A New Variable Step-Size Affine Projection Sign Algorithm Based on A Posteriori Estimation Error Analysis

In order to accelerate the convergence rate and reduce the steady-state misalignment of the affine projection sign algorithm (APSA), a novel variable step-size APSA based on a posteriori estimation error (APEE) analysis is proposed. The new algorithm modified the iterative process of the APSA in which only sign information of the output error is used. The variable step size is obtained by minimizing the L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{2}$$\end{document}-norm of the APEE. And the step size has a large value in the initial stage and a small value in the steady state, which can better reflect the working state of the robust adaptive filter than the APSA with fixed step sizes. Therefore, the proposed algorithm achieves a faster convergence and a lower steady-state misalignment than the APSA and its variable step-size versions. The simulation results provided in the paper confirm that the proposed algorithm retains both the advantages of the APSA with large and small step sizes without significantly increase the computational complexity.