Stochastic Modeling of the Transform-Domain εLMS Algorithm for Correlated Gaussian Data

This paper presents a stochastic analysis of the transform-domain epsilon least-mean-square (TD epsilon LMS) algorithm. The TDLMS algorithm is used as an alternative to the ordinary LMS algorithm to overcome the convergence problems under correlated input signals. Analytical models for the first and second moments of the adaptive filter weights are derived. The proposed model expressions are particularly focused on correlated Gaussian data, allowing for the time-varying nature of the normalized step-size parameter. A regularization parameter c is also considered in the proposed model derivation. Through simulation results, the accuracy of the proposed model is assessed. In addition, a procedure for computing high-order hyperelliptic integrals is presented.