Simulation of
Communication Systems
Michel C. Jeruchim
GE Aerospace
Philadelphia, Pennsylvania
Philip Balaban
A T& T Bell Laboratories
Holmdel, New Jersey
K. Sam Shanmugan
University of Kansas
Lawrence, Kansas
and Cadence Design Systems
San Jose, California
PLENUM PRESS • NEW YORK AND LONDON
Contents
Chapter 1.
Introduction
1.1. Methods of Performance Evaluation
1.2. Simulation Approach
1.3. The Application of Simulation to the Design of Communication
Systems
1.4. Historical Perspective
1.5. Outline of the Book
References
Chapter 2.
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Representation of Signals and Systems in Simulation
2.1.
Introduction
2.1.1. Signals
2.1.1.1. Continuous Signals
2.1.1.2. Discrete-Time Signals
2.1.2. Systems
2.1.2.1. Properties of Systems
2.1.2.2. Block Diagram Representation of Systems
2.2. Linear Time-Invariant Systems
2.2.1. Continuous Linear Time-Invariant Systems
2.2.1.1. The Impulse Response
2.2.1.2. The Convolution Integral
2.2.1.3. Properties of the Convolution
2.2.2. Discrete Linear Time-Invariant Systems
2.2.2.1. The Impulse Response
2.2.2.2. Convolution Sum (Discrete Convolution)
2.2.2.3. Properties of the Discrete Convolution
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2.3.
Frequency Domain Representation
2.3.1. The Fourier Transform
2.3.2. Frequency Domain Representation of Periodic Continuous
Signals
2.3.2.1. The Fourier Series
2.3.2.2. Parseval's Theorem for Periodic Signals
2.3.3. The Fourier Transform
2.3.3.1. Convergence
2.3.3.2. Properties of the Fourier Transform
2.3.4. The Frequency Response
2.3.4.1. Interconnection of Systems in the Frequency
*-• _ Domain
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2.3.4.2. Parseval's Theorem for Continuous Signals
2.3.5. Gibbs' Phenomenon
2.3.6. Relationship between the Fourier Transform and the Fourier
Series
2.3.6.1. Fourier Series Coefficients
2.3.7. The Fourier Transform of a Periodic Signal
2.3.7.1. Periodic Convolution
2.3.7.2. The Poisson Sumation Formula
2.4. Low-Pass Equivalent Signals and Systems
2.4.1. The Hilbert Transform
2.4.2. Properties of the Hilbert Transform
2.4.3. Low-Pass Equivalent Modulated Signals
2.4.4. Hilbert Transform in System Analysis
2.4.5. Practical Considerations in Modeling of Low-Pass
Equivalents for Simulation
2.5. Sampling and Interpolation
2.5.1. Impulse Sampling
2.5.2. Sampling Theorem
2.5.2.1. Interpolation
2.5.2.2. Aliasing: The Effect of Undersampling
2.6. Characterization of LTI Systems Using the Laplace Transform
2.6.1. The Laplace Transform
2.6.1.1. Convergence and Stability
2.6.2. Inverse Laplace Transform
2.6.3. Properties of the Laplace Transform
2.6.4. Transfer or System Function
2.6.5. Interconnections of LTI Systems (Block Diagrams)
2.6.6. Systems Characterized by Linear Constant-Coefficient
Differential Equations
2.6.6.1. Properties of the Transfer Function for Linear
Constant-Coefficient Differential Equations
2.6.6.2. Realizations of Rational Transfer Functions Using
Biquadratic Expansion
2.6.7. Frequency Response
2.6.8. Low-Pass Equivalents of Bandpass Filters Represented by
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Contents
Rational Functions
2.6.9. Continuous Classical Filters
2.6.9.1. Frequency Transformation
2.6.9.2. Low-Pass Equivalent Classical Filters
2.7. Representation of Continuous Systems by Discrete Transfer
Functions
2.7.1. The z-Transform
2.7.1.1. Convergence and Stability
2.7.1.2. Table of Simple z-Transforms
2.7.1.3. Properties of the z-Transform
2.7.2. Systems Characterized by Linear Constant-Coefficient
-'. Difference Equations
2.7.2.1. Structures of Recursive Discrete Filters
Implemented in Simulation Models
2.7.2.2. The Cascade Interconnections of Biquadratic
Canonic Sections
2.7.2.3. The Parallel Realization
2.7.3. Transformations between Continuous Time and Discrete
Time Systems Represented by Rational Functions
2.7.3.1. Impulse Invariant Transformation
2.7.3.2. The Bilinear Transformation
2.7.3.3. Effect of Mapping on Low-Pass Equivalent Filters
Represented by Rational Functions
2.7.4. Finite Impulse Response (FIR) Discrete Systems
2.7.4.1. Modeling of FIR Filters
2.7.4.2. Windowing
2.7.4.3. Realization of FIR Filters
2.7.4.4. Discussion on FIR Filter Modeling
2.7.4.5. Note on FIR Filter Design
2.8. Fourier Analysis for Discrete-Time Systems
2.8.1. Introduction
2.8.2. The Discrete Fourier Transform
2.8.3. The Fast Fourier Transform (FFT)
2.8.4. Properties of the Discrete Fourier Transform
2.8.4.1. Periodic or Circular Properties
2.8.4.2. The Periodic Time-Shift Property
2.8.4.3. The Periodic or Circular Convolution
2.8.4.4. The Discrete Periodic Convolution Theorem
2.8.4.5. The Discrete Frequency Response
2.8.4.6. Relationship between the Bandwidth and the
Duration of the Impulse Response
2.8.4.7. Relationship between the DFT and the z-Transform
').-.
2.8.4.8. Increasing the Frequency Resolution of the DFT ..
2.8.5. Discrete Signal Processing (FIR Filtering)
}•/'
2.8.6. Frequency Domain FIR Filtering for Nonperiodic Signals ..
;/'"
2.8.6.1. Difference between Periodic and Linear
Convolution
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Contents
2.8.6.2.
Linear Convolution for a Signal of Arbitrary
Duration via the FFT,
2.8.6.3. The Overlap-and-Add (OA) Method
2.8.6.4. The Overlap-and-Save (OS) Method
2.8.6.5. Efficiency of the Linear Convolution via the FFT . .
2.8.7. Implications of Frequency Domain FIR Filtering
2.8.7.1. Block Processing Using the OA and OS Methods ..
2.8.7.2. Gibbs' Phenomenon Distortion
2.9. The Process of Mapping Continuous Signals and Systems into
Discrete Signals and Systems for Simulation
2.9.1. Preparation of Signals and Systems for Discrete Simulation
2.9.HL. Mapping of Continuous Filters into Discrete Filters
2.9.2.1. Finite-Impulse-Response (FIR) Filters
2.9.2.2. Infinite-Impulse-Response (IIR) Filters
2.9.3. Effects of Finite Word Length in Simulation of Digital
Filters
2.9.3.1. Roundoff Noise in Simulations of IIR Filters
2.9.3.2. Roundoff Noise in Simulations of FIR Filters
2.9.3.3. Effects of Quantization in Computation of the FastFourier Transform
2.9.4. A Guide to the Selection of the Proper Method for Filter
Simulation
2.10. Linear Time-Variant (LTV) Systems
2.10.1. The Impulse Response
2.10.1.1. Computation of the Superposition for LTV Systems
2.10.2. Computation of the Impulse Response for a Linear
Differential Equation with Time-Variant Coefficients
2.10.3. Properties of Linear Time-Variant Systems
2.10.3.1. Frequency-Domain Representation of Time-Variant
Systems
2.10.3.2. Bandwidth Relations in Time-Variant Systems
2.10.3.3. Sampling Rate
2.10.4. Models for LTV Systems
2.10.4.1. Separable Models
2.10.4.2. Discrete (Sampling) Models
2.10.5. Interconnections of Time-Variant Linear Systems
2.10.5.1. The Algebra of LTV Systems
2.10.5.2. The Feedback System
2.10.6. Interconnections of LTV Systems in the Frequency Domain
2.11. Nonlinear Systems
2.11.1. Introduction
2.11.2. Simulation of Nonlinear Systems
2.11.3. Estimating the Sampling Rate for Nonlinear Systems
2.11.4. Modeling Considerations for Nonlinear Systems
2.11.5. Block Models for Memoryless Nonlinearities
2.11.5.1. Memoryless Baseband Nonlinearities
2.11.5.2. Memoryless Bandpass Nonlinearities
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2.11.5.3. Low-Pass Equivalent of a Bandpass Nonlinearity ..
2.11.5.4. The Limiter Family
2.11.5.5. Setting the Operating Point of a Memoryless
Nonlinearity
2.11.6. Block Models for Nonlinearities with Memory
2.11.7. Analytical Approach to Block Models
2.11.7.1. Modeling a Memoryless Baseband Nonlinearity . . .
2.11.7.2. Modeling a Memoryless Bandpass Nonlinearity . . .
2.11.7.3. Baseband Nonlinearity with Memory—Volterra
Series Model
2.11.7.4. Bandpass Nonlinearities with Memory—Volterra
Series Model
2.11.8. Nonlinear Differential Equations
2.11.8.1. Introduction
2.11.8.2. Outline of Numerical Methods
2.11.8.3. Truncation Error of Integration Formulas
2.11.8.4. Stability of Integration Formulas
2.11.8.5. The Use of Implicit and Explicit
Integration Formulas in Simulation
2.11.8.6. Accuracy and Stability Control
2.11.8.7. Application of Numerical Methods
2.12. Summary
2.13. Appendix
2.14. Problems and Projects
References
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Chapter 3.
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Simulation of Random Variables
and Random Processes
3.1. Introduction
3.2. Random Variables
3.2.1. Basic Concepts, Definitions, and Notations
3.2.1.1. Averages
3.2.2. Multidimensional Random Variables (Random Vectors) . . . .
3.2.3. Complex Random Variables
3.3. Univariate Models
3.3.1. Univariate Models—Discrete
3.3.1.1. Uniform
3.3.1.2. Binomial
3.3.1.3. Negative Binomial
3.3.1.4. Poisson
3.3.2. Univariate Models—Continuous
3.3.2.1. Uniform
3.3.2.2. Gaussian (Normal)
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3.3.2.3. Exponential
3.3.2.4. Gamma
3.3.2.5. Rayleigh
3.3.2.6. Chi-Square
3.3.2.7. Student's t
3.3.2.8. F-Distribution
3.3.2.9. Generalized Exponential
3.4. Multivariate Models
3.4.1. Multinomial
3.4.2. Multivariate Gaussian
3.4.2.1. Properties of the Multivariate Gaussian
*"- '
Distribution
3.4.2.2. Moments of Multivariate Gaussian pdf
3.5. Transformations (Functions) of Random Variables
3.5.1. Scalar-Valued Function of One Random Variable
3.5.1.1. Discrete Case
3.5.1.2. Continuous Case
3.5.2. Functions of Several Random Variables
3.5.2.1. Special Case—Linear Transformation
3.5.2.2. Sum of Random Variables
3.5.2.3. Order Statistics
3.5.3. Nonlinear Transformations
3.5.3.1. Moment-Based Techniques
3.5.3.2. Monte Carlo Simulation Techniques
3.6. Bounds and Approximations
3.6.1. Chebyshev's Inequality
3.6.2. Chernoff Bound
3.6.3. Union Bound
3.6.4. Central Limit Theorem
3.6.5. Approximate Computation of Expected Values
3.6.5.1. Series Expansion Technique
3.6.5.2. Moments of Finite Sums of Random Variables
3.6.5.3. Quadrature Approximations
3.7. Random Processes
3.7.1. Basic Definitions and Notations
3.7.2. Methods of Description
3.7.2.1. Joint Distribution
3.7.2.2. Analytical Description using Random Variables....
3.7.2.3. Average Values
3.7.2.4. Two or More Random Processes
3.7.3. Stationarity, Time Averaging and Ergodicity
3.7.3.1. Time Averages
3.7.3.2. Ergodicity
3.7.4. Correlation and Power Spectral Density Function of
Stationary Random Processes
3.7.4.1. Autocorrelation Function and its Properties
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Contents
3.8.
3.9.
3.10.
3.11.
3.7.4.2. Cross-Correlation Function and its Properties
3.7.4.3. Power Spectral Density
3.7.4.4. Low-Pass and Bandpass Processes
3.7.4.5. Power and Bandwidth Calculations
3.7.5. Cross-Power Spectral Density Function and its Properties . . .
3.7.6. Power Spectral Density Functions of Random Sequences . . .
Random Process Models
3.8.1. Random Sequences
3.8.1.1. Independent Sequences
3.8.1.2. Markov Sequences
3.8.1.3. Autoregressive and Moving Average (ARMA)
Sequences
3.8.2. M-ary Digital Waveforms
3.8.2.1. Random Binary Waveform
3.8.3. Poisson Process
3.8.4. Shot (Impulse) Noise
3.8.5. Gaussian Process
3.8.5.1. Definition of a Gaussian Process
3.8.5.2. Models of White and Band-Limited White Noise . .
3.8.5.3. Quadrature Representation of Bandpass (Gaussian)
Signals
Transformation of Random Processes
3.9.1. Response of Linear Time-Invariant Causal (LTIVC) System
3.9.1.1. Stationarity
3.9.1.2. Probability Distribution
3.9.1.3. Mean, Autocorrelation, and Power Spectral Density
Functions
3.9.2. Filtering
3.9.3. Integration
3.9.4. Response of Nonlinear and Time-Varying Systems
3.9.4.1. Nonlinear Systems
3.9.4.2. Time-Varying Systems
Sampling and Quantizing
3.10.1. Sampling
3.10.1.1. Sampling of Low-Pass Random Processes
3.10.1.2. Aliasing Effect
3.10.1.3. Sampling Rate for Simulations
3.10.1.4. Sampling of Bandpass Random Process
3.10.2. Quantization
3.10.2.1. Uniform Quantizing
3.10.2.2. Nonuniform Quantizer
Computer Generation of Random Numbers and Sequences
3.11.1. Generation of Uniform Random Numbers
3.11.2. Methods of Generating Random Numbers from an Arbitrary
pdf
3.11.2.1. Transform Method (Analytical)
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3.11.2.2. Transform Method (Empirical)
3.11.2.3. Transform Method for Discrete Random Variables
3.11.2.4. Acceptance/Rejection Method of Generating
Random Numbers
3.11.3. Generating Gaussian Random Variables
3.11.4. Generating Independent Random Sequences
3.11.4.1. White Gaussian Noise
3.11.4.2. Random Binary Sequence and Random Binary
Waveform
3.11.4.3. Pseudorandom Binary Sequences
3.11.4.4. M-ary PN Sequences
3.11.5^ Generating Correlated Random Sequences
3.12. Testing of Random Number Generators
3.12.1. Stationarity and Uncorrelatedness
3.12.2. Goodness-of-Fit Tests
3.13. Summary
3.14. Problems and Projects
References
Chapter 4.
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Modeling of Communication Systems
4.1. Introduction
4.2. Radiofrequency and Optical Sources
4.2.1. Radiofrequency Sources
4.2.2. Optical Sources
4.3. Information Sources
4.3.1. Analog Signals
4.3.2. Digital Signals
4.4. Source Encoders/Decoders
4.4.1. Quantization
4.4.2. Differential Quantization
4.4.3. Encoding the Output of Discrete Information Sources
4.5. Baseband Modulation: Formatting; Line Coding
4.5.1. Logical-to-Logical Mapping I: Binary Differential Encoding
4.5.2. Logical-to-Logical Mapping II: Correlative Coding
4.5.3. Logical-to-Real Mapping I: Non-Return-to-Zero (NRZ)
Binary Signaling
4.5.4. Logical-to-Real Mapping II: NRZ M-ary Signaling (PAM)
4.5.5. Logical-to-Real Mapping III: Return-to-Zero (RZ) Binary
Signaling
4.5.6. Logical-to-Real Mapping IV: Biphase Signaling or
Manchester Code
4.5.7. Logical-to-Real Mapping V: Miller Code or Delay
Modulation
4.5.8. Logical-to-Real Mapping VI: Partial Response Signaling
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4.6.
4.7.
4.8.
4.9.
4.10.
4.11.
RF and Optical Modulation
4.6.1. Analog Modulation ,
4.6.2. Digital Quadrature Modulation
4.6.3. Continuous Phase Modulation (CPM): CPFSK; MSK
4.6.3.1. Continuous Phase Modulation
4.6.3.2. Continuous-Phase Frequency-Shift-Keying: CPFSK
4.6.3.3. Minimum-Shift-Keying: MSK
4.6.4. Some Implementation Notes
Demodulation
4.7.1. Coherent Demodulation
4.7.2. Noncoherent Demodulation
4.7.2.1. Amplitude Demodulation
4.7.2.2. Discriminator Detection of PM/FM Signals
4.7.2.3. PLL Demodulation of PM/FM Signals
Filtering
4.8.1. Filters for Spectral Shaping
4.8.2. Filters for Pulse Shaping
4.8.3. Linear Minimum MSE Filters
4.8.4. Filters for Minimizing Noise and Distortion
4.8.5. Matched Filters
4.8.6. Adaptive Filtering (Equalization)
4.8.7. Filters Specified by Simple Functions in the Frequency
Domain
4.8.8. Tabular Filters for Masks and Measurements
Communication Channels and Models
4.9.1. The Almost Free-Space Channel
4.9.1.1. Clear-Air Atmospheric (Tropospheric) C h a n n e l . . . .
4.9.1.2. The Rainy-Atmospheric Channel
4.9.1.3. The Ionospheric Phase Channel
4.9.2. Conducting and Guided Wave Media
4.9.2.1. Rectangular Waveguide Medium
4.9.2.2. The Fiber Optic Channel
4.9.3. Multipath Channels
4.9.3.1. Discrete Multipath
4.9.3.2. Diffuse Multipath
4.9.3.3. Combined Discrete and Diffuse Multipath
4.9.3.4. Specific Multipath Models: Radio-Relay Link;
Mobile Radio Link
4.9.3.5. Simulation of Multipath Channels
4.9.4. Discrete Channel Models
4.9.4.1. Memoryless Channel
4.9.4.2. Channels with Memory
Multiplexing/Multiple Access
4.10.1. Basic Principles
4.10.2. Issues in the Simulation of Multiple Access Methods
Noise and Interference
4.11.1. Thermal (Gaussian) Noise
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4.12.
4.13.
4.14.
4.15.
4.16.
4.17.
Contents
4.11.2. Impulsive Noise
4.11.3. Interference
:
Error Control Coding
4.12.1. Block Codes: General Principles
4.12.1.1. Block Encoders
4.12.2. Convolutional Codes: General Principles
4.12.2.1. Convolutional Encoders
4.12.3. Block Decoders
4.12.4. Soft Decision Decoding
4.12.5. Convolutional Decoders
4.12.6. Interleaving, Nonbinary Codes and Concatenation
4.f2:?. "Simulation of Coded Communication Links
Synchronization
4.13.1. Carrier Recovery—BPSK
4.13.2. The Phase-Locked Loop
4.13.3. Timing Recovery Scheme—BPSK
4.13.4. Carrier Recovery—QPSK
4.13.5. Timing Recovery—QPSK
Spread Spectrum Techniques
Coded Modulation
Summary
Problems and Projects
References
Chapter 5. Estimation of Performance Measures from Simulation
5.1. Preliminaries
5.1.1. Random Process Model: Stationarity and Ergodicity
5.1.2. Basic Notation and Definitions
5.1.3. Quality of an Estimator: Bias, Variance, Confidence Interval
and Time-Reliability Product
5.1.3.1. Bias of an Estimator
5.1.3.2. Variance of an Estimator
5.1.3.3. Confidence Interval
5.1.3.4. Time-Reliability Product
5.2. Estimating the Average Level of a Waveform
5.2.1. Form of the Estimator
5.2.2. Expected (Mean) Value of the Estimator
5.2.3. Variance of the Estimator
5.2.4. Mixture (Signal Plus Noise) Processes
5.2.5. Confidence Interval Conditioned on the Signal
5.3. Estimating the Average Power (Mean-Square Value) of a Waveform
5.3.1. Form of the Estimator for Average Power
Contents
5.4.
5.5.
5.6.
5.7.
5.3.2. Expected Value of the Estimator
5.3.3. Variance of the Estimator
Estimating the Signal-to-Noise Ratio (SNR)
5.4.1. Introduction
5.4.2. Form of the Estimator
5.4.3. Statistical Properties of the Estimator
5.4.4. Implementing the Estimator
Estimating the Probability Density or Distribution Function of the
Amplitude of a Waveform
5.5.1. The Empirical Distribution
5.5.2. The Empirical Probability Density Function—Histogram....
5.5.2.1. Form of the Estimator
5.5.2.2. Expectation of the Estimator
5.5.2.3. Variance of the Estimator
Estimating the Error Probability (Bit-Error-Rate) of a Digital
System
5.6.1. The Monte Carlo Method
5.6.1.1. Confidence Interval: Binomial Distribution
5.6.1.2. Confidence Interval: Poisson Approximation
5.6.1.3. Confidence Interval: Normal Approximation
5.6.1.4. Mean and Variance of Monte Carlo Estimator
5.6.1.5. Effect of Dependent Errors
5.6.2. Importance Sampling
5.6.2.1. Form of the Estimator
5.6.2.2. Choosing a Biased Density
5.6.2.3. Implementation of the Estimator
5.6.2.4. Bias of the Estimator
5.6.2.5. Variance (Time-Reliability Product) of the
Estimator
5.6.2.6. Some Considerations on Implementing and Using
Importance Sampling
5.6.3. Extreme Value Theory
5.6.4. Tail Extrapolation
5.6.4.1. Form of the Estimator
5.6.4.2. Asymptotic Bias of the Estimator
5.6.4.3. Variance of the Estimator
5.6.4.4. Summary of the Simulation Procedure for
Implementing Tail Extrapolation
5.6.5. Quasianalytical (Semianalytic) Estimation
5.6.5.1. Form of the Estimator and Computational
Procedure for Binary or Quaternary Systems with a
Generalized Exponential Distribution
5.6.5.2. Reliability of the Estimator
5.6.5.3. Some Considerations on Implementing QA
5.6.6. Summary and Comparison of BER Estimation Techniques . .
Estimating the Power Spectral Density (PSD) of a Process
5.7.1. Form of the Estimator
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Contents
5.7.1.1. The Correlogram, or Indirect Method
5.7.1.2. The Periodogram or Direct Method
5.7.2. Modified Form of the Estimator: Windowing and Averaging
5.7.3. Expected Value of the Estimator
5.7.4. Variance of the Estimator
5.7.5. Some Considerations on Implementing PSD Estimators:
Summary of the Simulation Procedure
5.7.5.1. Welch Periodogram Procedure (Direct Method) . . .
5.7.5.2. Windowed Correlogram Procedure (Indirect
Method)
5.8. .Visual Indicators of Performance and Related Bounds
5*8.1. Eye Diagrams
5.8.2. Scatter Diagrams
5.9. Summary
5.10. Problems and Projects
References
Chapter 6. Simulation and Modeling Methodology
6.1. Simulation Environment
6.1.1. Features of the Software Environment
6.1.2. Components of the Software Environment
6.1.3. Hardware Environment
6.1.4. Miscellaneous
6.2. Modeling Considerations
6.2.1. Basic Concepts of Modeling
6.2.2. Cascaded Linear Elements
6.2.3. Hardwired Synchronization: Phase and Timing Bias
6.2.4. Distribution of Phase and Timing Jitter Processes:
Replacement by a Single Approximately Equivalent Process
6.2.5. Effect of Synchronization Errors by Statistical Averaging.. ..
6.2.6. Estimating Initial Carrier and Symbol Synchronization
6.2.7. Block Estimator Structures
6.2.8. Simulation of Feedback Loops: Application to Phase-Locked
Carrier Tracking Loop and Phase-Locked Demodulator . . . .
6.2.8.1. Modeling Considerations
6.2.8.2. Stand-Alone PLL Model
6.2.8.3. Assembled PLL Model
6.2.8.4. The Phased-Locked Loop as a Phase Tracker
6.2.8.5. The Phase-Locked Loop as an FM Demodulator...
6.2.8.6. Effect of Delay on the Performance of the
Assembled PLL Model
6.2.9. Multirate Sampling
6.2.10. Simulating a Hypothetical System
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6.3. Performance Evaluation Techniques
6.3.1. Basic QA Technique t ,(QA-l)
6.3.1.1. Basic QA Technique for QAM Signals (QA-1.1) . . .
6.3.2. Mixed QA Technique (QA-2)
6.3.2.1. MQA Variation 1 (QA-2.1)
6.3.2.2. MQA Variation 2 (QA-2.2)
6.3.3. QA Technique for Coded Systems with Hard Decision
Decoding (QA-3)
6.3.3.1. Independent-Error Channel (Interleaving): Method
QA-ll
6.3.3.2. Dependent-Error Channel: Method QA-3.2
6.3.4. QA Technique for Convolutionally Coded Systems with
Soft-Decision Decoding (QA-4)
6.3.5. QA Technique for Speeding up Equalizer Convergence
(QA-5)
6.3.6. Simulation-Based Moment Evaluation for Analytic
Performance Evaluation (QA-6)
6.4. Error Sources in Simulation
6.4.1. Errors in System Modeling
6.4.2. Errors in Device Modeling
6.4.3. Errors in Random Process Modeling
6.4.4. Processing Errors
6.5. Validation
6.5.1. Validating Models of Devices
6.5.2. Validating Random Process Models
6.5.3. Validating the System Model
6.5.4. Concluding Remarks
6.6. The Role of Simulation in Communication System Engineering . . . .
6.7. Summary
6.8. Appendix: The "Equivalent Phase Noise" Process
6.9. Problems and Projects
References
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Chapter 7. Three Case Studies
7.1. Case Study I: 64-QAM Equalized Digital Radio Link in a Fading
Environment
7.1.1. Methods of Performance Evaluation Using Simulation
7.1.1.1. Selected Channel Snapshot Methodology
7.1.1.2. Stochastic Channel Sequence Methodology
7.1.2. The Channel Model
7.1.3. The Equalizer Model
7.1.3.1. The Stochastic Gradient Algorithm
7.1.3.2. Covariance Matrix Inversion
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Contents
7.1.4.
The System Model
7.1.4.1. Modulator
:
7.1.4.2. Filters
7.1.4.3. Demodulator
7.1.4.4. Equalizer
7.1.4.5. Detector
7.1.4.6. Synchronization
7.1.5. The Selected Channel Snapshot Simulation
7.1.5.1. Simulation Procedure
7.1.5.2. Calibration Procedure
7.1.5.3. Estimation of Error Probability
"•"- 7.1.5.4. Simulation Results
7.1.6. The Stochastic Channel Sequence Simulation
7.1.6.1. Evaluation of Error Probability
7.1.6.2. Simulation Procedure
7.1.6.3. Evaluation of the Performance of Digital Radio
Using the Stochastic Channel Simulation
7.1.6.4. Simulation Results
7.1.7. Conclusions
7.2. Case Study II: Lightwave Communications Link
7.2.1. Block Diagram
7.2.2. Photodetector Modeling
7.2.3. Tradeoff Studies
7.2.3.1. System Assumptions
7.2.3.2. Model Validation
7.2.3.3. Nonideal Rise-and Fall-Time Sensitivity
7.2.3.4. WDM and Optical Filtering
7.2.3.5. Effects of LED Center Wavelength Drift
7.2.3.6. Photodetector Comparison
7.2.3.7. Timing Jitter Effects
7.3. Case Study III: A Satellite System Example
7.3.1. Transponder Simulation Block Diagram
7.3.2. System Simulation Block Diagram
7.3.3. Tradeoff Studies
References
Appendixes
A. A Collection of Useful Results for the Error Probability of Digital
Systems
B. Gaussian Tail Probabilities Q(x) and an Approximation Q(x)
C. Coefficients of the Hermite Polynomials
D. Some Abscissas and Weights for Gaussian Quadrature Integration....
E. Chi-Square Probabilities
Index
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