Communication Systems Modelling and Simulation

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Communication Systems Modelling and Simulation Using MATLAB and Simulink К С Raveendranathan Professor and Head Department of Electronics & Communication Engineering Government Engineering

1 Communication Systems Modelling and Simulation Using MATLAB and Simulink К С Raveendranathan Professor and Head Department of Electronics & Communication Engineering Government Engineering College Barton Hill Thiruvananthapuram Universities Press < CRC Press Taylor & Francis Croup Boca Raton London New York CRC is an imprint of the Taylor St Francis Croup, an informa business

Preface 1 Introduction to Systems, Models and Simulations 1.1 Systems Simulation: The Shortest Route to Applications 1.1.1 Introduction 1.1.2 Computer Simulation 1.2 Modelling and Simulation 1.

2 Preface 1 Introduction to Systems, Models and Simulations 1.1 Systems Simulation: The Shortest Route to Applications Introduction Computer Simulation 1.2 Modelling and Simulation 1.3 Types of Simulations Discrete Event Simulation Continuous Simulation Steady State Simulation Random Event simulation Social Simulation Web Enabled Simulation Parallel and Distributed Simulation 1.4 Discrete Event Systems (DES) 1.5 Determination of Time to Reach Steady State 1.6 Determination of the Desirable Number of Trials 1.7 Selection of Simulation Software 1.8 High Performance Simulation Tools 1.9 Conclusion Further Reading 2 Introduction to Programming in MATLAB 2.1 Introduction to MATLAB 2.2 Basic Features of MATLAB Starting MATLAB 2.3 Notation, Syntax, and Operations Variable names in MATLAB Numerical Conventions vii

viii 2.4 Importing and Exporting Information 23 2.4.1 Command Line Import 23 2.4.2 The Import Wizard 23 2.4.3 Other Import Functions 24 2.4.4 Export Functions 25 2.

3 viii 2.4 Importing and Exporting Information Command Line Import The Import Wizard Other Import Functions Export Functions Elements of MATLAB Programming Special Built-in Constants Linear Algebra Trigonometric Functions Hyperbolic Functions Logical Functions Exponential and Logarithmic Functions Complex Functions Round-off Functions Matrix Functions Polynomial Functions String Functions Plotting with MATLAB Specialised Plotting Plot Enhancement Commands Exporting of MATLAB Figures to Files Exporting of MATLAB Figures to Clipboard Specific Features of MATLAB M-files P-Code M-Book Control Flow Interactive Input Special MATLAB Functions Statistical Functions Signal Processing Functions Control System Functions Numerical Computations in MATLAB MATLAB Symbolic Math Toolbox Getting MATLAB Help Online Generating Executable Files in MATLAB Compiling and Calling External files from MATLAB Calling MATLAB Objects from External Programs Using Java Classes in MATLAB The MATLAB GUIDE 55

2.14.1 Editing a GUI 2.14.2 Code Attachment Process 2.14.3 Executing the GUI 2.15 Writing Efficient MATLAB Code 2.15.1 The MATLAB Profiler 2.15.2 Array Pre-allocation 2.15.3 JIT Acceleration 2.15.4 Vectorisation 2.

4 Editing a GUI Code Attachment Process Executing the GUI 2.15 Writing Efficient MATLAB Code The MATLAB Profiler Array Pre-allocation JIT Acceleration Vectorisation Mining Simple Functions Referencing Operations Numerical Integration Speeding Up Signal Processing Miscellaneous Tricks 2.16 MATLAB Clones 2.17 Parallel MATLAB Embarrassingly Parallel System Message Passing System Back-End Support System MATLAB Compilers Shared Memory System 2.18 Conclusion Further Reading Problems Simulink 3.1 Simulink as a Tool for Model-Based Design 3.2 Invoking Simulink 3.3 Concept of Signal and Logic Flow Connecting Blocks Sources and Sinks Continuous and Discrete Systems Discontinuities in Simulink Using Functions (written as.m,.c,.cpp, etc) Modelling a First Order System in Simulink Modelling a Second Order System Simulating the Response of a Transfer Function Modelling an Amplitude Modulator in Simulink Modelling a Zero-Crossing Detector in Simulink 3.4 Creating Sub-systems in Simulink Creating a Sub-system by Adding the Sub-system Block

X 3.4.2 Creating a Sub-system by Grouping Existing Blocks 104 3.4.3 Undoing a Sub-system 105 3.5 Conclusion 105 Further Reading 106 Problems 106 Simulation of Signals and Systems 110 4.

5 X Creating a Sub-system by Grouping Existing Blocks Undoing a Sub-system Conclusion 105 Further Reading 106 Problems 106 Simulation of Signals and Systems Continuous Time and Discrete Time Signals Basic Operations on Signals Periodic Signals and Sequences Even and Odd Signals Signal Decomposition Elementary Signals Continuous Time Complex Exponential Signal Discrete Time Complex Exponential Sequences Periodicity of Discrete Time Complex Exponential Sequences Unit Impulse and Unit Step Functions and Sequences Continuous Time and Discrete Time Systems Basic Properties of Systems Memory Invertibility of Systems Causality of Systems Stability of Systems Time Invariance Linearity of Systems Linear Time Invariant Systems Discrete Time LTI Systems and the Convolution Sum LTI Systems and the Convolution Integral Properties of LTI Systems Unit Step Response of an LTI System Linear Differential/Difference Equations The Fourier Series Representation A History of the Fourier Series and Transform Response of LTI Systems to Complex Exponentials Fourier Series Representation of Continuous Time Periodic Signals Properties of Continuous Time Fourier Series Fourier Series Representation of Discrete Time Periodic Sequences Properties of Discrete Time Fourier Series Fourier Transform of Aperiodic Signals Convergence of Fourier Transforms 160

$\\ 4.8.2 Properties of Fourier Transforms 161 4.8.3 Systems Characterised by Differential Equations 165 4.8.4 The Fourier Transform of Periodic Signals 166 4.$

6 \\ Properties of Fourier Transforms Systems Characterised by Differential Equations The Fourier Transform of Periodic Signals The Discrete Time Fourier Transform (DTFT) Properties of Di screte Time Fourier Transform Systems Characterised by Difference Equations Nyquist-Shannon Sampling Theorem Mathematical Proof of Sampling Theorem Aliasing Effects of Aliasing Avoidance of Aliasing Signal Reconstruction The Exact Reconstruction Procedure The Bilateral Laplace Transform Region of Convergence (ROC) Unilateral Laplace Transform Properties of Laplace Transform Analysis of LTI Systems Using Laplace Transforms Causality of LTI Systems Stability of an LTI System The Z-Transform Region of Convergence Inverse Z-Transform Properties of Z-Transform Analysis of LTI Systems Using Z-Transforms Causality Stability Unilateral Z-Transforms The Discrete Fourier Transform (DFT) Conclusion 200 Further Reading 201 Problems Simulation of Analog Modulation Systems Introduction Amplitude Modulation (AM) Amplitude Generation and Demodulation Mathematical Model of AM Amplitude Modulation with Multiple Sinusoidal Signals Power Contained in AM Components 208

xii 5.3 Simulation of Amplitude Modulation 209 5.3.1 AM Generation User Defined M-file 210 5.3.2 AM Generation Using Library Functions 211 5.4 Simulation of Other Variants of AM 212 5.4.1 Simulation of DSBSC 213 5.

7 xii 5.3 Simulation of Amplitude Modulation AM Generation User Defined M-file AM Generation Using Library Functions Simulation of Other Variants of AM Simulation of DSBSC Simulation of SSB Modulation Frequency Spectra Demodulation of Amplitude Modulation Demodulation of an SSB Modulation Noise Performance Normalised Transmission Bandwidth Noise in Baseband Systems Noise in AM Receivers Noise in Coherent DSBSC Receivers Noise in SSB Receivers Vestigial Sideband (VSB) System Measurement of Noise Performance Methods of Measuring Receiver Sensitivity Points to Note while Measuring SNR Conclusion 230 Further Reading 231 Problems 231 Simulation of Angle Modulation Systems Frequency Modulation (FM) The Frequency Spectrum of FM Simulation of Frequency Modulation Using MATLAB Use of modulate (. ) Function to Generate FM Frequency Modulation and Demodulation Using Communications Toolbox The FM Radio Frequency Band Bandwidth Requirements for FM Carson's Rule on FM Bandwidth Average Power Contained in a Sinusoidal FM Phase Modulation (PM) Comparison of FM and PM Waveforms Simulation of Phase Modulation and Demodulation Using Communications Toolbox Comparison Between Angle Modulations Bandwidth Requirements for PM Comparison Between FM and AM 254

xiii 6.4 FM Transmission and Noise 255 6.5 Noise in FM Receivers 255 6.5.1 Carrier-to-Noise Ratio 257 6.5.2 Processing Gain 257 6.6 Threshold Effect in FM Systems 258 6.6.1 FM Threshold Reduction 258 6.

8 xiii 6.4 FM Transmission and Noise Noise in FM Receivers Carrier-to-Noise Ratio Processing Gain Threshold Effect in FM Systems FM Threshold Reduction Comparison of Noise Performance in Continuous Wave Systems Pre-emphasis and De-emphasis Conclusion 260 Further Reading 260 Problems Simulation of Digital Modulation Systems Introduction to Digital Modulation Trading-off Simplicity and Bandwidth Comparison of Analog Modulation Schemes with Digital Modulation Quadrature Signals Representing Real Signals Using Complex Phasors Representing Quadrature Signals in the Frequency Domain The I/Q Formats in Digital Communication The I and Q Components in a Radio Transmitter The I and Q Components in a Radio Receiver The Need for I/Q Components Digital Modulation of a Carrier Wave Introduction to Digital Basebands Amplitude Shift Keying (ASK) Frequency Shift Keying (FSK) Binary Phase Shift Keying (PSK) Differential Phase Shift Keying (DPSK) M-ary Phase Shift Keying (MPSK) Quadrature Amplitude Modulation (QAM) Minimum Shift Keying (MSK) Simulation of MSK Waveforms Gaussian Minimum Shift Keying (GMSK) Theoretical Bandwidth Efficiency Limits Performance Comparison and Applications The Competing Goals of Spectral Efficiency and Power Consumption Square-Root-Raised-Cosine Filter (SRRC) The Raised-Cosine Filter (RCF) Eye Diagrams 306

xiv 7.3.17 Probability of Bit Error 309 7.4 Pulse Modulation Schemes 310 7.4.1 Pulse Amplitude Modulation (РАМ) 310 7.4.2 Pulse Width Modulation (PWM) 312 7.4.3 Pulse Position Modulation (PPM) 314 7.

9 xiv Probability of Bit Error Pulse Modulation Schemes Pulse Amplitude Modulation (РАМ) Pulse Width Modulation (PWM) Pulse Position Modulation (PPM) Pulse Code Modulation (PCM) Sampling Linear/Uniform Quantisation Non-Linear/Non-Uniform Quantisation Companding Differential Pulse Code Modulation (DPCM) Adaptive Differential PCM (ADPCM) Delta Modulation (DM) Adaptive Delta Modulation (ADM) Sigma Delta Modulation (SDM) Continuously Variable Slope Delta Modulation (CVSD) Performance Comparison and Applications Conclusion 332 Further Reading 334 Problems Probability and Random Processes Introduction Axioms of Probability Mutually Exclusive Events Definitions of Probability Simulation of Random Experiments in MATLAB Probability Space Joint Probability Equality of Events Conditional Probability Statistical Independence of Events Random Variables The Discrete Random Variable The Probability Mass Function (PMF) The Cumulative Distribution Function (CDF) The cdf (. ) Function in Statistics Toolbox The Continuous Random Variable The Probability Density Function (PDF) The pdf (. ) Function in Statistics Toolbox 353

XV 8.8 Some Discrete Random Variables 353 8.8.1 The Bernoulli Random Variable 353 8.8.2 The Binomial Random Variable 354 8.8.3 The Poisson Random Variable 355 8.8.4 The Geometric Random Variable 356 8.

10 XV 8.8 Some Discrete Random Variables The Bernoulli Random Variable The Binomial Random Variable The Poisson Random Variable The Geometric Random Variable The Pascal Random Variable Some Continuous Random Variables The Gaussian Random Variable The normcdf (. ) and normpdf (. ) Functions The Log-normal Random Variable The Uniform Random Variable The Exponential Random Variable The Laplace Random Variable The Gamma Random Variable The Erlang Random Variable The x 2 Random Variable The Rayleigh Random Variable The Rician Random Variable The Cauchy Random Variable The Weibull Random Variable The Nakagami-m Random Variable The Nakagami-q Random Variable The Logistic Random Variable The Log-logistic Random Variable The Hyperbolic Secant Random Variable Random Number Generators Pseudo Random Number Generators (PRNGs) True Random Number Generators (TRNGs) Algorithms for Pseudo Random Number Generation Random Number Generation in MATLAB The Expected Value (Mean) of a Random Variable Expected Values of Functions of Random Variables Conditional Distribution and Density Functions Conditional Expected Values Computing Expectations by Conditioning The Variance and Standard Deviation Computing Variances by Conditioning Operations on a Random Variable Moments Central Moments 401

xvi 8.16 Transformations of Random Variables 402 8.16.1 Monotonically Increasing Functions 402 8.16.2 Monotonically Decreasing Functions 403 8.16.3 Non-monotonic Functions 403 8.

11 xvi 8.16 Transformations of Random Variables Monotonically Increasing Functions Monotonically Decreasing Functions Non-monotonic Functions Characteristic Functions Probability Generating Functions (PGF) Moment Generating Functions Markov's Inequality Chebyshev's Inequality Chernoff Bound Joint Probability Distribution Functions Joint Probability Density Functions Joint Probability Mass Functions Independent Random Variables The Correlation Between Two Random Variables The Covariance The Correlation Coefficient The Joint Moment The Joint Central Moment Jointly Gaussian Random Variables Properties of Jointly Gaussian Random Variables The Central Limit Theorem Random Processes Strict Sense Stationary Random Process Wide Sense Stationary Random Process Conclusion 416 Further Readi ng 417 Problems 417 Index 419

PRINCIPLES OF COMMUNICATIONS

PRINCIPLES OF COMMUNICATIONS Systems, Modulation, and Noise SIXTH EDITION INTERNATIONAL STUDENT VERSION RODGER E. ZIEMER University of Colorado at Colorado Springs WILLIAM H. TRANTER Virginia Polytechnic