Main Simulation Of Communication Systems Modeling, Methodology And Techniques

Simulation Of Communication Systems Modeling, Methodology And Techniques

, ,
Since the first edition of this book was published seven years ago, the field of modeling and simulation of communication systems has grown and matured in many ways, and the use of simulation as a day-to-day tool is now even more common practice. With the current interest in digital mobile communications, a primary area of application of modeling and simulation is now in wireless systems of a different flavor from the `traditional' ones.
This second edition represents a substantial revision of the first, partly to accommodate the new applications that have arisen. New chapters include material on modeling and simulation of nonlinear systems, with a complementary section on related measurement techniques, channel modeling and three new case studies; a consolidated set of problems is provided at the end of the book.
Year: 2000
Edition: 2nd
Publisher: Springer
Language: english
Pages: 937
ISBN 10: 0306462672
ISBN 13: 9780306462672
Series: Information Technology: Transmission, Processing and Storage
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Simulation of
Communication Systems

Second Edition

Information Technology: Transmission, Processing, and Storage
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

William H. Tranter
Virginia Polytechnic Institute and State University
Blacksburg, Virginia

Multi-Carrier Digital Communications: Theory and Applications of OFDM
Ahmad R. S. Bahai and Burton R. Saltzberg
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
Communication Systems Second Edition
Modeling, Methodology, and Techniques

Michel C. Jeruchim
Lockheed Martin Management & Data Systems

Valley Forge, Pennsylvania

Philip Balaban
AT&T Laboratories
Holmdel, New Jersey

K. Sam Shanmugan
University of Kansas

Lawrence, Kansas

KLUWER ACADEMIC PUBLISHERS
NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

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To
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
—PB
Radha, Kannon, and Ravi
and to the memory of my parents

—KSS

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Preface

Since the first edition of the book was published, the field of modeling and simulation of
communication systems has grown and matured in many ways, and the use of simulation as a
day-to-day tool is now even more common practice. Many new modeling and simulation
approaches have been developed in the recent years, many more commercial simulation
packages are available, and the evolution of powerful general mathematical applications
packages has provided still more options for computer-aided design and analysis. With the
current interest in digital mobile communications, a primary area of application of modeling
and 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 and
performance of systems of current interest, the practice of simulation has naturally evolved
along 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 of
several disciplines, communication theory in particular, the practice of modeling and simulation is still very much grounded in those basics. It is these principles, along with the many
tricks of the trade that accompany their application, that still form the main focus of this
second edition.
This edition represents a substantial revision of the first, partly to accommodate the new
applications that have arisen. The text has been extensively reorganized and expanded. It now
contains 13 chapters instead of the previous 7. Some of the former chapters have been divided
into more logical units, edited for greater clarity where needed, and extended in coverage for
selected topics. This division was made in part to facilitate the use of this book as a teaching
text. Two new chapters were added on material only lightly covered in the first edition. One
new chapter, on modeling and simulation of nonlinear systems, provides a fairly extensive
discussion of “black-box” modeling of nonlinear systems with memory, and a complementary 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 usual
environment for wireless systems. As in the first edition, one chapter provides several case
studies as a means of illustrating different ways of approaching a problem and applying
specific modeling and computational techniques from the arsenal of possibilities available to
the simulation practitioner. The first case study is a thoroughly reworked version of a previous

vii

viii

Preface

one, and three new case studies are given. A consolidated set of problems can be found
following 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, we
have had again to rely on the generosity of friends and colleagues to provide us with advice
and material on various topics. First, we would like to reacknowledge the contributors to the
first 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 on
large-deviations theory (Section 11.2.5.3.2). Numerous contributions were also made by other
members of the Communications Analysis and Simulation Group at Lockheed Martin
M&DS. Aside from Bob Wolfe’s work just mentioned, Douglas Castor and Dr. Gregory
Maskarinec 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 the
figures 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 Mathematica to compute Table 11.1 and to generate Figures 11.23 and 11.24. We thank Paul
Beauvilliers for using his experience in simulating phase-locked loops to produce the material
for Example 8.12.2 and the associated figures. We also express our appreciation to Daniel
McGahey, who supplied the block diagram, its details, and the timing information that form
the 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 went
beyond the call of duty by providing the material on generalized Volterra models and polyspectral 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 be
thanked individually for writing Section 5.3.4.2 on nonlinear parametric discrete-time
models. We have also benefited from numerous discussions with Harvey Berger of TRW on
his published and unpublished work in nonlinear amplifier modeling.
Several individuals presently or formerly at AT&T Laboratories, or formerly with Bell
Laboratories, 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 are
most grateful to Dr. Thomas M. Willis III for contributing the material on shadow fading in
Chapter 9. We also express our gratitude to Dr. Seong (Sam) Kim for providing the material
and the figures on indoor channel modeling in Chapter 9. We also acknowledge many
discussions 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 the
material (and its iterations) on orthogonal frequency division multiplexing (OFDM) that

Preface

ix

appears in Section 8.7.2.2. We much appreciate the efforts of Prof. J. Keith Townsend of
North Carolina State University for many discussions on importance sampling, for inputs into
Section 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 accommodated for space reasons. We thank Dr. Faroukh Abrishamkar of Qualcomm for his advice
on CDMA system modeling and for providing some of the reference channel models in the
Appendix 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, and
likewise we are pleased to acknowledge Prof. Brian Woerner of Virginia Polytechnic Institute
for providing us with a number of projects following Chapter 12.
Finally, we renew our acknowledgment to our families for bearing with us—a second
time—through this long process.

Michel C. Jeruchim
Philip Balaban
K. Sam Shanmugan

7KLVSDJHLQWHQWLRQDOO\OHIWEODQN

Contents

Chapter 1. Introduction
1.1. Methods of Performance Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.........................................
1.1.1. Introduction.
1.1.2. Hierarchical View. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. Simulation Approach: Waveform-Level Simulation of Communication Systems. . . . . .
1.3. The Application of Simulation to the Design of Communication Systems . . . . . . . . .
1.4. Historical Perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5. Outline of the Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
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Chapter 2. Simulation and Modeling Methodology
2.1.
2.2.
2.3.

2.4.
2.5.

2.6.

2.7.

Some General Remarks on Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methodology of Problem Solving for Simulation . . . . . . . . . . . . . . . . . . . . . . . .
Basic Concepts of Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1. System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
......................................
2.3.2. Device Modeling
................................
2.3.3. Random Process Modeling
2.3.4. Modeling Hypothetical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5. Simulation with Hardware in the Loop . . . . . . . . . . . . . . . . . . . . . . . . .
Performance Evaluation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Error Sources in Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1. Errors in System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2. Errors in Device Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3. Errors in Random Process Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.4. Processing Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1. Validating Models of Devices or Subsystems . . . . . . . . . . . . . . . . . . . . .
2.6.2. Validating Random Process Models . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.3. Validating the System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation Environment and Software Issues . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.1. Features of the Software Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.2. Components of the Software Environment . . . . . . . . . . . . . . . . . . . . . . .
2.7.3. Hardware Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.4. Miscellaneous
........................................
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2.8. The Role of Simulation in Communication System Engineering . . . . . . . . . . . . . . .
2.9. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3. Representation of Signals and Systems in Simulation: Analytic
Fundamentals
3.1. Introduction to Deterministic Signals and Systems . . . . . . . . . . . . . . . . . . . . . . .
3.1.1. Continuous Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2. Discrete-Time Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3. Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3.1. Properties of Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3.2. Block Diagram Representation of Systems . . . . . . . . . . . . . . . . .
3.2. Linear Time-Invariant Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1. Continuous Linear Time-Invariant Systems. . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1.1. The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1.2. The Convolution Integral, . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2. Discrete Linear Time-Invariant Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2.1. The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2.2. Convolution Sum (Discrete Convolution) . . . . . . . . . . . . . . . . . . . . . .
3.3. Frequency-Domain Representation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1. The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1.1. The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1.2. The Convolution Integral. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2. Frequency-Domain Representation of Periodic Continuous Signals. . . . . . . . .
3.3.2.1. The Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2.2. Parseval’s Theorem for Periodic Signals. . . . . . . . . . . . . . . . . . . . . . .
3.3.3. The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...................................
3.3.3.1. Convergence
3.3.3.2. Properties of the Fourier Transform . . . . . . . . . . . . . . . . . . . . .
3.3.4. The Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4.1. Interconnection of Systems in the Frequency Domain . . . . . . . . . .
3.3.4.2. Parseval’s Theorem for Continuous Signals. . . . . . . . . . . . . . . . . . . .
3.3.5. The Gibbs Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.6. Relationship between the Fourier Transform and the Fourier Series . . . . . . . .
3.3.6.1. Introduction.
...................................
3.3.6.2. Fourier Series Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.7. The Fourier Transform of a Periodic Signal . . . . . . . . . . . . . . . . . . . . . .
3.3.7.1. Periodic Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.7.2. The Poisson Sum Formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4. Lowpass-Equivalent Signals and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1. The Hilbert Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2. Properties of the Hilbert Transform . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3. Lowpass-Equivalent Modulated Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.4. Hilbert Transform in System Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...................................
3.4.4.1. Introduction.
3.4.4.2. Lowpass Equivalent of a Bandpass Filter . . . . . . . . . . . . . . . . . .
3.4.5. Practical Considerations in Modeling of Lowpass Equivalents for Simulation. . .
.......................................
3.4.5.1. Signals
3.4.5.2. Filters
.......................................
3.5. Sampling and Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.5.1. Impulse Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5.2. Sampling Theorem
.......................................
3.5.3. Multirate Sampling and Sampling Conversion . . . . . . . . . . . . . . . . . . . . .
3.5.4. Interpolation
.........................................
3.5.4.1. Introduction.
...................................
3.5.4.2. Interpolator Structures for Integer Upconversion. . . . . . . . . . . . . . . . . . .
3.5.4.3. Bandlimited and Windowed Bandlimited Interpolation . . . . . . . . . .
3.5.4.4. Linear Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.4.5. Spline Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6. Characterization of Linear Time-Invariant Systems Using the Laplace Transform. . . . .
3.6.1. The Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1.1. Introduction.
...................................
3.6.1.2. Convergence and Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2. Inverse Laplace Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3. Properties of the Laplace Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.4. Transfer or System Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.5. Interconnections of LTI Systems (Block Diagrams) . . . . . . . . . . . . . . . . . . . . .
3.6.6. Systems Characterized by Linear Constant-Coefficient Differential Equations. . .

3.7.

3.8.

3.9.
3.10.

3.6.6.1. Properties of the Transfer Function for Linear Constant-Coefficient
Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.6.2. 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. Convergence and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.1.2. Table of Simple z-Transforms . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.1.3. Properties of the z-Transform . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.1.4. Discrete Transfer or System Function . . . . . . . . . . . . . . . . . . . .
Fourier Analysis for Discrete-Time Systems . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.1. Introduction.
.........................................
3.8.2. The Discrete Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.3. The Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.4. Properties of the Discrete Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.4.1. Periodic or Circular Properties . . . . . . . . . . . . . . . . . . . . . . . .
3.8.4.2. The Periodic Time-Shift Property. . . . . . . . . . . . . . . . . . . . . . .
3.8.4.3. The Periodic or Circular Convolution . . . . . . . . . . . . . . . . . . . .
3.8.4.4. The Discrete Periodic Convolution Theorem . . . . . . . . . . . . . . . .
3.8.4.5. The Discrete Frequency Response . . . . . . . . . . . . . . . . . . . . . .
3.8.4.6. Relationship between the Bandwidth and the Duration of the
Impulse Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.4.7. Relationship between the Discrete Fourier Transform and the
z-Transform.
...................................
3.8.4.8. Increasing the Frequency Resolution of the Discrete Fourier
Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix: A Brief Summary of Some Transforms and Theorems Useful in
Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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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. LTI Filters: Description, Specification, and Approximation . . . . . . . . . . . . .
4.1.1.1. Filter Descriptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1.2. Continuous Classical Filters . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1.3. Frequency Transformations . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1.4. Lowpass Equivalents of Bandpass Filters Represented by Rational
Functions
.....................................
4.1.1.5. Filter Specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1.6. Approximating Continuous Structures in Discrete Time for
Simulation
....................................
4.1.2. Simulation of Filtering with Finite Impulse Response Filters . . . . . . . . . . . .
4.1.2.1. Simulation of FIR Filtering in the Time Domain . . . . . . . . . . . . .
4.1.2.1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2.1.2. Windowing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2.2. Simulation of FIR Filtering in the Frequency Domain . . . . . . . . . .
4.1.2.2.1. Difference between Periodic and Linear Convolution....
4.1.2.2.2. Linear Convolution for a Signal of Arbitrary Duration
via the FFT. . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2.2.3. The Overlap-and-Add (OA) Method. . . . . . . . . . . . . . . . .
4.1.2.2.4. The Overlap-and-Save (OS) Method. . . . . . . . . . . . . . . . .
4.1.2.2.5. Efficiency of the Linear Convolution via the FFT. . . . . . . .
4.1.2.2.6. Implications of Frequency-Domain FIR Filtering . . . . . .
4.1.2.3. Mapping of Continuous Filters into Discrete FIR Filters . . . . . . . . .
4.1.2.3.1. FIR Filters Defined in the Time Domain . . . . . . . . . . .
4.1.2.3.2. FIR Filters Defined in the Frequency Domain . . . . . . . .
4.1.2.4. Comparison of Time-Domain (Impulse Response) and

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Frequency-Domain (FFT) Implementations for FIR Filtering . . . . . .

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4.1.3. Simulation of Filtering with IIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3.1. Systems Characterized by Linear Constant-Coefficient Difference
Equations
.....................................
4.1.3.2. Structures of Recursive Discrete Filters Implemented in Simulation
Models
......................................
4.1.3.2.1. Direct-Form (Canonic) Realization. . . . . . . . . . . . . . . . . . .
4.1.3.2.2. The Cascade Interconnections of Biquadratic Canonic
Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3.2.3. The Parallel Realization . . . . . . . . . . . . . . . . . . . . .
4.1.3.3. Transformations between Continuous-Time and Discrete-Time Systems
Represented by Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3.3.1. Impulse-Invariant Transformation. . . . . . . . . . . . . . . .
4.1.3.3.2. The Bilinear Transformation. . . . . . . . . . . . . . . . . . .
4.1.3.3.3. Effect of Mapping on Lowpass-Equivalent Filters
Represented by Rational Functions. . . . . . . . . . . . . . .
4.1.3.3.4. Guide for Mapping Recursive Filters Specified in
Frequency Domain

........................

4.1.4. Effects of Finite Word Length in Simulation of Digital Filters . . . . . . . . . . .
4.1.4.1. Roundoff Noise in Simulations of IIR Filters. . . . . . . . . . . . . . . .
4.1.4.2. Roundoff Noise in Simulations of FIR Filters . . . . . . . . . . . . . . .
4.1.4.3. Effects of Quantization in Computation of the Fast Fourier
Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

into Discrete Signals and Systems for Simulation . . . . . . . . . . . . . . . . . . .
4.1.5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.5.2. A Guide to the Selection of the Proper Method of Filter Simulation. .
4.2. Time-Varying Linear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1. Examples of Time-Varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2.2. Time-Domain Description for Linear Time-Varying Systems . . . . . . . . . . . .
4.2.2.1. The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2.2. The Superposition Integral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3. Frequency-Domain Representations of Time-Varying Systems . . . . . . . . . . .
4.2.3.1. Two-Dimensional Frequency Response . . . . . . . . . . . . . . . . . . .
4.2.3.2. Bandwidth Relations in Time-Varying Systems . . . . . . . . . . . . . .
4.2.3.3. Sampling Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4. Properties of Linear Time-Varying Systems. . . . . . . . . . . . . . . . . . . . . . .
4.2.4.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4.2. Interconnections of Linear Time-Varying Systems. . . . . . . . . . . . . . . .
4.2.5. Models for LTV Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.5.1. Linear Differential Equation with Time-Varying Coefficients . . . . . .
4.2.5.2. Separable Models
................................
4.2.5.3. Tapped Delay-Line Channel Models . . . . . . . . . . . . . . . . . . . . .
4.3. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4. Appendix: Biquadratic Factors for Classical Filters . . . . . . . . . . . . . . . . . . . . . . .

References

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Chapter 5. Modeling and Simulation of Nonlinear Systems
5.1. Modeling Considerations for Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Memoryless Nonlinearities.
.....................................
5.2.1. Memoryless Baseband Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2. Estimating the Sampling Rate for Nonlinear Systems. . . . . . . . . . . . . . . . .
5.2.3. Memoryless Bandpass Nonlinearities: Analytically Based Models . . . . . . . . .

5.2.3.1. The Limiter Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3.2. Power Series Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4. Memoryless Bandpass Amplifiers: Empirically Based Models . . . . . . . . . . .
5.2.4.1. Description and Interpretation of AM/AM and AM/PM
Characteristics for Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4.2. Lowpass Equivalent of a Bandpass Amplifier . . . . . . . . . . . . . . .
5.2.4.3. Alternative Approaches to Defining AM/AM and AM/PM
Characteristics
..................................
5.2.4.4. Multiple Carriers and Intel-modulation Products . . . . . . . . . . . . . .
5.2.4.5. Setting the Operating Point of a Memoryless Nonlinearity. . . . . . . .
5.3. Nonlinearities with Memory (NLWM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1. NLWM Modeling I: Fitting Swept-Tone AM/AM and AM/PM
Measurements
........................................
5.3.1.1. The Poza–Sarokozy–Berger (PSB) Model. . . . . . . . . . . . . . . . . .
5.3.1.1.1. AM/AM Characteristics . . . . . . . . . . . . . . . . . . . . .
5.3.1.1.2. AM/PM Characteristics . . . . . . . . . . . . . . . . . . . . .
5.3.1.1.3. Combined Model . . . . . . . . . . . . . . . . . . . . . . . . .
................................
5.3.1.2. The Saleh Model
5.3.1.3. The Abuelma’atti Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2. NLWM Modeling II: Fitting Preset Structures . . . . . . . . . . . . . . . . . . . . .

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5.3.2.1. One Filter–One Nonlinearity (Two-Box) Models. . . . . . . . . . . . . .
5.3.2.1.1. Filter–Nonlinearity with Least-Squares Fit . . . . . . . . . .

5.3.2.1.2. Filter–Nonlinearity ARMA Model. . . . . . . . . . . . . . . . . .
5.3.2.1.3. Filter–Nonlinearity with Small-Signal Transfer Function. . .
5.3.2.1.4. Nonlinearity–Filter with Least-Squares Fit . . . . . . . . . .
5.3.2.2. Filter–Nonlinearity–Filter (Three-Box) Models. . . . . . . . . . . . . . .
5.3.2.2.1. Three-Box Model with Least-Squares Fit . . . . . . . . . . .
5.3.2.2.2. Three-Box Model with Specified Characteristics. . . . . . .
5.3.3. NLWM Modeling III: Analytical Models . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3.1. Volterra Series Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3.2. Polyspectral Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3.2.1. Nonlinearity–Filter Polyspectral Model . . . . . . . . . . . .
5.3.3.2.2. Filter–Nonlinearity Polyspectral Model . . . . . . . . . . . .
5.3.4. NLWM Modeling IV: Miscellaneous Models. . . . . . . . . . . . . . . . . . . . . .
5.3.4.1. Power-Dependent Transfer Function Model. . . . . . . . . . . . . . . . . . . .
5.3.4.2. Nonlinear Parametric Discrete-Time Models . . . . . . . . . . . . . . . .
5.3.4.3. Instantaneous Frequency Model. . . . . . . . . . . . . . . . . . . . . . . .
5.3.5. Setting the Operating Point for a Nonlinearity with Memory . . . . . . . . . . . .
5.4. Nonlinear Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1. Outline of Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2. Families of Numerical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2.1. Solution Using Explicit Methods . . . . . . . . . . . . . . . . . . . . . . .
5.4.2.2. Solution Using Implicit Methods . . . . . . . . . . . . . . . . . . . . . . .

5.4.2.2.1. Iterated Predictor–Corrector Method. . . . . . . . . . . . . . . . .
5.4.2.2.2. Root Finding Using Newton–Raphson Method . . . . . . .
5.4.3. Properties of Numerical Methods: Accuracy and Stability . . . . . . . . . . . . . .

5.4.3.1. Order of a Method: Computation of Local or Truncation Error. . . . . . .
5.4.3.2. Absolute Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.4. Computational Considerations: Methods of Quality Control . . . . . . . . . . . . . . . .
5.4.5. Application of Numerical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.5.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.5.2. Stand-Alone Model for a Traveling-Wave Semiconductor Amplifier. . .
5.5. Measurement Technique for Nonlinear Components . . . . . . . . . . . . . . . . . . . . . .
5.5.1. The Vector Network Analyzer Single-Tone Measurement . . . . . . . . . . . . . .
5.5.2. Dynamic AM/AM and AM/PM Measurement Techniques Using a
Periodically Modulated Signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.3. Time-Domain Measurement Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
................................................
5.6. Summary
References
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Chapter 6. Fundamentals of Random Variables and Random Processes
for Simulation
..............................................
6.1. Introduction
6.2. Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1. Basic Concepts, Definitions, and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1.2. Statistical Averages or Expected Values . . . . . . . . . . . . . . . . . . .
6.2.2. Multidimensional Random Variables (Random Vectors) . . . . . . . . . . . . . . .
6.2.3. Complex Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...........................................
6.3. Univariate Models

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6.3.1. Univariate Models–Discrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1.1. Uniform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1.2. Binomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1.3. Negative Binomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1.4. Poisson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2. Univariate Models—Continuous. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.1. Uniform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.2. Gaussian (Normal). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.3. Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.4. Gamma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.5. Rayleigh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.6. Chi-Square. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.7. Student’s t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.8. F Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2.9. Generalized Exponential. . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4. Multivariate Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1. Multinomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2. Multivariate Gaussian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2.1. Properties of the Multivariate Gaussian Distribution . . . . . . . . . . .
6.4.2.2. Moments of Multivariate Gaussian pdf. . . . . . . . . . . . . . . . . . .
6.5. Transformations (Functions) of Random Variables. . . . . . . . . . . . . . . . . . . . . . .
6.5.1. Scalar-Valued Function of One Random Variable . . . . . . . . . . . . . . . . . . .
6.5.1.1. Discrete Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1.2. Continuous Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.2. Functions of Several Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Special Case—Linear Transformation. . . . . . . . . . . . . . . . . . . .
6.5.2.2. Sum of Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.2.1.

6.5.2.3. Order Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.3. Nonlinear Transformations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.3.1. Moment-Based Techniques. . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.3.2. Monte Carlo Simulation Techniques . . . . . . . . . . . . . . . . . . . .
6.6. Bounds and Approximations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1. Chebyshev’s Inequality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.2. Chernoff Bound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.3. Union Bound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.4. Central Limit Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.5. Approximate Computation of Expected Values. . . . . . . . . . . . . . . . . . . . .

6.6.5.1. Series Expansion Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.5.2. Moments of Finite Sums of Random Variables. . . . . . . . . . . . . . .
6.6.5.3. Quadrature Approximations . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7. Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.1. Basic Definitions and Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.2. Methods of Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.2.1. Joint Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.2.2. Analytical Description Using Random Variables . . . . . . . . . . . . . . . . .
6.7.2.3. Average Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.2.4. Two or More Random Processes. . . . . . . . . . . . . . . . . . . . . . .
6.7.3. Stationarity, Time Averaging, and Ergodicity. . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.3.1. Time Averages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.3.2. Ergodicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.4. Correlation and Power Spectral Density Function of Stationary Random
Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6.7.4.1. Autocorrelation Function and Its Properties. . . . . . . . . . . . . . . . .

6.7.4.2. Cross-Correlation Function and Its Properties . . . . . . . . . . . . . . .
6.7.4.3. Power Spectral Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7.4.4. Lowpass and Bandpass Processes. . . . . . . . . . . . . . . . . . . . . . .
6.7.4.5. Power and Bandwidth Calculations. . . . . . . . . . . . . . . . . . . . . .
6.7.5. Cross-Power Spectral Density Function and Its Properties . . . . . . . . . . . . . .
6.7.6. Power Spectral Density Functions of Random Sequences . . . . . . . . . . . . . .
6.8. Random Process Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8.1. Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8.1.1. Independent Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8.1.2. Markov Sequences (First Order) . . . . . . . . . . . . . . . . . . . . . . .
6.8.1.3. Autoregressive and Moving Average (ARMA) Sequences . . . . . . . .
.................................
6.8.2. M-ary Digital Waveforms
6.8.2.1. Introduction.
...................................
6.8.2.2. Random Binary Waveform. . . . . . . . . . . . . . . . . . . . . . . . . . .
.......................................
6.8.3. Poisson Process
6.8.4. Shot Noise and Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8.4.1. Shot Noise
....................................
6.8.4.2. Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
......................................
6.8.5. Gaussian Process
6.8.5.1. Definition of a Gaussian Process . . . . . . . . . . . . . . . . . . . . . . .
6.8.5.2. Models of White and Bandlimited White Noise . . . . . . . . . . . . . .
6.8.5.3. Quadrature Representation of Bandpass (Gaussian) Signals . . . . . . .
6.9. Transformation of Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9.1. Response of Linear Time-Invariant Causal (LTIVC) System. . . . . . . . . . . . .
....................................
6.9.1.1. Stationarity
6.9.1.2. Probability Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9.1.3. Mean, Autocorrelation, and Power Spectral Density Functions . . . . .
...........................................
6.9.2. Filtering.
..........................................
6.9.3. Integration
6.9.4. Response of Nonlinear and Time-Varying Systems . . . . . . . . . . . . . . . . . .
6.9.4.1. Nonlinear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.9.4.2. Time-Varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10. Sampling of Stationary Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10.1. Sampling
...........................................

6.10.1.1. Sampling of Lowpass Random Processes . . . . . . . . . . . . . . . . .
6.10.1.2. Aliasing Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10.1.3. Sampling Rate for Simulations . . . . . . . . . . . . . . . . . . . . . . .
6.10.1.4. Sampling of Bandpass Random Process . . . . . . . . . . . . . . . . . .
6.10.2. Quantization
.........................................
6.10.2.1. Uniform Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.10.2.2. Nonuniform Quantizer . . . . . . . . . . . . . . . . . . . . . . . . . . . .
................................................
6.11. Summary
References
...............................................

335
335
336
337
338
338
339
340
340
340
340
342
344
344
345
346
346
346
348
350
351

352
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357
357
357
357
357
358
360
361
361
362
362
362
362
363
365
365
366
367
368
369
369

Chapter 7. Monte Carlo Simulation and Generation of Random Numbers
7.1. Principle of Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1. Definition of Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.2. Variations of Monte Carlo Simulation—Quasianalytical

Monte Carlo Simulation

..................................

371
371
373

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....................................
7.2. Random Number Generation
7.2.1. Generation of Uniform Random Numbers . . . . . . . . . . . . . . . . . . . . . . .
...........................
7.2.1.1. Wichman–Hill Algorithm
7.2.1.2. Marsaglia–Zaman Algorithm . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2. Methods of Generating Random Numbers from an Arbitrary pdf . . . . . . . . . .
7.2.2.1. Transform Method ( Analytical) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2.2. Transform Method (Empirical) . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2.3. Transform Method for Discrete Random Variables . . . . . . . . . . . .
7.2.2.4. Acceptance/Rejection Method of Generating Random Numbers . . . .
7.2.3. Generating Gaussian Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.2.3.1. Sum-of-12 Method
...............................
7.2.3.2. Box Müller Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3. Generating Independent Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . .
...................................
7.3.1. White Gaussian Noise
7.3.2. Random Binary Sequences and Random Binary Waveforms . . . . . . . . . . . .
7.3.3. Pseudorandom Binary Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.4. M-ary Pseudo noise Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4. Generation of Correlated Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.1. Correlated Gaussian Sequences: Scalar Case. . . . . . . . . . . . . . . . . . . . . . . .

7.4.1.1. Autoregressive Moving Average (ARMA) Models. . . . . . . . . . . . .
........................
7.4.2. Correlated Gaussian Vector Sequences . . . . . . . . . . . . . . . . . . . . . . . . .
...................................
7.4.2.1. Special Case
7.4.2.2. General Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.3. Correlated Non-Gaussian Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.1.2. Spectral Factorization Method.

7.5. Testing of Random Number Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5.1. Stationarity and Uncorrelatedness . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...................................
7.5.1.1. Introduction.

7.5.1.2. Durbin Watson Test for Correlation . . . . . . . . . . . . . . . . . . . . .
...................................
7.6. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References
...............................................
7.5.2. Goodness-of-Fit Tests.

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

Chapter 8. Modeling of Communication Systems: Transmitter
and Receiver Subsystems
8.1. Introduction
..............................................
8.2. Information Sources
.........................................
8.2.1. Analog Sources
.......................................
8.2.1.1. Single Test Tone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.1.2. Multiple Test Tones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.1.3. Filtered Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.1.4. Stored Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.2. Digital Sources.
.......................................
.....................................
8.3. Formatting/Source Coding
8.3.1. Analog-to-Digital (A/D) Conversion. . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.2. On Simulating the FSC Subsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4. Digital Waveforms: Baseband Modulation (I) . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5. Line Coding: Baseband Modulation (II). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5.1. Logical-to-Logical Mapping I: Binary Differential Encoding . . . . . . . . . . . .

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

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Contents

8.5.2. Logical-to-Logical Mapping II: Correlative Coding . . . . . . . . . . . . . . . . . .
8.5.3. Logical-to-Logical Mapping III: Miller Code. . . . . . . . . . . . . . . . . . . . . . . .
8.5.4. Logical-to-Real Mapping I: Non-Return to Zero (NRZ) Binary Signaling . . . .
8.5.5. Logical-to-Real Mapping II: NRZ M-ary Signaling (PAM) . . . . . . . . . . . . .
8.5.6. Logical-to-Real Mapping III: Return-to-Zero (RZ) Binary Signaling. . . . . . . .
8.5.7. Logical-to-Real Mapping IV: Biphase Signaling or Manchester Code . . . . . . .
8.5.8. Logical-to-Real Mapping V: Miller Code or Delay Modulation. . . . . . . . . . . . . . .
8.5.9. Logical-to-Real Mapping VI: Partial Response Signaling . . . . . . . . . . . . . .
8.6. Channel Coding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.6.1. Computational Load for Block Coding/Decoding. . . . . . . . . . . . . . . . . . . . . . . .
8.6.2. Computational Load for Convolutional Coding/Decoding . . . . . . . . . . . . . .
8.7. Radiofrequency and Optical Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.7.1. Analog Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.7.2. Digital Quadrature Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.7.2.1.
QPSK: Differential Quaternary Phase-Shift-Keying (DQSK). . . .
8.7.2.2. Multitone Modulation/OFDM. . . . . . . . . . . . . . . . . . . . . . . . .
8.7.3. Continuous Phase Modulation CPFSK, MSK, GMSK . . . . . . . . . . . . . . . .
8.7.3.1. Continuous Phase Modulation. . . . . . . . . . . . . . . . . . . . . . . . .
8.7.3.2. Continuous-Phase Frequency-Shift-Keying . . . . . . . . . . . . . . . . .
8.7.3.3. Minimum-Shift-Keying. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

421
421
422
423
423
423
423
425
425
428
431
433

8.7.3.4. Gaussian Minimum-Shift-Keying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

447

8.7.4. Coded Modulation.
.....................................
8.7.5. Modeling Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.8. Demodulation and Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.8.1. Coherent Demodulation
..................................
8.8.2. Noncoherent Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.8.2.1. Amplitude Demodulation. . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.8.2.2. Discriminator Detection of PM/FM Signals . . . . . . . . . . . . . . . .
8.8.2.3. PLL Demodulation of PM/FM Signals . . . . . . . . . . . . . . . . . . .
.................................................
8.9. Filtering
8.9.1. Filters for Spectral Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.9.2. Filters for Pulse Shaping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.9.3. Linear Minimum MSE Filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.9.4. Filters for Minimizing Noise and Distortion . . . . . . . . . . . . . . . . . . . . . .
8.9.5. Matched Filters
.......................................
8.9.6. Adaptive Filtering ( Equalization) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.9.6.1. Tap-Gain Adaptation for Minimizing MSE . . . . . . . . . . . . . . . . .
8.9.6.2. Covariance Matrix Inversion Method. . . . . . . . . . . . . . . . . . . . .
8.9.6.3. Simulation Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.9.7. Filters Specified by Simple Functions in the Frequency Domain . . . . . . . . . .
8.9.8. Tabular Filter for Masks and Measurements . . . . . . . . . . . . . . . . . . . . . .
...................................
8.10. Multiplexing/Multiple Access
8.10.1. Issues in the Simulation of Multiple-Access Methods. . . . . . . . . . . . . . . . . . .
8.10.1.1. SDMA and PDMA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.10.1.2. FDMA
.....................................
.....................................
8.10.1.3. TDMA
8.10.1.4. CDMA (Spread Spectrum Techniques) . . . . . . . . . . . . . . . . . .
8.11. Radiofrequency and Optical Carrier Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.................................
8.11.1. Radiofrequency Sources
8.11.2. Optical Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
............................................
8.12. Synchronization
8.12.1. Approaches to Including Synchronization in Simulation . . . . . . . . . . . . . . .

434

435
438
439
443
443
445
446
449
451
455

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480
481
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491
491
492
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Contents

8.12.2.
8.12.3.
8.12.4.
8.12.5.
8.12.6.
8.12.7.
8.12.8.

xxi

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 . . . . . . . . . . . . . . . . . . . . .
8.12.8.1. Modeling Considerations for the PLL . . . . . . . . . . . . . . . . . . . .
8.12.8.2. Stand-Alone PLL Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.12.8.3. Assembled PLL Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.12.8.4. The Phase-Locked Loop as a Phase Tracker . . . . . . . . . . . . . . . .
8.12.8.5. The Phase-Locked Loop as an FM Demodulator . . . . . . . . . . . . .
8.12.8.6. Effect of Delay on the Performance of the Assembled PLL Model. . .

8.13. Calibration of Simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.13.1. Introduction.
.........................................
8.13.2. Calibration of Signal-to-Noise Ratio or
for Digital S i g n a l i n g . . . . . . . .
8.13.2.1. Signal Power Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.13.2.2. Noise Power Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.13.2.3. Calibrating Signal-to-Noise Ratio and
................
8.14. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References
...............................................

500
502
504
506
510
513
514
514
515
522
528
529
531
534
534
535
535
538
538
539
540

Chapter 9. Communication Channels and Models
9.1. Fading and Multipath Channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9.1.1. Introduction.
.........................................
9.1.2. Shadow Fading.
.......................................
......................................
9.1.3. Multipath Fading
9.1.3.1. Lowpass-Equivalent Characterization of Multipath Channels . . . . . .
9.1.3.2. Statistical Characterization of Multipath Channels. . . . . . . . . . . . . . . .
9.1.3.3. Statistical Characterization of the Time-Variant Behavior. . . . . . . . . . .
9.1.3.4. Statistical Characterization: The WSSUS Model. . . . . . . . . . . . . .
9.1.3.4.1. The Delay Power Profile . . . . . . . . . . . . . . . . . . . . . . . .
9.1.3.4.2. The Spaced-Frequency Correlation Function. . . . . . . . . . . .
9.1.3.4.3. The Time-Varying Channel . . . . . . . . . . . . . . . . . . .
9.1.3.5. Structural Models for Multipath Fading Channels . . . . . . . . . . . . .
9.1.3.5.1. Diffuse Multipath Channel Model . . . . . . . . . . . . . . .
9.1.3.5.2. Statistical Tap-Gain Models. . . . . . . . . . . . . . . . . . . . .
9.1.3.5.3. Generation of Tap-Gain Processes . . . . . . . . . . . . . . .
9.1.3.6. Indoor Wireless Channels . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.1.3.6.1. Factory and Open-Plan-Building Model. . . . . . . . . . . .
9.1.3.6.2. Office Building Model. . . . . . . . . . . . . . . . . . . . . . . .
9.1.3.6.3 Ray-Tracing Prediction Model. . . . . . . . . . . . . . . . . . . .
9.1.3.7. Radio-Relay Line-of-Sight (LOS) Discrete Multipath Fading
Channel Model.
.................................
9.2. The Almost Free-Space Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1. Clear-Air Atmospheric (Troposphenc) Channel . . . . . . . . . . . . . . . . . . . .
9.2.2. The Rainy-Atmospheric Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.3. The Ionospheric Phase Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

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Contents

9.3. Conducting and Guided Wave Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.1. Rectangular Waveguide Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.2. The Fiber Optic Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
....................................
9.4. Finite-State Channel Models
9.4.1. Finite-State Memoryless Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4.2. Finite-State Models with Memory: Hidden Markov Models ( H M M ) . . . . . . . .
9.4.2.1. N-State Markov Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4.2.2. First-Order Markov Process . . . . . . . . . . . . . . . . . . . . . . . . . .
....................................
9.4.2.3. Stationarity
9.4.3. Types of Hidden Markov Models: Gilbert and Fritchman Model. . . . . . . . . . . .
9.4.4. Estimation of the Parameters of a Markov Model. . . . . . . . . . . . . . . . . . . . .
9.5. Methodology for Simulating Communication Systems Operating over
Fading Channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5.1. Waveform-Level Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5.2. Symbol-Level Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.................................
9.5.3. Speech Coder Simulation
................................................
9.6. Summary
9.7. Appendix Reference Models for Mobile Channels . . . . . . . . . . . . . . . . . . . . . . .
9.A.1. Reference Channel Models for GSM Applications . . . . . . . . . . . . . . . . . .
9.A.2. Reference Models for PCS Applications . . . . . . . . . . . . . . . . . . . . . . . .
9.A.3. Reference Channel Models for UMTS-IMT-2000 Applications. . . . . . . . . . . . . . .

9.A.3.1. Path Loss Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.A.3.1.1. Path Loss Model for Indoor Office Test Environment. . .
9.A.3.1.2. Path Loss Model for Outdoor-to-Indoor and
Pedestrian Test Environments . . . . . . . . . . . . . . . . .
9.A.3.1.3. Path Loss Model for Vehicular Test Environments . . . .
9.A.3.1.4. Decorrelation Length of the Long-Term Fading . . . . . .
9.A.3.2. Channel Impulse Response Model . . . . . . . . . . . . . . . . . . . . .

References

...............................................

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

Chapter 10. Estimation of Parameters in Simulation
10.1. Preliminaries
.............................................
10.1.1. Random Process Model: Stationarity and Ergodicity. . . . . . . . . . . . . . . . . . . .
10.1.2. Basic Notation and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.3. Quality of an Estimator: Bias, Variance, Confidence Interval,
and Time Reliability Product. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.3.1. Bias of an Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.3.2. Variance of an Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.3.3. Confidence Interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.3.4. Time–Reliability Product . . . . . . . . . . . . . . . . . . . . . . . . .
10.1.3.5. Normalized Measures . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2. Estimating the Average Level of a Waveform. . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.1. Form of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.2. Expected (Mean) Value of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.3. Variance of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.4. Mixture (Signal Plus Noise) Processes . . . . . . . . . . . . . . . . . . . . . . . .
10.2.5. Confidence Interval Conditioned on the Signal. . . . . . . . . . . . . . . . . . . . . .
10.3. Estimating the Average Power (Mean-Square Value) of a Waveform. . . . . . . . . . . . . . .
10.3.1. Form of the Estimator for Average Power . . . . . . . . . . . . . . . . . . . . . .

626
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626
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631
631
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10.3.2. Expected Value of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.3. Variance of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4. Estimating the Probability Density or Distribution Function of the Amplitude

10.5.

10.6.

10.7.
10.8.

of a Waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.1. The Empirical Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.2. The Empirical Probability Density Function—Histogram . . . . . . . . . . . . .
10.4.2.1. Form of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.2.2. Expectation of the Estimator . . . . . . . . . . . . . . . . . . . . . . .
10.4.2.3. Variance of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . .
Estimating the Power Spectral Density (PSD) of a Process. . . . . . . . . . . . . . . . . . . . .
10.5.1. Form of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.5.1.1. The Correlogram or Indirect Method . . . . . . . . . . . . . . . . . .
10.5.1.2. The Periodogram or Direct Method . . . . . . . . . . . . . . . . . . .
10.5.2. Modified Form of the Estimator: Windowing and Averaging. . . . . . . . . . . . . .
10.5.3. Expected Value of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.5.4. Variance of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.5.5. Some Considerations on Implementing PSD Estimators: Summary
of the Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.5.5.1. Welch Periodogram Procedure (Direct Method) . . . . . . . . . . . . . . .
10.5.5.2. Windowed Correlogram Procedure (Indirect Method) . . . . . . . .
Estimating Delay and Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6.1. Estimating Carrier Phase and Timing Synchronization in the
Noiseless Case
......................................
10.6.2. Block Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6.2.1. Block Delay Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6.2.2. Block Phase Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.6.3. Distribution of PLL-Based Phase and Timing Estimators . . . . . . . . . . . . .
10.6.3.1. Distribution of the Phase Estimator . . . . . . . . . . . . . . . . . . . .
10.6.3.2. Distribution of the Timing Estimator . . . . . . . . . . . . . . . . . . .
Visual Indicators of Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.7.1. Eye Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.7.2. Scatter Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References
..............................................

xxiii

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

Chapter 11. Estimation of Performance Measures from Simulation

11.1. Estimation of Signal-to-Noise Ratio

...............................
11.1.1. Derivation of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1.2. Form of the Estimator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1.3. Statistical Properties of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.1.4. Implementing the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2. Estimating Performance Measures for Digital Systems . . . . . . . . . . . . . . . . . . . .
11.2.1. Performance Characterization for Digital Systems and Run-Time
Implications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.2. A Conceptual Framework for Performance Estimation. . . . . . . . . . . . . . . . . . .
11.2.3. The Monte Carlo Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.3.1 Confidence Interval: Binomial Distribution . . . . . . . . . . . . . . .
11.2.3.2. Confidence Interval: Poisson Approximation. . . . . . . . . . . . . . . . . . .
11.2.3.3. Confidence Interval: Normal Approximation. . . . . . . . . . . . . . . . . . .

670
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673
673
675
678
679
683
686
688
691
691

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Contents

11.2.3.4.
11.2.3.5.
11.2.3.6.
11.2.3.7.

Mean and Variance of the Monte Carlo Estimator . . . . . . . . . .
Effect of Dependent Errors . . . . . . . . . . . . . . . . . . . . . . . .
Sequential Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . .
Estimation of Interval Measures . . . . . . . . . . . . . . . . . . . . .
11.2.3.7.1. Using a Generative Model. . . . . . . . . . . . . . . . . . .
11.2.3.7.2. Using a Descriptive Model . . . . . . . . . . . . . . . .

11.2.3.7.3. Interval Simulation . . . . . . . . . . . . . . . . . . . . .
11.2.4. Tail Extrapolation.
....................................
11.2.4.1. Form of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.4.2. Asymptotic Bias of the Estimator . . . . . . . . . . . . . . . . . . . .
11.2.4.3. Variance of the Estimator . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.4.4. Summary of the Simulation Procedure for Implementing Tail
Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.5. Importance Sampling
..................................
11.2.5.1. Formulating IS for Simulation Implementation . . . . . . . . . . . .
11.2.5.2. Properties of the Importance Sampling Estimator. . . . . . . . . . . . . .
11.2.5.3. Choosing Biasing Densities. . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.5.3.1. A Heuristic Approach . . . . . . . . . . . . . . . . . . .
11.2.5.3.2. A Formal Approach. . . . . . . . . . . . . . . . . . . . .
11.2.5.4. Stochastic Importance Sampling . . . . . . . . . . . . . . . . . . . . .
11.2.6. Efficient Simulation Using Importance Splitting . . . . . . . . . . . . . . . . . .
11.2.6.1. Introduction
.................................
11.2.6.2. Application of DPR-Based Splitting Simulation. . . . . . . . . . . . . . . .
11.2.7. Quasianalytical (Semianalytic) Estimation . . . . . . . . . . . . . . . . . . . . . .
11.2.7.1 General Scheme for the QA Method. . . . . . . . . . . . . . . . . . . . . .
11.2.7.2. QA Method for Binary Systems . . . . . . . . . . . . . . . . . . . . .
11.2.7.3. QA Method for Single-Dimensional Multiamplitude Modulation. . .
11.2.7.4. QA Method for QAM Modulation. . . . . . . . . . . . . . . . . . . .
11.2.7.5. QA Method for PSK Modulation . . . . . . . . . . . . . . . . . . . .
11.2.7.6. QA Techniques for Coded Systems with Hard-Decision
Decoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.7.6.1. Independent-Error Channel . . . . . . . . . . . . . . . .
11.2.7.6.2. Dependent-Error Channel . . . . . . . . . . . . . . . . .
11.2.7.7. QA Method for Convolutionally Coded Systems with

Soft-Decision Decoding

..........................

11.2.7.8. Incorporating Jitter in the QA Technique . . . . . . . . . . . . . . . .
11.2.7.9. Mixed QA Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...............................................
11.3. Summary

References

..............................................

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

Chapter 12. Four Case Studies
12.1. Case Study I: 64-QAM Equalized Line-of-Sight Digital Radio Link in a

Fading Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
........................................
12.1.1. Introduction
12.1.2. The System Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.2.1. The Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.2.2. Modulator
..................................
12.1.2.3. Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.2.4. The Transmitted Signal . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.2.5. The Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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12.1.2.6.
12.1.2.7.
12.1.2.8.
12.1.2.9.
12.1.2.10.

Receiver Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Demodulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Receiver Noise
...............................
Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The Detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12.1.3. The Selected Channel Snapshot Simulation . . . . . . . . . . . . . . . . . . . . .
12.1.3.1. Simulation Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12.1.3.2. Calibration Procedure

...........................

12.1.3.3. Estimation of Error Probability. . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.3.4. Selected Simulation Results. . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.4. The Stochastic Channel Sequence Simulation. . . . . . . . . . . . . . . . . . . . . . . . .
12.1.4.1. Stochastic Channel Sequence Generation. . . . . . . . . . . . . . . . . . . .
12.1.4.2. Evaluation of Error Probability: Fast Quasianalytical
Method 1 (FQA-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.4.3. Evaluation of Error Probability: Fast Quasianalytical
Method 2 (FQA-2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.4.4. Evaluation of Error Probability: The Moment Method
(Gaussian Quadrature) . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.4.5. Simulation Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.4.6. Evaluation of the Outage Probability . . . . . . . . . . . . . . . . . .
12.1.4.7. Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.1.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2. Case Study II: Phase Noise and Its Effect on Block-Coded Systems. . . . . . . . . . . . . .
........................................
12.2.1. Introduction
12.2.2. Analytical Formulation: Demodulated Signal . . . . . . . . . . . . . . . . . . . .
12.2.3. Quadrupling Loop Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2.4. Residual Phase Noise Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2.4.2. Calibrating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2.5. Residual Phase Noise Random Number Generator . . . . . . . . . . . . . . . . .
12.2.6. A Quasianalytical Generator for the Error Sequence . . . . . . . . . . . . . . . .
12.2.7. Postprocessing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2.8. Conclusions
........................................
12.3. Case Study III: Exploring the Effects of Linear and Nonlinear Distortions
and Their Interactions on MSK-Modulated Signals: A Visual Approach. . . . . . . . . .
........................................
12.3.1. Introduction
12.3.2. Linear Filter Distortions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2.1. Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2.2. Bandlimiting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2.3. Linear Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2.4. Parabolic Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2.5. Parabolic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2.6. Cubic Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2.7. Residual Amplitude and Phase . . . . . . . . . . . . . . . . . . . . . .
12.3.2.8. Combined Effects of Linear Filter Distortions . . . . . . . . . . . . .
12.3.3. Memoryless Nonlinear AM/AM and AM/PM Distortions . . . . . . . . . . . .
12.3.4. Nonlinear Filter Distortions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
........................................
12.3.5. Conclusions
12.4. Case Study IV: Performance Evaluation of a CDMA Cellular Radio System. . . . . . .
12.4.1. Introduction
........................................
12.4.2. Brief Description of a CDMA Cellular System . . . . . . . . . . . . . . . . . . .
12.4.3. Reverse Radio Link Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

770
771
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796
798
799
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802
803
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12.4.3.1. The Simulation Model of the Reverse Radio Link . . . . . . . . . .

12.4.3.1.1. The Transmitter . . . . . . . . . . . . . . . . . . . . . . .
12.4.3.1.2. The Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.3.1.3. The Receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.3.2. Simulation Run-Length Requirement . . . . . . . . . . . . . . . . . .
12.4.3.3. Simulation Runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.4. The Forward Radio Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.4.1. The Simulation Model of the Forward Radio L i n k . . . . . . . . . .
12.4.4.1.1. The Transmitter . . . . . . . . . . . . . . . . . . . . . . .
12.4.4.1.2. The Receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.4.2. QA Performance Evaluation of the Forward Link in a
Bursty Environment
............................
12.4.4.3. Simulation Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.5. Finite-State Channel Characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.5.1. HMM Parameter Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.5.2. Discrete Channel Modeling . . . . . . . . . . . . . . . . . . . . . . . .
12.4.5.2.1. The Reverse Link. . . . . . . . . . . . . . . . . . . . . . . .
12.4.5.2.2. The Forward Link. . . . . . . . . . . . . . . . . . . . . . . .
12.4.5.3. The Number of States . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.5.4. Probability Distribution of Error-Free Intervals . . . . . . . . . . . .
12.4.5.5. Probability Distribution of the Number of Errors in a Block . . . .
12.4.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.5. Appendix: Simulation of the Tap-Gain Functions for a Rayleigh Fading Channel. . . . . .
........................................
12A.1. Introduction
12A.2. Estimation of the Sampling Rates and Expansion Rates . . . . . . . . . . . . . . . .
12A.3. The Channel Shaping Filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12A.4. FIR Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12A.5. IIR Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12A.6. Comparison of IIR and FIR Filter Implementation . . . . . . . . . . . . . . . . .
12A.7. Sampling Rate Expansion and Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . .
References
..............................................

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

Problems and Projects
Chapter

3

..............................................

Chapter
Chapter

4
5

...............................................
...............................................

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

...............................................
...............................................
...............................................
...............................................
..............................................
..............................................

851
854
856
863
865
868
871
873
874

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. . . . . . . . . . . . . . . . . . . .

879
891
893
895

Appendixes
A.
B.
C.
D.

Contents

xxvii

E.

Chi-Square Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

897

.....................................................

899

Index

7KLVSDJHLQWHQWLRQDOO\OHIWEODQN

1
Introduction

The complexity of communication and signal processing systems has grown considerably
during the past decades. During the same time, the emergence of a variety of new technologies such as fast and inexpensive hardware for digital signal processing, fiber optics, integrated optical devices, and monolithic microwave integrated circuits has had significant
impact on the implementation of communication systems. While the growth in complexity of
communication systems increases the time and effort required for analysis and design, the
need to insert new technologies into commercial products quickly requires that the design be
done in a timely, cost-effective, and effort-free manner. These demands can be met only
through 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). These
computer-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 incorporates
analytical 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
communication systems.

1.1. Methods of Performance Evaluation
1.1.1. Introduction
The performance of communication systems can be evaluated using formula-based
calculations, waveform-level simulation, or through hardware prototyping and measurements.
(This classification is not meant to imply that the three methods are mutually exclusive;
indeed, the best approach is often one that combines all three.)
Formula-based techniques, which are based on simplified models, provide considerable
insight into the relationship between design parameters and system performance, and they are
useful 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

2

Chapter 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 of
designs is of course an accurate and credible method, and is useful during the later stages of
the 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 alternatives
may 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 actual
signals 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 environment for analysis and design of communication and signal-processing systems, an environment in which software models can be combined with hardware data and real signals to
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 simulation
techniques.
1.1.2. Hierarchical View

In a broad sense, the term “communication system” might refer to a global communication network, a geosynchronous communication satellite, a terrestrial microwave transmission 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 algorithm
implemented 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 various
layers 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 network
throughput, response time, and resource utilization are estimated as a function of network
parameters like processor speeds, buffer sizes at nodes, and link capacities. Network simulations are used to establish specifications for the processors, protocols, and the communication links.
Communication links deal with the transmission of information-bearing waveforms over
different types of communication channels (free space, cables, wires, optical fibers, etc.). For
digital 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

Introduction

3

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 filters
and 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 simulations
establish the specifications for implementation, and simulation at the implementation level is
used to provide behavioral models which are exported back to the link level. An example of a
behavioral model is the transfer function for a filter.
The focus of this book is on waveform-level simulation of communication links (middle
layer 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 the
simplified model of a “generic” digital communication system shown in Figure 1.2. This
model shows only a subset of the functional blocks in a typical digital communication system,

4

Chapter 1

Figure 1.2. Simulation example.

and for discussion purposes let us assume that we are interested in evaluating the error-rate
performance of this system as a function of the parameters of the filters (orders and bandwidths), the nonlinear amplifier (saturation level or peak power and operating point), and the
signal-to-noise ratios for the two Gaussian noise sources. We are assuming that the performance of the system is determined by the signal distortions introduced by the filters and the
nonlinear 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 interference, and the presence of noise before the nonlinearity leads to non-Gaussian and
nonadditive effects, which are very difficult to characterize and analyze. Some approximations can be made by neglecting the effects of the filter preceding the nonlinearity and by
combining the first noise source with the second noise source and treating the overall effect of
the two noise sources as additive and Gaussian. These and other simplifications, while useful

Introduction

5

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 and
the two noise processes).
2. Process these samples through models for the filter and the nonlinearity, and generate
sampled values of the output of the system.
3. Estimate the error rate by comparing the simulated values of the input sequence and
the 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 increasing
signal 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 performancesensitivity 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 the
waveform level also makes it easy to incorporate in a simulation the measured values of
device 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 one
imposes the top-level specifications such as information rate and performance objectives. The
performance of any communication system is governed by two important factors: the signalto-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 degradations are obtained using simpler models and educated guesses. For example, to calculate
SNR, 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 performance
objectives, then the design proceeds to the next phase. Otherwise, the topology of the
candidate designs might have to be changed (say, by adding a filter or changing the encoder/
decoder) and the distortion parameters must be modified.

6

Chapter 1

The next phase in the design is the development of detailed specification for subsystems
and 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 bandwidthsymbol time product of 0.7 (as opposed to an ideal lowpass filter with an allocation of 2.0 dB
for signal distortion for link budget calculation), then waveform-level simulation can be used
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 some
other component. Otherwise, additional savings will have to be sought from other components. Simulation is flexible and efficient and is often the only method available for
performing these tradeoff studies and establishing detailed specifications for hardware
development.
The initial step in hardware development involves the building and testing of critical
components/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 results
are 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 the
system using postulated characteristics of key components due to aging. The validated
simulation model can also be used during operational stages for trouble shooting and for
providing answers to “what if” scenarios.
Thus, simulation can play an important role at any point in the life cycle of a
communication system: at the conceptual definition stage, where top-level specifications are
derived; as an ongoing part of design and development, in concert with hardware development to finalize specifications and check the influence of an as-built subsystem on the system
performance as a whole; out to the operational scenario, where simulation can be used as a
trouble-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 weapons
systems.(8) An analog computer is a simulator of continuous systems composed of modular
components interconnected via a patchboard into a block diagram configuration representing
the system. The linear elements, such as integrators and adders, are realized using feedback
DC operational amplifiers. Nonlinear modules such as multipliers and trigonometric functions
were first realized by electromechanical servo systems and later by piecewise linear
approximations. 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 a
block diagram made up of components of the analog computer. By wiring the components

Introduction

7

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 the
analog 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 dynamic
range 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. These
simulation languages emulated the behavior of analog computers on a component-bycomponent basis. For example, a summer is replaced by the code for addition, and an integrator is replaced by an integration subroutine. The interconnections between the components
are specified by a block-oriented language just as the analog computer patchboard electrically
links analog computing components. Block-oriented simulation languages draw their motivation from the analog block diagram as a simple and convenient way of describing
continuous 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 techniques
and 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 and
designed 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 these
packages, simulations were performed on a mainframe or a super-minicomputer, and graphics
terminals were used to provide a limited amount of interactive preprocessing as well as
postprocessing.
Computer hardware and software technologies have since undergone significant changes. Powerful workstations and personal computers offer very friendly computing environments 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 userfriendly framework for simulation-based analysis and design of communication systems. The
current generation of simulation software packages (SPW,(22) COSSAP,(23) MATLAB/
SIMULINK(24) and others) offer interactive, graphical, and user-friendly frameworks for
developing simulation models in a hierarchical fashion using graphical block diagram
representations, and permit the user to configure and execute waveform-level simulations,
review the results of simulations, and perform design iterations. These tools also provide
database 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
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 current
generation of simulation frameworks, attention is now focused on important issues such as
modeling and simulation techniques, estimation of performance measures, and computational
efficiency, which are the subject matter of this book. We assume that the reader’s primary

8

Chapter 1

interest is in understanding modeling and simulation techniques, problem formulation, and
using simulations for analysis of proposed designs, and not in building simulation frameworks or tools as such. This book is intended to provide the conceptual underpinnings for
such 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 and
noise, processing these sampled values through discrete-time models of functional blocks in
those 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 major
aspects 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 of
theoretical considerations that are especially relevant to simulation. Nevertheless, since such
considerations are not our principal focus, this coverage is given in a condensed, review
fashion with adequate references for the reader who might want to explore the theory in
greater 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 general
concepts of modeling and modeling hierarchy, and the central notion of validation. This
chapter should be useful in acquiring the right mindset for those with relatively little
experience 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 simul