Regularization of the RLS Algorithm

Abstract

SUMMARY Regularization plays a fundamental role in adaptive filter-ing. There are, very likely, many different ways to regularize an adaptivefilter. In this letter, we propose one possible way to do it based on a con-dition that makes intuitively sense. From this condition, we show how toregularize the recursive least-squares (RLS) algorithm. key words: echo cancellation, adaptive filters, regularization, recursiveleast-squares (RLS) algorithm 1. Introduction It is well known that regularization is a must in all prob-lems when a noisy linear system of equations needs to besolved [1]. Any adaptive filter has a linear system of equa-tions to solve, explicitly or implicitly, so that regularizationis required in order that the algorithm converges smoothlyand consistently to the optimal Wiener solution, especiallyin the presence of additive noise.In many adaptive filters [2],[3], the regularization pa-rameter is chosen as δ=βσ 2 x ,whereσ x = Ex 2 ( n )is thevariance of the zero-mean input signal