Adaptive Filtering Under Minimum Mean p‑Power Error Criterion

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Symbols and Abbreviations
Preface
1 Introduction
	1.1 Basic Knowledge of Adaptive Filtering Algorithms
		1.1.1 AF Framework
		1.1.2 Adaptive Criteria
		1.1.3 Typical Algorithms
			1.1.3.1 Linear Adaptive Filtering Algorithms
			1.1.3.2 Nonlinear AFAs
	1.2 AFAs under MMPE Criterion
		1.2.1 MMPE Criterion
		1.2.2 MMPE Criterion based AFAs
			1.2.2.1 Linear AFAs under MMPE Criterion
			1.2.2.2 Nonlinear AFAs under MMPE Criterion
			1.2.2.3 AFAs under KMPE Criterion
	1.3 Outline of the Book
2 Adaptive Filtering Algorithms under MMSE Criterion
	2.1 LMS Algorithm
	2.2 Recursive Least Square Algorithm
		2.2.1 Original RLS Algorithm
		2.2.2 Exponentially Weighted RLS Algorithm
	2.3 KLMS Algorithm
		2.3.1 Kernel Method
		2.3.2 Kernel Least Mean Square
	2.4 KRLS Algorithm
	Appendix A: Block Matrix Inversion Lemma
	Appendix B: Reproducing Kernel Hilbert Spaces
	Appendix C: Mercer Kernel
3 MMPE Family Criteria
	3.1 Basic MMPE Criterion
		3.1.1 Mean p-Power Error Criterion
		3.1.2 Properties of MPE Criterion
			3.1.2.1 Convexity of MPE Criterion
			3.1.2.2 Performance Function of Gaussian Process
	3.2 Adaptive MMPE Criterion
	3.3 Mixture MMPE Criterion
	3.4 Smoothed MMPE Criterion
		3.4.1 Smoothed MMPE Criterion
		3.4.2 Properties of the SMPE Criterion
	3.5 MMPE in Kernel Space
		3.5.1 Kernel Mean p-Power Error Criterion
			3.5.1.1 Definition of KMPE
			3.5.1.2 Properties of KMPE
		3.5.2 q-Gaussian Kernel Mean p-Power Error
		3.5.3 Kernel Mixture Mean p-Power Error Criterion
			3.5.3.1 Definition
			3.5.3.2 Properties
4 Adaptive Filtering Algorithms under MMPE
	4.1 The Original Least Mean p-Power Algorithm
		4.1.1 Derivation of the LMP Algorithm
		4.1.2 Convergence Analysis
		4.1.3 Steady-State MSE Analysis
			4.1.3.1 EMSE Analysis for Complex LMP Algorithm
			4.1.3.2 EMSE Analysis for Real LMP Algorithm
		4.1.4 Simulation Results
	4.2 Adaptive Filtering Algorithm under Adaptive MMPE
		4.2.1 Adaptive LMP Algorithm
		4.2.2 Mean-Square Convergence Analysis
		4.2.3 Simulation Results
	4.3 Adaptive Filtering Algorithm with Variable Normalization under MMPE
		4.3.1 Variable Normalization LMP Algorithm
		4.3.2 Convergence Analysis
		4.3.3 Simulation Results
			4.3.3.1 Theoretical Validation
			4.3.3.2 Performance Comparison
	4.4 Adaptive Filtering Algorithm under Smoothed MMPE
		4.4.1 Smoothed LMP Algorithm
		4.4.2 Convergence Performance
		4.4.3 Simulation Results
			4.4.3.1 Theoretical and Simulated Steady-State Performance
			4.4.3.2 Stability Problems
			4.4.3.3 Performance Comparison
	4.5 Sparsity-Aware Adaptive Filtering Algorithm under MMPE
		4.5.1 LMP Algorithm with Sparsity Constrained Term
			4.5.1.1 Sparsity Constrained Terms
			4.5.1.2 Sparsity-Aware LMP Algorithms
			4.5.1.3 Convergence Analysis
			4.5.1.4 Simulation Results
		4.5.2 Proportionate LMP Algorithm
			4.5.2.1 Formulation of PLMP Algorithm
			4.5.2.2 Convergence Analysis
			4.5.2.3 Simulation Results
	4.6 Diffusion Adaptive Filtering Algorithm under MMPE
		4.6.1 Diffusion LMP Algorithm
			4.6.1.1 General Diffusion LMP Algorithm
			4.6.1.2 ATC and CTA Diffusion LMP
			4.6.1.3 Simulation Results
		4.6.2 Robust Diffusion NLMP Algorithm
			4.6.2.1 Diffusion NLMP Algorithm
			4.6.2.2 Robust DNLMP Algorithm
			4.6.2.3 Performance Analysis
			4.6.2.4 Simulation Results
	4.7 Constrained Adaptive Filtering Algorithm under MMPE
		4.7.1 Constrained LMP Algorithm
		4.7.2 Convergence Analysis
		4.7.3 Simulation Results
	Appendix D: Alpha-Stable Distribution
	Appendix E
	Appendix F
	Appendix G
5 Recursive Adaptive Filtering Algorithms under MMPE
	5.1 Recursive AFAs under MMPE
		5.1.1 Recursive Least Mean p-Power Error Algorithm
		5.1.2 Enhanced Recursive Mean p-Power Error Algorithm
		5.1.3 Performance Analysis of the ET-RLpN Algorithm
			5.1.3.1 Mean Stability
			5.1.3.2 Steady State Analysis
			5.1.3.3 Verification of MSE
		5.1.4 Simulation Results
			5.1.4.1 Performance Comparison under Contaminated Gaussian Noise
			5.1.4.2 Performance Comparison under Alpha-Stable Noise
	5.2 Sparsity-Aware Recursive Adaptive Filtering Algorithms under MMPE
		5.2.1 RLMP Algorithm with Sparsity Constraints
			5.2.1.1 Derivation of the Algorithm
			5.2.1.2 Special Cases of the SRLMP Algorithm
		5.2.2 Simulation Results
	5.3 Diffusion Recursive Adaptive Filtering Algorithm under MMPE
		5.3.1 Diffusion RLP Algorithm
		5.3.2 Simulation Results
	5.4 Constrained Recursive Adaptive Filtering Algorithm under MMPE
		5.4.1 CRLP Algorithm
		5.4.2 Simulation Results
	Appendix H
6 Nonlinear Filtering Algorithms under MMPE
	6.1 Kernel Adaptive Filtering Algorithms under MMPE Criterion
		6.1.1 Kernel Least Mean p-Power Algorithm
		6.1.2 Projected KLMP Algorithm
			6.1.2.1 PKLMP Algorithm
			6.1.2.2 Convergence Analyses
			6.1.2.3 Simulation Results
		6.1.3 Kernel Recursive Least Mean p-Power Algorithm
			6.1.3.1 KRLP Algorithm
			6.1.3.2 Simulation Results
		6.1.4 Random Fourier Features Extended KRLP Algorithm
			6.1.4.1 Approximation of Gaussian Kernel Functions with Random Fourier Features
			6.1.4.2 Fourier Features Extended KRLP Algorithm
			6.1.4.3 Simulation Results
	6.2 ELM Models under MMPE
		6.2.1 Extreme Learning Machine
		6.2.2 Least Mean p-Power ELM
		6.2.3 Recursive Least Mean p-Power ELM
			6.2.3.1 RLMP-ELM Algorithm
			6.2.3.2 Simulation Results
		6.2.4 Sparse RLMP-ELM
			6.2.4.1 Sparse Recursive Least Mean p-power ELM
			6.2.4.2 Simulation Results
	6.3 BLS Models under MMPE
		6.3.1 Broad Learning System
		6.3.2 BLS under MMPE Criterion
			6.3.2.1 Derivation of Least p-norm Based BLS
			6.3.2.2 Simulation Results
		6.3.3 BLS under Mixture MMPE Criterion
			6.3.3.1 Model Formulation
			6.3.3.2 Model Optimization
			6.3.3.3 Simulation Results
7 Adaptive Filtering Algorithms under Mixture MMPE
	7.1 Adaptive Filtering Algorithm under Mixture MMPE
	7.2 Special Cases of Linear Adaptive Filtering Algorithms under Mixture MMPE
		7.2.1 LMMN Adaptive Filtering Algorithm
			7.2.1.1 LMMN Algorithm
			7.2.1.2 Local Exponential Stability of the LMMN Algorithm
			7.2.1.3 Steady-State Behavior of LMMN
			7.2.1.4 Simulation Results
		7.2.2 Robust Mixed-Norm Adaptive Filtering Algorithm
			7.2.2.1 RMN Algorithm
			7.2.2.2 Convergence Analysis
			7.2.2.3 Simulation Results
		7.2.3 A Mixed l[sub(2)]–l[sub(p)] Adaptive Filtering Algorithm
			7.2.3.1 L2LP Algorithm
			7.2.3.2 Convergence Analysis
			7.2.3.3 Simulation Results
	7.3 Sparsity-Aware Adaptive Filtering Algorithms under Mixture MMPE
		7.3.1 Sparse Mixed L2LP Algorithm
			7.3.1.1 Zero-Attracting L2LP Algorithm
			7.3.1.2 Reweighting Zero-Attracting L2LP Algorithm
			7.3.1.3 CIM L2LP Algorithm
		7.3.2 Convergence Analysis
			7.3.2.1 First Moment Behavior of the Weight Error Vector
			7.3.2.2 Second Moment Behavior of the Weight Error Vector
		7.3.3 Simulation Results
			7.3.3.1 Convergence and Steady-State Analysis
			7.3.3.2 Estimation Performance Comparison Under a UWB Channel at CM1 Mode
	7.4 Diffusion Adaptive Filtering Algorithm under Mixture MMPE
		7.4.1 Diffusion General Mixed-Norm Algorithm
		7.4.2 Convergence Performance Analysis
			7.4.2.1 Signal Modeling
			7.4.2.2 Mean Performance
			7.4.2.3 Mean Square Performance
			7.4.2.4 Steady-State Analysis
		7.4.3 Simulation Results
			7.4.3.1 Gaussian Noise
			7.4.3.2 Mixture Noise
	7.5 Kernel Adaptive Filters under Mixture MMPE
		7.5.1 Kernel Normalized Mixed-Norm Algorithm
			7.5.1.1 KNMN Algorithm
			7.5.1.2 Mean Square Convergence Analysis
			7.5.1.3 Simulation Results
		7.5.2 Kernel Recursive Generalized Mixed-Norm Algorithm
			7.5.2.1 KRGMN Algorithm
			7.5.2.2 Simulation Results
	Appendix I
8 Adaptive Filtering Algorithms under KMPE Family Criteria
	8.1 Adaptive Filtering Algorithm under Original KMPE
		8.1.1 KMPE-Based Adaptive Filtering Algorithm
		8.1.2 Recursive Adaptive Filtering Algorithm under KMPE Criterion
		8.1.3 Simulation Results
			8.1.3.1 Performance Comparison
			8.1.3.2 Performance Evaluation under Sudden Changes
	8.2 Kernel Adaptive Filtering Algorithm under q-Gaussian KMPE
		8.2.1 RQKMP Algorithm
		8.2.2 Simulation Results
			8.2.2.1 Testing the Effects under Different Parameters
			8.2.2.2 Performance Comparison
			8.2.2.3 Testing the Performance of the RQKMP Algorithm under Larger Outliers
	8.3 Kernel Adaptive Filtering Algorithm under KMMPE
		8.3.1 NysRMKMP Algorithm
			8.3.1.1 Nyström Method
			8.3.1.2 NysRMKMP Algorithm
		8.3.2 Simulation Results
			8.3.2.1 Parameter Selection
			8.3.2.2 Performance Comparison
	8.4 Extreme Learning Machine under KMPE
		8.4.1 ELM-KMPE
		8.4.2 Simulation Results
			8.4.2.1 Function Estimation with Synthetic Data
			8.4.2.2 Regression and Classification on Benchmark Datasets
References
Index