On the Stochastic Modeling of the NSVR–IAF–PNLMS Algorithm for Correlated Gaussian Input Data

Abstract

This paper presents a stochastic model for the normalized smoothed variation rate individual-activation-factor proportionate normalized least-mean-square (NSVR-IAF-PNLMS) algorithm. Specifically, taking into account correlated Gaussian input data, model expressions are derived for predicting the mean weight vector, gain distribution matrix, NSVR metric, learning curve, weight-error correlation matrix, and steady-state excess mean-square error. Such expressions are obtained by considering the time-varying characteristics of the gain distribution matrix. Simulation results are shown confirming the accuracy of the proposed model for different operating conditions. Keywords Adaptive filtering • Proportionate normalized least-mean-square algorithm • Stochastic model 1 Introduction Although the least-mean-square (LMS) and the normalized LMS (NLMS) algorithms have been commonly used in many real-world applications (Sayed 2009; Farhang-Boroujeny 2013; Haykin 2014), these algorithms exhibit slow conver-B Rui Seara