Variable Step Size Norm-Constrained Adaptive Filtering Algorithms

Variable step size norm-constrained adaptive filtering algorithms are proposed in the paper. A variable step size is derived by minimizing the variance of the noise-free a posterior error. Thus, the update equation can obtain a reasonable step size at each iteration. Due to the introduction of variable step size, the proposed algorithms based on the constrained conditions of L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{1}$$\end{document} and L0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{0}$$\end{document} norm have a significant advantage that the convergence rate is faster than some well-known algorithms in the sparse system. The simulation results illustrate the good performance of the proposed algorithms.