Nonlinear Distortion in Wireless Systems

Khaled M. Gharaibeh, Yarmouk University, JordanKhaled M. Gharaibeh received his B.S. and M.S. in Electrical Engineering in 1995 and 1998, respectively, both from Jordan University of Science and Technology, Irbid, Jordan. He received his Ph.D. in Electrical Engineering from North Carolina State University in 2004. From 1996 to 2000, he was a planning Engineer at Jordan Telecom, Amman, Jordan. From January 2004 to 2005, he was a research associate post-doctorate at the Department Electrical and Computer Engineering, North Carolina State University. Currently he is an Assistant Professor of Electrical Engineering at the Hijawi faculty for Engineering Technology of Yarmouk University, Irbid, Jordan. His research interests are in nonlinear system identification, behavioural modelling of nonlinear RF circuits and wireless communications. He is a senior member of the Institute of Electrical and Electronics Engineering (IEEE) and the honour society Eta Kappa Nu.

• Preface xv List of Abbreviations xviiList of Figures xixList of Tables xxviiAcknowledgements xxix1 Introduction 11.1 Nonlinearity in Wireless Communication Systems 11.1.1 Power Amplifiers 21.1.2 Low-Noise Amplifiers (LNAs) 41.1.3 Mixers 61.2 Nonlinear Distortion in Wireless Systems 61.2.1 Adjacent-Channel Interference 81.2.2 Modulation Quality and Degradation of System Performance 91.2.3 Receiver Desensitization and Cross-Modulation 111.3 Modeling and Simulation of Nonlinear Systems 121.3.1 Modeling and Simulation in Engineering 121.3.2 Modeling and Simulation for Communication System Design 141.3.3 Behavioral Modeling of Nonlinear Systems 151.3.4 Simulation of Nonlinear Circuits 161.4 Organization of the Book 191.5 Summary 202 Wireless Communication Systems, Standards and Signal Models 212.1 Wireless System Architecture 212.1.1 RF Transmitter Architectures 232.1.2 Receiver Architecture 262.2 Digital Signal Processing in Wireless Systems 302.2.1 Digital Modulation 312.2.2 Pulse Shaping 372.2.3 Orthogonal Frequency Division Multiplexing (OFDM) 392.2.4 Spread Spectrum Modulation 412.3 Mobile System Standards 452.3.1 Second-Generation Mobile Systems 462.3.2 Third-Generation Mobile Systems 482.3.3 Fourth-Generation Mobile Systems 512.3.4 Summary 512.4 Wireless Network Standards 522.4.1 First-Generation Wireless LANs 522.4.2 Second-Generation Wireless LANs 522.4.3 Third-Generation Wireless Networks (WMANs) 532.5 Nonlinear Distortion in Different Wireless Standards 552.6 Summary 563 Modeling of Nonlinear Systems 593.1 Analytical Nonlinear Models 603.1.1 General Volterra Series Model 603.1.2 Wiener Model 623.1.3 Single-Frequency Volterra Models 633.1.4 The Parallel Cascade Model 653.1.5 Wiener–Hammerstein Models 663.1.6 Multi-Input Single-Output (MISO) Volterra Model 673.1.7 The Polyspectral Model 673.1.8 Generalized Power Series 683.1.9 Memory Polynomials 693.1.10 Memoryless Models 703.1.11 Power-Series Model 703.1.12 The Limiter Family of Models 723.2 Empirical Nonlinear Models 743.2.1 The Three-Box Model 743.2.2 The Abuelma’ati Model 753.2.3 Saleh Model 763.2.4 Rapp Model 763.3 Parameter Extraction of Nonlinear Models from Measured Data 763.3.1 Polynomial Models 773.3.2 Three-Box Model 793.3.3 Volterra Series 803.4 Summary 804 Nonlinear Transformation of Deterministic Signals 834.1 Complex Baseband Analysis and Simulations 844.1.1 Complex Envelope of Modulated Signals 854.1.2 Baseband Equivalent of Linear System Impulse Response 894.2 Complex Baseband Analysis of Memoryless Nonlinear Systems 904.2.1 Power-Series Model 924.2.2 Limiter Model 924.3 Complex Baseband Analysis of Nonlinear Systems with Memory 944.3.1 Volterra Series 944.3.2 Single-Frequency Volterra Models 954.3.3 Wiener-Hammerstein Model 964.4 Complex Envelope Analysis with Multiple Bandpass Signals 974.4.1 Volterra Series 974.4.2 Single-Frequency Volterra Models 994.4.3 Wiener-Hammerstein Model 1004.4.4 Multi-Input Single-Output Nonlinear Model 1034.4.5 Memoryless Nonlinearity-Power-Series Model 1044.5 Examples–Response of Power-Series Model to Multiple Signals 1064.5.1 Single Tone 1074.5.2 Two-Tone Signal 1074.5.3 Single-Bandpass Signal 1084.5.4 Two-Bandpass Signals 1084.5.5 Single Tone and a Bandpass Signal 1094.5.6 Multisines 1104.5.7 Multisine Analysis Using the Generalized Power-Series Model 1114.6 Summary 1115 Nonlinear Transformation of Random Signals 1135.1 Preliminaries 1145.2 Linear Systems with Stochastic Inputs 1145.2.1 White Noise 1155.2.2 Gaussian Processes 1165.3 Response of a Nonlinear System to a Random Input Signal 1165.3.1 Power-Series Model 1165.3.2 Wiener–Hammerstein Models 1185.4 Response of Nonlinear Systems to Gaussian Inputs 1195.4.1 Limiter Model 1205.4.2 Memoryless Power-Series Model 1235.5 Response of Nonlinear Systems to Multiple Random Signals 1235.5.1 Power-Series Model 1245.5.2 Wiener–Hammerstein Model 1265.6 Response of Nonlinear Systems to a Random Signal and a Sinusoid 1285.7 Summary 1296 Nonlinear Distortion 1316.1 Identification of Nonlinear Distortion in Digital Wireless Systems 1326.2 Orthogonalization of the Behavioral Model 1346.2.1 Orthogonalization of the Volterra Series Model 1366.2.2 Orthogonalization of Wiener Model 1376.2.3 Orthogonalization of the Power-Series Model 1396.3 Autocorrelation Function and Spectral Analysis of the Orthogonalized Model 1406.3.1 Output Autocorrelation Function 1426.3.2 Power Spectral Density 1426.4 Relationship Between System Performance and Uncorrelated Distortion 1446.5 Examples 1466.5.1 Narrowband Gaussian Noise 1466.5.2 Multisines with Deterministic Phases 1486.5.3 Multisines with Random Phases 1526.6 Measurement of Uncorrelated Distortion 1546.7 Summary 1557 Nonlinear System Figures of Merit 1577.1 Analogue System Nonlinear Figures of Merit 1587.1.1 Intermodulation Ratio 1587.1.2 Intercept Points 1597.1.3 1-dB Compression Point 1607.2 Adjacent-Channel Power Ratio (ACPR) 1617.3 Signal-to-Noise Ratio (SNR) 1617.4 CDMA Waveform Quality Factor (ρ) 1637.5 Error Vector Magnitude (EVM) 1637.6 Co-Channel Power Ratio (CCPR) 1647.7 Noise-to-Power Ratio (NPR) 1647.7.1 NPR of Communication Signals 1657.7.2 NBGN Model for Input Signal 1667.8 Noise Figure in Nonlinear Systems 1677.8.1 Nonlinear Noise Figure 1697.8.2 NBGN Model for Input Signal and Noise 1717.9 Summary 1738 Communication System Models and Simulation in MATLAB® 1758.1 Simulation of Communication Systems 1768.1.1 Random Signal Generation 1768.1.2 System Models 1768.1.3 Baseband versus Passband Simulations 1778.2 Choosing the Sampling Rate in MATLAB® Simulations 1788.3 Random Signal Generation in MATLAB® 1788.3.1 White Gaussian Noise Generator 1788.3.2 Random Matrices 1798.3.3 Random Integer Matrices 1798.4 Pulse-Shaping Filters 1808.4.1 Raised Cosine Filters 1808.4.2 Gaussian Filters 1828.5 Error Detection and Correction 1838.6 Digital Modulation in MATLAB® 1848.6.1 Linear Modulation 1848.6.2 Nonlinear Modulation 1868.7 Channel Models in MATLAB® 1888.8 Simulation of System Performance in MATLAB® 1888.8.1 BER 1908.8.2 Scatter Plots 1958.8.3 Eye Diagrams 1968.9 Generation of Communications Signals in MATLAB® 1988.9.1 Narrowband Gaussian Noise 1988.9.2 OFDM Signals 1998.9.3 DS-SS Signals 2038.9.4 Multisine Signals 2068.10 Example 2108.11 Random Signal Generation in Simulink® 2118.11.1 Random Data Sources 2118.11.2 Random Noise Generators 2128.11.3 Sequence Generators 2138.12 Digital Modulation in Simulink® 2148.13 Simulation of System Performance in Simulink® 2148.13.1 Example 1: Random Sources and Modulation 2168.13.2 Example 2: CDMA Transmitter 2178.13.3 Simulation of Wireless Standards in Simulink® 2208.14 Summary 2209 Simulation of Nonlinear Systems in MATLAB® 2219.1 Generation of Nonlinearity in MATLAB® 2219.1.1 Memoryless Nonlinearity 2219.1.2 Nonlinearity with Memory 2229.2 Fitting a Nonlinear Model to Measured Data 2249.2.1 Fitting a Memoryless Polynomial Model to Measured Data 2249.2.2 Fitting a Three-Box Model to Measured Data 2289.2.3 Fitting a Memory Polynomial Model to a Simulated Nonlinearity 2349.3 Autocorrelation and Spectrum Estimation 2359.3.1 Estimation of the Autocorrelation Function 2359.3.2 Plotting the Signal Spectrum 2379.3.3 Power Measurements from a PSD 2399.4 Spectrum of the Output of a Memoryless Nonlinearity 2409.4.1 Single Channel 2409.4.2 Two Channels 2439.5 Spectrum of the Output of a Nonlinearity with Memory 2469.5.1 Three-Box Model 2469.5.2 Memory Polynomial Model 2499.6 Spectrum of Orthogonalized Nonlinear Model 2519.7 Estimation of System Metrics from Simulated Spectra 2569.7.1 Signal-to-Noise and Distortion Ratio (SNDR) 2579.7.2 EVM 2609.7.3 ACPR 2629.8 Simulation of Probability of Error 2639.9 Simulation of Noise-to-Power Ratio 2689.10 Simulation of Nonlinear Noise Figure 2719.11 Summary 27810 Simulation of Nonlinear Systems in Simulink® 27910.1 RF Impairments in Simulink® 28010.1.1 Communications Blockset 28010.1.2 The RF Blockset 28010.2 Nonlinear Amplifier Mathematical Models in Simulink® 28310.2.1 The “Memoryless Nonlinearity” Block-Communications Blockset 28310.2.2 Cubic Polynomial Model 28410.2.3 Hyperbolic Tangent Model 28410.2.4 Saleh Model 28510.2.5 Ghorbani Model 28510.2.6 Rapp Model 28510.2.7 Example 28610.2.8 The “Amplifier” Block–The RF Blockset 28610.3 Nonlinear Amplifier Physical Models in Simulink® 28910.3.1 “General Amplifier” Block 29010.3.2 “S-Parameter Amplifier” Block 29610.4 Measurements of Distortion and System Metrics 29710.4.1 Adjacent-Channel Distortion 29710.4.2 In-Band Distortion 29710.4.3 Signal-to-Noise and Distortion Ratio 30010.4.4 Error Vector Magnitude 30010.5 Example: Performance of Digital Modulation with Nonlinearity 30110.6 Simulation of Noise-to-Power Ratio 30210.7 Simulation of Noise Figure in Nonlinear Systems 30410.8 Summary 306Appendix A Basics of Signal and System Analysis 307A.1 Signals 308A.2 Systems 308Appendix B Random Signal Analysis 311B.1 Random Variables 312B.1.1 Examples of Random Variables 312B.1.2 Functions of Random Variables 312B.1.3 Expectation 313B.1.4 Moments 314B.2 Two Random Variables 314B.2.1 Independence 315B.2.2 Joint Statistics 315B.3 Multiple Random Variables 316B.4 Complex Random Variables 317B.5 Gaussian Random Variables 318B.5.1 Single Gaussian Random Variable 318B.5.2 Moments of Single Gaussian Random Variable 319B.5.3 Jointly Gaussian Random Variables 319B.5.4 Price’s Theorem 320B.5.5 Multiple Gaussian Random Variable 320B.5.6 Central Limit Theorem 321B.6 Random Processes 321B.6.1 Stationarity 322B.6.2 Ergodicity 323B.6.3 White Processes 323B.6.4 Gaussian Processes 324B.7 The Power Spectrum 324B.7.1 White Noise Processes 325B.7.2 Narrowband Processes 326Appendix C Introduction to MATLAB® 329C.1 MATLAB® Scripts 329C.2 MATLAB® Structures 330C.3 MATLAB® Graphics 330C.4 Random Number Generators 330C.5 Moments and Correlation Functions of Random Sequences 332C.6 Fourier Transformation 332C.7 MATLAB® Toolboxes 333C.7.1 The Communication Toolbox 334C.7.2 The RF Toolbox 334C.8 Simulink® 335C.8.1 The Communication Blockset 339C.8.2 The RF Blockset 339References 341Index 347

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