research-article

Analysis of a Diffusion LMS Algorithm with Probing Delays for Cyclostationary White Gaussian and Non-Gaussian Inputs

Authors:

Jose C.M. Bermudez,

Neil J. BershadAuthors Info & Claims

Volume 219, Issue C

https://doi.org/10.1016/j.sigpro.2024.109428

Published: 01 June 2024 Publication History

Highlights

•

Behavior of the diffusion LMS algorithm is analyzed in the presence of delays in probing the unknown system.

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Cyclostationary white Gaussian and non-Gaussian nodal inputs are considered.

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The types of input distribution and the probing delays can be different for different nodes.

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The derived models facilitate the understanding of the algorithm dependence upon the network parameters.

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Significant differences are found between the algorithm behavior for equal and unequal probing delays.

Abstract

The paper studies the behavior of the diffusion least mean square (DLMS) algorithm in the presence of delays in probing the unknown system by the nodes. The types of input distribution and the probing delays can be different for different nodes. The analysis is done for a network having a central combiner. This structure reduces the dimensionality of the resulting stochastic models while preserving important diffusion properties. Communication delays between the nodes and the central combiner are also considered in the analysis. The analysis is done for system identification for cyclostationary white nodal inputs. Mean and mean-square behaviors of the algorithm are analyzed. The derived models consist of simple scalar recursions. These recursions facilitate the understanding of the algorithm mean and mean-square dependence upon the 1) nodal input kurtosis, 2) nodal probing delays, 3) communication delays between the nodes and the central combiner, 4) nodal noise powers, and 5) nodal weighting coefficients. Significant differences are found between the algorithm behavior for equal probing delays and that for unequal probing delays. Results for unequal probing delays are surprising. Simulations are in excellent agreement with the theory.

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Published In

cover image Signal Processing

Signal Processing Volume 219, Issue C

Jun 2024

404 pages

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Elsevier B.V.

Publisher

Elsevier North-Holland, Inc.

United States

Publication History

Published: 01 June 2024

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