Leaky-FXLMS algorithm: Stochastic analysis for Gaussian data and secondary path modeling error

This paper presents a stochastic analysis of the leaky filtered-X least-mean-square (LFXLMS) algorithm. The version with leakage of the adaptive algorithm is used in practical implementations aiming to reduce undesirable effects due to numerical errors in finite-precision machines, overload of the secondary source, among others. Based on new analysis assumptions, instead of the ordinary independence theory frequently used in classical LMS analysis, an analytical model for the first and second moments of the adaptive filter weights has been derived. In addition, the proposed theoretical models consider the situation in which the secondary path is imperfectly modeled. Experimental results demonstrate the accuracy of the proposed model as compared with the classical analysis.