Fast Affine Projection Adaptation Algorithms With Stable and Robust Symmetric Linear System Slovers

Abstract

This paper proposes two noniterative approaches to solve a symmetric linear system associated with the fast affine projection adaptation algorithm. The first approach, using matrix LDL <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> factorization, can provide an exact solution at a moderate complexity, in contrast with the fact that existing stable approaches are all approximate. Based on a reciprocating recursion scheme, the second approach has a very low complexity and gives a good approximate solution. Steady-state and transient properties of the proposed and certain previous FAP algorithms are studied in detail. Being stable and optimal under all step size conditions, fast affine projection algorithms incorporating the proposed approaches are promising in telecom and other applications of adaptive filtering