Stochastic analysis of the diffusion LMS algorithm for cyclostationary white Gaussian inputs

• Published in: Signal processing Vol. 185; p. 108081
• Main Authors: Bershad, Neil J., Eweda, Eweda, Bermudez, Jose C.M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2021
• Subjects: Adaptive filters; Analysis; LMS algorithm; Stochastic diffusion algorithms; LMS algorithm; Adaptive filters; Analysis; Stochastic diffusion algorithms
• ISSN: 0165-1684
• DOI: 10.1016/j.sigpro.2021.108081

•Derived a relatively simple theory for the mean square deviation behavior of the fusion center for the diffusion LMS algorithm.•The fusion center behavior is a special case of the diffusion LMS algorithm where the fusion center and nodes only communicate with each other.•The theory is shown to be the same for both Combine-then-Adapt and Adapt-then-Combine diffusion strategies.•The theory can be used to predict the behavior of the fusion center weights for any collection of nodal weights, nodal step sizes, nodal frequencies and nodal noise powers.•The nodes help each other (alluded to in many of the referenced publications) is demonstrated by comparing the mean square deviation behavior of one node vs. ten nodes. This paper studies the stochastic behavior of a specific version of the Diffusion Least-Mean Square (DLMS) algorithm in a system identification framework for a cyclostationary white Gaussian input. The considered DLMS version has a fusion center. The input cyclostationary signal is modeled by a white random process with periodically time-varying power. The system parameters vary according to a random walk model. The paper focusses on the behavior of the fusion center for DLMS for the special case when the nodes communicate only with the fusion center and vice versa. Mathematical models are derived for the mean and mean-square-deviation (MSD) behavior of the fusion center adaptive weights as a function of the input cyclostationarity. It is shown that the behavior of the fusion center is the same for both Combine-Then-Adapt (CTA) and Adapt-Then-Combine (ATC) diffusion strategies. Monte Carlo simulations are shown in excellent agreement with the theory. Finally the model is used to study the design of the DLMS algorithm for different nodal step-sizes, cyclostationarities, noise powers and weighting coefficients.