Stochastic analysis of the modified DNLMS algorithm for Gaussian data

This paper proposes a stochastic model for the modified delayed normalized least-mean-square (MDNLMS) algorithm. This algorithm uses the a posteriori error to perform the adaptation and a normalized step-size parameter. The MDNLMS algorithm is an alternative to the standard delayed LMS (DLMS) one to obtain a faster and delay-independent convergence speed. Analytical models for the first moment of the adaptive filter weight vector and the learning curve are obtained. Furthermore, the time-varying nature of normalized step size is considered in the models. The proposed approach is derived without invoking the simplifying assumption of an independent input signal. Without considering such an assumption, a high-order hyperelliptic integral has to be computed. The proposed model is based on tackling the solution of such an integral. Numerical simulation results permit to assess the accuracy of the proposed analytical models.