Behavioral Modeling and Predistortion of Wideband Wireless Transmitters

Fadhel M. Ghannouchi University of Calgary, CanadaOualid Hammi King Fahd University of Petroleum and Minerals, Saudi ArabiaMohamed Helaoui University of Calgary, Canada

• About the Authors xiPreface xiiiAcknowledgments xv1 Characterization of Wireless Transmitter Distortions 11.1 Introduction 11.1.1 RF Power Amplifier Nonlinearity 21.1.2 Inter-Modulation Distortion and Spectrum Regrowth 21.2 Impact of Distortions on Transmitter Performances 61.3 Output Power versus Input Power Characteristic 91.4 AM/AM and AM/PM Characteristics 101.5 1 dB Compression Point 121.6 Third and Fifth Order Intercept Points 151.7 Carrier to Inter-Modulation Distortion Ratio 161.8 Adjacent Channel Leakage Ratio 181.9 Error Vector Magnitude 19References 212 Dynamic Nonlinear Systems 232.1 Classification of Nonlinear Systems 232.1.1 Memoryless Systems 232.1.2 Systems with Memory 242.2 Memory in Microwave Power Amplification Systems 252.2.1 Nonlinear Systems without Memory 252.2.2 Weakly Nonlinear and Quasi-Memoryless Systems 262.2.3 Nonlinear System with Memory 272.3 Baseband and Low-Pass Equivalent Signals 272.4 Origins and Types of Memory Effects in Power Amplification Systems 292.4.1 Origins of Memory Effects 292.4.2 Electrical Memory Effects 302.4.3 Thermal Memory Effects 332.5 Volterra Series Models 38References 403 Model Performance Evaluation 433.1 Introduction 433.2 Behavioral Modeling versus Digital Predistortion 433.3 Time Domain Metrics 463.3.1 Normalized Mean Square Error 463.3.2 Memory Effects Modeling Ratio 473.4 Frequency Domain Metrics 483.4.1 Frequency Domain Normalized Mean Square Error 483.4.2 Adjacent Channel Error Power Ratio 493.4.3 Weighted Error Spectrum Power Ratio 503.4.4 Normalized Absolute Mean Spectrum Error 513.5 Static Nonlinearity Cancelation Techniques 523.5.1 Static Nonlinearity Pre-Compensation Technique 523.5.2 Static Nonlinearity Post-Compensation Technique 563.5.3 Memory Effect Intensity 593.6 Discussion and Conclusion 61References 624 Quasi-Memoryless Behavioral Models 634.1 Introduction 634.2 Modeling and Simulation of Memoryless/Quasi-Memoryless Nonlinear Systems 634.3 Bandpass to Baseband Equivalent Transformation 674.4 Look-Up Table Models 694.4.1 Uniformly Indexed Loop-Up Tables 694.4.2 Non-Uniformly Indexed Look-Up Tables 704.5 Generic Nonlinear Amplifier Behavioral Model 714.6 Empirical Analytical Based Models 734.6.1 Polar Saleh Model 734.6.2 Cartesian Saleh Model 744.6.3 Frequency-Dependent Saleh Model 764.6.4 Ghorbani Model 764.6.5 Berman and Mahle Phase Model 774.6.6 Thomas–Weidner–Durrani Amplitude Model 774.6.7 Limiter Model 784.6.8 ARCTAN Model 794.6.9 Rapp Model 814.6.10 White Model 824.7 Power Series Models 824.7.1 Polynomial Model 824.7.2 Bessel Function Based Model 834.7.3 Chebyshev Series Based Model 844.7.4 Gegenbauer Polynomials Based Model 844.7.5 Zernike Polynomials Based Model 85References 865 Memory Polynomial Based Models 895.1 Introduction 895.2 Generic Memory Polynomial Model Formulation 905.3 Memory Polynomial Model 915.4 Variants of the Memory Polynomial Model 915.4.1 Orthogonal Memory Polynomial Model 915.4.2 Sparse-Delay Memory Polynomial Model 935.4.3 Exponentially Shaped Memory Delay Profile Memory Polynomial Model 955.4.4 Non-Uniform Memory Polynomial Model 965.4.5 Unstructured Memory Polynomial Model 975.5 Envelope Memory Polynomial Model 985.6 Generalized Memory Polynomial Model 1015.7 Hybrid Memory Polynomial Model 1065.8 Dynamic Deviation Reduction Volterra Model 1085.9 Comparison and Discussion 111References 1136 Box-Oriented Models 1156.1 Introduction 1156.2 Hammerstein and Wiener Models 1156.2.1 Wiener Model 1166.2.2 Hammerstein Model 1176.3 Augmented Hammerstein and Weiner Models 1186.3.1 Augmented Wiener Model 1186.3.2 Augmented Hammerstein Model 1196.4 Three-Box Wiener–Hammerstein Models 1206.4.1 Wiener–Hammerstein Model 1206.4.2 Hammerstein–Wiener Model 1206.4.3 Feedforward Hammerstein Model 1216.5 Two-Box Polynomial Models 1236.5.1 Models’ Descriptions 1236.5.2 Identification Procedure 1246.6 Three-Box Polynomial Models 1246.6.1 Parallel Three-Blocks Model: PLUME Model 1246.6.2 Three Layered Biased Memory Polynomial Model 1256.6.3 Rational Function Model for Amplifiers 1276.7 Polynomial Based Model with I/Q and DC Impairments 1286.7.1 Parallel Hammerstein (PH) Based Model for the Alleviation of Various Imperfections in Direct Conversion Transmitters 1296.7.2 Two-Box Model with I/Q and DC Impairments 129References 1307 Neural Network Based Models 1337.1 Introduction 1337.2 Basics of Neural Networks 1337.3 Neural Networks Architecture for Modeling of Complex Static Systems 1377.3.1 Single-Input Single-Output Feedforward Neural Network (SISO-FFNN) 1377.3.2 Dual-Input Dual-Output Feedforward Neural Network (DIDO-FFNN) 1387.3.3 Dual-Input Dual-Output Coupled Cartesian Based Neural Network (DIDO-CC-NN) 1397.4 Neural Networks Architecture for Modeling of Complex Dynamic Systems 1407.4.1 Complex Time-Delay Recurrent Neural Network (CTDRNN) 1417.4.2 Complex Time-Delay Neural Network (CTDNN) 1427.4.3 Real Valued Time-Delay Recurrent Neural Network (RVTDRNN) 1427.4.4 Real Valued Time-Delay Neural Network (RVTDNN) 1447.5 Training Algorithms 1477.6 Conclusion 150References 1518 Characterization and Identification Techniques 1538.1 Introduction 1538.2 Test Signals for Power Amplifier and Transmitter Characterization 1558.2.1 Characterization Using Continuous Wave Signals 1558.2.2 Characterization Using Two-Tone Signals 1568.2.3 Characterization Using Multi-Tone Signals 1578.2.4 Characterization Using Modulated Signals 1588.2.5 Characterization Using Synthetic Modulated Signals 1608.2.6 Discussion: Impact of Test Signal on the Measured AM/AM and AM/PM Characteristics 1608.3 Data De-Embedding in Modulated Signal Based Characterization 1638.4 Identification Techniques 1708.4.1 Moving Average Techniques 1708.4.2 Model Coefficient Extraction Techniques 1728.5 Robustness of System Identification Algorithms 1798.5.1 The LS Algorithm 1798.5.2 The LMS Algorithm 1798.5.3 The RLS Algorithm 1808.6 Conclusions 181References 1819 Baseband Digital Predistortion 1859.1 The Predistortion Concept 1859.2 Adaptive Digital Predistortion 1889.2.1 Closed Loop Adaptive Digital Predistorters 1889.2.2 Open Loop Adaptive Digital Predistorters 1899.3 The Predistorter’s Power Range in Indirect Learning Architectures 1919.3.1 Constant Peak Power Technique 1939.3.2 Constant Average Power Technique 1939.3.3 Synergetic CFR and DPD Technique 1949.4 Small Signal Gain Normalization 1949.5 Digital Predistortion Implementations 2019.5.1 Baseband Digital Predistortion 2019.5.2 RF Digital Predistortion 2049.6 The Bandwidth and Power Scalable Digital Predistortion Technique 2059.7 Summary 206References 20710 Advanced Modeling and Digital Predistortion 20910.1 Joint Quadrature Impairment and Nonlinear Distortion Compensation Using Multi-Input DPD 20910.1.1 Modeling of Quadrature Modulator Imperfections 21010.1.2 Dual-Input Polynomial Model for Memoryless Joint Modeling of Quadrature Imbalance and PA Distortions 21110.1.3 Dual-Input Memory Polynomial for Joint Modeling of Quadrature Imbalance and PA Distortions Including Memory Effects 21210.1.4 Dual-Branch Parallel Hammerstein Model for Joint Modeling of Quadrature Imbalance and PA Distortions with Memory 21310.1.5 Dual-Conjugate-Input Memory Polynomial for Joint Modeling of Quadrature Imbalance and PA Distortions Including Memory Effects 21610.2 Modeling and Linearization of Nonlinear MIMO Systems 21610.2.1 Impairments in MIMO Systems 21610.2.2 Crossover Polynomial Model for MIMO Transmitters 22110.2.3 Dual-Input Nonlinear Polynomial Model for MIMO Transmitters 22210.2.4 MIMO Transmitters Nonlinear Multi-Variable Polynomial Model 22310.3 Modeling and Linearization of Dual-Band Transmitters 22710.3.1 Generalization of the Polynomial Model to the Dual-Band Case 22810.3.2 Two-Dimensional (2-D) Memory Polynomial Model for Dual-Band Transmitters 23010.3.3 Phase-Aligned Multi-band Volterra DPD 23110.4 Application of MIMO and Dual-Band Models in Digital Predistortion 23510.4.1 Linearization of MIMO Systems with Nonlinear Crosstalk 23610.4.2 Linearization of Concurrent Dual-Band Transmitters Using a 2-D Memory Polynomial Model 23810.4.3 Linearization of Concurrent Tri-Band Transmitters Using 3-D Phase-Aligned Volterra Model 240References 242Index 247