On the variance of the LMS algorithm squared-error sample curve

Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean value of the squared error. Behavior models based on average measures models are useful for understanding the algorithm behavior under different environments and can be used for design. Ne...

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Bibliographic Details
Published inSignal processing Vol. 238; p. 110168
Main Authors Maruo, Marcos H., Almeida, Sérgio J.M., Bermudez, José C.M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2026
Subjects
Adaptive filtering
Least mean-square (LMS) algorithm
Real-time system
Sample function
Adaptive filtering
Real-time system
Least mean-square (LMS) algorithm
Sample function
Online AccessGet full text
ISSN0165-1684
DOI10.1016/j.sigpro.2025.110168

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Summary:Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean value of the squared error. Behavior models based on average measures models are useful for understanding the algorithm behavior under different environments and can be used for design. Nevertheless, from a practical point of view, the adaptive filter user has only one realization of the algorithm to obtain the desired result. This article derives a model for the variance of the squared-error sample curve of the least-mean-square (LMS) adaptive algorithm, so that the achievable cancellation level can be predicted based on the properties of the steady-state squared error. The derived results provide the user with useful design guidelines.
ISSN:0165-1684
DOI:10.1016/j.sigpro.2025.110168