Behavioral Modeling and Predistortion of Wideband Wireless Transmitters

Fadhel M. Ghannouchi University of Calgary, Canada Oualid Hammi King Fahd University of Petroleum and Minerals, Saudi Arabia Mohamed Helaoui University of Calgary, Canada

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