Nonlinear Distortion in Wireless Systems – Modeling and Simulation with MATLAB (R)

This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems with stochastic inputs and establishes the performance metrics of communication systems with regard to nonlinearity. In addition, the author also discusses the problem of how to embed models of distortion in system-level simulators such as MATLAB and MATLAB Simulink and provides practical techniques that professionals can use on their own projects. Finally, the book explores simulation and programming issues and provides a comprehensive reference of simulation tools for nonlinearity in wireless communication systems. Key Features: * Covers the theory, models and simulation tools needed for understanding nonlinearity and nonlinear distortion in wireless systems * Presents simulation and modeling techniques for nonlinear distortion in wireless channels using MATLAB * Uses random process theory to develop simulation tools for predicting nonlinear system performance with real-world wireless communication signals * Focuses on simulation examples of real-world communication systems under nonlinearity * Includes an accompanying website containing MATLAB code This book will be an invaluable reference for researchers, RF engineers, and communication system engineers working in the field. Graduate students and professors undertaking related courses will also find the book of interest.

Table of Contents:
Preface xv List of Abbreviations xvii List of Figures xix List of Tables xxvii Acknowledgements xxix 1 Introduction 1 1.1 Nonlinearity in Wireless Communication Systems 1 1.1.1 Power Amplifiers 2 1.1.2 Low-Noise Amplifiers (LNAs) 4 1.1.3 Mixers 6 1.2 Nonlinear Distortion in Wireless Systems 6 1.2.1 Adjacent-Channel Interference 8 1.2.2 Modulation Quality and Degradation of System Performance 9 1.2.3 Receiver Desensitization and Cross-Modulation 11 1.3 Modeling and Simulation of Nonlinear Systems 12 1.3.1 Modeling and Simulation in Engineering 12 1.3.2 Modeling and Simulation for Communication System Design 14 1.3.3 Behavioral Modeling of Nonlinear Systems 15 1.3.4 Simulation of Nonlinear Circuits 16 1.4 Organization of the Book 19 1.5 Summary 20 2 Wireless Communication Systems, Standards and Signal Models 21 2.1 Wireless System Architecture 21 2.1.1 RF Transmitter Architectures 23 2.1.2 Receiver Architecture 26 2.2 Digital Signal Processing in Wireless Systems 30 2.2.1 Digital Modulation 31 2.2.2 Pulse Shaping 37 2.2.3 Orthogonal Frequency Division Multiplexing (OFDM) 39 2.2.4 Spread Spectrum Modulation 41 2.3 Mobile System Standards 45 2.3.1 Second-Generation Mobile Systems 46 2.3.2 Third-Generation Mobile Systems 48 2.3.3 Fourth-Generation Mobile Systems 51 2.3.4 Summary 51 2.4 Wireless Network Standards 52 2.4.1 First-Generation Wireless LANs 52 2.4.2 Second-Generation Wireless LANs 52 2.4.3 Third-Generation Wireless Networks (WMANs) 53 2.5 Nonlinear Distortion in Different Wireless Standards 55 2.6 Summary 56 3 Modeling of Nonlinear Systems 59 3.1 Analytical Nonlinear Models 60 3.1.1 General Volterra Series Model 60 3.1.2 Wiener Model 62 3.1.3 Single-Frequency Volterra Models 63 3.1.4 The Parallel Cascade Model 65 3.1.5 Wiener Hammerstein Models 66 3.1.6 Multi-Input Single-Output (MISO) Volterra Model 67 3.1.7 The Polyspectral Model 67 3.1.8 Generalized Power Series 68 3.1.9 Memory Polynomials 69 3.1.10 Memoryless Models 70 3.1.11 Power-Series Model 70 3.1.12 The Limiter Family of Models 72 3.2 Empirical Nonlinear Models 74 3.2.1 The Three-Box Model 74 3.2.2 The Abuelma ati Model 75 3.2.3 Saleh Model 76 3.2.4 Rapp Model 76 3.3 Parameter Extraction of Nonlinear Models from Measured Data 76 3.3.1 Polynomial Models 77 3.3.2 Three-Box Model 79 3.3.3 Volterra Series 80 3.4 Summary 80 4 Nonlinear Transformation of Deterministic Signals 83 4.1 Complex Baseband Analysis and Simulations 84 4.1.1 Complex Envelope of Modulated Signals 85 4.1.2 Baseband Equivalent of Linear System Impulse Response 89 4.2 Complex Baseband Analysis of Memoryless Nonlinear Systems 90 4.2.1 Power-Series Model 92 4.2.2 Limiter Model 92 4.3 Complex Baseband Analysis of Nonlinear Systems with Memory 94 4.3.1 Volterra Series 94 4.3.2 Single-Frequency Volterra Models 95 4.3.3 Wiener-Hammerstein Model 96 4.4 Complex Envelope Analysis with Multiple Bandpass Signals 97 4.4.1 Volterra Series 97 4.4.2 Single-Frequency Volterra Models 99 4.4.3 Wiener-Hammerstein Model 100 4.4.4 Multi-Input Single-Output Nonlinear Model 103 4.4.5 Memoryless Nonlinearity-Power-Series Model 104 4.5 Examples Response of Power-Series Model to Multiple Signals 106 4.5.1 Single Tone 107 4.5.2 Two-Tone Signal 107 4.5.3 Single-Bandpass Signal 108 4.5.4 Two-Bandpass Signals 108 4.5.5 Single Tone and a Bandpass Signal 109 4.5.6 Multisines 110 4.5.7 Multisine Analysis Using the Generalized Power-Series Model 111 4.6 Summary 111 5 Nonlinear Transformation of Random Signals 113 5.1 Preliminaries 114 5.2 Linear Systems with Stochastic Inputs 114 5.2.1 White Noise 115 5.2.2 Gaussian Processes 116 5.3 Response of a Nonlinear System to a Random Input Signal 116 5.3.1 Power-Series Model 116 5.3.2 Wiener Hammerstein Models 118 5.4 Response of Nonlinear Systems to Gaussian Inputs 119 5.4.1 Limiter Model 120 5.4.2 Memoryless Power-Series Model 123 5.5 Response of Nonlinear Systems to Multiple Random Signals 123 5.5.1 Power-Series Model 124 5.5.2 Wiener Hammerstein Model 126 5.6 Response of Nonlinear Systems to a Random Signal and a Sinusoid 128 5.7 Summary 129 6 Nonlinear Distortion 131 6.1 Identification of Nonlinear Distortion in Digital Wireless Systems 132 6.2 Orthogonalization of the Behavioral Model 134 6.2.1 Orthogonalization of the Volterra Series Model 136 6.2.2 Orthogonalization of Wiener Model 137 6.2.3 Orthogonalization of the Power-Series Model 139 6.3 Autocorrelation Function and Spectral Analysis of the Orthogonalized Model 140 6.3.1 Output Autocorrelation Function 142 6.3.2 Power Spectral Density 142 6.4 Relationship Between System Performance and Uncorrelated Distortion 144 6.5 Examples 146 6.5.1 Narrowband Gaussian Noise 146 6.5.2 Multisines with Deterministic Phases 148 6.5.3 Multisines with Random Phases 152 6.6 Measurement of Uncorrelated Distortion 154 6.7 Summary 155 7 Nonlinear System Figures of Merit 157 7.1 Analogue System Nonlinear Figures of Merit 158 7.1.1 Intermodulation Ratio 158 7.1.2 Intercept Points 159 7.1.3 1-dB Compression Point 160 7.2 Adjacent-Channel Power Ratio (ACPR) 161 7.3 Signal-to-Noise Ratio (SNR) 161 7.4 CDMA Waveform Quality Factor ( ) 163 7.5 Error Vector Magnitude (EVM) 163 7.6 Co-Channel Power Ratio (CCPR) 164 7.7 Noise-to-Power Ratio (NPR) 164 7.7.1 NPR of Communication Signals 165 7.7.2 NBGN Model for Input Signal 166 7.8 Noise Figure in Nonlinear Systems 167 7.8.1 Nonlinear Noise Figure 169 7.8.2 NBGN Model for Input Signal and Noise 171 7.9 Summary 173 8 Communication System Models and Simulation in MATLAB(R) 175 8.1 Simulation of Communication Systems 176 8.1.1 Random Signal Generation 176 8.1.2 System Models 176 8.1.3 Baseband versus Passband Simulations 177 8.2 Choosing the Sampling Rate in MATLAB(R) Simulations 178 8.3 Random Signal Generation in MATLAB(R) 178 8.3.1 White Gaussian Noise Generator 178 8.3.2 Random Matrices 179 8.3.3 Random Integer Matrices 179 8.4 Pulse-Shaping Filters 180 8.4.1 Raised Cosine Filters 180 8.4.2 Gaussian Filters 182 8.5 Error Detection and Correction 183 8.6 Digital Modulation in MATLAB(R) 184 8.6.1 Linear Modulation 184 8.6.2 Nonlinear Modulation 186 8.7 Channel Models in MATLAB(R) 188 8.8 Simulation of System Performance in MATLAB(R) 188 8.8.1 BER 190 8.8.2 Scatter Plots 195 8.8.3 Eye Diagrams 196 8.9 Generation of Communications Signals in MATLAB(R) 198 8.9.1 Narrowband Gaussian Noise 198 8.9.2 OFDM Signals 199 8.9.3 DS-SS Signals 203 8.9.4 Multisine Signals 206 8.10 Example 210 8.11 Random Signal Generation in Simulink(R) 211 8.11.1 Random Data Sources 211 8.11.2 Random Noise Generators 212 8.11.3 Sequence Generators 213 8.12 Digital Modulation in Simulink(R) 214 8.13 Simulation of System Performance in Simulink(R) 214 8.13.1 Example 1: Random Sources and Modulation 216 8.13.2 Example 2: CDMA Transmitter 217 8.13.3 Simulation of Wireless Standards in Simulink(R) 220 8.14 Summary 220 9 Simulation of Nonlinear Systems in MATLAB(R) 221 9.1 Generation of Nonlinearity in MATLAB(R) 221 9.1.1 Memoryless Nonlinearity 221 9.1.2 Nonlinearity with Memory 222 9.2 Fitting a Nonlinear Model to Measured Data 224 9.2.1 Fitting a Memoryless Polynomial Model to Measured Data 224 9.2.2 Fitting a Three-Box Model to Measured Data 228 9.2.3 Fitting a Memory Polynomial Model to a Simulated Nonlinearity 234 9.3 Autocorrelation and Spectrum Estimation 235 9.3.1 Estimation of the Autocorrelation Function 235 9.3.2 Plotting the Signal Spectrum 237 9.3.3 Power Measurements from a PSD 239 9.4 Spectrum of the Output of a Memoryless Nonlinearity 240 9.4.1 Single Channel 240 9.4.2 Two Channels 243 9.5 Spectrum of the Output of a Nonlinearity with Memory 246 9.5.1 Three-Box Model 246 9.5.2 Memory Polynomial Model 249 9.6 Spectrum of Orthogonalized Nonlinear Model 251 9.7 Estimation of System Metrics from Simulated Spectra 256 9.7.1 Signal-to-Noise and Distortion Ratio (SNDR) 257 9.7.2 EVM 260 9.7.3 ACPR 262 9.8 Simulation of Probability of Error 263 9.9 Simulation of Noise-to-Power Ratio 268 9.10 Simulation of Nonlinear Noise Figure 271 9.11 Summary 278 10 Simulation of Nonlinear Systems in Simulink(R) 279 10.1 RF Impairments in Simulink(R) 280 10.1.1 Communications Blockset 280 10.1.2 The RF Blockset 280 10.2 Nonlinear Amplifier Mathematical Models in Simulink(R) 283 10.2.1 The Memoryless Nonlinearity Block-Communications Blockset 283 10.2.2 Cubic Polynomial Model 284 10.2.3 Hyperbolic Tangent Model 284 10.2.4 Saleh Model 285 10.2.5 Ghorbani Model 285 10.2.6 Rapp Model 285 10.2.7 Example 286 10.2.8 The Amplifier Block The RF Blockset 286 10.3 Nonlinear Amplifier Physical Models in Simulink(R) 289 10.3.1 General Amplifier Block 290 10.3.2 S-Parameter Amplifier Block 296 10.4 Measurements of Distortion and System Metrics 297 10.4.1 Adjacent-Channel Distortion 297 10.4.2 In-Band Distortion 297 10.4.3 Signal-to-Noise and Distortion Ratio 300 10.4.4 Error Vector Magnitude 300 10.5 Example: Performance of Digital Modulation with Nonlinearity 301 10.6 Simulation of Noise-to-Power Ratio 302 10.7 Simulation of Noise Figure in Nonlinear Systems 304 10.8 Summary 306 Appendix A Basics of Signal and System Analysis 307 A.1 Signals 308 A.2 Systems 308 Appendix B Random Signal Analysis 311 B.1 Random Variables 312 B.1.1 Examples of Random Variables 312 B.1.2 Functions of Random Variables 312 B.1.3 Expectation 313 B.1.4 Moments 314 B.2 Two Random Variables 314 B.2.1 Independence 315 B.2.2 Joint Statistics 315 B.3 Multiple Random Variables 316 B.4 Complex Random Variables 317 B.5 Gaussian Random Variables 318 B.5.1 Single Gaussian Random Variable 318 B.5.2 Moments of Single Gaussian Random Variable 319 B.5.3 Jointly Gaussian Random Variables 319 B.5.4 Price s Theorem 320 B.5.5 Multiple Gaussian Random Variable 320 B.5.6 Central Limit Theorem 321 B.6 Random Processes 321 B.6.1 Stationarity 322 B.6.2 Ergodicity 323 B.6.3 White Processes 323 B.6.4 Gaussian Processes 324 B.7 The Power Spectrum 324 B.7.1 White Noise Processes 325 B.7.2 Narrowband Processes 326 Appendix C Introduction to MATLAB(R) 329 C.1 MATLAB(R) Scripts 329 C.2 MATLAB(R) Structures 330 C.3 MATLAB(R) Graphics 330 C.4 Random Number Generators 330 C.5 Moments and Correlation Functions of Random Sequences 332 C.6 Fourier Transformation 332 C.7 MATLAB(R) Toolboxes 333 C.7.1 The Communication Toolbox 334 C.7.2 The RF Toolbox 334 C.8 Simulink(R) 335 C.8.1 The Communication Blockset 339 C.8.2 The RF Blockset 339 References 341 Index 347