Stochastic analysis of the NLMS algorithm for nonstationary environment and deficient length adaptive filter

This paper presents a stochastic model of the normalized least-mean-square (NLMS) algorithm assuming nonstationary environment, deficient length adaptive filter, as well as white and correlated Gaussian input data. Specifically, considering a system identification setup, the proposed stochastic model takes into account scenarios in which the adaptive filter may have lower order than the time-varying plant to be identified. Such an assumption (which is consistent with practical conditions) has not been considered in the research works discussed so far in the literature about stochastic analysis of adaptive algorithms operating under nonstationary environments. So, a stochastic model capable of describing the NLMS algorithm behavior in more realistic operating scenarios is presented. Based on the proposed model, some interesting behaviors of the NLMS algorithm are verified due to the mismatch between the order of the adaptive filter and the plant. In addition, the impact of the algorithm parameters on its performance is discussed, aiming to provide some useful design guidelines. The effectiveness of the proposed model is assessed through simulation results for different operating conditions. (C) 2019 Elsevier B.V. All rights reserved.