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stochastic analysis of the diffusion least mean square and normalized least mean square algorithms for cyclostationary white Gaussian and non-Gaussian inputs

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2021年第12期35卷 2466-2486页

作者： Eweda, Eweda Bershad, Neil J. Bermudez, Jose C. M. Future Univ Dept Elect Engn Cairo Egypt Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA USA Univ Fed Santa Catarina Dept Elect Engn Florianopolis SC Brazil

The diffusion least mean square (DLMS) and the diffusion normalized least mean square (DNLMS) algorithms are analyzed for a network having a fusion center. This structure reduces the dimensionality of the resulting stochastic models while preserving important diffusion properties. The analysis is done in a system identification framework for cyclostationary white nodal inputs. The system parameters vary according to a random walk model. The cyclostationarity is modeled by periodic time variations of the nodal input powers. The analysis holds for all types of nodal input distributions except for distributions with infinite variance. The derived models consist of simple scalar recursions. These recursions facilitate the understanding of the network mean and mean-square dependence upon the 1) nodal weighting coefficients, 2) nodal input kurtosis and cyclostationarities, 3) nodal noise powers, and 4) the unknown system mean-square parameter increments. Optimization of the node weighting coefficients is studied. Also investigated is the stability dependence of the two algorithms upon the nodal input kurtosis and weighting coefficients. Significant differences are found between the behaviors of the DLMS and DNLMS algorithms for non-Gaussian nodal inputs. Simulations provide strong support for the theory.

关键词： adaptive filters least mean square algorithm normalized least mean square algorithm stochastic diffusion algorithms

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

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SIGNAL PROCESSING 2021年 185卷

作者： Bershad, Neil J. Eweda, Eweda Bermudez, Jose C. M. Univ Calif Irvine Dept Elect Engn & Comp Sci 1621 Santiago Dr Newport Beach CA 92660 USA Future Univ Dept Elect Engn New Cairo Egypt Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil

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 co-efficients. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Adaptive filters Analysis LMS algorithm stochastic diffusion algorithms

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

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SIGNAL PROCESSING 2024年 219卷

作者： Eweda, Eweda Bermudez, Jose C. M. Bershad, Neil J. Future Univ Dept Elect Engn Cairo Egypt Univ Fed Santa Catarina Dept Elect Engn Florianopolis SC Brazil Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92660 USA

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.

关键词： Adaptive filters Analysis LMS algorithm stochastic diffusion algorithms

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