Daniel Gilio Tiglea, Renato Candido, Magno T. M. Silva. Bias-Variance Decomposition of the Mean-Square Deviation of the LMS Algorithm: Transient and Steady-State Analysis. Circuits, Systems, and Signal Processing, 2025.

Abstract

In this paper, we perform the bias-variance decomposition of the mean-square deviation of the least-mean-squares algorithm during both the transient and steady-state phases. Although this solution has been extensively studied, to the best of our knowledge, this type of analysis has not been done before explicitly in this manner. We analyze a wide range of scenarios, including cases in which the filter length is not equal to that of the optimal solution and situations in the presence of impulsive noise. The conclusions thus obtained provide novel insights into the inner workings of the algorithm, and are supported by simulations. Moreover, we conduct experiments with real-world data considering an acoustic echo cancellation application, which show that the theoretical model thus obtained may perform reasonably well even when many of the assumptions made in the analysis do not hold.

Keywords

Adaptive filtering, bias-variance decomposition, least-mean-squares, mean-square deviation, transient analysis.

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