A Novel Variable Step-Size LMS Algorithm for Decentralized Incremental Distributed Networks

• https://link.springer.com/article/10.1007/s00034-023-02426-y

Variable step-size, Least mean square algorithm, Incremental algorithm, Mean squared deviation, Theoretical analysis, Quotient form

This work proposes a variable step-size strategy for estimation over distributed networks using the incremental scheme. The proposed algorithm employs the ratio of filtered squared instantaneous error to the squared instantaneous error in a windowed format. This reduces the dependency on the error power which is particularly beneficial in low signal-to-noise power ratio situations. A comprehensive theoretical analysis has been performed, and closed-form solutions of mean squared error, excess mean squared error and mean squared deviation have been derived. The theoretical results are verified via simulation results. Extensive testing has been done through experiments under various scenarios to show the supremacy of the proposed algorithm in comparison with several other algorithms.