Convergence analysis of the sign algorithm for adaptive filtering

Author

Masry, Elias ; Bullo, Francesco

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA, USA

Volume

41

Issue

2

fYear

1995

fDate

3/1/1995 12:00:00 AM

Firstpage

489

Lastpage

495

Abstract

We consider the convergence analysis of the sign algorithm for adaptive filtering when the input processes are uncorrelated and Gaussian and a fixed step size μ>0 is used. Exact recursive equations for the covariance matrix of the deviation error are established for any step size μ>0. Asymptotic time-averaged convergence for the mean-absolute deviation error, mean-square deviation error, and for the signal mean-square estimation error are established. These results are shown to hold for arbitrary step size μ>0

Keywords

Gaussian processes; adaptive estimation; adaptive filters; convergence of numerical methods; covariance matrices; error analysis; filtering theory; adaptive filtering; adaptive linear estimation; asymptotic time-averaged convergence; convergence analysis; covariance matrix; exact recursive equations; input processes; mean-absolute deviation error; mean-square deviation error; sign algorithm; signal mean-square estimation error; step size; uncorrelated Gaussian input process; Adaptive filters; Algorithm design and analysis; Convergence; Covariance matrix; Equations; Estimation error; Filtering algorithms; Least squares approximation; Noise cancellation; Nonlinear filters;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.370150

Filename

370150