Simulation of Communication Systems
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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 simu-
lation 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 comple-
mentary section on related measurement techniques. As hinted above, perhaps the most
dramatic change in the communications/telecommunications industry since the first edition
has been the explosion of wireless services. In consequence, we have included a new chapter
on channel modeling, the bulk of which deals with multipath and fading channels, the 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 Mathe-
matica 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 poly-
spectral models in Section 5.3.3, as well as the material in Section 5.2.4.3, supplying several
of the related problems, and thoroughly reviewing Chapter 5. Chris Clark is also to 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 accom-
modated 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.
1.2.
1.3.
1.4.
1.5.
Methods of Performance Evaluation
1.1.1.
1.1.2.
Introduction.
Hierarchical View
Simulation Approach: Waveform-Level Simulation of Communication Systems.
The
Application
of
Simulation
to the
Design
of
Communication
Systems
Historical Perspective
Outline of the Book
References
Chapter 2. Simulation and Modeling Methodology
2.1.
2.2.
2.3.
Some General Remarks on Methodology
Methodology of Problem Solving for Simulation
Basic Concepts of Modeling
2.3.1.
2.3.2.
2.3.3.
2.3.4.
2.3.5.
System Modeling
Device Modeling
Random Process Modeling
Modeling Hypothetical Systems
Simulation with Hardware in the Loop
2.4.
2.5.
Performance Evaluation Techniques
Error Sources in Simulation
2.5.1.
2.5.2.
2.5.3.
2.5.4.
Errors in System Modeling
Errors in Device Modeling.
Errors in Random Process Modeling.
Processing Errors
2.6.
Validation
2.6.1.
2.6.2.
2.6.3.
Validating Models of Devices or Subsystems
Validating Random Process Models
Validating the System Model
2.7.
Simulation Environment and Software Issues
2.7.1.
2.7.2.
2.7.3.
2.7.4.
Features of the Software Environment
Components of the Software Environment
Hardware Environment
Miscellaneous
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2
3
5
6
8
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45
45
Contents
2.8.
2.9.
The Role of Simulation in Communication System Engineering
Summary
References
Chapter 3. Representation of Signals and Systems in Simulation: Analytic
Fundamentals
3.1.
3.2.
3.3.
3.4.
3.5.
Introduction to Deterministic Signals and Systems
3.1.1.
3.1.2.
3.1.3.
Continuous Signals
Discrete-Time Signals
Systems
3.1.3.1.
3.1.3.2.
Properties of Systems
Block Diagram Representation of Systems
Linear Time-Invariant Systems
3.2.1.
Continuous Linear Time-Invariant Systems
3.2.1.1.
3.2.1.2.
The Impulse Response
The Convolution Integral,
3.2.2.
Discrete Linear Time-Invariant Systems
3.2.2.1.
3.2.2.2.
The Impulse Response
Convolution Sum (Discrete Convolution)
Frequency-Domain Representation
3.3.1.
The Fourier Transform
3.3.1.1.
3.3.1.2.
The Impulse Response
The Convolution Integral.
3.3.2.
Frequency-Domain Representation of Periodic Continuous Signals.
3.3.2.1.
3.3.2.2.
The Fourier Series
Parseval’s Theorem for Periodic Signals
3.3.3.
The Fourier Transform
3.3.3.1.
3.3.3.2.
Convergence
Properties
of the
Fourier
Transform
3.3.4.
The Frequency Response
3.3.4.1.
3.3.4.2.
Interconnection of Systems in the Frequency Domain
Parseval’s Theorem for Continuous Signals
3.3.5.
3.3.6.
3.3.7.
The Gibbs Phenomenon
Relationship
between
the
Fourier
Transform
and the
Fourier
Series
3.3.6.1.
3.3.6.2.
Introduction.
Fourier Series Coefficients
The
Fourier
Transform
of a
Periodic
Signal
3.3.7.1.
3.3.7.2.
Periodic Convolution
The Poisson Sum Formula
Lowpass-Equivalent Signals and Systems
3.4.1.
3.4.2.
3.4.3.
3.4.4.
3.4.5.
The Hilbert Transform
Properties
of the
Hilbert
Transform
Lowpass-Equivalent Modulated Signals
Hilbert Transform in System Analysis
3.4.4.1.
3.4.4.2.
Introduction.
Lowpass Equivalent of a Bandpass Filter
Practical Considerations in Modeling of Lowpass Equivalents for Simulation. . .
3.4.5.1.
3.4.5.2.
Signals
Filters
Sampling and Interpolation
49
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xii
Contents
xiii
3.5.1.
3.5.2.
3.5.3.
3.5.4.
Impulse Sampling
Sampling Theorem
Multirate Sampling and Sampling Conversion
Interpolation
3.5.4.1.
3.5.4.2.
3.5.4.3.
3.5.4.4.
3.5.4.5.
Introduction.
Interpolator Structures for Integer Upconversion
Bandlimited
and
Windowed
Bandlimited
Interpolation
Linear Interpolation
Spline Interpolation
3.6.
3.7.
3.8.
3.9.
3.10.
Characterization of Linear Time-Invariant Systems Using the Laplace Transform
3.6.1.
3.6.2.
3.6.3.
3.6.4.
3.6.5.
3.6.6.
The Laplace Transform
3.6.1.1.
3.6.1.2.
Introduction.
Convergence and Stability
Inverse Laplace Transform.
Properties of the Laplace Transform
Transfer
or
System
Function.
Interconnections of LTI Systems (Block Diagrams)
Systems Characterized by Linear Constant-Coefficient Differential Equations. . .
3.6.6.1.
3.6.6.2.
Properties of the Transfer Function for Linear Constant-Coefficient
Differential
Equations.
Realizations of Rational Transfer Functions Using Biquadratic
Expansion.
3.6.7.
Frequency Response
Representation
of
Continuous
Systems
by
Discrete
Transfer
Functions
3.7.1.
The
z
-Transform
3.7.1.1.
3.7.1.2.
3.7.1.3.
3.7.1.4.
Convergence
and
Stability
Table
of
Simple
z
-Transforms
Properties of the
z
-Transform
Discrete
Transfer
or
System
Function
Fourier Analysis for Discrete-Time Systems
3.8.1.
3.8.2.
3.8.3.
3.8.4.
Introduction.
The Discrete Fourier Transform.
The
Fast
Fourier
Transform
Properties of the Discrete Fourier Transform
3.8.4.1.
3.8.4.2.
3.8.4.3.
3.8.4.4.
3.8.4.5.
3.8.4.6.
3.8.4.7.
3.8.4.8.
Periodic or Circular Properties
The Periodic Time-Shift Property.
The Periodic or Circular Convolution
The Discrete Periodic Convolution Theorem
The Discrete Frequency Response
Relationship between the Bandwidth and the Duration of the
Impulse Response
Relationship between the Discrete Fourier Transform and the
z-Transform.
Increasing the Frequency Resolution of the Discrete Fourier
Transform.
Summary
Appendix: A Brief Summary of Some Transforms and Theorems Useful in
Simulation
References
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90
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96
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106
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107
108
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112
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xiv
Contents
Chapter 4. Modeling and Simulation of Linear Time-Invariant and
Time-Varying Systems
4.1.
Modeling and Simulation of Linear Time-Invariant Systems
4.1.1.
4.1.2.
4.1.3.
4.1.4.
LTI Filters: Description, Specification, and Approximation
4.1.1.1.
4.1.1.2.
4.1.1.3.
4.1.1.4.
4.1.1.5.
4.1.1.6.
Filter Descriptions
Continuous Classical Filters
Frequency Transformations
Lowpass Equivalents of Bandpass Filters Represented by Rational
Functions
Filter Specifications
Approximating Continuous Structures in Discrete Time for
Simulation
Simulation of Filtering with Finite Impulse Response Filters
4.1.2.1.
4.1.2.2.
4.1.2.3.
4.1.2.4.
Simulation of FIR Filtering in the Time Domain
4.1.2.1.1.
4.1.2.1.2.
Introduction
Windowing
Simulation of FIR Filtering in the Frequency Domain
4.1.2.2.1.
4.1.2.2.2.
4.1.2.2.3.
4.1.2.2.4.
4.1.2.2.5.
4.1.2.2.6.
Difference between Periodic and Linear Convolution
Linear Convolution for a Signal of Arbitrary Duration
via the FFT
The Overlap-and-Add (OA) Method
The Overlap-and-Save (OS) Method
Efficiency of the Linear Convolution via the FFT
Implications
of
Frequency-Domain
FIR
Filtering
Mapping of Continuous Filters into Discrete FIR Filters
4.1.2.3.1.
4.1.2.3.2.
FIR Filters Defined in the Time Domain
FIR Filters Defined in the Frequency Domain
Comparison of Time-Domain (Impulse Response) and
Frequency-Domain (FFT) Implementations for FIR Filtering
Simulation of Filtering with IIR Filters
4.1.3.1.
4.1.3.2.
Systems Characterized by Linear Constant-Coefficient Difference
Equations
Structures of Recursive Discrete Filters Implemented in Simulation
Models
4.1.3.2.1.
4.1.3.2.2.
4.1.3.2.3.
Direct-Form (Canonic) Realization
The Cascade Interconnections of Biquadratic Canonic
Sections.
The Parallel Realization
4.1.3.3.
Transformations between Continuous-Time and Discrete-Time Systems
Represented by Rational Functions
4.1.3.3.1.
4.1.3.3.2.
4.1.3.3.3.
4.1.3.3.4.
Impulse-Invariant Transformation.
The Bilinear Transformation.
Effect of Mapping on Lowpass-Equivalent Filters
Represented by Rational Functions.
Guide for Mapping Recursive Filters Specified in
Frequency Domain
Effects
of
Finite
Word
Length
in
Simulation
of
Digital
Filters
4.1.4.1.
4.1.4.2.
4.1.4.3.
Roundoff Noise in Simulations of IIR Filters.
Roundoff Noise in Simulations of FIR Filters
Effects of Quantization in Computation of the Fast Fourier
Transform
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Contents
xv
4.1.5.
Summary of the Process of Mapping Continuous Signals and Systems
into Discrete Signals and Systems for Simulation
4.1.5.1.
4.1.5.2.
Introduction
A Guide to the Selection of the Proper Method of Filter Simulation. .
4.2.
4.3.
4.4.
Time-Varying
Linear
Systems.
4.2.1.
4.2.2.
4.2.3.
4.2.4.
4.2.5.
Examples
of
Time-Varying
Systems
Time-Domain Description for Linear Time-Varying Systems
4.2.2.1.
4.2.2.2.
The Impulse Response
The Superposition Integral
Frequency-Domain
Representations
of
Time-Varying
Systems
4.2.3.1.
4.2.3.2.
4.2.3.3.
Two-Dimensional
Frequency
Response
Bandwidth Relations in Time-Varying Systems
Sampling
Rate
Properties of Linear Time-Varying Systems.
4.2.4.1.
4.2.4.2.
Introduction
Interconnections of Linear Time-Varying Systems
Models for LTV Systems
4.2.5.1.
4.2.5.2.
4.2.5.3.
Linear
Differential
Equation
with
Time-Varying
Coefficients
Separable Models
Tapped
Delay-Line
Channel
Models
Summary
Appendix: Biquadratic Factors for Classical Filters
References
Chapter 5. Modeling and Simulation of Nonlinear Systems
5.1.
5.2.
5.3.
Modeling Considerations for Nonlinear Systems
Memoryless Nonlinearities.
5.2.1.
5.2.2.
5.2.3.
5.2.4.
Memoryless Baseband Nonlinearities
Estimating
the
Sampling
Rate
for
Nonlinear
Systems.
Memoryless
Bandpass
Nonlinearities:
Analytically
Based
Models
5.2.3.1.
5.2.3.2.
The
Limiter
Family
Power Series Model
Memoryless
Bandpass
Amplifiers:
Empirically
Based
Models
5.2.4.1.
5.2.4.2.
5.2.4.3.
5.2.4.4.
5.2.4.5.
Description and Interpretation of AM/AM and AM/PM
Characteristics for Simulation
Lowpass
Equivalent
of a
Bandpass
Amplifier
Alternative Approaches to Defining AM/AM and AM/PM
Characteristics
Multiple
Carriers
and
Intel-modulation
Products
Setting
the
Operating
Point
of a
Memoryless
Nonlinearity.
Nonlinearities
with
Memory
(NLWM).
5.3.1.
5.3.2.
NLWM Modeling I: Fitting Swept-Tone AM/AM and AM/PM
Measurements
5.3.1.1.
5.3.1.2.
5.3.1.3.
The
Poza–Sarokozy–Berger
(PSB)
Model.
5.3.1.1.1.
5.3.1.1.2.
5.3.1.1.3.
AM/AM Characteristics
AM/PM Characteristics . . .
Combined Model
The Saleh Model
The Abuelma’atti Model
NLWM
Modeling
II:
Fitting
Preset
Structures
182
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234
xvi
Contents
5.3.2.1.
5.3.2.2.
One
Filter–One
Nonlinearity
(Two-Box)
Models.
5.3.2.1.1.
5.3.2.1.2.
5.3.2.1.3.
5.3.2.1.4.
Filter–Nonlinearity
with
Least-Squares
Fit
Filter–Nonlinearity ARMA Model
Filter–Nonlinearity with Small-Signal Transfer Function. . .
Nonlinearity–Filter with Least-Squares Fit
Filter–Nonlinearity–Filter (Three-Box) Models.
5.3.2.2.1.
5.3.2.2.2.
Three-Box Model with Least-Squares Fit
Three-Box
Model
with
Specified
Characteristics.
5.3.3.
5.3.4.
5.3.5.
NLWM Modeling III: Analytical Models
5.3.3.1.
5.3.3.2.
Volterra Series Modeling
Polyspectral Models
5.3.3.2.1.
5.3.3.2.2.
Nonlinearity–Filter Polyspectral Model . . .
Filter–Nonlinearity Polyspectral Model
NLWM
Modeling
IV:
Miscellaneous
Models.
5.3.4.1.
5.3.4.2.
5.3.4.3.
Power-Dependent Transfer Function Model
Nonlinear Parametric Discrete-Time Models
Instantaneous Frequency Model.
Setting the Operating Point for a Nonlinearity with Memory
5.4.
5.5.
5.6.
Nonlinear
Differential
Equations
5.4.1.
5.4.2.
5.4.3.
5.4.4.
5.4.5.
Outline of Numerical Methods
Families of Numerical Methods
5.4.2.1.
5.4.2.2.
Solution Using Explicit Methods
Solution Using Implicit Methods
5.4.2.2.1.
5.4.2.2.2.
Iterated Predictor–Corrector Method
Root
Finding
Using
Newton–Raphson
Method
Properties of Numerical Methods: Accuracy and Stability
5.4.3.1.
5.4.3.2.
Order of a Method: Computation of Local or Truncation Error
Absolute Stability
Computational Considerations: Methods of Quality Control
Application of Numerical Methods
5.4.5.1.
5.4.5.2.
Introduction.
Stand-Alone Model for a Traveling-Wave Semiconductor Amplifier. . .
Measurement Technique for Nonlinear Components
5.5.1.
5.5.2.
5.5.3.
The Vector Network Analyzer Single-Tone Measurement
Dynamic AM/AM and AM/PM Measurement Techniques Using a
Periodically Modulated Signal.
Time-Domain Measurement Techniques
Summary .
References
234
234
235
235
236
236
236
237
237
237
245
246
249
252
252
253
255
256
257
257
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266
268
269
270
271
271
272
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275
277
280
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285
289
291
291
291
293
294
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297
Chapter 6. Fundamentals of Random Variables and Random Processes
for Simulation
6.1.
6.2.
6.3.
Introduction
Random Variables
6.2.1.
6.2.2.
6.2.3.
Basic Concepts, Definitions, and Notations
6.2.1.1.
6.2.1.2.
Introduction.
Statistical Averages or Expected Values
Multidimensional Random Variables (Random Vectors)
Complex Random Variables
Univariate Models
Contents
xvii
6.3.1.
Univariate Models–Discrete
6.3.1.1.
6.3.1.2.
6.3.1.3.
6.3.1.4.
Uniform
Binomial
Negative Binomial
Poisson
6.3.2.
Univariate Models—Continuous
6.3.2.1.
6.3.2.2.
6.3.2.3.
6.3.2.4.
6.3.2.5.
6.3.2.6.
6.3.2.7.
6.3.2.8.
6.3.2.9.
Uniform.
Gaussian (Normal)
Exponential
Gamma
Rayleigh
Chi-Square
Student’s
t.
F Distribution
Generalized Exponential
6.4.
Multivariate Models
6.4.1.
6.4.2.
Multinomial
Multivariate Gaussian
6.4.2.1.
6.4.2.2.
Properties of the Multivariate Gaussian Distribution
Moments of Multivariate Gaussian pdf
6.5.
Transformations (Functions) of Random Variables
6.5.1.
6.5.2.
6.5.3.
Scalar-Valued Function of One Random Variable
6.5.1.1.
6.5.1.2.
Discrete Case
Continuous Case
Functions of Several Random Variables
6.5.2.1.
6.5.2.2.
6.5.2.3.
Special Case—Linear Transformation
Sum of Random Variables
Order Statistics
Nonlinear Transformations
6.5.3.1.
6.5.3.2.
Moment-Based Techniques
Monte Carlo Simulation Techniques
6.6.
Bounds and Approximations
6.6.1.
6.6.2.
6.6.3.
6.6.4.
6.6.5.
Chebyshev’s Inequality
Chernoff Bound
Union Bound
Central Limit Theorem
Approximate Computation of Expected Values.
6.6.5.1.
6.6.5.2.
6.6.5.3.
Series Expansion Technique
Moments
of
Finite
Sums
of
Random
Variables.
Quadrature Approximations
6.7.
Random Processes
6.7.1.
6.7.2.
Basic Definitions and Notations
Methods of Description
6.7.2.1.
6.7.2.2.
6.7.2.3.
6.7.2.4.
Joint Distribution
Analytical Description Using Random Variables
Average Values
Two or More Random Processes
6.7.3.
Stationarity, Time Averaging, and Ergodicity
6.7.3.1.
6.7.3.2.
Time Averages
Ergodicity.
6.7.4.
Correlation and Power Spectral Density Function of Stationary Random
Processes
298
298
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299
299
300
300
301
301
302
302
303
303
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304
304
305
305
308
308
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313
313
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315
316
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318
318
320
321
321
322
323
326
326
328
328
328
329
330
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333
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xviii
Contents
6.7.4.1.
6.7.4.2.
6.7.4.3.
6.7.4.4.
6.7.4.5.
Autocorrelation Function and Its Properties.
Cross-Correlation Function and Its Properties
Power Spectral
Density
Lowpass and Bandpass Processes.
Power and Bandwidth Calculations.
6.7.5.
6.7.6.
Cross-Power Spectral Density Function and Its Properties
Power Spectral Density Functions of Random Sequences
6.8.
6.9.
6.10.
6.11.
Random Process Models
6.8.1.
6.8.2.
6.8.3.
6.8.4.
6.8.5.
Random Sequences
6.8.1.1.
6.8.1.2.
6.8.1.3.
Independent Sequences
Markov Sequences (First Order)
Autoregressive and Moving Average (ARMA) Sequences
M-ary Digital Waveforms
6.8.2.1.
6.8.2.2.
Introduction.
Random Binary Waveform.
Poisson Process
Shot Noise and Impulsive Noise
6.8.4.1.
6.8.4.2.
Shot Noise
Impulsive Noise
Gaussian Process
6.8.5.1.
6.8.5.2.
6.8.5.3.
Definition of a Gaussian Process
Models of White and Bandlimited White Noise
Quadrature Representation of Bandpass (Gaussian) Signals
Transformation of Random Processes
6.9.1.
6.9.2.
6.9.3.
6.9.4.
Response
of
Linear
Time-Invariant
Causal
(LTIVC)
System.
6.9.1.1.
6.9.1.2.
6.9.1.3.
Stationarity
Probability Distribution.
Mean, Autocorrelation, and Power Spectral Density Functions
Filtering.
Integration
Response of Nonlinear and Time-Varying Systems
6.9.4.1.
6.9.4.2.
Nonlinear Systems.
Time-Varying Systems
Sampling of Stationary Random Processes
6.10.1.
6.10.2.
Sampling
6.10.1.1.
6.10.1.2.
6.10.1.3.
6.10.1.4.
Sampling of Lowpass Random Processes
Aliasing Effect
Sampling Rate for Simulations
Sampling of Bandpass Random Process
Quantization
6.10.2.1.
6.10.2.2.
Uniform Quantization
Nonuniform
Quantizer
Summary
References
Chapter 7. Monte Carlo Simulation and Generation of Random Numbers
7.1.
Principle of Monte Carlo Simulation
7.1.1.
7.1.2.
Definition
of
Monte
Carlo
Simulation
Variations of Monte Carlo Simulation—Quasianalytical
Monte Carlo Simulation
335
335
336
337
338
338
339
340
340
340
340
342
344
344
345
346
346
346
348
350
351
352
354
357
357
357
357
357
358
360
361
361
362
362
362
362
363
365
365
366
367
368
369
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371
373
Contents
xix
7.2.
7.3.
7.4.
7.5.
7.6.
Random Number Generation
7.2.1.
7.2.2.
7.2.3.
Generation
of
Uniform
Random
Numbers
7.2.1.1.
7.2.1.2.
Wichman–Hill Algorithm
Marsaglia–Zaman Algorithm
Methods
of
Generating
Random
Numbers
from
an
Arbitrary
pdf .
7.2.2.1.
7.2.2.2.
7.2.2.3.
7.2.2.4.
Transform Method ( Analytical)
Transform Method (Empirical)
Transform Method for Discrete Random Variables
Acceptance/Rejection Method of Generating Random Numbers
Generating Gaussian Random Variables
7.2.3.1.
7.2.3.2.
Sum-of-12 Method
Box Müller Method
Generating Independent Random Sequences
7.3.1.
7.3.2.
7.3.3.
7.3.4.
White Gaussian Noise
Random
Binary
Sequences
and
Random
Binary
Waveforms
Pseudorandom Binary Sequences
M-
ary
Pseudo
noise
Sequences
Generation of Correlated Random Sequences
7.4.1.
7.4.2.
7.4.3.
Correlated Gaussian Sequences: Scalar Case
7.4.1.1.
7.4.1.2.
Autoregressive Moving Average (ARMA) Models.
Spectral Factorization Method.
Correlated Gaussian Vector Sequences
7.4.2.1.
7.4.2.2.
Special Case
General Case
Correlated Non-Gaussian Sequences
Testing of Random Number Generators
7.5.1.
Stationarity and Uncorrelatedness
7.5.1.1.
7.5.1.2.
Introduction.
Durbin Watson Test for Correlation
7.5.2.
Goodness-of-Fit Tests.
Summary
References
Chapter 8. Modeling of Communication Systems: Transmitter
and Receiver Subsystems
8.1.
8.2.
8.3.
8.4.
8.5.
Introduction
Information Sources
8.2.1.
8.2.2.
Analog Sources
8.2.1.1.
8.2.1.2.
8.2.1.3.
8.2.1.4.
Single Test Tone
Multiple Test Tones
Filtered Random Processes.
Stored
Experimental
Data
Digital Sources.
Formatting/Source Coding
8.3.1.
8.3.2.
Analog-to-Digital (A/D) Conversion.
On
Simulating
the FSC
Subsystem.
Digital
Waveforms:
Baseband
Modulation
(I)
Line
Coding:
Baseband
Modulation
(II).
8.5.1.
Logical-to-Logical
Mapping
I:
Binary
Differential
Encoding
373
374
376
376
377
377
379
380
381
383
383
383
384
384
385
386
389
392
393
393
395
397
397
398
399
400
400
400
401
402
405
406
407
411
411
412
412
413
413
413
414
414
416
417
420
420
xx
Contents
8.5.2.
8.5.3.
8.5.4.
8.5.5.
8.5.6.
8.5.7.
8.5.8.
8.5.9.
Logical-to-Logical Mapping II: Correlative Coding
Logical-to-Logical Mapping III: Miller Code
Logical-to-Real Mapping I: Non-Return to Zero (NRZ) Binary Signaling . . . .
Logical-to-Real Mapping II: NRZ M-ary Signaling (PAM)
Logical-to-Real
Mapping
III:
Return-to-Zero
(RZ)
Binary
Signaling.
Logical-to-Real Mapping IV: Biphase Signaling or Manchester Code
Logical-to-Real Mapping V: Miller Code or Delay Modulation
Logical-to-Real Mapping VI: Partial Response Signaling
8.6.
8.7.
8.8.
8.9.
8.10.
8.11.
8.12.
Channel Coding
8.6.1.
8.6.2.
Computational Load for Block Coding/Decoding
Computational Load for Convolutional Coding/Decoding
Radiofrequency and Optical Modulation
8.7.1.
8.7.2.
8.7.3.
8.7.4.
8.7.5.
Analog Modulation
Digital Quadrature Modulation
8.7.2.1.
8.7.2.2.
QPSK: Differential Quaternary Phase-Shift-Keying (DQSK). . . .
Multitone Modulation/OFDM.
Continuous Phase Modulation CPFSK, MSK, GMSK
8.7.3.1.
8.7.3.2.
8.7.3.3.
8.7.3.4.
Continuous Phase Modulation.
Continuous-Phase Frequency-Shift-Keying
Minimum-Shift-Keying.
Gaussian Minimum-Shift-Keying
Coded Modulation.
Modeling Considerations
Demodulation and Detection
8.8.1.
8.8.2.
Coherent Demodulation
Noncoherent Demodulation
8.8.2.1.
8.8.2.2.
8.8.2.3.
Amplitude Demodulation.
Discriminator Detection of PM/FM Signals
PLL Demodulation of PM/FM Signals
Filtering
8.9.1.
8.9.2.
8.9.3.
8.9.4.
8.9.5.
8.9.6.
8.9.7.
8.9.8.
Filters for Spectral Shaping
Filters for Pulse Shaping
Linear Minimum MSE Filters
Filters for Minimizing Noise and Distortion
Matched Filters
Adaptive Filtering ( Equalization)
8.9.6.1.
8.9.6.2.
8.9.6.3.
Tap-Gain Adaptation for Minimizing MSE
Covariance Matrix Inversion Method.
Simulation Considerations
Filters Specified by Simple Functions in the Frequency Domain
Tabular Filter for Masks and Measurements
Multiplexing/Multiple Access
8.10.1.
Issues in the Simulation of Multiple-Access Methods
8.10.1.1.
8.10.1.2.
8.10.1.3.
8.10.1.4.
SDMA and PDMA.
FDMA
TDMA
CDMA (Spread Spectrum Techniques)
Radiofrequency and Optical Carrier Sources
8.11.1.
8.11.2.
Radiofrequency Sources
Optical Sources
Synchronization
8.12.1.
Approaches to Including Synchronization in Simulation
421
421
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423
423
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425
425
428
431
433
434
435
438
439
443
443
445
446
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474
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479
480
481
483
484
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484
486
487
489
491
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492
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498
Contents
xxi
8.12.2.
8.12.3.
8.12.4.
8.12.5.
8.12.6.
8.12.7.
8.12.8.
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.
8.12.8.2.
8.12.8.3.
8.12.8.4.
8.12.8.5.
8.12.8.6.
Modeling Considerations for the PLL
Stand-Alone PLL Model
Assembled PLL Model
The
Phase-Locked
Loop
as a
Phase
Tracker
The
Phase-Locked
Loop
as an FM
Demodulator
Effect of Delay on the Performance of the Assembled PLL Model. . .
8.13.
8.14.
Calibration of Simulations
8.13.1.
8.13.2.
Introduction.
Calibration of Signal-to-Noise Ratio or for Digital Signaling
8.13.2.1.
8.13.2.2.
8.13.2.3.
Signal Power Level
Noise
Power
Level
Calibrating
Signal-to-Noise
Ratio
and
Summary
References
Chapter 9. Communication Channels and Models
9.1.
9.2.
Fading
and
Multipath
Channels.
9.1.1.
9.1.2.
9.1.3.
Introduction.
Shadow Fading.
Multipath Fading
9.1.3.1.
9.1.3.2.
9.1.3.3.
9.1.3.4.
9.1.3.5.
9.1.3.6.
9.1.3.7.
Lowpass-Equivalent
Characterization
of
Multipath
Channels
Statistical Characterization of Multipath Channels
Statistical Characterization of the Time-Variant Behavior.
Statistical Characterization: The WSSUS Model.
9.1.3.4.1.
9.1.3.4.2.
9.1.3.4.3.
The Delay Power Profile
The Spaced-Frequency Correlation Function
The Time-Varying Channel
Structural Models for Multipath Fading Channels
9.1.3.5.1.
9.1.3.5.2.
9.1.3.5.3.
Diffuse
Multipath
Channel
Model
Statistical Tap-Gain Models
Generation of Tap-Gain Processes
Indoor Wireless Channels
9.1.3.6.1.
9.1.3.6.2.
9.1.3.6.3
Factory and Open-Plan-Building Model
Office Building Model
Ray-Tracing Prediction Model
Radio-Relay Line-of-Sight (LOS) Discrete Multipath Fading
Channel Model.
The Almost Free-Space Channel
9.2.1.
9.2.2.
9.2.3.
Clear-Air
Atmospheric
(Troposphenc)
Channel
The Rainy-Atmospheric Channel
The Ionospheric Phase Channel
500
502
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506
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514
514
515
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538
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575
576
577
578
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583
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587
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589
xxii
Contents
9.3.
9.4.
9.5.
9.6.
9.7.
Conducting and Guided Wave Media
9.3.1.
9.3.2.
Rectangular Waveguide Medium
The Fiber Optic Channel
Finite-State Channel Models
9.4.1.
9.4.2.
9.4.3.
9.4.4.
Finite-State Memoryless Models
Finite-State Models with Memory: Hidden Markov Models (HMM)
9.4.2.1.
9.4.2.2.
9.4.2.3.
N-State Markov Model
First-Order Markov Process
Stationarity
Types of Hidden Markov Models: Gilbert and Fritchman Model. .
Estimation of the Parameters of a Markov Model
Methodology for Simulating Communication Systems Operating over
Fading Channels
9.5.1.
9.5.2.
9.5.3.
Waveform-Level Simulation
Symbol-Level Simulation
Speech Coder Simulation
Summary
Appendix Reference Models for Mobile Channels
9.A.1.
9.A.2.
9.A.3.
Reference Channel Models for GSM Applications
Reference Models for PCS Applications
Reference Channel Models for UMTS-IMT-2000 Applications
9.A.3.1.
9.A.3.2.
Path Loss Models
9.A.3.1.1.
9.A.3.1.2.
9.A.3.1.3.
9.A.3.1.4.
Path Loss Model for Indoor Office Test Environment. . .
Path Loss Model for Outdoor-to-Indoor and
Pedestrian Test Environments
Path Loss Model for Vehicular Test Environments
Decorrelation Length of the Long-Term Fading
Channel Impulse Response Model
References
Chapter 10. Estimation of Parameters in Simulation
10.1.
10.2.
10.3.
Preliminaries
10.1.1.
10.1.2.
10.1.3.
Random Process Model: Stationarity and Ergodicity
Basic Notation and Definitions
Quality of an Estimator: Bias, Variance, Confidence Interval,
and Time Reliability Product
10.1.3.1.
10.1.3.2.
10.1.3.3.
10.1.3.4.
10.1.3.5.
Bias of an Estimator
Variance of an Estimator
Confidence Interval
Time–Reliability Product
Normalized Measures
Estimating the Average Level of a Waveform.
10.2.1.
10.2.2.
10.2.3.
10.2.4.
10.2.5.
Form of the Estimator
Expected (Mean) Value of the Estimator
Variance of the Estimator
Mixture (Signal Plus Noise) Processes
Confidence Interval Conditioned on the Signal
Estimating the Average Power (Mean-Square Value) of a Waveform
10.3.1.
Form of the Estimator for Average Power
591
591
593
596
597
599
600
601
601
604
606
610
611
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613
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632
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635
636
637
Contents
xxiii
10.3.2.
10.3.3.
Expected Value of the Estimator
Variance of the Estimator
10.4.
10.5.
10.6.
10.7.
10.8.
Estimating the Probability Density or Distribution Function of the Amplitude
of a Waveform
10.4.1.
10.4.2.
The Empirical Distribution
The Empirical Probability Density Function—Histogram
10.4.2.1.
10.4.2.2.
10.4.2.3.
Form of the Estimator
Expectation of the Estimator
Variance
of the
Estimator
Estimating the Power Spectral Density (PSD) of a Process
10.5.1.
10.5.2.
10.5.3.
10.5.4.
10.5.5.
Form of the Estimator
10.5.1.1.
10.5.1.2.
The Correlogram or Indirect Method
The Periodogram or Direct Method
Modified Form of the Estimator: Windowing and Averaging
Expected Value of the Estimator
Variance of the Estimator
Some Considerations on Implementing PSD Estimators: Summary
of the Simulation Procedure
10.5.5.1.
10.5.5.2.
Welch Periodogram Procedure (Direct Method)
Windowed
Correlogram
Procedure
(Indirect
Method)
Estimating
Delay
and
Phase
10.6.1.
10.6.2.
10.6.3.
Estimating Carrier Phase and Timing Synchronization in the
Noiseless Case
Block
Estimators
10.6.2.1.
10.6.2.2.
Block Delay Estimator
Block Phase Estimator
Distribution
of
PLL-Based
Phase
and
Timing
Estimators
10.6.3.1.
10.6.3.2.
Distribution
of the
Phase
Estimator
Distribution
of the
Timing
Estimator
Visual
Indicators
of
Performance
10.7.1.
10.7.2.
Eye
Diagrams
Scatter Diagrams
Summary
References
Chapter 11. Estimation of Performance Measures from Simulation
11.1.
11.2.
Estimation of Signal-to-Noise Ratio
11.1.1.
11.1.2.
11.1.3.
11.1.4.
Derivation of the Estimator
Form of the Estimator
Statistical Properties of the Estimator
Implementing the Estimator
Estimating
Performance
Measures
for
Digital
Systems
11.2.1.
11.2.2.
11.2.3.
Performance Characterization for Digital Systems and Run-Time
Implications
A Conceptual Framework for Performance Estimation
The Monte Carlo Method
11.2.3.1
11.2.3.2.
11.2.3.3.
Confidence
Interval:
Binomial
Distribution
Confidence Interval: Poisson Approximation
Confidence Interval: Normal Approximation
637
638
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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
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670
673
673
675
678
679
683
686
688
691
691
xxiv
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.
11.2.3.7.2.
11.2.3.7.3.
Using a Generative Model
Using a Descriptive Model
Interval Simulation
11.2.4.
11.2.5.
11.2.6.
11.2.7.
Tail Extrapolation.
11.2.4.1.
11.2.4.2.
11.2.4.3.
11.2.4.4.
Form of the Estimator
Asymptotic Bias of the Estimator
Variance of the Estimator
Summary of the Simulation Procedure for Implementing Tail
Extrapolation
Importance Sampling
11.2.5.1.
11.2.5.2.
11.2.5.3.
11.2.5.4.
Formulating IS for Simulation Implementation
Properties of the Importance Sampling Estimator
Choosing Biasing Densities
11.2.5.3.1.
11.2.5.3.2.
A Heuristic Approach
A Formal Approach.
Stochastic Importance Sampling
Efficient Simulation Using Importance Splitting
11.2.6.1.
11.2.6.2.
Introduction
Application of DPR-Based Splitting Simulation
Quasianalytical (Semianalytic) Estimation
11.2.7.1
11.2.7.2.
11.2.7.3.
11.2.7.4.
11.2.7.5.
11.2.7.6.
11.2.7.7.
11.2.7.8.
11.2.7.9.
General Scheme for the QA Method
QA Method for Binary Systems
QA Method for Single-Dimensional Multiamplitude Modulation. . .
QA Method for QAM Modulation.
QA Method for PSK Modulation
QA Techniques for Coded Systems with Hard-Decision
Decoding
11.2.7.6.1.
11.2.7.6.2.
Independent-Error Channel
Dependent-Error Channel
QA Method for Convolutionally Coded Systems with
Soft-Decision Decoding
Incorporating Jitter in the QA Technique
Mixed QA Technique
11.3.
Summary
References
Chapter 12. Four Case Studies
12.1.
Case Study I: 64-QAM Equalized Line-of-Sight Digital Radio Link in a
Fading Environment
12.1.1.
12.1.2.
Introduction
The System Model
12.1.2.1.
12.1.2.2.
12.1.2.3.
12.1.2.4.
12.1.2.5.
The Source. . .
Modulator
Filters
The Transmitted Signal
The Channel
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