A New Robust Variable Step-Size NLMS Algorithm

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A new framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost function subject to a time-dependent constraint on the norm of the filter update. Particularly, we present a robust variable step-size NLMS algorithm which optimizes the square of the <emphasis emphasistype="boldital">a posteriori</emphasis> error. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. In addition, a theoretical model for predicting the transient and steady-state behavior and a proof of almost sure filter convergence are provided. The algorithm is then tested in different environments for system identification and acoustic echo cancelation applications. </para>