On the diffusion NLMS algorithm applied to adaptive networks: Stochastic modeling and performance comparisons

This paper aims to develop an accurate stochastic model for the diffusion normalized least-mean-square (dNLMS) algorithm operating with both combine-then-adapt (CTA) and adapt-then-combine (ATC) strategies, aiming to provide a theoretical basis for supporting the study of this algorithm. In particular, considering uncorrelated and correlated Gaussian input data, model expressions are derived for predicting the mean and mean-square behavior of either an individual node or the whole adaptive network for both transient and steady-state phases. Based on these expressions, the impact of the diffusion strategy along with a combination rule on the algorithm performance is assessed and discussed. In addition, examples are presented to demonstrate how model expressions can help the designer in the adjustment of the algorithm parameters without the need of extensive trial-and-error procedures, making performance comparisons less laborious. The effectiveness of the proposed model is assessed through simulation results covering different operating conditions, network topologies, combination rules, step-size values, as well as for a wide range of eigenvalue spreads of the input data correlation matrix and signal-to-noise ratio (SNR) values. (C) 2021 Elsevier Inc. All rights reserved.