On the stochastic modeling of a VSS-NLMS algorithm with high immunity against measurement noise

This paper presents a comprehensive study of the variable step-size normalized least-mean-square (VSS-NLMS) algorithm introduced by Zipf, Tobias, and Seara [IEEE International Telecommunications Symposium (September 2010)]. Specifically, taking into account white and correlated Gaussian input data, a stochastic model is developed to predict the algorithm behavior for both transient and steady-state phases. Based on the proposed model, some interesting characteristics of the considered algorithm are verified, ratifying the robustness of the step-size adjustment rule against uncorrelated measurement noise. In addition, the impact of the smoothing parameter (used in the step-size adjustment rule) on the algorithm performance is discussed, aiming to provide some useful design guidelines. Through simulation results, the accuracy of the proposed model and some features of the algorithm are verified for different operating scenarios. Moreover, performance comparisons between the considered VSS-NLMS algorithm and other important and recent algorithms from the literature are presented.