral Density

Lowpass and Bandpass Processes .

Power and Bandwidth Calculations .

6.7.5 6.7.6 Cross-Power Spectral Density Function and Its Properties

Power Spectral Density Functions of Random Sequences

6.8 6.9 6.10 6.11 Random Process Models

6.8.1 6.8.2 6.8.3 6.8.4 6.8.5. Random Sequences

6.8.1.1 6.8.1.2 6.8.1.3. Independent Sequences

Markov Sequences (First Order)

Autoregressive and Moving Average (ARMA) Sequences

M-ary Digital Waveforms

6.8.2.1 6.8.2.2 Introduction .

Random Binary Waveform .

Poisson Process

Shot Noise and Impulsive Noise

6.8.4.1 6.8.4.2 Shot Noise

Impulsive Noise

Gaussian Process

6.8.5.1 6.8.5.2 6.8.5.3 Definition of a Gaussian Process

Models of White and Bandlimited White Noise

Quadrature Representation of Bandpass (Gaussian) Signals

Transformation of Random Processes

6.9.1 6.9.2 6.9.3 6.9.4 Response of Linear Time-Invariant Causal (LTIVC) System .

6.9.1.1 6.9.1.2 6.9.1.3 Stationarity

Probability Distribution .

Mean, Autocorrelation, and Power Spectral Density Functions

Filtering .

Integration

Response of Nonlinear and Time-Varying Systems

6.9.4.1 6.9.4.2. Nonlinear Systems

Time-Varying Systems

Sampling of Stationary Random Processes

6.10.1 6.10.2. Sampling

6.10.1.1 6.10.1.2 6.10.1.3 6.10.1.4. Sampling of Lowpass Random Processes

Aliasing Effect

Sampling Rate for Simulations

Sampling of Bandpass Random Process

Quantization

6.10.2.1 6.10.2.2 Uniform Quantization .

Nonuniform Quantizer

Summary

References

Chapter 7 Monte Carlo Simulation and Generation of Random Numbers 7.1. Principle of Monte Carlo Simulation

7.1.1 7.1.2 Definition of Monte Carlo Simulation

Variations of Monte Carlo Simulation—Quasianalytical Monte Carlo Simulation

335 335 336 337 338 338 339 340 340 340 340 342 344 344 345 346 346 346 348 350 351 352 354 357 357 357 357 357 358 360 361 361 362 362 362 362 363 365 365 366 367 368 369 369

371 371 373

7.3.

7.4.

7.5.

7.6.

Random Number Generation

7.2.1 7.2.2 7.2.3 Generation of Uniform Random Numbers

7.2.1.1 7.2.1.2. Wichman–Hill Algorithm

Marsaglia–Zaman Algorithm

Methods of Generating Random Numbers from an Arbitrary pdf

7.2.2.1 7.2.2.2 7.2.2.3 7.2.2.4. Transform Method ( Analytical)

Transform Method (Empirical)

Transform Method for Discrete Random Variables

Acceptance/Rejection Method of Generating Random Numbers

Generating Gaussian Random Variables

7.2.3.1 7.2.3.2. Sum-of-12 Method

Box Müller Method

Generating Independent Random Sequences

7.3.1 7.3.2 7.3.3 7.3.4 White Gaussian Noise

Random Binary Sequences and Random Binary Waveforms

Pseudorandom Binary Sequences .

M-ary Pseudo noise Sequences

Generation of Correlated Random Sequences

7.4.1 7.4.2 7.4.3. Correlated Gaussian Sequences: Scalar Case

7.4.1.1 7.4.1.2. Autoregressive Moving Average (ARMA) Models

Spectral Factorization Method

Correlated Gaussian Vector Sequences

7.4.2.1 7.4.2.2. Special Case

General Case

Correlated Non-Gaussian Sequences

Testing of Random Number Generators

7.5.1. Stationarity and Uncorrelatedness

7.5.1.1 7.5.1.2 Introduction .

Durbin Watson Test for Correlation

7.5.2. Goodness-of-Fit Tests

Summary

References

Chapter 8 Modeling of Communication Systems: Transmitter and Receiver Subsystems 8.1 8.2 8.3 8.4 8.5 Introduction

Information Sources

8.2.1 8.2.2 Analog Sources

8.2.1.1 8.2.1.2 8.2.1.3 8.2.1.4. Single Test Tone

Multiple Test Tones

Filtered Random Processes

Stored Experimental Data

Digital Sources

Formatting/Source Coding

8.3.1 8.3.2. Analog-to-Digital (A/D) Conversion

On Simulating the FSC Subsystem .

Digital Waveforms: Baseband Modulation (I)

Line Coding: Baseband Modulation (II) .

8.5.1 Logical-to-Logical Mapping I: Binary Differential Encoding

373 374 376 376 377 377 379 380 381 383 383 383 384 384 385 386 389 392 393 393 395 397 397 398 399 400 400 400 401 402 405 406

407 411 411 412 412 413 413 413 414 414 416 417 420 420

8.5.3.

8.5.4.

8.5.5.

8.5.6.

8.5.7.

8.5.8.

8.5.9.

Logical-to-Logical Mapping II: Correlative Coding

Logical-to-Logical Mapping III: Miller Code .

Logical-to-Real Mapping I: Non-Return to Zero (NRZ) Binary Signaling

Logical-to-Real Mapping II: NRZ M-ary Signaling (PAM)

Logical-to-Real Mapping III: Return-to-Zero (RZ) Binary Signaling .

Logical-to-Real Mapping IV: Biphase Signaling or Manchester Code

Logical-to-Real Mapping V: Miller Code or Delay Modulation .

Logical-to-Real Mapping VI: Partial Response Signaling

8.6 8.7 8.8 8.9 8.10 8.11 8.12 Channel Coding .

8.6.1 8.6.2 Computational Load for Block Coding/Decoding .

Computational Load for Convolutional Coding/Decoding

Radiofrequency and Optical Modulation

8.7.1 8.7.2 8.7.3 8.7.4 8.7.5 Analog Modulation

Digital Quadrature Modulation

8.7.2.1 8.7.2.2 QPSK: Differential Quaternary Phase-Shift-Keying (DQSK) .

Multitone Modulation/OFDM

Continuous Phase Modulation CPFSK, MSK, GMSK

8.7.3.1 8.7.3.2 8.7.3.3 8.7.3.4. Continuous Phase Modulation

Continuous-Phase Frequency-Shift-Keying

Minimum-Shift-Keying

Gaussian Minimum-Shift-Keying .

Coded Modulation .

Modeling Considerations .

Demodulation and Detection

8.8.1 8.8.2 Coherent Demodulation

Noncoherent Demodulation

8.8.2.1 8.8.2.2 8.8.2.3. Amplitude Demodulation

Discriminator Detection of PM/FM Signals

PLL Demodulation of PM/FM Signals

Filtering

8.9.1 8.9.2 8.9.3 8.9.4 8.9.5 8.9.6 8.9.7 8.9.8 Filters for Spectral Shaping

Filters for Pulse Shaping

Linear Minimum MSE Filters .

Filters for Minimizing Noise and Distortion

Matched Filters

Adaptive Filtering ( Equalization)

8.9.6.1 8.9.6.2 8.9.6.3 Tap-Gain Adaptation for Minimizing MSE

Covariance Matrix Inversion Method .

Simulation Considerations

Filters Specified by Simple Functions in the Frequency Domain

Tabular Filter for Masks and Measurements

Multiplexing/Multiple Access

8.10.1. Issues in the Simulation of Multiple-Access Methods

8.10.1.1 8.10.1.2 8.10.1.3 8.10.1.4 SDMA and PDMA .

FDMA

TDMA

CDMA (Spread Spectrum Techniques)

Radiofrequency and Optical Carrier Sources

8.11.1 8.11.2 Radiofrequency Sources

Optical Sources

Synchronization

8.12.1 Approaches to Including Synchronization in Simulation

421 421 422 423 423 423 423 425 425 428 431 433 434 435 438 439 443 443 445 446 447 449 451 455 457 460 460 461 465 467 467 468 470 471 472 474 476 479 480 481 483 484 484 484 486 487 489 491 491 492 495 498

Hardwired Synchronization: Phase and Timing Bias

Synchronization Using an Equivalent Random Process Model Carrier Recovery—BPSK Timing Recovery—BPSK .Carrier Recovery—QPSK .Timing Recovery—QPSK .Simulation of Feedback Loops: Application to the Phase-Locked Loop,

Phase-Locked Demodulator, and Costas Loop

The Phase-Locked Loop as an FM Demodulator

Effect of Delay on the Performance of the Assembled PLL Model .8.13

8.13.2.1

8.13.2.2

8.13.2.3.

Signal Power Level

Noise Power Level

Calibrating Signal-to-Noise Ratio and Summary .References

Chapter 9 Communication Channels and Models

Multipath Fading 9.1.3.1.

9.1.3.4.2

9.1.3.4.3.

The Delay Power Profile

The Spaced-Frequency Correlation Function .The Time-Varying Channel Structural Models for Multipath Fading Channels 9.1.3.5.1

9.1.3.5.2

9.1.3.5.3.

Diffuse Multipath Channel Model Statistical Tap-Gain Models .Generation of Tap-Gain Processes Indoor Wireless Channels 9.1.3.6.1

9.1.3.6.2

9.1.3.6.3

Factory and Open-Plan-Building Model .Office Building Model .Ray-Tracing Prediction Model .Radio-Relay Line-of-Sight (LOS) Discrete Multipath Fading

506 510 513 514 514 515 522 528 529 531 534 534 535 535 538 538 539 540

546 546 547 549 550 551 551 553 554 557 558 561 561 572 575 576 577 578 582 583 586 587 587 589

Rectangular Waveguide Medium

The Fiber Optic Channel Finite-State Channel Models 9.4.1.

Types of Hidden Markov Models: Gilbert and Fritchman Model .

Estimation of the Parameters of a Markov Model

Methodology for Simulating Communication Systems Operating over

Fading Channels 9.5.1.

9.5.2.

9.5.3.

Waveform-Level Simulation Symbol-Level Simulation Speech Coder Simulation

Decorrelation Length of the Long-Term Fading

Channel Impulse Response Model

10.1.2.

10.1.3.

Random Process Model: Stationarity and Ergodicity .

Basic Notation and Definitions .Quality of an Estimator: Bias, Variance, Confidence Interval,

and Time Reliability Product .

Time–Reliability Product Normalized Measures

Estimating the Average Level of a Waveform 10.2.1.

Variance of the Estimator

Mixture (Signal Plus Noise) Processes

Confidence Interval Conditioned on the Signal

Estimating the Average Power (Mean-Square Value) of a Waveform .

10.3.1 Form of the Estimator for Average Power

591 591 593 596 597 599 600 601 601 604 606 610 611 612 613 613 614 614 617 618 618 618 618 618 619 619 621

626 626 626 628 628 629 629 631 631 631 631 632 632 635 635 636 637

10.4.2.3

Form of the Estimator Expectation of the Estimator

Variance of the Estimator

Estimating the Power Spectral Density (PSD) of a Process

Expected Value of the Estimator

Variance of the Estimator

Some Considerations on Implementing PSD Estimators: Summary

of the Simulation Procedure 10.5.5.1

10.5.5.2

Welch Periodogram Procedure (Direct Method) Windowed Correlogram Procedure (Indirect Method) Estimating Delay and Phase 10.6.1

10.6.2

10.6.3

Estimating Carrier Phase and Timing Synchronization in the

Noiseless Case Block Estimators 10.6.2.1

10.6.2.2.

Block Delay Estimator

Block Phase Estimator .

Distribution of PLL-Based Phase and Timing Estimators 10.6.3.1

10.6.3.2

Distribution of the Phase Estimator

Distribution of the Timing Estimator Visual Indicators of Performance 10.7.1

10.7.2

Eye Diagrams .Scatter Diagrams

Derivation of the Estimator

Form of the Estimator

Statistical Properties of the Estimator

Implementing the Estimator Estimating Performance Measures for Digital Systems 11.2.1

11.2.2

11.2.3

Performance Characterization for Digital Systems and Run-Time

Implications

A Conceptual Framework for Performance Estimation

The Monte Carlo Method

11.2.3.1

11.2.3.2.

11.2.3.3.

Confidence Interval: Binomial Distribution

Confidence Interval: Poisson Approximation .

Confidence Interval: Normal Approximation

637 638 640 640 641 642 643 644 645 646 646 647 648 651 652 653 653 654 655 655 657 658 660 661 662 664 664 664 666 667 667

670 670 673 673 675 678 679 683 686 688 691 691

11.2.3.7.2.

11.2.3.7.3.

Using a Generative Model

Using a Descriptive Model Interval Simulation 11.2.4.

11.2.5.1.

11.2.5.2.

11.2.5.3.

11.2.5.4.

Formulating IS for Simulation Implementation

Properties of the Importance Sampling Estimator .Choosing Biasing Densities

11.2.5.3.1.

11.2.5.3.2.

A Heuristic Approach

A Formal Approach Stochastic Importance Sampling Efficient Simulation Using Importance Splitting

11.2.6.1.

11.2.6.2.

Introduction Application of DPR-Based Splitting Simulation

Quasianalytical (Semianalytic) Estimation

General Scheme for the QA Method

QA Method for Binary Systems

QA Method for Single-Dimensional Multiamplitude Modulation

QA Method for QAM Modulation .

QA Method for PSK Modulation

QA Techniques for Coded Systems with Hard-Decision Decoding 11.2.7.6.1.

11.2.7.6.2.

Independent-Error Channel Dependent-Error Channel

QA Method for Convolutionally Coded Systems with

Soft-Decision Decoding Incorporating Jitter in the QA Technique

Mixed QA Technique 11.3 Summary

References

Chapter 12 Four Case Studies

12.1 Case Study I: 64-QAM Equalized Line-of-Sight Digital Radio Link in a

694

696 697 697 698 700 701 703 706 707 707 709 710 713 717 719 719 724 732 734 734 736 737 739 740 743 744 745 748 748 751 753 753 754 757 758

763 763 765 766 767 767 769 769

Method 2 (FQA-2) Evaluation of Error Probability: The Moment Method

(Gaussian Quadrature) Simulation Procedure Evaluation of the Outage Probability Simulation Results Conclusions 12.2.

Residual Phase Noise Model

12.2.4.1.

12.2.4.2.

Introduction Calibrating the Model Residual Phase Noise Random Number Generator

A Quasianalytical Generator for the Error Sequence Postprocessing Conclusions Case Study III: Exploring the Effects of Linear and Nonlinear Distortions

and Their Interactions on MSK-Modulated Signals: A Visual Approach 12.3.1.

Parabolic Amplitude

Parabolic Phase Cubic Phase

Residual Amplitude and Phase

Combined Effects of Linear Filter Distortions

Memoryless Nonlinear AM/AM and AM/PM Distortions

Nonlinear Filter Distortions Conclusions

Case Study IV: Performance Evaluation of a CDMA Cellular Radio System

12.4.1.

12.4.2.

12.4.3.

Introduction

Brief Description of a CDMA Cellular System

Reverse Radio Link Simulation

770 771 773 774 777 777 777 778 779 781 782 785 786 787 787 790 791 792 793 793 793 796 798 799 799 802 803 806 807 809 809 809 812 812 814 814 816 816 817 818 818 818 820 822 822 822 825 826

Simulation Run-Length Requirement Simulation Runs 12.4.4.

Finite-State Channel Characterization

12.4.5.2.1.

12.4.5.2.2.

The Reverse Link

The Forward Link .

The Number of States

Probability Distribution of Error-Free Intervals Probability Distribution of the Number of Errors in a Block

The Channel Shaping Filter

FIR Implementation IIR Implementation .

Comparison of IIR and FIR Filter Implementation

Sampling Rate Expansion and Interpolation .

References

Problems and Projects

Chapter 3

Chapter 4 Chapter 5

Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11

A Collection of Useful Results for the Error Probability of Digital Systems .

Gaussian Tail Probabilities Q(x) and an Approximation Coefficients of the Hermite Polynomials

Some Abscissas and Weights for Gaussian Quadrature Integration .

826 826 828 829 831 831 832 832 832 833 835 836 836 837 838 838 839 839 840 840 841 845 845 845 846 846 847 847 848 848

851 854 856 863 865 868 871 873 874

879 891 893 895

E Chi-Square Probabilities .

Index

897 899

Introduction

The complexity of communication and signal processing systems has grown considerablyduring the past decades During the same time, the emergence of a variety of new technol-ogies such as fast and inexpensive hardware for digital signal processing, fiber optics, inte-grated optical devices, and monolithic microwave integrated circuits has had significantimpact on the implementation of communication systems While the growth in complexity ofcommunication systems increases the time and effort required for analysis and design, theneed to insert new technologies into commercial products quickly requires that the design bedone in a timely, cost-effective, and effort-free manner These demands can be met onlythrough the use of powerful computer-aided analysis and design tools

A large body of computer-aided techniques has been developed in recent years to assist

in the process of modeling, analyzing, and designing communication systems (1–7) Thesecomputer-aided techniques fall into two categories: formula-based approaches, where the

computer is used to evaluate complex formulas, and simulation-based approaches, where the computer is used to simulate the waveforms or signals that flow through the system The

second approach, which involves “waveform”-level simulation (and often incorporatesanalytical techniques), is the subject of this book

Since performance evaluation and trade off studies are the central issues in the analysis

and design of communication systems, we will focus on the use of simulation for evaluating

the performance of analog and digital communication systems with the emphasis on digital

Formula-based techniques, which are based on simplified models, provide considerableinsight into the relationship between design parameters and system performance, and they areuseful in the early stages of the design for broadly exploring the design space However,except for some idealized and oversimplified cases, it is extremely difficult to evaluate the

1

performance of complex communication systems using analytical techniques alone with the

degree of accuracy needed for finer exploration of the design space

Performance evaluation based on measurements obtained from hardware prototypes ofdesigns is of course an accurate and credible method, and is useful during the later stages ofthe design when the design choices are limited to a small subset This approach is in general

very costly and time-consuming and not very flexible It is clearly not feasible to use this

approach during the earlier stage of the design cycle when the number of design alternativesmay be large

With simulation-based approaches to performance evaluation, systems can be modeled

with almost any level of detail desired (subject, of course, to certain limitations) and the

design space can be explored more finely than is possible with formula-based approaches

or measurements With a simulation-based approach, one can combine mathematical and

empirical models easily, and incorporate measured characteristics of devices and actualsignals into analysis and design Simulated waveforms can also be used as test signals for

verifying the functionality of hardware

Indeed, a simulation-based approach can be used to create a rapid prototyping

onment for analysis and design of communication and signal-processing systems, an onment in which software models can be combined with hardware data and real signals to

envir-produce designs that are timely, cost-effective, and error-free

The primary disadvantage of the simulation approach is the computational burden,which can be reduced by a careful choice of modeling and simulation techniques A

substantial part of this book is devoted to the topics of simulation models and simulationtechniques

1.1.2 Hierarchical View

In a broad sense, the term “communication system” might refer to a global nication network, a geosynchronous communication satellite, a terrestrial microwave trans-

commu-mission system, or a built-in modem in a personal computer A hierarchical view that is often

used to describe communication systems is shown in Figure 1.1 The top level in this

representation is a communication network, which is made up of communication nodes(processors) interconnected via communication links or transmission systems as represented

in the layer below A communication link is made up of elements like modulators, encoders,

filters, amplifiers, decoders, and demodulators and other components which perform signal

processing operations These elements can be analog circuits, digital circuits, or an algorithmimplemented on a programmable digital signal processor (DSP) Details of these elements are

represented in the bottom layer of the hierarchy shown in Figure 1.1

A variety of simulation techniques are used to evaluate the performance of the variouslayers in Figure 1.1 At the network level, the flow of packets and messages over the network

is simulated using an event-driven simulator, and performance measures such as networkthroughput, response time, and resource utilization are estimated as a function of networkparameters like processor speeds, buffer sizes at nodes, and link capacities Network simu-lations are used to establish specifications for the processors, protocols, and the commu-nication links

Communication links deal with the transmission of information-bearing waveforms over

different types of communication channels (free space, cables, wires, optical fibers, etc.) Fordigital transmission systems, the performance of communication links is measured in terms of

bit error characteristics, and the bit error rate performance is estimated by simulating the flow

Figure 1.1 Hierarchical view of communication systems.

of waveforms using models for functional blocks such as modulators, encoders, filters,amplifiers, and channels Whereas network simulations are used to establish specifications for

communication links, link-level simulations are used to verify that the link design meets these

specifications The performance parameters obtained at the link-level simulation are exported

up to the network-level simulator to verify the performance of the network

The bottom layer in Figure 1.1 deals with implementation of components such as filtersand equalizers using either analog or digital technologies Circuit simulators like Spice or

digital simulators like HDL (Hardware Description Language) are used to simulate, verify

functionality, and characterize the behavior of the components Link-level simulationsestablish the specifications for implementation, and simulation at the implementation level isused to provide behavioral models which are exported back to the link level An example of abehavioral model is the transfer function for a filter

The focus of this book is on waveform-level simulation of communication links (middlelayer in Figure 1.1)

1.2 Simulation Approach: Waveform-Level Simulation of Communication Systems

To illustrate the approach used in waveform-level simulations, let us consider thesimplified model of a “generic” digital communication system shown in Figure 1.2 Thismodel shows only a subset of the functional blocks in a typical digital communication system,

Figure 1.2 Simulation example.

and for discussion purposes let us assume that we are interested in evaluating the error-rateperformance of this system as a function of the parameters of the filters (orders and band-

widths), the nonlinear amplifier (saturation level or peak power and operating point), and thesignal-to-noise ratios for the two Gaussian noise sources We are assuming that the perfor-mance of the system is determined by the signal distortions introduced by the filters and thenonlinear amplifier, and by the two noise sources

Analytical evaluation of the performance of this system is difficult because of the

presence of the nonlinearity and the filters Bandlimiting filters introduce intersymbol

inter-ference, and the presence of noise before the nonlinearity leads to non-Gaussian andnonadditive effects, which are very difficult to characterize and analyze Some approxima-tions can be made by neglecting the effects of the filter preceding the nonlinearity and bycombining the first noise source with the second noise source and treating the overall effect ofthe two noise sources as additive and Gaussian These and other simplifications, while useful

for obtaining a “first-order” estimate of system performance, are often not accurate enough

for performing detailed performance tradeoff analysis

Estimation of the error rate via simulation involves the following steps:

1 Generate sampled values of the input processes (waveforms) (the source output andthe two noise processes)

2 Process these samples through models for the filter and the nonlinearity, and generatesampled values of the output of the system

3 Estimate the error rate by comparing the simulated values of the input sequence andthe output waveform

Examples of simulated waveforms are shown in Figure 1.2 along with sensitivity curves,which show the relationship between the performance measure (error rate) and design

parameters such as the operating point of the amplifier and the receive-filter bandwidth.Smaller values of the receive-filter bandwidth reduce the effects of the noise while increasingsignal distortion, whereas a larger bandwidth leads to larger noise power and smaller amounts

of signal distortion The “optimum” value of the bandwidth is chosen using the

performance-sensitivity curves shown in Figure 1.2

Note that simulated waveforms can closely mimic the waveforms that might exist in the

real system Hence, it is possible to use simulated waveforms as test signals in the real system

as well as real signals to “drive” portions of the simulations This close correspondence at thewaveform level also makes it easy to incorporate in a simulation the measured values ofdevice characteristics, such as the frequency response of filters or the transfer characteristics

of amplifiers

1.3 The Application of Simulation to the Design of Communication Systems

Simulation can play an important role during all phases of the design and engineering of

communication systems, from the early stages of conceptual design through the various

stages of implementation, testing, and fielding of the system

The design process typically is initiated by the “concept definition” phase, where oneimposes the top-level specifications such as information rate and performance objectives Theperformance of any communication system is governed by two important factors: the signal-to-noise ratio (SNR) and the accumulated signal distortions Generally, these are interactive

and some tradeoffs are necessary For example, with respect to the system shown in Figure

1.2, filter bandwidths affect both SNR and distortion In most communication systems, a

spread-sheet-like table called a link budget is used to keep track of factors that affect overall

SNR

The system designer starts with a candidate system and a list of design parameters

During the early phase of the design, estimates of signal-to-noise ratios and signal

degra-dations are obtained using simpler models and educated guesses For example, to calculateSNR, a filter may be modeled as an ideal lowpass filter with a certain bandwidth, and the

distortion introduced by the actual filter may be assigned an equivalent “degradation” of, say,

2.0 dB in SNR If the initial design produces candidate systems that meet performanceobjectives, then the design proceeds to the next phase Otherwise, the topology of thecandidate designs might have to be changed (say, by adding a filter or changing the encoder/decoder) and the distortion parameters must be modified

The next phase in the design is the development of detailed specification for subsystemsand components, and verification of signal distortions Simulation plays an important role

here For example, if a filter is specified as a third-order Butterworth filter with a symbol time product of 0.7 (as opposed to an ideal lowpass filter with an allocation of 2.0 dBfor signal distortion for link budget calculation), then waveform-level simulation can be used

bandwidth-to verify the extent of degradation introduced by the filter If the degradation obtained via

simulation is less than 2.0 dB, then the saving can be used to relax the specification on someother component Otherwise, additional savings will have to be sought from other compo-

nents Simulation is flexible and efficient and is often the only method available forperforming these tradeoff studies and establishing detailed specifications for hardwaredevelopment

The initial step in hardware development involves the building and testing of criticalcomponents/subsystems that involve risky or new technologies The measured characteristics

of these prototype hardware components are then used in the simulations to verify the

end-to-end performance of the system Note that, at this step, simulation involves models for

components yet to be built, and actual characteristics of components already built and tested.

If simulations produce satisfactory values for performance objectives, then the remaining

hardware components are built and a prototype hardware for the entire system is “wired

together” and tested Otherwise, specifications are modified and parts of the design are

redone

When the hardware prototype of the system is completed, it is tested and the test resultsare compared with simulation results The degree of closeness between the hardware and

simulation results is the basis for declaring whether or not the simulation is “valid.” The

validated simulation model can be used to predict the end-of-life (EOL) performance of thesystem using postulated characteristics of key components due to aging The validated

simulation model can also be used during operational stages for trouble shooting and forproviding answers to “what if” scenarios

Thus, simulation can play an important role at any point in the life cycle of acommunication system: at the conceptual definition stage, where top-level specifications arederived; as an ongoing part of design and development, in concert with hardware develop-

ment to finalize specifications and check the influence of an as-built subsystem on the systemperformance as a whole; out to the operational scenario, where simulation can be used as atrouble-shooting tool; and to predict EOL performance of the system

1.4 Historical Perspective

Waveform-level simulation started with the invention of analog computers in the 1940s,which were first used to simulate the behavior of control systems used in aircraft and weaponssystems.(8) An analog computer is a simulator of continuous systems composed of modularcomponents interconnected via a patchboard into a block diagram configuration representingthe system The linear elements, such as integrators and adders, are realized using feedback

DC operational amplifiers Nonlinear modules such as multipliers and trigonometric functionswere first realized by electromechanical servo systems and later by piecewise linearapproximations Any system whose behavior is described by a linear or nonlinear differential

equation with constant coefficients or with time-varying coefficients can be reduced to ablock diagram made up of components of the analog computer By wiring the components

according to the block diagram and exciting the model with appropriate signals, one can

simulate the dynamic behavior of a broad range of linear and nonlinear systems using theanalog computer

The development of high-speed digital computers and the availability of large-capacity

memory enabled their usage in simulation applications This development opened the field of

modeling to new disciplines such as numerical analysis and programming The large dynamicrange of floating point number representation freed the user from the drudgery of signal

scaling General frameworks for digital simulation originated with block-oriented languages

such as MIDAS, SCADS, and CSMP,(9,10) which were developed in the early 1960s Thesesimulation languages emulated the behavior of analog computers on a component-by-component basis For example, a summer is replaced by the code for addition, and an inte-

grator is replaced by an integration subroutine The interconnections between the components

are specified by a block-oriented language just as the analog computer patchboard electricallylinks analog computing components Block-oriented simulation languages draw their moti-vation from the analog block diagram as a simple and convenient way of describingcontinuous systems

Applications of digital computers to circuit analysis and simulation with programs such

as ECAP and SPICE(11) in the mid 1960s led to advances in numerical integration techniquesand topological simplification of signal flowgraphs

Advances in discrete-time systems and digital signal processing have led to new

approaches for digital simulation of systems Software packages for simulations based upon

transform domain techniques (Fast Fourier transform for frequency domain techniques and

bilinear-Z transform for time domain techniques) began to emerge in the late 1960s and the

early 1970s SYSTID,(12,13) CSMP, CHAMP,(14,15) LINK,16 and others(17,18) were developed

during this period for aiding in the analysis and design of satellite communication links.While the initial versions of SYSTID and similar packages were language-oriented anddesigned to operate in a batch mode, later versions of SYSTID, and other packages such

as ICSSM and ICS,(19,20) were interactive and menu driven, at least in part With thesepackages, simulations were performed on a mainframe or a super-minicomputer, and graphicsterminals were used to provide a limited amount of interactive preprocessing as well aspostprocessing

Computer hardware and software technologies have since undergone significant

chan-ges Powerful workstations and personal computers offer very friendly computing

environ-ments with highly visual and graphical interfaces The Boss(21) software package was the first

to take advantage of the advances in workstation technologies to create a graphical friendly framework for simulation-based analysis and design of communication systems Thecurrent generation of simulation software packages (SPW,(22) COSSAP,(23) MATLAB/SIMULINK(24) and others) offer interactive, graphical, and user-friendly frameworks fordeveloping simulation models in a hierarchical fashion using graphical block diagramrepresentations, and permit the user to configure and execute waveform-level simulations,review the results of simulations, and perform design iterations These tools also providedatabase management, on-line help, on-line documentation, and other services and features.These features minimize the amount of effort the communication system engineer has to put

user-into the creation and debugging of simulation programs, and other mundane details associated

with the mechanics of simulating communication systems With the availability of the currentgeneration of simulation frameworks, attention is now focused on important issues such asmodeling and simulation techniques, estimation of performance measures, and computationalefficiency, which are the subject matter of this book We assume that the reader’s primary

interest is in understanding modeling and simulation techniques, problem formulation, andusing simulations for analysis of proposed designs, and not in building simulation frame-works or tools as such This book is intended to provide the conceptual underpinnings forsuch tools.

Many of the commercial packages like SPW, COSSAP, and Matlab provide interfaces to

network simulators and also links to circuit design and other implementation tools While we

will briefly describe some of these interfaces; detailed discussion of network simulation and

links to implementation tools is beyond the scope of this book

1.5 Outline of the Book

Simulation of communication systems involves generating sampled values of signals andnoise, processing these sampled values through discrete-time models of functional blocks inthose systems, and estimating certain properties of the signal at various points in the system,with particular emphasis on performance measures at the output The validity and accuracy of

simulation results will depend on the correctness of the modeling and estimation techniques

and generally, but not always, on the length of a simulation This book covers all majoraspects of the modeling and simulation of communication systems (that is, the middle layer as

defined in Figure 1.1) with emphasis on providing a practical introduction rather than a

theoretical discourse By practical we mean those countless hints, tricks of the trade, and

how-to information that will permit an individual with little previous background actually to

put together a useful simulation, or to thoroughly appreciate the underpinnings of commercial

software packages On the other hand, “practical” does not mean that we have no interest in

theory Indeed, the discipline is grounded on theoretical concepts and we provide coverage oftheoretical considerations that are especially relevant to simulation Nevertheless, since such

considerations are not our principal focus, this coverage is given in a condensed, reviewfashion with adequate references for the reader who might want to explore the theory ingreater detail In this section we provide a broad-brush overview of the following chapters A

detailed topical description is contained in the Contents

We begin, in the next chapter, with a discussion of the methodology of modeling and

simulation The term methodology implies ways of dealing with and thinking about a subject,

and in that sense Chapter 2 underlies the remainder of the book Methodology includes both

qualitative and quantitative aspects of the discipline, which we shall label, respectively, the

“art” and the “science” of simulation Important aspects of methodology include generalconcepts of modeling and modeling hierarchy, and the central notion of validation Thischapter should be useful in acquiring the right mindset for those with relatively littleexperience in simulation, and it may be profitable to revisit or browse through from time to

time when reading other chapters

Chapter 3 reviews and collects some basic topics in linear system theory, with emphasis

on the representation of signals and linear time-invariant (LTI) systems in the simulationcontext Although many of the topics covered are traditional, we strive to emphasize the

connection between theoretical constructs and their practical application to the actual process

of simulation Simulation using the digital computer requires us to deal with discrete-time orsampled versions of continuous-time signals and systems Thus, the core topic dealt with inthis chapter is the link between continuous-time signals and systems and their discrete-time

counterparts This link is provided by the well-known sampling theorem We enlarge the

typical discussion of sampling to include the important practical situation where multiratesampling is appropriate, and also discuss the related topic of interpolation We introduce

standard techniques for processing discrete-time signals, such as the z-transform and the

discrete Fourier transform, and in the process expose and contrast various time- andfrequency-domain relationships for discrete-time and continuous-time signals and systems.Another important practical topic addressed here is the complex lowpass representation,which is critical to the efficient simulation of bandpass signals and systems

Probably the most ubiquitous linear operation is filtering; indeed, every linear operation

can be thought of as a form of filtering In the first part of Chapter 4, we examine in somedetail how to perform time-invariant filtering within simulation Although there are manyways of describing filters, a very important characterization from the point of view ofsimulation techniques is whether the impulse response has a finite duration (FIR) or aninfinite duration (IIR) This dichotomy leads to fairly distinct sets of approaches FIR filteringitself is divided into two approaches that are often referred to as time-domain and frequency-domain processing The latter is most often used, and is based on the use of the discrete

Fourier transform in its “fast” version, the FFT IIR filtering is based on certain s-domain to

z-domain mappings which result in recursive difference equations We present a class of

continuous filters, called the classical filters, that frequently serve as the s-domain structures

that are converted to digital equivalents In this portion of the chapter, we also provide by-step summaries of the process of filtering according to the several methods mentioned

step-The second part of Chapter 4 deals with linear but time-varying (LTV) systems A brief

review is provided of various relationships in the time and frequency domains between theinput and output of such systems The time variations preclude the relatively simple input-output relationships that apply in the LTI case The main result of this chapter portion is thederivation of a tapped delay-line model for LTV systems that is practical to implement insimulation For the type of applications in which we are interested, the LTV “system” istypically a communication channel, such as the mobile channel However, such a channel is a

randomly time-varying system The tapped delay-line model just mentioned is deterministic,

but will be reinterpreted to apply in the random case when we get to Chapter 9

Chapter 5 deals with the modeling and simulation of nonlinear systems, generally themost intractable to treat analytically Generally, nonlinear systems are not especially difficult

to simulate, given the model Obtaining a high-fidelity model is where the main difficulty lies.Toward this goal, we define categories of models that depend largely on the ratio of signalbandwidth to system (or device) bandwidth When that ratio is small, models called

“memoryless” are often adequate and relatively easy to arrive at Nonlinear memorylessdevices are specified by input-power/output-power and input-power/output-phase char-acteristics that are conventionally measured If the ratio of signal bandwidth to systembandwidth is relatively large, models “with memory” will typically have to be be used It isgenerally a difficult task to develop a model with memory that has validity for a wide range ofsignals We outline various approaches for developing models with memory, all of themdependent to a greater or lesser degree on some type of measurement Since measurementsare central to the development of nonlinear models, we also provide in this section a primer

on related measurement techniques Such measurements, incidentally, can be used to inferwhether the appropriate modeling construct is one with or without memory A nonlinearsystem is one whose behavior is governed by a nonlinear differential equation In commu-nications, the most common forms of such systems are synchronization and tracking loops

We provide an overview of numerical methods that can be used to simulate such equationsdirectly

Information-bearing signals, noise, and interference in communication systems arerandom in nature In addition, the characteristics of some elements of a communicationsystem can change randomly over time Such elements could be manufactured equipment,whose behavior is influenced by age and environment, or they could be the environment itself,for example, a fading channel These phenomena, as well as signals, noise, and interference,are modeled using random variables and random processes Consequently, a review of themain elements of the theory of random variables and processes is provided in Chapter 6,along with a short catalog of distributions that are commonly encountered.

In simulation, random processes such as noise must be generated in some fashion, since

by their nature their values at sampling times are not given Generating sequences of numbersthat appear to behave as if they were samples of a typical path of a random process reliesmainly on techniques of random number generation, which forms a discipline distinct fromthe theory of random processes itself Consequently, we study such techniques in Chapter 7

An algorithm for generating a sequence that imitates a particular random process is called arandom number generator (RNG) Each type of random process must have a correspondingRNG, but for any particular process there can be more than one distinct algorithm Algo-rithms can differ in their properties in different ways The most desirable ones, of course,imitate most closely the process they are intended to reproduce and are computationallyefficient In this chapter we look at several ways in which RNGs can be constructed andsupply a number of algorithms for generating sequences of numbers having different types ofdistributions A brief look at methods for testing the quality of RNGs is also given A subclass

of algorithms for generating “pseudorandom” sequences of digital symbols, often called

shift-register sequences, is also presented, both for binary as well as M-ary symbols.

One of the central activities related to simulation is to develop models for the variousbuilding blocks of a communication system as well as for the signal and noise processes that

are the stimuli to any system A model is any description of the functioning or behavior of an

element of a system that forms the basis for the representation of that element in a simulation.With regard to signal and noise processes, the model consists simply in deciding what the

nature of the process is The construction of the model in this case would be the synthesis of a

proper RNG A similar approach holds for random channels, in which the modeling per seconsists in choosing a suitable set of probabilistic properties, which then have to be imple-

mented with some RNG In some cases, we may decide to use deterministic test signals or

patterns as inputs to a system, which may have no resemblance to the actual signals This, ofcourse, is often done in practice, and the generation of such test signals is straightforward

Primarily, however, Chapter 8 deals with models of transmitter and receiver subsystems In

terms of the modeling hierarchy of Chapter 2, subsystems are the modeling entities closest tothe entity of interest, namely, the system Modeling at that level will generally result in themost computationally economical program In formulating subsystem models, we advocate

a “functional” approach that allows, wherever possible, the incorporation of “knobs” in themodel to allow for real-life departures from ideal behavior We discuss in varying degrees ofdetail a number of important subsystems in digital communications links: source formatting,modulators, demodulators, filters, equalizers, encoders/decoders, and synchronizationsubsystems

All signals in communication links travel through some sort of medium, which can be

“wired” or “wireless.” Such media can be the performance-limiting element of a link, andtheir effect must of course be included in a simulation Most media can be considered linear,but some are time-invariant, or can be considered to be so for an application, and others aretime-varying We look at two examples of LTI wired media, namely waveguides and optical

fibers, and provide equations for their transfer functions These can essentially be treated asfilters in the same manner as those discussed earlier We also look at some examples ofwireless media that can be considered as LTI or slowly varying, namely the ionosphere and

the troposphere Most of Chapter 9, however, is devoted to a discussion of the multipath

fading channel which generally dominates the design considerations for mobile, cellular, and

personal communication systems (PCS) both indoors and outdoors We present a general

model for such channels, only the parameters of which have to be tailored for specificapplications We look at three specific multipath channels: outdoor mobile, indoor, and radio-relay For convenience, we include certain reference channel models proposed by standards

bodies for system studies We also describe in this chapter finite-state (discrete) channel

models We describe the burst errors encountered in fading channels The characterization ofchannels in the form of finite-state Markov models is extremely useful for network layer

simulations

The next two chapters are devoted to statistical aspects of simulation, to be distinguishedfrom the material covered in Chapters 6 and 7

In particular, we mean by this the estimation of quantities that one might normally wish

to measure in an actual system, but are subject to statistical variations for various reasons Wedivide the quantities to be estimated into two categories: parameters and performancemeasures In Chapter 10 we concentrate on estimation of parameters; these may be descriptors

of a waveform, such as the average power; they may be quantities inherently estimated in areal system, such as phase and timing references; or they may be rough indicators of asystem’s health, like eye diagrams

Most system-level simulations are run to obtain an estimate of a performance measure A

performance measure is an indicator of the quality of signal transmission Chapter 11 is

devoted to this topic For analog signals, the quality indicator that is almost universallyaccepted is the signal-to-noise ratio (SNR), and in general the SNR is a useful indicator of thenoisiness of a signal We derive the form for an SNR estimator for a general system and

describe its implementation in simulation in one of two forms, a time-domain version and a

frequency-domain version The bulk of Chapter 11, however, is concerned with the mance estimation problem for digital transmissions Performance measures for digital signalsare invariably framed in terms of some description of the errors to be found in the recovered

perfor-symbol (bit) stream The traditional indicator has been the average number of errors per

transmitted symbol, otherwise known as the bit-error-rate, or BER, but other measures may

be even more relevant, depending on context For example, one may be more interested in theprobability of an error in a block or frame than in the BER per se

Even though in practice it is often not thought of in this fashion, it is necessary to cast

the performance estimation problem as a statistical one It is, of course, a statistical problem:any estimate of the indicator will vary from one measurement to another because thewaveforms involved are random In many (perhaps even most) practical situations, this is not

a problem because the real time involved to reduce the statistical fluctuations to negligiblelevels is very short In simulation this is typically not the case: computational time per

processed symbol is not real time Therefore, it is important to bear in mind the statisticalaspect and quantify it The standard Monte Carlo technique is too slow for many problems of

interest, and more clever alternatives have to be considered Chapter 11 discusses a number of

such alternatives and attempts to quantify the corresponding run-time requirements

Chapter 12 contains four case studies that are intended to illustrate the application of as

wide a range of simulation techniques and ideas as possible The first case study deals with

performance estimation for a terrestrial radio-relay system in which fading occurs, and