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I. Introduction
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I. Introduction
by Kurt L. Kosbar, William H. Tranter, Theodore S. Rappaport, K. Sam Shanmugan
Principles of Communication Systems Simulation with Wireless Applications
Copyright
Dedication
Prentice Hall Communications Engineering and Emerging Technologies Series
Preface
Acknowledgments
I. Introduction
1. The Role of Simulation
1.1. Examples of Complexity
1.1.1. The Analytically Tractable System
1.1.2. The Analytically Tedious System
1.1.3. The Analytically Intractable System
1.2. Multidisciplinary Aspects of Simulation
1.3. Models
1.4. Deterministic and Stochastic Simulations
1.4.1. An Example of a Deterministic Simulation
1.4.2. An Example of a Stochastic Simulation
1.5. The Role of Simulation
1.5.1. Link Budget and System-Level Specification Process
1.5.2. Implementation and Testing of Key Components
1.5.3. Completion of the Hardware Prototype and Validation of the Simulation Model
1.5.4. End-of-Life Predictions
1.6. Software Packages for Simulation
1.7. A Word of Warning
1.8. The Use of MATLAB
1.9. Outline of the Book
1.10. Further Reading
2. Simulation Methodology
2.1. Introduction
2.2. Aspects of Methodology
2.2.1. Mapping a Problem into a Simulation Model
Hierarchical Representation
Partitioning and Conditioning
Simplifications and Approximations
2.2.2. Modeling of Individual Blocks
Lowpass Equivalent Representation
Sampling
Linear versus Nonlinear Models
Time Invariance
Memory
Time-Domain and Frequency-Domain Simulations
Block Processing
Variable Step-Size Processing
Parameterization
Interface to Other Blocks
2.2.3. Random Process Modeling and Simulation
Gaussian Approximation
Equivalent Process Representation
Slow versus Fast Processes
2.3. Performance Estimation
2.4. Summary
2.5. Further Reading
2.6. Problems
II. Fundamental Concepts and Techniques
3. Sampling and Quantizing
3.1. Sampling
3.1.1. The Lowpass Sampling Theorem
3.1.2. Sampling Lowpass Random Signals
3.1.3. Bandpass Sampling
The Bandpass Sampling Theorem
Sampling Direct/Quadrature Signals
3.2. Quantizing
Fixed-Point Arithmetic
Floating-Point Arithmetic
3.3. Reconstruction and Interpolation
3.3.1. Ideal Reconstruction
3.3.2. Upsampling and Downsampling
Upsampling and Interpolation
Downsampling (Decimation)
3.4. The Simulation Sampling Frequency
3.4.1. General Development
3.4.2. Independent Data Symbols
3.4.3. Simulation Sampling Frequency
3.5. Summary
3.6. Further Reading
3.7. References
3.8. Problems
4. Lowpass Simulation Models for Bandpass Signals and Systems
4.1. The Lowpass Complex Envelope for Bandpass Signals
4.1.1. The Complex Envelope: The Time-Domain View
4.1.2. The Complex Envelope: The Frequency-Domain View
4.1.3. Derivation of Xd(f) and Xq(f) from
4.1.4. Energy and Power
4.1.5. Quadrature Models for Random Bandpass Signals
4.1.6. Signal-to-Noise Ratios
4.2. Linear Bandpass Systems
4.2.1. Linear Time-Invariant Systems
4.2.2. Derivation of hd(t) and hq(t) from H(f)
4.3. Multicarrier Signals
4.4. Nonlinear and Time-Varying Systems
4.4.1. Nonlinear Systems
4.4.2. Time-Varying Systems
4.5. Summary
4.6. Further Reading
4.7. References
4.8. Problems
4.9. Appendix A: MATLAB Program QAMDEMO
4.9.1. Main Program: c4_qamdemo.m
4.9.2. Supporting Routines
qam.m
mary.m
4.10. Appendix B: Proof of Input-Output Relationship
5. Filter Models and Simulation Techniques
5.1. Introduction
5.2. IIR and FIR Filters
5.2.1. IIR Filters
5.2.2. FIR Filters
5.2.3. Synthesis and Simulation
5.3. IIR and FIR Filter Implementations
5.3.1. Direct Form II and Transposed Direct Form II Implementations
5.3.2. FIR Filter Implementation
5.4. IIR Filters: Synthesis Techniques and Filter Characteristics
5.4.1. Impulse-Invariant Filters
5.4.2. Step-Invariant Filters
5.4.3. Bilinear z-Transform Filters
Synthesis Technique
Special Case: Trapezoidal Integration
5.4.4. Computer-Aided Design of IIR Digital Filters
5.4.5. Error Sources in IIR Filters
5.5. FIR Filters: Synthesis Techniques and Filter Characteristics
5.5.1. Design from the Amplitude Response
5.5.2. Design from the Impulse Response
5.5.3. Implementation of FIR Filter Simulation Models
5.5.4. Computer-Aided Design of FIR Digital Filters
5.5.5. Comments on FIR Design
5.6. Summary
5.7. Further Reading
5.8. References
5.9. Problems
5.10. Appendix A: Raised Cosine Pulse Example
5.10.1. Main program c5_rcosdemo.m
5.10.2. Function file c5_rcos.m
5.11. Appendix B: Square Root Raised Cosine Pulse Example
5.11.1. Main Program c5_sqrcdemo.m
5.11.2. Function file c5_sqrc.m
5.12. Appendix C: MATLAB Code and Data for Example 5.11
5.12.1. c5_FIRFilterExample.m
5.12.2. FIR_Filter_AMP_Delay.m
5.12.3. shift_ifft.m
5.12.4. log_psd.m
6. Case Study: Phase-Locked Loops and Differential Equation Methods
6.1. Basic Phase-Locked Loop Concepts
6.1.1. PLL Models
6.1.2. The Nonlinear Phase Model
6.1.3. Nonlinear Model with Complex Input
6.1.4. The Linear Model and the Loop Transfer Function
6.2. First-Order and Second-Order Loops
6.2.1. The First-Order PLL
6.2.2. The Second-Order PLL
6.3. Case Study: Simulating the PLL
6.3.1. The Simulation Architecture
6.3.2. The Simulation
6.3.3. Simulation Results
6.3.4. Error Sources in the Simulation
The Analytical Model
The Simulation Model
6.4. Solving Differential Equations Using Simulation
6.4.1. Simulation Diagrams
6.4.2. The PLL Revisited
6.5. Summary
6.6. Further Reading
6.7. References
6.8. Problems
6.9. Appendix A: PLL Simulation Program
6.10. Appendix B: Preprocessor for PLL Example Simulation
6.11. Appendix C: PLL Postprocessor
6.11.1. Main Program
6.11.2. Called Routines
Script File ppplot.m
Function pplane.m
6.12. Appendix D: MATLAB Code for Example 6.3
7. Generating and Processing Random Signals
7.1. Stationary and Ergodic Processes
7.2. Uniform Random Number Generators
7.2.1. Linear Congruence
Technique A: The Mixed Congruence Algorithm
Technique B: The Multiplicative Algorithm With Prime Modulus
Technique C: The Multiplicative Algorithm with Nonprime Modulus
7.2.2. Testing Random Number Generators
Scatterplots
The Durbin-Watson Test
7.2.3. Minimum Standards
Lewis, Goodman, and Miller Minimum Standard
The Wichmann-Hill Algorithm
7.2.4. MATLAB Implementation
7.2.5. Seed Numbers and Vectors
7.3. Mapping Uniform RVs to an Arbitrary pdf
7.3.1. The Inverse Transform Method
7.3.2. The Histogram Method
7.3.3. Rejection Methods
7.4. Generating Uncorrelated Gaussian Random Numbers
7.4.1. The Sum of Uniforms Method
7.4.2. Mapping a Rayleigh RV to a Gaussian RV
7.4.3. The Polar Method
7.4.4. MATLAB Implementation
7.5. Generating Correlated Gaussian Random Numbers
7.5.1. Establishing a Given Correlation Coefficient
7.5.2. Establishing an Arbitrary PSD or Autocorrelation Function
7.6. Establishing a pdf and a PSD
7.7. PN Sequence Generators
7.8. Signal Processing
7.8.1. Input/Output Means
7.8.2. Input/Output Cross-Correlation
7.8.3. Output Autocorrelation Function
7.8.4. Input/Output Variances
7.9. Summary
7.10. Further Reading
7.11. References
7.12. Problems
7.13. Appendix A: MATLAB Code for Example 7.11
7.14. Main Program: c7_Jakes.m
7.14.1. Supporting Routines
Jakes_filter.m
linear_fft.m
log_psd.m
8. Postprocessing
8.1. Basic Graphical Techniques
8.1.1. A System Example—π/4 DQPSK Transmission
8.1.2. Waveforms, Eye Diagrams, and Scatter Plots
Eye Diagrams
8.2. Estimation
8.2.1. Histograms
8.2.2. Power Spectral Density Estimation
The Periodogram
The Periodogram With a Data Window
Segmented Periodograms
8.2.3. Gain, Delay, and Signal-to-Noise Ratios
Theoretical Development for Real Lowpass Signals
8.3. Coding
8.3.1. Analytic Approach to Block Coding
8.3.2. Analytic Approach to Convolutional Coding
8.4. Summary
8.5. Further Reading
8.6. References
8.7. Problems
8.8. Appendix A: MATLAB Code for Example 8.1
8.8.1. Main Program: c8_pi4demo.m
8.8.2. Supporting Routines
sigcon.m
dqeye.m
dqplot.m
9. Introduction to Monte Carlo Methods
9.1. Fundamental Concepts
9.1.1. Relative Frequency
9.1.2. Unbiased and Consistent Estimators
9.1.3. Monte Carlo Estimation
9.1.4. The Estimation of π
9.2. Application to Communications Systems—The AWGN Channel
9.2.1. The Binomial Distribution
9.2.2. Two Simple Monte Carlo Simulations
9.3. Monte Carlo Integration
9.3.1. Basic Concepts
9.3.2. Convergence
9.3.3. Confidence Intervals
9.4. Summary
9.5. Further Reading
9.6. References
9.7. Problems
10. Monte Carlo Simulation of Communication Systems
10.1. Two Monte Carlo Examples
10.2. Semianalytic Techniques
10.2.1. Basic Considerations
10.2.2. Equivalent Noise Sources
10.2.3. Semianalytic BER Estimation for PSK
10.2.4. Semianalytic BER Estimation for QPSK
10.2.5. Choice of Data Sequence
10.3. Summary
10.4. References
10.5. Problems
10.6. Appendix A: Simulation Code for Example 10.1
10.6.1. Main Program
10.6.2. Supporting Program: random_binary.m
10.7. Appendix B: Simulation Code for Example 10.2
10.7.1. Main Program
10.7.2. Supporting Programs
10.7.3. vxcorr.m
10.8. Appendix C: Simulation Code for Example 10.3
10.8.1. Main Program: c10_PSKSA.m
10.8.2. Supporting Programs
psk_berest
q.m
10.9. Appendix D: Simulation Code for Example 10.4
10.9.1. Supporting Programs
qpsk_berest
11. Methodology for Simulating a Wireless System
11.1. System-Level Simplifications and Sampling Rate Considerations
Sampling Rate
11.2. Overall Methodology
11.2.1. Methodology for Simulation of the Analog Portion of the System
Details of the Simulation Model
Pure Monte Carlo Approach to Performance Estimation
Semianalytic Approach to Performance Estimation
Faster Semianalytic Technique
Moment Method for BER Estimation
11.2.2. Summary of Methodology for Simulating the Analog Portion of the System
11.2.3. Estimation of the Coded BER
11.2.4. Estimation of Voice-Quality Metric
11.2.5. Summary of Overall Methodology
11.3. Summary
11.4. Further Reading
11.5. References
11.6. Problems
III. Advanced Models and Simulation Techniques
12. Modeling and Simulation of Nonlinearities
12.1. Introduction
12.1.1. Types of Nonlinearities and Models
12.1.2. Simulation of Nonlinearities—Factors to Consider
Sampling Rate
Cascading
Nonlinear Feedback Loops
Variable Sampling Rate and Interpolation
12.2. Modeling and Simulation of Memoryless Nonlinearities
12.2.1. Baseband Nonlinearities
12.2.2. Bandpass Nonlinearities—Zonal Bandpass Model
12.2.3. Lowpass Complex Envelope (AM-to-AM and AM-to-PM) Models
Analytical Derivation of AM–to-AM and AM-to-PM Characteristics
Measurement of AM-to-AM and AM-to-PM Characteristics
Analytical Forms of AM-to-AM and AM-to-PM Characteristics
12.2.4. Simulation of Complex Envelope Models
12.2.5. The Multicarrier Case
The Multicarrier Model
Intermodulation Distortion in Multicarrier Systems
12.3. Modeling and Simulation of Nonlinearities with Memory
12.3.1. Empirical Models Based on Swept Tone Measurements
Poza’s Model
Saleh’s Model
12.3.2. Other Models
12.4. Techniques for Solving Nonlinear Differential Equations
12.4.1. State Vector Form of the NLDE
12.4.2. Recursive Solutions of NLDE-Scalar Case
Explicit Techniques
Implicit Techniques
Implicit Solution Using the Predictor-Corrector Method
Implicit Solution Using Newton-Raphson Method
12.4.3. General Form of Multistep Methods
12.4.4. Accuracy and Stability of Numerical Integration Methods
Accuracy
Stability
12.4.5. Solution of Higher-Order NLDE-Vector Case
12.5. PLL Example
12.5.1. Integration Methods
Forward Euler (Explicit Method)
Backward Euler (Implicit Method with Predictor-Corrector)
Backward Euler (Implicit Method with N-R Iterations)
12.6. Summary
12.7. Further Reading
12.8. References
12.9. Problems
12.10. Appendix A: Saleh’s Model
12.11. Appendix B: MATLAB Code for Example 12.2
12.11.1. Supporting Routines
13. Modeling and Simulation of Time-Varying Systems
13.1. Introduction
13.1.1. Examples of Time-Varying Systems
13.1.2. Modeling and Simulation Approach
13.2. Models for LTV Systems
13.2.1. Time-Domain Description for LTV System
13.2.2. Frequency Domain Description of LTV Systems
13.2.3. Properties of LTV Systems
Associative Property
Commutative Property
Distributive Property
13.3. Random Process Models
13.4. Simulation Models for LTV Systems
13.4.1. Tapped Delay Line Model
Simplification of the TDL Model
Generation of Tap Gain Processes
13.5. MATLAB Examples
13.5.1. MATLAB Example 1
13.5.2. MATLAB Example 2
13.6. Summary
13.7. Further Reading
13.8. References
13.9. Problems
13.10. Appendix A: Code for MATLAB Example 1
13.10.1. Supporting Program
13.11. Appendix B: Code for MATLAB Example 2
13.11.1. Supporting Routines
13.11.2. mpsk_pulses.m
14. Modeling and Simulation of Waveform Channels
14.1. Introduction
14.1.1. Models of Communication Channels
14.1.2. Simulation of Communication Channels
14.1.3. Discrete Channel Models
14.1.4. Methodology for Simulating Communication System Performance
14.1.5. Outline of Chapter
14.2. Wired and Guided Wave Channels
14.3. Radio Channels
14.3.1. Tropospheric Channel
14.3.2. Rain Effects on Radio Channels
14.4. Multipath Fading Channels
14.4.1. Introduction
14.4.2. Example of a Multipath Fading Channel
14.4.3. Discrete Versus Diffused Multipath
14.5. Modeling Multipath Fading Channels
14.6. Random Process Models
14.6.1. Models for Temporal Variations in the Channel Response (Fading)
14.6.2. Important Parameters
Multipath Spread
Doppler Bandwidth
14.7. Simulation Methodology
14.7.1. Simulation of Diffused Multipath Fading Channels
Special Cases
Sampling
Generation of Tap Gain Processes
Delay Power Profiles and Doppler Power Spectral Densities
Correlated Tap Gain Model
14.7.2. Simulation of Discrete Multipath Fading Channels
Uniformly Spaced TDL Model for Discrete Multipath Fading Channels
14.7.3. Examples of Discrete Multipath Fading Channel Models
Rummler’s Model for LOS Terrestrial Microwave Channels
Models for Mobile Channels
Discrete Channel Models for GSM Applications
Discrete Models for PCS Applications
Discrete Multipath Channel Models for 3G Wideband CDMA Systems
14.7.4. Models for Indoor Wireless Channels
14.8. Summary
14.9. Further Reading
14.10. References
14.11. Problems
14.12. Appendix A: MATLAB Code for Example 14.1
14.12.1. Main Program
14.12.2. Supporting Functions
14.13. Appendix B: MATLAB Code for Example 14.2
14.13.1. Main Program
14.13.2. Supporting Functions
jakes_filter.m
linear_psd.m
15. Discrete Channel Models
15.1. Introduction
15.2. Discrete Memoryless Channel Models
15.3. Markov Models for Discrete Channels with Memory
15.3.1. Two-State Model
15.3.2. N-state Markov Model
15.3.3. First-Order Markov Process
15.3.4. Stationarity
15.3.5. Simulation of the Markov Model
15.4. Example HMMs—Gilbert and Fritchman Models
15.5. Estimation of Markov Model Parameters
15.5.1. Scaling
15.5.2. Convergence and Stopping Criteria
15.5.3. Block Equivalent Markov Models
15.6. Two Examples
15.7. Summary
15.8. Further Reading
15.9. References
15.10. Problems
15.11. Appendix A: Error Vector Generation
15.11.1. Program: c15_errvector.m
15.11.2. Program: c15_hmmtest.m
15.12. Appendix B: The Baum-Welch Algorithm
15.13. Appendix C: The Semi-Hidden Markov Model
15.14. Appendix D: Run-Length Code Generation
15.15. Appendix E: Determination of Error-Free Distribution
15.15.1. c15_intervals1.m
15.15.2. c15_intervals2.m
16. Efficient Simulation Techniques
16.1. Tail Extrapolation
16.2. pdf Estimators
16.3. Importance Sampling
16.3.1. Area of an Ellipse
Monte Carlo Estimators Revisited
Selecting Bounding Boxes for MC Simulations
Optimal Bounding Regions
Nonuniform pdfs and Weighting Functions
16.3.2. Sensitivity to the pdf
16.3.3. A Final Twist
16.3.4. The Communication Problem
16.3.5. Conventional and Improved Importance Sampling
16.4. Summary
16.5. Further Reading
16.6. References
16.7. Problems
16.8. Appendix A: MATLAB Code for Example 16.3
16.8.1. Supporting Routines
cgpdf.m
17. Case Study: Simulation of a Cellular Radio System
17.1. Introduction
17.2. Cellular Radio System
17.2.1. System-Level Description
17.2.2. Modeling a Cellular Communication System
Trunking and Grade of Service
Channel Model
Sectorized Cells
Total Co-Channel Interference
Effects of Sectoring
17.3. Simulation Methodology
17.3.1. The Simulation
Definition of the Target System to Be Simulated
Propagation characteristics (channel parameters)
Locations of co-channel cells
Generation of Snapshots of Mobiles’ Locations and Computation of SIR
Step 1: A mobile is placed within each cell
Step 2: Determination of the distances between mobiles and base stations
Step 3: Determination of the statistics of SIR on both links
17.3.2. Processing the Simulation Results
Outage Probability
System Performance over the Cell Area
17.4. Summary
17.5. Further Reading
17.6. References
17.7. Problems
17.8. Appendix A: Program for Generating the Erlang B Chart
17.9. Appendix B: Initialization Code for Simulation
17.10. Appendix C: Modeling Co-Channel Interference
17.10.1. Wilkinson’s Method
17.10.2. Schwartz and Yeh’s Method
17.11. Appendix D: MATLAB Code for Wilkinson’s Method
18. Two Example Simulations
18.1. A Code-Division Multiple Access System
18.1.1. The System
18.1.2. The Simulation Program
18.1.3. Example Simulations
Baseline Validation
Performance as a Function of Eb/N0 and the Ricean K-factor
18.1.4. Development of Markov Models
Program 1: c18_cdmahmm1.m
Program 2: c18_cdmahmm2.m
Program 3: c18_cdmahmm3
18.2. FDM System with a Nonlinear Satellite Transponder
18.2.1. System Description and Simulation Objectives
18.2.2. The Overall Simulation Model
18.2.3. Uplink FDM Signal Generation
18.2.4. Satellite Transponder Model
18.2.5. Receiver Model and Semianalytic BER Estimator
18.2.6. Simulation Results
Baseline Validation
Nonlinear and Noise Effects −5 FDM Carriers
18.2.7. Summary and Conclusions
18.3. References
18.4. Appendix A: MATLAB Code for CDMA Example
18.4.1. Supporting Functions
MSquence.m
LinearFeedbackShiftRegiater,m
18.5. Appendix B: Preprocessors for CDMA Application
18.5.1. Validation Run
18.5.2. Study Illustrating the Effect of the Ricean K-Factor
18.6. Appendix C: MATLAB Function c18_errvector.m
18.7. Appendix D: MATLAB Code for Satellite FDM Example
18.7.1. Supporting Functions
mpsk_impulses.m
sqrc_time.m
sqrc_freq_nosinc.m
delayr1.m
twt_model.m
twtdata1.m
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