A new robust variable step-size NLMS algorithm

Abstract—A new framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost func-tion 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 a posteriori error. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. In addition, a theoret-ical model for predicting the transient and steady-state behavior and a proof of almost sure filter convergence are provided. The al-gorithm is then tested in different environments for system identi-fication and acoustic echo cancelation applications. Index Terms—Acoustic echo cancelation, adaptive filtering, im-pulsive noise, normalized least-mean-square (NLMS) algorithm, robust filtering. I