Fadhel M. Ghannouchi, Oualid Hammi, Mohamed Helaoui
Behavioral Modeling and Predistortion of Wideband Wireless Transmitters (eBook, ePUB)
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Fadhel M. Ghannouchi, Oualid Hammi, Mohamed Helaoui
Behavioral Modeling and Predistortion of Wideband Wireless Transmitters (eBook, ePUB)
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Covers theoretical and practical aspects related to the behavioral modelling and predistortion of wireless transmitters and power amplifiers. It includes simulation software that enables the users to apply the theory presented in the book. In the first section, the reader is given the general background of nonlinear dynamic systems along with their behavioral modelling from all its aspects. In the second part, a comprehensive compilation of behavioral models formulations and structures is provided including memory polynomial based models, box oriented models such as Hammerstein-based and…mehr
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Covers theoretical and practical aspects related to the behavioral modelling and predistortion of wireless transmitters and power amplifiers. It includes simulation software that enables the users to apply the theory presented in the book. In the first section, the reader is given the general background of nonlinear dynamic systems along with their behavioral modelling from all its aspects. In the second part, a comprehensive compilation of behavioral models formulations and structures is provided including memory polynomial based models, box oriented models such as Hammerstein-based and Wiener-based models, and neural networks-based models. The book will be a valuable resource for design engineers, industrial engineers, applications engineers, postgraduate students, and researchers working on power amplifiers modelling, linearization, and design.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 272
- Erscheinungstermin: 12. Mai 2015
- Englisch
- ISBN-13: 9781119004448
- Artikelnr.: 42887797
- Verlag: John Wiley & Sons
- Seitenzahl: 272
- Erscheinungstermin: 12. Mai 2015
- Englisch
- ISBN-13: 9781119004448
- Artikelnr.: 42887797
Fadhel M. Ghannouchi University of Calgary, Canada Oualid Hammi King Fahd University of Petroleum and Minerals, Saudi Arabia Mohamed Helaoui University of Calgary, Canada
Preface Chapter 1: Characterization of Wireless Transmitter Distortions 1.1 Introduction 1.1.1 RF Power Amplifiers Nonlinearity 1.1.2 Inter-modulation Distortion and Spectrum Regrowth 1.2 Impact of the Distortions on Transmitter Performances 1.3 Output Power versus Input Power Characteristic 1.4 AM/AM and AM/PM Characteristics 1.5 1dB Compression Point 1.6 Third and Fifth Order Intercept Points 1.7 Carrier to Inter-Modulation Distortion Ratio 1.8 Adjacent Channel Leakage Ratio 1.9 Error Vector Magnitude References Chapter 2: Dynamic Nonlinear Systems 2.1 Classification of Nonlinear Systems 2.1.1 Memoryless Systems 2.1.2 Systems with Memory 2.2 Memory in Microwave Power Amplification Systems 2.2.1 Nonlinear Systems without Memory 2.2.2 Weakly nonlinear and Quasi-Memoryless Systems 2.2.3 Nonlinear System with Memory 2.3 Baseband and Low-Pass Equivalent Signals 2.4 Origins and Types of Memory Effects in Power Amplification Systems 2.4.1 Origins of Memory Effects 2.4.2 Electrical Memory Effects 2.4.3 Thermal Memory Effects 2.5 Volterra Series Models References Chapter 3: Model Performance Evaluation 3.1 Introduction 3.2 Behavioral Modeling vs Digital Predistortion 3.3 Time Domain Metrics 3.3.1 Normalized Mean Square Error 3.3.2 Memory Effects Modeling Ratio 3.4 Frequency Domain Metrics 3.4.1 Frequency Domain Normalized Mean Square Error 3.4.2 Adjacent Channel Error Power Ratio 3.4.3 Weighted Error Spectrum Power Ratio 3.4.4 Normalized Absolute Mean Spectrum Error 3.5 Static Nonlinearity Cancellation Techniques 3.5.1 Static Nonlinearity Pre-Compensation Technique 3.5.2 Static Nonlinearity Post-Compensation Technique 3.5.3 Memory Effects Intensity 3.6 Discussion and Conclusion References Chapter 4: Quasi-Memoryless Behavior Models 4.1 Introduction 4.2 Modeling and Simulation of Memoryless/Quasi-Memoryless Nonlinear Systems 4.3 Bandpass to Baseband Equivalent Transformation 4.4 Look-up Table Models 4.4.1 Non-uniform Indexed Look-up Tables 4.5 Empirical Analytical Based Models 4.5.1 Class AB Amplifier Behavior Model 4.6 Saleh Based Models 4.6.1 Polar Saleh Model 4.6.2 Cartesian Saleh Model 4.6.3 Frequency-dependent Saleh Model 4.6.4 Ghorbani Model 4.6.5 Berman & Mahle Phase Model 4.6.6 Thomas-Weidner-Durrani Amplitude Model 4.6.7 Limiter Model 4.6.8 ARCTAN Model 4.6.9 Rapp Model 4.6.10 White Model 4.7 Power Series Models 4.7.1 Polynomial Model 4.7.2 Bessel Function Based Model 4.7.3 Chebyshev Series Based Model 4.7.4 Gegenbauer Polynomials Based Model 4.7.5 Zernike Polynomials Based Model References Chapter 5: Memory Polynomial Based Models 5.1 Introduction 5.2 Generic Memory Polynomial Model Formulation 5.3 Memory Polynomial Model 5.4 Variants of the Memory Polynomial Model 5.4.1 Orthogonal Memory Polynomial Model 5.4.2 Sparse-Delay Memory Polynomial Model 5.4.3 Exponentially Shaped Memory Delay Profile Memory Polynomial Model 5.4.4 Non-uniform Memory Polynomial Model 5.4.5 Unstructured Memory Polynomial Model 5.5 Envelope Memory Polynomial Model 5.6 Generalized Memory Polynomial Model 5.7 Hybrid Memory Polynomial Model 5.8 Dynamic Deviation Reduction Volterra Model 5.9 Comparison and Discussion References Chapter 6: Box-Oriented Models 6.1 Introduction 6.2 Hammerstein and Wiener Models 6.2.1 Wiener Model 6.2.2 Hammerstein Model 6.3 Augmented Hammerstein and Weiner Models 6.3.1 Augmented Wiener Model 6.3.2 Augmented Hammerstein Model 6.4 Three-Box Wiener-Hammerstein Models 6.4.1 Wiener-Hammerstein Model 6.4.2 Hammerstein-Wiener Model 6.4.3 Feed-Forward Hammerstein Model 6.5 Two-Box Polynomial Models 6.5.1 Models Description 6.5.2 Identification Procedure 6.6 Three-Box Polynomial Models 6.6.1 Parallel Three-blocks Model - Plume Model 6.6.2 Three layered biased memory polynomial Model 6.6.3 Rational Function Model for Amplifiers 6.7 Polynomial based Model with I/Q and DC impairments 6.7.1 Parallel Hammerstein (PH) based model for the alleviation of various imperfections in Direct Conversion transmitters 6.7.2 Two-Box Model with I/Q and DC Impairments References Chapter 7: Neural Network Based Models 7.1 Introduction 7.2 Basics of Neural Networks 7.3 Neural Networks Architecture for Modeling of Complex Static Systems 7.3.1 Single-Input Single-Output Feedforward Neural Network (SISO-FFNN) 7.3.2 Dual-Input Dual-Output Feedforward Neural Network (DIDO-FFNN) 7.3.3 Dual-Input Dual-Output Coupled Cartesian based Neural Network (DIDO-CC-NN) 7.4 Neural Networks Architectures for Modeling of Complex Dynamic Systems 7.4.1 Complex Time-Delay Recurrent Neural Network (CTDRNN) 7.4.2 Complex Time-Delay Neural Network (CTDNN) 7.4.3 Real Valued Time-Delay Recurrent Neural Network (RVTDRNN) 7.4.4 Real Valued Time-Delay Neural Network (RVTDNN) 7.5 Training Algorithms 7.6 Conclusion References Chapter 8: Characterization and Identification Techniques 8.1 Introduction 8.2 Test Signals for Power Amplifiers and Transmitters Characterization 8.2.1 Characterization using Continuous Wave Signals 8.2.2 Characterization using Two-Tone Signals 8.2.3 Characterization using Multi-Tone Signals 8.2.4 Characterization using Modulated Signals 8.2.5 Characterization using Synthetic Modulated Signals 8.2.6 Discussion: Impact of Test Signal on the Measured AM/AM and AM/PM Characteristics 8.3 Data De-embedding in Modulated Signals Based Characterization 8.4 Identification Techniques 8.4.1 Moving average Techniques 8.4.2 Model Coefficient Extraction Techniques 8.5 Robustness of System Identification Algorithms 8.5.1 The LS Algorithm 8.5.2 The LMS Algorithm 8.5.3 The RLS Algorithm 8.6 Conclusions References Chapter 9: Baseband Digital Predistortion 9.1 The Predistortion Concept 9.2 Adaptive Digital Predistortion 9.2.1 Closed Loop Adaptive Digital Predistorters 9.2.2 Open Loop Adaptive Digital Predistorters 9.3 The Predistorter's Power Range in Indirect Learning Architectures 9.3.1 Constant Peak Power Technique 9.3.2 Constant Average Power Technique 9.3.3 Synergetic CFR and DPD Technique 9.4 Small Signal Gain Normalization 9.5 Digital Predistortion Implementations 9.5.1 Baseband Digital Predistortion 9.5.2 RF Digital Predistortion 9.6 The Bandwidth and Power Scalable Digital Predistortion Technique References Chapter 10: Advanced Modeling and Digital Predistortion 10.1 Joint Quadrature Impairment and Nonlinear Distortion Compensation 10.1.1 Modeling of Quadrature Modulator Imperfections 10.1.2 Dual-Input Polynomial Model for Memoryless Joint Modeling of Quadrature Imbalance and PA Distortions 10.1.3 Dual-Input Memory Polynomial for Joint Modeling of Quadrature Imbalance and PA Distortions Including Memory Effects 10.1.4 Dual-Branch Parallel Hammerstein Model for Joint Modeling of Quadrature Imbalance and PA Distortions with Memory 10.1.5 Dual-Conjugate-Input Memory Polynomial for Joint Modeling of Quadrature Imbalance and PA Distortions Including Memory Effects 10.2 Modelling and Linearization of Nonlinear MIMO Systems 10.2.1 Impairments in MIMO Systems 10.2.2 Crossover Polynomial Model for MIMO Transmitters 10.2.3 Dual-Input Nonlinear Polynomial Model for MIMO Transmitters 10.2.4 MIMO Transmitters Nonlinear Multi-variable Polynomial Model 10.3 Modelling and Linearization of Dual Band Transmitters 10.3.1 Generalization of the Polynomial Model to Dual-Band Case 10.3.2 Two-Dimensional (2-D) Memory Polynomial Model for Dual-Band Transmitters 10.3.3 Phase-Aligned Multi-band Volterra DPD 10.4 Application of MIMO and Dual-band Models in Digital Predisortion 10.4.1 Linearization of MIMO Systems with Nonlinear Crosstalk 10.4.2 Linearization of Concurrent Dual-Band Transmitters using 2D Memory Polynomial Model 10.4.3 Linearization of Concurrent Tri-Band Transmitters using 3D Phase-Aligned Volterra Model 10.5 References Index
About the Authors xi Preface xiii Acknowledgments xv 1 Characterization of
Wireless Transmitter Distortions 1 1.1 Introduction 1 1.1.1 RF Power
Amplifier Nonlinearity 2 1.1.2 Inter-Modulation Distortion and Spectrum
Regrowth 2 1.2 Impact of Distortions on Transmitter Performances 6 1.3
Output Power versus Input Power Characteristic 9 1.4 AM/AM and AM/PM
Characteristics 10 1.5 1 dB Compression Point 12 1.6 Third and Fifth Order
Intercept Points 15 1.7 Carrier to Inter-Modulation Distortion Ratio 16 1.8
Adjacent Channel Leakage Ratio 18 1.9 Error Vector Magnitude 19 References
21 2 Dynamic Nonlinear Systems 23 2.1 Classification of Nonlinear Systems
23 2.1.1 Memoryless Systems 23 2.1.2 Systems with Memory 24 2.2 Memory in
Microwave Power Amplification Systems 25 2.2.1 Nonlinear Systems without
Memory 25 2.2.2 Weakly Nonlinear and Quasi-Memoryless Systems 26 2.2.3
Nonlinear System with Memory 27 2.3 Baseband and Low-Pass Equivalent
Signals 27 2.4 Origins and Types of Memory Effects in Power Amplification
Systems 29 2.4.1 Origins of Memory Effects 29 2.4.2 Electrical Memory
Effects 30 2.4.3 Thermal Memory Effects 33 2.5 Volterra Series Models 38
References 40 3 Model Performance Evaluation 43 3.1 Introduction 43 3.2
Behavioral Modeling versus Digital Predistortion 43 3.3 Time Domain Metrics
46 3.3.1 Normalized Mean Square Error 46 3.3.2 Memory Effects Modeling
Ratio 47 3.4 Frequency Domain Metrics 48 3.4.1 Frequency Domain Normalized
Mean Square Error 48 3.4.2 Adjacent Channel Error Power Ratio 49 3.4.3
Weighted Error Spectrum Power Ratio 50 3.4.4 Normalized Absolute Mean
Spectrum Error 51 3.5 Static Nonlinearity Cancelation Techniques 52 3.5.1
Static Nonlinearity Pre-Compensation Technique 52 3.5.2 Static Nonlinearity
Post-Compensation Technique 56 3.5.3 Memory Effect Intensity 59 3.6
Discussion and Conclusion 61 References 62 4 Quasi-Memoryless Behavioral
Models 63 4.1 Introduction 63 4.2 Modeling and Simulation of
Memoryless/Quasi-Memoryless Nonlinear Systems 63 4.3 Bandpass to Baseband
Equivalent Transformation 67 4.4 Look-Up Table Models 69 4.4.1 Uniformly
Indexed Loop-Up Tables 69 4.4.2 Non-Uniformly Indexed Look-Up Tables 70 4.5
Generic Nonlinear Amplifier Behavioral Model 71 4.6 Empirical Analytical
Based Models 73 4.6.1 Polar Saleh Model 73 4.6.2 Cartesian Saleh Model 74
4.6.3 Frequency-Dependent Saleh Model 76 4.6.4 Ghorbani Model 76 4.6.5
Berman and Mahle Phase Model 77 4.6.6 Thomas-Weidner-Durrani Amplitude
Model 77 4.6.7 Limiter Model 78 4.6.8 ARCTAN Model 79 4.6.9 Rapp Model 81
4.6.10 White Model 82 4.7 Power Series Models 82 4.7.1 Polynomial Model 82
4.7.2 Bessel Function Based Model 83 4.7.3 Chebyshev Series Based Model 84
4.7.4 Gegenbauer Polynomials Based Model 84 4.7.5 Zernike Polynomials Based
Model 85 References 86 5 Memory Polynomial Based Models 89 5.1 Introduction
89 5.2 Generic Memory Polynomial Model Formulation 90 5.3 Memory Polynomial
Model 91 5.4 Variants of the Memory Polynomial Model 91 5.4.1 Orthogonal
Memory Polynomial Model 91 5.4.2 Sparse-Delay Memory Polynomial Model 93
5.4.3 Exponentially Shaped Memory Delay Profile Memory Polynomial Model 95
5.4.4 Non-Uniform Memory Polynomial Model 96 5.4.5 Unstructured Memory
Polynomial Model 97 5.5 Envelope Memory Polynomial Model 98 5.6 Generalized
Memory Polynomial Model 101 5.7 Hybrid Memory Polynomial Model 106 5.8
Dynamic Deviation Reduction Volterra Model 108 5.9 Comparison and
Discussion 111 References 113 6 Box-Oriented Models 115 6.1 Introduction
115 6.2 Hammerstein and Wiener Models 115 6.2.1 Wiener Model 116 6.2.2
Hammerstein Model 117 6.3 Augmented Hammerstein and Weiner Models 118 6.3.1
Augmented Wiener Model 118 6.3.2 Augmented Hammerstein Model 119 6.4
Three-Box Wiener-Hammerstein Models 120 6.4.1 Wiener-Hammerstein Model 120
6.4.2 Hammerstein-Wiener Model 120 6.4.3 Feedforward Hammerstein Model 121
6.5 Two-Box Polynomial Models 123 6.5.1 Models' Descriptions 123 6.5.2
Identification Procedure 124 6.6 Three-Box Polynomial Models 124 6.6.1
Parallel Three-Blocks Model: PLUME Model 124 6.6.2 Three Layered Biased
Memory Polynomial Model 125 6.6.3 Rational Function Model for Amplifiers
127 6.7 Polynomial Based Model with I/Q and DC Impairments 128 6.7.1
Parallel Hammerstein (PH) Based Model for the Alleviation of Various
Imperfections in Direct Conversion Transmitters 129 6.7.2 Two-Box Model
with I/Q and DC Impairments 129 References 130 7 Neural Network Based
Models 133 7.1 Introduction 133 7.2 Basics of Neural Networks 133 7.3
Neural Networks Architecture for Modeling of Complex Static Systems 137
7.3.1 Single-Input Single-Output Feedforward Neural Network (SISO-FFNN) 137
7.3.2 Dual-Input Dual-Output Feedforward Neural Network (DIDO-FFNN) 138
7.3.3 Dual-Input Dual-Output Coupled Cartesian Based Neural Network
(DIDO-CC-NN) 139 7.4 Neural Networks Architecture for Modeling of Complex
Dynamic Systems 140 7.4.1 Complex Time-Delay Recurrent Neural Network
(CTDRNN) 141 7.4.2 Complex Time-Delay Neural Network (CTDNN) 142 7.4.3 Real
Valued Time-Delay Recurrent Neural Network (RVTDRNN) 142 7.4.4 Real Valued
Time-Delay Neural Network (RVTDNN) 144 7.5 Training Algorithms 147 7.6
Conclusion 150 References 151 8 Characterization and Identification
Techniques 153 8.1 Introduction 153 8.2 Test Signals for Power Amplifier
and Transmitter Characterization 155 8.2.1 Characterization Using
Continuous Wave Signals 155 8.2.2 Characterization Using Two-Tone Signals
156 8.2.3 Characterization Using Multi-Tone Signals 157 8.2.4
Characterization Using Modulated Signals 158 8.2.5 Characterization Using
Synthetic Modulated Signals 160 8.2.6 Discussion: Impact of Test Signal on
the Measured AM/AM and AM/PM Characteristics 160 8.3 Data De-Embedding in
Modulated Signal Based Characterization 163 8.4 Identification Techniques
170 8.4.1 Moving Average Techniques 170 8.4.2 Model Coefficient Extraction
Techniques 172 8.5 Robustness of System Identification Algorithms 179 8.5.1
The LS Algorithm 179 8.5.2 The LMS Algorithm 179 8.5.3 The RLS Algorithm
180 8.6 Conclusions 181 References 181 9 Baseband Digital Predistortion 185
9.1 The Predistortion Concept 185 9.2 Adaptive Digital Predistortion 188
9.2.1 Closed Loop Adaptive Digital Predistorters 188 9.2.2 Open Loop
Adaptive Digital Predistorters 189 9.3 The Predistorter's Power Range in
Indirect Learning Architectures 191 9.3.1 Constant Peak Power Technique 193
9.3.2 Constant Average Power Technique 193 9.3.3 Synergetic CFR and DPD
Technique 194 9.4 Small Signal Gain Normalization 194 9.5 Digital
Predistortion Implementations 201 9.5.1 Baseband Digital Predistortion 201
9.5.2 RF Digital Predistortion 204 9.6 The Bandwidth and Power Scalable
Digital Predistortion Technique 205 9.7 Summary 206 References 207 10
Advanced Modeling and Digital Predistortion 209 10.1 Joint Quadrature
Impairment and Nonlinear Distortion Compensation Using Multi-Input DPD 209
10.1.1 Modeling of Quadrature Modulator Imperfections 210 10.1.2 Dual-Input
Polynomial Model for Memoryless Joint Modeling of Quadrature Imbalance and
PA Distortions 211 10.1.3 Dual-Input Memory Polynomial for Joint Modeling
of Quadrature Imbalance and PA Distortions Including Memory Effects 212
10.1.4 Dual-Branch Parallel Hammerstein Model for Joint Modeling of
Quadrature Imbalance and PA Distortions with Memory 213 10.1.5
Dual-Conjugate-Input Memory Polynomial for Joint Modeling of Quadrature
Imbalance and PA Distortions Including Memory Effects 216 10.2 Modeling and
Linearization of Nonlinear MIMO Systems 216 10.2.1 Impairments in MIMO
Systems 216 10.2.2 Crossover Polynomial Model for MIMO Transmitters 221
10.2.3 Dual-Input Nonlinear Polynomial Model for MIMO Transmitters 222
10.2.4 MIMO Transmitters Nonlinear Multi-Variable Polynomial Model 223 10.3
Modeling and Linearization of Dual-Band Transmitters 227 10.3.1
Generalization of the Polynomial Model to the Dual-Band Case 228 10.3.2
Two-Dimensional (2-D) Memory Polynomial Model for Dual-Band Transmitters
230 10.3.3 Phase-Aligned Multi-band Volterra DPD 231 10.4 Application of
MIMO and Dual-Band Models in Digital Predistortion 235 10.4.1 Linearization
of MIMO Systems with Nonlinear Crosstalk 236 10.4.2 Linearization of
Concurrent Dual-Band Transmitters Using a 2-D Memory Polynomial Model 238
10.4.3 Linearization of Concurrent Tri-Band Transmitters Using 3-D
Phase-Aligned Volterra Model 240 References 242 Index 247
Wireless Transmitter Distortions 1 1.1 Introduction 1 1.1.1 RF Power
Amplifier Nonlinearity 2 1.1.2 Inter-Modulation Distortion and Spectrum
Regrowth 2 1.2 Impact of Distortions on Transmitter Performances 6 1.3
Output Power versus Input Power Characteristic 9 1.4 AM/AM and AM/PM
Characteristics 10 1.5 1 dB Compression Point 12 1.6 Third and Fifth Order
Intercept Points 15 1.7 Carrier to Inter-Modulation Distortion Ratio 16 1.8
Adjacent Channel Leakage Ratio 18 1.9 Error Vector Magnitude 19 References
21 2 Dynamic Nonlinear Systems 23 2.1 Classification of Nonlinear Systems
23 2.1.1 Memoryless Systems 23 2.1.2 Systems with Memory 24 2.2 Memory in
Microwave Power Amplification Systems 25 2.2.1 Nonlinear Systems without
Memory 25 2.2.2 Weakly Nonlinear and Quasi-Memoryless Systems 26 2.2.3
Nonlinear System with Memory 27 2.3 Baseband and Low-Pass Equivalent
Signals 27 2.4 Origins and Types of Memory Effects in Power Amplification
Systems 29 2.4.1 Origins of Memory Effects 29 2.4.2 Electrical Memory
Effects 30 2.4.3 Thermal Memory Effects 33 2.5 Volterra Series Models 38
References 40 3 Model Performance Evaluation 43 3.1 Introduction 43 3.2
Behavioral Modeling versus Digital Predistortion 43 3.3 Time Domain Metrics
46 3.3.1 Normalized Mean Square Error 46 3.3.2 Memory Effects Modeling
Ratio 47 3.4 Frequency Domain Metrics 48 3.4.1 Frequency Domain Normalized
Mean Square Error 48 3.4.2 Adjacent Channel Error Power Ratio 49 3.4.3
Weighted Error Spectrum Power Ratio 50 3.4.4 Normalized Absolute Mean
Spectrum Error 51 3.5 Static Nonlinearity Cancelation Techniques 52 3.5.1
Static Nonlinearity Pre-Compensation Technique 52 3.5.2 Static Nonlinearity
Post-Compensation Technique 56 3.5.3 Memory Effect Intensity 59 3.6
Discussion and Conclusion 61 References 62 4 Quasi-Memoryless Behavioral
Models 63 4.1 Introduction 63 4.2 Modeling and Simulation of
Memoryless/Quasi-Memoryless Nonlinear Systems 63 4.3 Bandpass to Baseband
Equivalent Transformation 67 4.4 Look-Up Table Models 69 4.4.1 Uniformly
Indexed Loop-Up Tables 69 4.4.2 Non-Uniformly Indexed Look-Up Tables 70 4.5
Generic Nonlinear Amplifier Behavioral Model 71 4.6 Empirical Analytical
Based Models 73 4.6.1 Polar Saleh Model 73 4.6.2 Cartesian Saleh Model 74
4.6.3 Frequency-Dependent Saleh Model 76 4.6.4 Ghorbani Model 76 4.6.5
Berman and Mahle Phase Model 77 4.6.6 Thomas-Weidner-Durrani Amplitude
Model 77 4.6.7 Limiter Model 78 4.6.8 ARCTAN Model 79 4.6.9 Rapp Model 81
4.6.10 White Model 82 4.7 Power Series Models 82 4.7.1 Polynomial Model 82
4.7.2 Bessel Function Based Model 83 4.7.3 Chebyshev Series Based Model 84
4.7.4 Gegenbauer Polynomials Based Model 84 4.7.5 Zernike Polynomials Based
Model 85 References 86 5 Memory Polynomial Based Models 89 5.1 Introduction
89 5.2 Generic Memory Polynomial Model Formulation 90 5.3 Memory Polynomial
Model 91 5.4 Variants of the Memory Polynomial Model 91 5.4.1 Orthogonal
Memory Polynomial Model 91 5.4.2 Sparse-Delay Memory Polynomial Model 93
5.4.3 Exponentially Shaped Memory Delay Profile Memory Polynomial Model 95
5.4.4 Non-Uniform Memory Polynomial Model 96 5.4.5 Unstructured Memory
Polynomial Model 97 5.5 Envelope Memory Polynomial Model 98 5.6 Generalized
Memory Polynomial Model 101 5.7 Hybrid Memory Polynomial Model 106 5.8
Dynamic Deviation Reduction Volterra Model 108 5.9 Comparison and
Discussion 111 References 113 6 Box-Oriented Models 115 6.1 Introduction
115 6.2 Hammerstein and Wiener Models 115 6.2.1 Wiener Model 116 6.2.2
Hammerstein Model 117 6.3 Augmented Hammerstein and Weiner Models 118 6.3.1
Augmented Wiener Model 118 6.3.2 Augmented Hammerstein Model 119 6.4
Three-Box Wiener-Hammerstein Models 120 6.4.1 Wiener-Hammerstein Model 120
6.4.2 Hammerstein-Wiener Model 120 6.4.3 Feedforward Hammerstein Model 121
6.5 Two-Box Polynomial Models 123 6.5.1 Models' Descriptions 123 6.5.2
Identification Procedure 124 6.6 Three-Box Polynomial Models 124 6.6.1
Parallel Three-Blocks Model: PLUME Model 124 6.6.2 Three Layered Biased
Memory Polynomial Model 125 6.6.3 Rational Function Model for Amplifiers
127 6.7 Polynomial Based Model with I/Q and DC Impairments 128 6.7.1
Parallel Hammerstein (PH) Based Model for the Alleviation of Various
Imperfections in Direct Conversion Transmitters 129 6.7.2 Two-Box Model
with I/Q and DC Impairments 129 References 130 7 Neural Network Based
Models 133 7.1 Introduction 133 7.2 Basics of Neural Networks 133 7.3
Neural Networks Architecture for Modeling of Complex Static Systems 137
7.3.1 Single-Input Single-Output Feedforward Neural Network (SISO-FFNN) 137
7.3.2 Dual-Input Dual-Output Feedforward Neural Network (DIDO-FFNN) 138
7.3.3 Dual-Input Dual-Output Coupled Cartesian Based Neural Network
(DIDO-CC-NN) 139 7.4 Neural Networks Architecture for Modeling of Complex
Dynamic Systems 140 7.4.1 Complex Time-Delay Recurrent Neural Network
(CTDRNN) 141 7.4.2 Complex Time-Delay Neural Network (CTDNN) 142 7.4.3 Real
Valued Time-Delay Recurrent Neural Network (RVTDRNN) 142 7.4.4 Real Valued
Time-Delay Neural Network (RVTDNN) 144 7.5 Training Algorithms 147 7.6
Conclusion 150 References 151 8 Characterization and Identification
Techniques 153 8.1 Introduction 153 8.2 Test Signals for Power Amplifier
and Transmitter Characterization 155 8.2.1 Characterization Using
Continuous Wave Signals 155 8.2.2 Characterization Using Two-Tone Signals
156 8.2.3 Characterization Using Multi-Tone Signals 157 8.2.4
Characterization Using Modulated Signals 158 8.2.5 Characterization Using
Synthetic Modulated Signals 160 8.2.6 Discussion: Impact of Test Signal on
the Measured AM/AM and AM/PM Characteristics 160 8.3 Data De-Embedding in
Modulated Signal Based Characterization 163 8.4 Identification Techniques
170 8.4.1 Moving Average Techniques 170 8.4.2 Model Coefficient Extraction
Techniques 172 8.5 Robustness of System Identification Algorithms 179 8.5.1
The LS Algorithm 179 8.5.2 The LMS Algorithm 179 8.5.3 The RLS Algorithm
180 8.6 Conclusions 181 References 181 9 Baseband Digital Predistortion 185
9.1 The Predistortion Concept 185 9.2 Adaptive Digital Predistortion 188
9.2.1 Closed Loop Adaptive Digital Predistorters 188 9.2.2 Open Loop
Adaptive Digital Predistorters 189 9.3 The Predistorter's Power Range in
Indirect Learning Architectures 191 9.3.1 Constant Peak Power Technique 193
9.3.2 Constant Average Power Technique 193 9.3.3 Synergetic CFR and DPD
Technique 194 9.4 Small Signal Gain Normalization 194 9.5 Digital
Predistortion Implementations 201 9.5.1 Baseband Digital Predistortion 201
9.5.2 RF Digital Predistortion 204 9.6 The Bandwidth and Power Scalable
Digital Predistortion Technique 205 9.7 Summary 206 References 207 10
Advanced Modeling and Digital Predistortion 209 10.1 Joint Quadrature
Impairment and Nonlinear Distortion Compensation Using Multi-Input DPD 209
10.1.1 Modeling of Quadrature Modulator Imperfections 210 10.1.2 Dual-Input
Polynomial Model for Memoryless Joint Modeling of Quadrature Imbalance and
PA Distortions 211 10.1.3 Dual-Input Memory Polynomial for Joint Modeling
of Quadrature Imbalance and PA Distortions Including Memory Effects 212
10.1.4 Dual-Branch Parallel Hammerstein Model for Joint Modeling of
Quadrature Imbalance and PA Distortions with Memory 213 10.1.5
Dual-Conjugate-Input Memory Polynomial for Joint Modeling of Quadrature
Imbalance and PA Distortions Including Memory Effects 216 10.2 Modeling and
Linearization of Nonlinear MIMO Systems 216 10.2.1 Impairments in MIMO
Systems 216 10.2.2 Crossover Polynomial Model for MIMO Transmitters 221
10.2.3 Dual-Input Nonlinear Polynomial Model for MIMO Transmitters 222
10.2.4 MIMO Transmitters Nonlinear Multi-Variable Polynomial Model 223 10.3
Modeling and Linearization of Dual-Band Transmitters 227 10.3.1
Generalization of the Polynomial Model to the Dual-Band Case 228 10.3.2
Two-Dimensional (2-D) Memory Polynomial Model for Dual-Band Transmitters
230 10.3.3 Phase-Aligned Multi-band Volterra DPD 231 10.4 Application of
MIMO and Dual-Band Models in Digital Predistortion 235 10.4.1 Linearization
of MIMO Systems with Nonlinear Crosstalk 236 10.4.2 Linearization of
Concurrent Dual-Band Transmitters Using a 2-D Memory Polynomial Model 238
10.4.3 Linearization of Concurrent Tri-Band Transmitters Using 3-D
Phase-Aligned Volterra Model 240 References 242 Index 247
Preface Chapter 1: Characterization of Wireless Transmitter Distortions 1.1 Introduction 1.1.1 RF Power Amplifiers Nonlinearity 1.1.2 Inter-modulation Distortion and Spectrum Regrowth 1.2 Impact of the Distortions on Transmitter Performances 1.3 Output Power versus Input Power Characteristic 1.4 AM/AM and AM/PM Characteristics 1.5 1dB Compression Point 1.6 Third and Fifth Order Intercept Points 1.7 Carrier to Inter-Modulation Distortion Ratio 1.8 Adjacent Channel Leakage Ratio 1.9 Error Vector Magnitude References Chapter 2: Dynamic Nonlinear Systems 2.1 Classification of Nonlinear Systems 2.1.1 Memoryless Systems 2.1.2 Systems with Memory 2.2 Memory in Microwave Power Amplification Systems 2.2.1 Nonlinear Systems without Memory 2.2.2 Weakly nonlinear and Quasi-Memoryless Systems 2.2.3 Nonlinear System with Memory 2.3 Baseband and Low-Pass Equivalent Signals 2.4 Origins and Types of Memory Effects in Power Amplification Systems 2.4.1 Origins of Memory Effects 2.4.2 Electrical Memory Effects 2.4.3 Thermal Memory Effects 2.5 Volterra Series Models References Chapter 3: Model Performance Evaluation 3.1 Introduction 3.2 Behavioral Modeling vs Digital Predistortion 3.3 Time Domain Metrics 3.3.1 Normalized Mean Square Error 3.3.2 Memory Effects Modeling Ratio 3.4 Frequency Domain Metrics 3.4.1 Frequency Domain Normalized Mean Square Error 3.4.2 Adjacent Channel Error Power Ratio 3.4.3 Weighted Error Spectrum Power Ratio 3.4.4 Normalized Absolute Mean Spectrum Error 3.5 Static Nonlinearity Cancellation Techniques 3.5.1 Static Nonlinearity Pre-Compensation Technique 3.5.2 Static Nonlinearity Post-Compensation Technique 3.5.3 Memory Effects Intensity 3.6 Discussion and Conclusion References Chapter 4: Quasi-Memoryless Behavior Models 4.1 Introduction 4.2 Modeling and Simulation of Memoryless/Quasi-Memoryless Nonlinear Systems 4.3 Bandpass to Baseband Equivalent Transformation 4.4 Look-up Table Models 4.4.1 Non-uniform Indexed Look-up Tables 4.5 Empirical Analytical Based Models 4.5.1 Class AB Amplifier Behavior Model 4.6 Saleh Based Models 4.6.1 Polar Saleh Model 4.6.2 Cartesian Saleh Model 4.6.3 Frequency-dependent Saleh Model 4.6.4 Ghorbani Model 4.6.5 Berman & Mahle Phase Model 4.6.6 Thomas-Weidner-Durrani Amplitude Model 4.6.7 Limiter Model 4.6.8 ARCTAN Model 4.6.9 Rapp Model 4.6.10 White Model 4.7 Power Series Models 4.7.1 Polynomial Model 4.7.2 Bessel Function Based Model 4.7.3 Chebyshev Series Based Model 4.7.4 Gegenbauer Polynomials Based Model 4.7.5 Zernike Polynomials Based Model References Chapter 5: Memory Polynomial Based Models 5.1 Introduction 5.2 Generic Memory Polynomial Model Formulation 5.3 Memory Polynomial Model 5.4 Variants of the Memory Polynomial Model 5.4.1 Orthogonal Memory Polynomial Model 5.4.2 Sparse-Delay Memory Polynomial Model 5.4.3 Exponentially Shaped Memory Delay Profile Memory Polynomial Model 5.4.4 Non-uniform Memory Polynomial Model 5.4.5 Unstructured Memory Polynomial Model 5.5 Envelope Memory Polynomial Model 5.6 Generalized Memory Polynomial Model 5.7 Hybrid Memory Polynomial Model 5.8 Dynamic Deviation Reduction Volterra Model 5.9 Comparison and Discussion References Chapter 6: Box-Oriented Models 6.1 Introduction 6.2 Hammerstein and Wiener Models 6.2.1 Wiener Model 6.2.2 Hammerstein Model 6.3 Augmented Hammerstein and Weiner Models 6.3.1 Augmented Wiener Model 6.3.2 Augmented Hammerstein Model 6.4 Three-Box Wiener-Hammerstein Models 6.4.1 Wiener-Hammerstein Model 6.4.2 Hammerstein-Wiener Model 6.4.3 Feed-Forward Hammerstein Model 6.5 Two-Box Polynomial Models 6.5.1 Models Description 6.5.2 Identification Procedure 6.6 Three-Box Polynomial Models 6.6.1 Parallel Three-blocks Model - Plume Model 6.6.2 Three layered biased memory polynomial Model 6.6.3 Rational Function Model for Amplifiers 6.7 Polynomial based Model with I/Q and DC impairments 6.7.1 Parallel Hammerstein (PH) based model for the alleviation of various imperfections in Direct Conversion transmitters 6.7.2 Two-Box Model with I/Q and DC Impairments References Chapter 7: Neural Network Based Models 7.1 Introduction 7.2 Basics of Neural Networks 7.3 Neural Networks Architecture for Modeling of Complex Static Systems 7.3.1 Single-Input Single-Output Feedforward Neural Network (SISO-FFNN) 7.3.2 Dual-Input Dual-Output Feedforward Neural Network (DIDO-FFNN) 7.3.3 Dual-Input Dual-Output Coupled Cartesian based Neural Network (DIDO-CC-NN) 7.4 Neural Networks Architectures for Modeling of Complex Dynamic Systems 7.4.1 Complex Time-Delay Recurrent Neural Network (CTDRNN) 7.4.2 Complex Time-Delay Neural Network (CTDNN) 7.4.3 Real Valued Time-Delay Recurrent Neural Network (RVTDRNN) 7.4.4 Real Valued Time-Delay Neural Network (RVTDNN) 7.5 Training Algorithms 7.6 Conclusion References Chapter 8: Characterization and Identification Techniques 8.1 Introduction 8.2 Test Signals for Power Amplifiers and Transmitters Characterization 8.2.1 Characterization using Continuous Wave Signals 8.2.2 Characterization using Two-Tone Signals 8.2.3 Characterization using Multi-Tone Signals 8.2.4 Characterization using Modulated Signals 8.2.5 Characterization using Synthetic Modulated Signals 8.2.6 Discussion: Impact of Test Signal on the Measured AM/AM and AM/PM Characteristics 8.3 Data De-embedding in Modulated Signals Based Characterization 8.4 Identification Techniques 8.4.1 Moving average Techniques 8.4.2 Model Coefficient Extraction Techniques 8.5 Robustness of System Identification Algorithms 8.5.1 The LS Algorithm 8.5.2 The LMS Algorithm 8.5.3 The RLS Algorithm 8.6 Conclusions References Chapter 9: Baseband Digital Predistortion 9.1 The Predistortion Concept 9.2 Adaptive Digital Predistortion 9.2.1 Closed Loop Adaptive Digital Predistorters 9.2.2 Open Loop Adaptive Digital Predistorters 9.3 The Predistorter's Power Range in Indirect Learning Architectures 9.3.1 Constant Peak Power Technique 9.3.2 Constant Average Power Technique 9.3.3 Synergetic CFR and DPD Technique 9.4 Small Signal Gain Normalization 9.5 Digital Predistortion Implementations 9.5.1 Baseband Digital Predistortion 9.5.2 RF Digital Predistortion 9.6 The Bandwidth and Power Scalable Digital Predistortion Technique References Chapter 10: Advanced Modeling and Digital Predistortion 10.1 Joint Quadrature Impairment and Nonlinear Distortion Compensation 10.1.1 Modeling of Quadrature Modulator Imperfections 10.1.2 Dual-Input Polynomial Model for Memoryless Joint Modeling of Quadrature Imbalance and PA Distortions 10.1.3 Dual-Input Memory Polynomial for Joint Modeling of Quadrature Imbalance and PA Distortions Including Memory Effects 10.1.4 Dual-Branch Parallel Hammerstein Model for Joint Modeling of Quadrature Imbalance and PA Distortions with Memory 10.1.5 Dual-Conjugate-Input Memory Polynomial for Joint Modeling of Quadrature Imbalance and PA Distortions Including Memory Effects 10.2 Modelling and Linearization of Nonlinear MIMO Systems 10.2.1 Impairments in MIMO Systems 10.2.2 Crossover Polynomial Model for MIMO Transmitters 10.2.3 Dual-Input Nonlinear Polynomial Model for MIMO Transmitters 10.2.4 MIMO Transmitters Nonlinear Multi-variable Polynomial Model 10.3 Modelling and Linearization of Dual Band Transmitters 10.3.1 Generalization of the Polynomial Model to Dual-Band Case 10.3.2 Two-Dimensional (2-D) Memory Polynomial Model for Dual-Band Transmitters 10.3.3 Phase-Aligned Multi-band Volterra DPD 10.4 Application of MIMO and Dual-band Models in Digital Predisortion 10.4.1 Linearization of MIMO Systems with Nonlinear Crosstalk 10.4.2 Linearization of Concurrent Dual-Band Transmitters using 2D Memory Polynomial Model 10.4.3 Linearization of Concurrent Tri-Band Transmitters using 3D Phase-Aligned Volterra Model 10.5 References Index
About the Authors xi Preface xiii Acknowledgments xv 1 Characterization of
Wireless Transmitter Distortions 1 1.1 Introduction 1 1.1.1 RF Power
Amplifier Nonlinearity 2 1.1.2 Inter-Modulation Distortion and Spectrum
Regrowth 2 1.2 Impact of Distortions on Transmitter Performances 6 1.3
Output Power versus Input Power Characteristic 9 1.4 AM/AM and AM/PM
Characteristics 10 1.5 1 dB Compression Point 12 1.6 Third and Fifth Order
Intercept Points 15 1.7 Carrier to Inter-Modulation Distortion Ratio 16 1.8
Adjacent Channel Leakage Ratio 18 1.9 Error Vector Magnitude 19 References
21 2 Dynamic Nonlinear Systems 23 2.1 Classification of Nonlinear Systems
23 2.1.1 Memoryless Systems 23 2.1.2 Systems with Memory 24 2.2 Memory in
Microwave Power Amplification Systems 25 2.2.1 Nonlinear Systems without
Memory 25 2.2.2 Weakly Nonlinear and Quasi-Memoryless Systems 26 2.2.3
Nonlinear System with Memory 27 2.3 Baseband and Low-Pass Equivalent
Signals 27 2.4 Origins and Types of Memory Effects in Power Amplification
Systems 29 2.4.1 Origins of Memory Effects 29 2.4.2 Electrical Memory
Effects 30 2.4.3 Thermal Memory Effects 33 2.5 Volterra Series Models 38
References 40 3 Model Performance Evaluation 43 3.1 Introduction 43 3.2
Behavioral Modeling versus Digital Predistortion 43 3.3 Time Domain Metrics
46 3.3.1 Normalized Mean Square Error 46 3.3.2 Memory Effects Modeling
Ratio 47 3.4 Frequency Domain Metrics 48 3.4.1 Frequency Domain Normalized
Mean Square Error 48 3.4.2 Adjacent Channel Error Power Ratio 49 3.4.3
Weighted Error Spectrum Power Ratio 50 3.4.4 Normalized Absolute Mean
Spectrum Error 51 3.5 Static Nonlinearity Cancelation Techniques 52 3.5.1
Static Nonlinearity Pre-Compensation Technique 52 3.5.2 Static Nonlinearity
Post-Compensation Technique 56 3.5.3 Memory Effect Intensity 59 3.6
Discussion and Conclusion 61 References 62 4 Quasi-Memoryless Behavioral
Models 63 4.1 Introduction 63 4.2 Modeling and Simulation of
Memoryless/Quasi-Memoryless Nonlinear Systems 63 4.3 Bandpass to Baseband
Equivalent Transformation 67 4.4 Look-Up Table Models 69 4.4.1 Uniformly
Indexed Loop-Up Tables 69 4.4.2 Non-Uniformly Indexed Look-Up Tables 70 4.5
Generic Nonlinear Amplifier Behavioral Model 71 4.6 Empirical Analytical
Based Models 73 4.6.1 Polar Saleh Model 73 4.6.2 Cartesian Saleh Model 74
4.6.3 Frequency-Dependent Saleh Model 76 4.6.4 Ghorbani Model 76 4.6.5
Berman and Mahle Phase Model 77 4.6.6 Thomas-Weidner-Durrani Amplitude
Model 77 4.6.7 Limiter Model 78 4.6.8 ARCTAN Model 79 4.6.9 Rapp Model 81
4.6.10 White Model 82 4.7 Power Series Models 82 4.7.1 Polynomial Model 82
4.7.2 Bessel Function Based Model 83 4.7.3 Chebyshev Series Based Model 84
4.7.4 Gegenbauer Polynomials Based Model 84 4.7.5 Zernike Polynomials Based
Model 85 References 86 5 Memory Polynomial Based Models 89 5.1 Introduction
89 5.2 Generic Memory Polynomial Model Formulation 90 5.3 Memory Polynomial
Model 91 5.4 Variants of the Memory Polynomial Model 91 5.4.1 Orthogonal
Memory Polynomial Model 91 5.4.2 Sparse-Delay Memory Polynomial Model 93
5.4.3 Exponentially Shaped Memory Delay Profile Memory Polynomial Model 95
5.4.4 Non-Uniform Memory Polynomial Model 96 5.4.5 Unstructured Memory
Polynomial Model 97 5.5 Envelope Memory Polynomial Model 98 5.6 Generalized
Memory Polynomial Model 101 5.7 Hybrid Memory Polynomial Model 106 5.8
Dynamic Deviation Reduction Volterra Model 108 5.9 Comparison and
Discussion 111 References 113 6 Box-Oriented Models 115 6.1 Introduction
115 6.2 Hammerstein and Wiener Models 115 6.2.1 Wiener Model 116 6.2.2
Hammerstein Model 117 6.3 Augmented Hammerstein and Weiner Models 118 6.3.1
Augmented Wiener Model 118 6.3.2 Augmented Hammerstein Model 119 6.4
Three-Box Wiener-Hammerstein Models 120 6.4.1 Wiener-Hammerstein Model 120
6.4.2 Hammerstein-Wiener Model 120 6.4.3 Feedforward Hammerstein Model 121
6.5 Two-Box Polynomial Models 123 6.5.1 Models' Descriptions 123 6.5.2
Identification Procedure 124 6.6 Three-Box Polynomial Models 124 6.6.1
Parallel Three-Blocks Model: PLUME Model 124 6.6.2 Three Layered Biased
Memory Polynomial Model 125 6.6.3 Rational Function Model for Amplifiers
127 6.7 Polynomial Based Model with I/Q and DC Impairments 128 6.7.1
Parallel Hammerstein (PH) Based Model for the Alleviation of Various
Imperfections in Direct Conversion Transmitters 129 6.7.2 Two-Box Model
with I/Q and DC Impairments 129 References 130 7 Neural Network Based
Models 133 7.1 Introduction 133 7.2 Basics of Neural Networks 133 7.3
Neural Networks Architecture for Modeling of Complex Static Systems 137
7.3.1 Single-Input Single-Output Feedforward Neural Network (SISO-FFNN) 137
7.3.2 Dual-Input Dual-Output Feedforward Neural Network (DIDO-FFNN) 138
7.3.3 Dual-Input Dual-Output Coupled Cartesian Based Neural Network
(DIDO-CC-NN) 139 7.4 Neural Networks Architecture for Modeling of Complex
Dynamic Systems 140 7.4.1 Complex Time-Delay Recurrent Neural Network
(CTDRNN) 141 7.4.2 Complex Time-Delay Neural Network (CTDNN) 142 7.4.3 Real
Valued Time-Delay Recurrent Neural Network (RVTDRNN) 142 7.4.4 Real Valued
Time-Delay Neural Network (RVTDNN) 144 7.5 Training Algorithms 147 7.6
Conclusion 150 References 151 8 Characterization and Identification
Techniques 153 8.1 Introduction 153 8.2 Test Signals for Power Amplifier
and Transmitter Characterization 155 8.2.1 Characterization Using
Continuous Wave Signals 155 8.2.2 Characterization Using Two-Tone Signals
156 8.2.3 Characterization Using Multi-Tone Signals 157 8.2.4
Characterization Using Modulated Signals 158 8.2.5 Characterization Using
Synthetic Modulated Signals 160 8.2.6 Discussion: Impact of Test Signal on
the Measured AM/AM and AM/PM Characteristics 160 8.3 Data De-Embedding in
Modulated Signal Based Characterization 163 8.4 Identification Techniques
170 8.4.1 Moving Average Techniques 170 8.4.2 Model Coefficient Extraction
Techniques 172 8.5 Robustness of System Identification Algorithms 179 8.5.1
The LS Algorithm 179 8.5.2 The LMS Algorithm 179 8.5.3 The RLS Algorithm
180 8.6 Conclusions 181 References 181 9 Baseband Digital Predistortion 185
9.1 The Predistortion Concept 185 9.2 Adaptive Digital Predistortion 188
9.2.1 Closed Loop Adaptive Digital Predistorters 188 9.2.2 Open Loop
Adaptive Digital Predistorters 189 9.3 The Predistorter's Power Range in
Indirect Learning Architectures 191 9.3.1 Constant Peak Power Technique 193
9.3.2 Constant Average Power Technique 193 9.3.3 Synergetic CFR and DPD
Technique 194 9.4 Small Signal Gain Normalization 194 9.5 Digital
Predistortion Implementations 201 9.5.1 Baseband Digital Predistortion 201
9.5.2 RF Digital Predistortion 204 9.6 The Bandwidth and Power Scalable
Digital Predistortion Technique 205 9.7 Summary 206 References 207 10
Advanced Modeling and Digital Predistortion 209 10.1 Joint Quadrature
Impairment and Nonlinear Distortion Compensation Using Multi-Input DPD 209
10.1.1 Modeling of Quadrature Modulator Imperfections 210 10.1.2 Dual-Input
Polynomial Model for Memoryless Joint Modeling of Quadrature Imbalance and
PA Distortions 211 10.1.3 Dual-Input Memory Polynomial for Joint Modeling
of Quadrature Imbalance and PA Distortions Including Memory Effects 212
10.1.4 Dual-Branch Parallel Hammerstein Model for Joint Modeling of
Quadrature Imbalance and PA Distortions with Memory 213 10.1.5
Dual-Conjugate-Input Memory Polynomial for Joint Modeling of Quadrature
Imbalance and PA Distortions Including Memory Effects 216 10.2 Modeling and
Linearization of Nonlinear MIMO Systems 216 10.2.1 Impairments in MIMO
Systems 216 10.2.2 Crossover Polynomial Model for MIMO Transmitters 221
10.2.3 Dual-Input Nonlinear Polynomial Model for MIMO Transmitters 222
10.2.4 MIMO Transmitters Nonlinear Multi-Variable Polynomial Model 223 10.3
Modeling and Linearization of Dual-Band Transmitters 227 10.3.1
Generalization of the Polynomial Model to the Dual-Band Case 228 10.3.2
Two-Dimensional (2-D) Memory Polynomial Model for Dual-Band Transmitters
230 10.3.3 Phase-Aligned Multi-band Volterra DPD 231 10.4 Application of
MIMO and Dual-Band Models in Digital Predistortion 235 10.4.1 Linearization
of MIMO Systems with Nonlinear Crosstalk 236 10.4.2 Linearization of
Concurrent Dual-Band Transmitters Using a 2-D Memory Polynomial Model 238
10.4.3 Linearization of Concurrent Tri-Band Transmitters Using 3-D
Phase-Aligned Volterra Model 240 References 242 Index 247
Wireless Transmitter Distortions 1 1.1 Introduction 1 1.1.1 RF Power
Amplifier Nonlinearity 2 1.1.2 Inter-Modulation Distortion and Spectrum
Regrowth 2 1.2 Impact of Distortions on Transmitter Performances 6 1.3
Output Power versus Input Power Characteristic 9 1.4 AM/AM and AM/PM
Characteristics 10 1.5 1 dB Compression Point 12 1.6 Third and Fifth Order
Intercept Points 15 1.7 Carrier to Inter-Modulation Distortion Ratio 16 1.8
Adjacent Channel Leakage Ratio 18 1.9 Error Vector Magnitude 19 References
21 2 Dynamic Nonlinear Systems 23 2.1 Classification of Nonlinear Systems
23 2.1.1 Memoryless Systems 23 2.1.2 Systems with Memory 24 2.2 Memory in
Microwave Power Amplification Systems 25 2.2.1 Nonlinear Systems without
Memory 25 2.2.2 Weakly Nonlinear and Quasi-Memoryless Systems 26 2.2.3
Nonlinear System with Memory 27 2.3 Baseband and Low-Pass Equivalent
Signals 27 2.4 Origins and Types of Memory Effects in Power Amplification
Systems 29 2.4.1 Origins of Memory Effects 29 2.4.2 Electrical Memory
Effects 30 2.4.3 Thermal Memory Effects 33 2.5 Volterra Series Models 38
References 40 3 Model Performance Evaluation 43 3.1 Introduction 43 3.2
Behavioral Modeling versus Digital Predistortion 43 3.3 Time Domain Metrics
46 3.3.1 Normalized Mean Square Error 46 3.3.2 Memory Effects Modeling
Ratio 47 3.4 Frequency Domain Metrics 48 3.4.1 Frequency Domain Normalized
Mean Square Error 48 3.4.2 Adjacent Channel Error Power Ratio 49 3.4.3
Weighted Error Spectrum Power Ratio 50 3.4.4 Normalized Absolute Mean
Spectrum Error 51 3.5 Static Nonlinearity Cancelation Techniques 52 3.5.1
Static Nonlinearity Pre-Compensation Technique 52 3.5.2 Static Nonlinearity
Post-Compensation Technique 56 3.5.3 Memory Effect Intensity 59 3.6
Discussion and Conclusion 61 References 62 4 Quasi-Memoryless Behavioral
Models 63 4.1 Introduction 63 4.2 Modeling and Simulation of
Memoryless/Quasi-Memoryless Nonlinear Systems 63 4.3 Bandpass to Baseband
Equivalent Transformation 67 4.4 Look-Up Table Models 69 4.4.1 Uniformly
Indexed Loop-Up Tables 69 4.4.2 Non-Uniformly Indexed Look-Up Tables 70 4.5
Generic Nonlinear Amplifier Behavioral Model 71 4.6 Empirical Analytical
Based Models 73 4.6.1 Polar Saleh Model 73 4.6.2 Cartesian Saleh Model 74
4.6.3 Frequency-Dependent Saleh Model 76 4.6.4 Ghorbani Model 76 4.6.5
Berman and Mahle Phase Model 77 4.6.6 Thomas-Weidner-Durrani Amplitude
Model 77 4.6.7 Limiter Model 78 4.6.8 ARCTAN Model 79 4.6.9 Rapp Model 81
4.6.10 White Model 82 4.7 Power Series Models 82 4.7.1 Polynomial Model 82
4.7.2 Bessel Function Based Model 83 4.7.3 Chebyshev Series Based Model 84
4.7.4 Gegenbauer Polynomials Based Model 84 4.7.5 Zernike Polynomials Based
Model 85 References 86 5 Memory Polynomial Based Models 89 5.1 Introduction
89 5.2 Generic Memory Polynomial Model Formulation 90 5.3 Memory Polynomial
Model 91 5.4 Variants of the Memory Polynomial Model 91 5.4.1 Orthogonal
Memory Polynomial Model 91 5.4.2 Sparse-Delay Memory Polynomial Model 93
5.4.3 Exponentially Shaped Memory Delay Profile Memory Polynomial Model 95
5.4.4 Non-Uniform Memory Polynomial Model 96 5.4.5 Unstructured Memory
Polynomial Model 97 5.5 Envelope Memory Polynomial Model 98 5.6 Generalized
Memory Polynomial Model 101 5.7 Hybrid Memory Polynomial Model 106 5.8
Dynamic Deviation Reduction Volterra Model 108 5.9 Comparison and
Discussion 111 References 113 6 Box-Oriented Models 115 6.1 Introduction
115 6.2 Hammerstein and Wiener Models 115 6.2.1 Wiener Model 116 6.2.2
Hammerstein Model 117 6.3 Augmented Hammerstein and Weiner Models 118 6.3.1
Augmented Wiener Model 118 6.3.2 Augmented Hammerstein Model 119 6.4
Three-Box Wiener-Hammerstein Models 120 6.4.1 Wiener-Hammerstein Model 120
6.4.2 Hammerstein-Wiener Model 120 6.4.3 Feedforward Hammerstein Model 121
6.5 Two-Box Polynomial Models 123 6.5.1 Models' Descriptions 123 6.5.2
Identification Procedure 124 6.6 Three-Box Polynomial Models 124 6.6.1
Parallel Three-Blocks Model: PLUME Model 124 6.6.2 Three Layered Biased
Memory Polynomial Model 125 6.6.3 Rational Function Model for Amplifiers
127 6.7 Polynomial Based Model with I/Q and DC Impairments 128 6.7.1
Parallel Hammerstein (PH) Based Model for the Alleviation of Various
Imperfections in Direct Conversion Transmitters 129 6.7.2 Two-Box Model
with I/Q and DC Impairments 129 References 130 7 Neural Network Based
Models 133 7.1 Introduction 133 7.2 Basics of Neural Networks 133 7.3
Neural Networks Architecture for Modeling of Complex Static Systems 137
7.3.1 Single-Input Single-Output Feedforward Neural Network (SISO-FFNN) 137
7.3.2 Dual-Input Dual-Output Feedforward Neural Network (DIDO-FFNN) 138
7.3.3 Dual-Input Dual-Output Coupled Cartesian Based Neural Network
(DIDO-CC-NN) 139 7.4 Neural Networks Architecture for Modeling of Complex
Dynamic Systems 140 7.4.1 Complex Time-Delay Recurrent Neural Network
(CTDRNN) 141 7.4.2 Complex Time-Delay Neural Network (CTDNN) 142 7.4.3 Real
Valued Time-Delay Recurrent Neural Network (RVTDRNN) 142 7.4.4 Real Valued
Time-Delay Neural Network (RVTDNN) 144 7.5 Training Algorithms 147 7.6
Conclusion 150 References 151 8 Characterization and Identification
Techniques 153 8.1 Introduction 153 8.2 Test Signals for Power Amplifier
and Transmitter Characterization 155 8.2.1 Characterization Using
Continuous Wave Signals 155 8.2.2 Characterization Using Two-Tone Signals
156 8.2.3 Characterization Using Multi-Tone Signals 157 8.2.4
Characterization Using Modulated Signals 158 8.2.5 Characterization Using
Synthetic Modulated Signals 160 8.2.6 Discussion: Impact of Test Signal on
the Measured AM/AM and AM/PM Characteristics 160 8.3 Data De-Embedding in
Modulated Signal Based Characterization 163 8.4 Identification Techniques
170 8.4.1 Moving Average Techniques 170 8.4.2 Model Coefficient Extraction
Techniques 172 8.5 Robustness of System Identification Algorithms 179 8.5.1
The LS Algorithm 179 8.5.2 The LMS Algorithm 179 8.5.3 The RLS Algorithm
180 8.6 Conclusions 181 References 181 9 Baseband Digital Predistortion 185
9.1 The Predistortion Concept 185 9.2 Adaptive Digital Predistortion 188
9.2.1 Closed Loop Adaptive Digital Predistorters 188 9.2.2 Open Loop
Adaptive Digital Predistorters 189 9.3 The Predistorter's Power Range in
Indirect Learning Architectures 191 9.3.1 Constant Peak Power Technique 193
9.3.2 Constant Average Power Technique 193 9.3.3 Synergetic CFR and DPD
Technique 194 9.4 Small Signal Gain Normalization 194 9.5 Digital
Predistortion Implementations 201 9.5.1 Baseband Digital Predistortion 201
9.5.2 RF Digital Predistortion 204 9.6 The Bandwidth and Power Scalable
Digital Predistortion Technique 205 9.7 Summary 206 References 207 10
Advanced Modeling and Digital Predistortion 209 10.1 Joint Quadrature
Impairment and Nonlinear Distortion Compensation Using Multi-Input DPD 209
10.1.1 Modeling of Quadrature Modulator Imperfections 210 10.1.2 Dual-Input
Polynomial Model for Memoryless Joint Modeling of Quadrature Imbalance and
PA Distortions 211 10.1.3 Dual-Input Memory Polynomial for Joint Modeling
of Quadrature Imbalance and PA Distortions Including Memory Effects 212
10.1.4 Dual-Branch Parallel Hammerstein Model for Joint Modeling of
Quadrature Imbalance and PA Distortions with Memory 213 10.1.5
Dual-Conjugate-Input Memory Polynomial for Joint Modeling of Quadrature
Imbalance and PA Distortions Including Memory Effects 216 10.2 Modeling and
Linearization of Nonlinear MIMO Systems 216 10.2.1 Impairments in MIMO
Systems 216 10.2.2 Crossover Polynomial Model for MIMO Transmitters 221
10.2.3 Dual-Input Nonlinear Polynomial Model for MIMO Transmitters 222
10.2.4 MIMO Transmitters Nonlinear Multi-Variable Polynomial Model 223 10.3
Modeling and Linearization of Dual-Band Transmitters 227 10.3.1
Generalization of the Polynomial Model to the Dual-Band Case 228 10.3.2
Two-Dimensional (2-D) Memory Polynomial Model for Dual-Band Transmitters
230 10.3.3 Phase-Aligned Multi-band Volterra DPD 231 10.4 Application of
MIMO and Dual-Band Models in Digital Predistortion 235 10.4.1 Linearization
of MIMO Systems with Nonlinear Crosstalk 236 10.4.2 Linearization of
Concurrent Dual-Band Transmitters Using a 2-D Memory Polynomial Model 238
10.4.3 Linearization of Concurrent Tri-Band Transmitters Using 3-D
Phase-Aligned Volterra Model 240 References 242 Index 247