Bursting in the LMS algorithm

Author

Rupp, Markus

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

43

Issue

10

fYear

1995

fDate

10/1/1995 12:00:00 AM

Firstpage

2414

Lastpage

2417

Abstract

The least mean square (LMS) algorithm is known to converge in the mean and in the mean square. However, during short time periods, the error sequence can blow up and cause severe disturbances, especially for non-Gaussian processes. The paper discusses potential short time unstable behavior of the LMS algorithm for spherically invariant random processes (SIRP) like Gaussian, Laplacian, and K₀. The result of this investigation is that the probability for bursting decreases with the step size. However, since a smaller step size also causes a slower convergence rate, one has to choose a tradeoff between convergence speed and the frequence of bursting

Keywords

Gaussian processes; Laplace equations; error analysis; least mean squares methods; numerical stability; probability; random processes; sequences; signal processing; Gaussian process; K₀ process; LMS algorithm; Laplacian process; bursting; convergence rate; disturbances; error sequence; least mean squares; nonGaussian processes; short time unstable behavior; spherically invariant random processes; step size; Algorithm design and analysis; Convergence; Filters; Frequency; Laplace equations; Least squares approximation; Probability; Random processes; Signal processing algorithms; Statistical analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.469846

Filename

469846