A Volterra Approach to Digital Predistortion: Sparse Identification and Estimation

Acronyms
Chapter 1 Overview of Nonlinear Effects in Wireless Communication Systems
	1.1 Wireless Communication Systems
		1.1.1 Transmitters and Receivers
		1.1.2 Real‐valued Continuous‐time RF Signals and Complex‐valued Discrete‐time Baseband Signals
	1.2 Modeling Power Amplifiers
	1.3 Modeling Mixers and Modulators
	1.4 Circuit Models of Nonlinear Devices
		1.4.1 Nonlinear Circuit Elements Representation
		1.4.2 Large‐signal Models for FET Devices
			1.4.2.1 Angelov Model for the Drain Current Characteristics
			1.4.2.2 Models for the Gate Capacitances
			1.4.2.3 Simplified Nonlinear Models for FET Amplifiers
	1.5 Experimental Evaluation of Nonlinear Circuits: Classical Methods
		1.5.1 One‐tone Characterization Tests
			1.5.1.1 Implementation of One‐tone Tests
		1.5.2 Two‐tone Characterization Tests
			1.5.2.1 In‐band Intermodulation Distortion
			1.5.2.2 Out‐of‐band Components
			1.5.2.3 Implementation of Two‐tone Tests
		1.5.3 Memory Effects
	1.6 Behavioral Modeling and Linearization of Nonlinear Systems
		1.6.1 Harmonic Balance
		1.6.2 Volterra Series
		1.6.3 Neural Networks
	1.7 Regression
	1.8 Structure of the Book
	Bibliography
Chapter 2 Volterra Series Approach
	2.1 Introduction
	2.2 Volterra Series
		2.2.1 Properties of the Volterra Series
			2.2.1.1 Convergence
			2.2.1.2 Homogeneous Nonlinear Systems
			2.2.1.3 Linearity in Nonlinear Systems
			2.2.1.4 Memory and Memoryless Systems
			2.2.1.5 Volterra Series for Complex‐valued Systems
	2.3 Volterra Series Applied to RF Amplifier Modeling
		2.3.1 Response of an Amplifier to a Single Sine Wave
			2.3.1.1 Volterra‐based, Yet Simple, Analysis of Conventional Amplifier Modes
			2.3.1.2 Class‐A Mode
			2.3.1.3 Class‐B Mode
		2.3.2 Determining Nonlinear Transfer Functions
			2.3.2.1 Nonlinear Currents Method
			2.3.2.2 Harmonic Input Method
	2.4 Volterra Series in the Frequency Domain
	2.5 Two‐block Models: Wiener and Hammerstein
	2.6 Double Volterra Series
		2.6.1 The Double Volterra Series in the Analysis of Mixers
			2.6.1.1 FET Resistive Mixer
	2.7 Analysis of Intermodulation Distortion
		2.7.1 Example of Volterra IMD Analysis in FET Amplifiers
	2.8 Baseband Volterra Model
	Bibliography
Chapter 3 Discrete‐time Volterra Models
	3.1 Introduction
	3.2 Discrete‐time Volterra Models for Power Amplifiers
		3.2.1 Volterra Models for Real‐valued Systems
		3.2.2 The Equivalent Baseband Volterra Model
		3.2.3 Multidimensional Signal Processing
			3.2.3.1 Frequency‐domain Characterization of Discrete Signals and Systems
	3.3 Reducing the Volterra Model Complexity
		3.3.1 Need for Model Pruning
		3.3.2 Heuristic Reduction of the Volterra Model Complexity
			3.3.2.1 The Univariate Zero‐memory Volterra Model
			3.3.2.2 The Univariate Memory Polynomial Model
			3.3.2.3 The Univariate Generalized Memory Polynomial Model
	3.4 Discrete‐time Double Volterra Model
		3.4.1 Double Volterra Model Properties
	3.5 Volterra–Parafac Model
		3.5.1 Basis of Tensor Algebra
			3.5.1.1 Special Forms of Tensors
		3.5.2 Baseband Volterra–Parafac Model
	3.6 Volterra Models in the Frequency Domain
		3.6.1 The Baseband Volterra Model in the Frequency Domain
		3.6.2 Volterra–Parafac Models in the Frequency Domain
		3.6.3 Application of a Frequency Domain MP Model to Linearization in OFDM Transmissions
	3.7 Complex‐valued Volterra Model
	3.8 Figures of Merit for Experimental Methods in Modeling and Linearization
		3.8.1 Normalized Mean Squared Error
		3.8.2 Adjacent Channel Power Ratio
		3.8.3 Noise Power Ratio
		3.8.4 Adjacent Channel Error Power Ratio
		3.8.5 Error Vector Magnitude
	Bibliography
Chapter 4 Volterra Models Pruning Based on Circuit Knowledge
	4.1 Introduction
	4.2 Heuristic Pruning of Volterra Models
		4.2.1 Memory Polynomial (MP) Model
		4.2.2 Generalized Memory Polynomial (GMP) Model
		4.2.3 Dynamic Deviation Reduction (DDR) Model
		4.2.4 Other Heuristic Pruning Proposals
	4.3 Pruning Based on Equivalent Circuit Knowledge
		4.3.1 Structure of the Kernels
			4.3.1.1 First‐Order Kernel
			4.3.1.2 Third‐Order Kernel
			4.3.1.3 Fifth‐Order Kernel
		4.3.2 Volterra Behavioral Model for Wideband Amplifiers
			4.3.2.1 Extension of the VBW
	4.4 Circuit Knowledge Model with Electrothermal Effects
		4.4.1 Third‐Order Kernel
		4.4.2 Fifth‐Order Kernel
	4.5 Circuit Knowledge in Bivariate Volterra Models
		4.5.1 The Bivariate FV Model
		4.5.2 The Bivariate‐CKV Model
		4.5.3 Model for Concurrent Dual‐Band Signal
	4.6 Volterra Models for I/Q Modulators
		4.6.1 Two‐Tone Test for I/Q Modulators
		4.6.2 Widely Nonlinear Approach for I/Q Modulators
			4.6.2.1 Analysis of the I Branch
			4.6.2.2 Analysis of the Q Branch
			4.6.2.3 Discrete‐Time Baseband Model of the I/Q Modulator
			4.6.2.4 Model Structure of a Transmitter in the Presence of I/Q Impairments
	Bibliography
Chapter 5 Regression of Volterra Models
	5.1 Introduction
	5.2 Least Squares Algorithm
		5.2.1 The Measurement Equation
		5.2.2 The Least Squares Method
		5.2.3 The Autocorrelation and Crossvariance Matrices
			5.2.3.1 Autocovariance Matrix
			5.2.3.2 Definition of Least Squares (LS) in Terms of the Crosscorrelation and Crossvariance Matrices
		5.2.4 Centering, Normalization, and Standardization
		5.2.5 Performance Indicators
		5.2.6 A Practical Regression
	5.3 Regularization
		5.3.1 Ridge Regression (ℓ2‐Norm Minimization)
		5.3.2 LASSO (ℓ1‐Norm Minimization)
	5.4 Adaptive Optimization and Iterative Regression
		5.4.1 Steepest Descent
		5.4.2 The Least Mean Squares (LMS) Algorithm
	Bibliography
Chapter 6 Sparse Machine Learning
	6.1 Introduction
	6.2 Thresholding
	6.3 Local Search: Hill Climbing
	6.4 Greedy Pursuits
		6.4.1 Orthogonal Matching Pursuit (OMP)
		6.4.2 Principal Component Analysis (PCA)
		6.4.3 Doubly Orthogonal Matching Pursuit (DOMP)
	6.5 Stopping Criteria
		6.5.1 Custom Target
		6.5.2 Bayesian Information Criterion
	6.6 Sparse Bayesian Learning
		6.6.1 Sparse Bayesian Pursuit (SBP)
		6.6.2 Deselecting Regressors
			6.6.2.1 Reconfiguring an Amplifier Model
		6.6.3 Bayesian Upgrading
			6.6.3.1 SBL Comparison to Other Techniques
			6.6.3.2 Two Cases of Model Upgrading
	6.7 A Practical Sparse Regression
	Bibliography
Chapter 7 Transmitter Linearization with Digital Predistorters
	7.1 Introduction
	7.2 Digital Predistortion
	7.3 Indirect Learning Architecture
	7.4 Direct Learning Architecture
	7.5 Some Practical Digital Predistortion Results
		7.5.1 Case 1: Basic Digital Predistorter with Indirect Learning Architecture
		7.5.2 Case 2: Digital Predistorter with Coefficients Selection and Indirect Learning Architecture
		7.5.3 Case 3: Linearization for an Input Power Sweep with Indirect Learning Architecture
		7.5.4 Case 4: Basic Digital Predistorter with Direct Learning Architecture
		7.5.5 Case 5: Digital Predistorter with Coefficients Selection and Direct Learning Architecture
		7.5.6 Case 6: Linearization for an Input Power Sweep with Direct Learning Architecture
	Bibliography
Index