Asymptotic properties of an adaptive beam former algorithm

Author

Yin, G.

Author_Institution

Dept. of Math., Wayne State Univ., Detroit, MI, USA

Volume

35

Issue

4

fYear

1989

fDate

7/1/1989 12:00:00 AM

Firstpage

859

Lastpage

867

Abstract

The asymptotic properties of a recursive adaptive beam former algorithm are studied. Both decreasing-gain and constant-gain cases are treated. For the case of decreasing gain the mean square convergence result is obtained, whereas for constant gain a sharp bound is derived, and asymptotic analysis for the normalized error is carried out. The analysis provides a clear picture of the local behaviour of the iterates near the optimal value. A sequence of scale deviations or normalized errors is shown to converge to a Gauss-Markov diffusion process which satisfies a stochastic differential equation

Keywords

adaptive filters; filtering and prediction theory; signal processing; Gauss-Markov diffusion process; adaptive beam former algorithm; adaptive filter; array processing; asymptotic properties; constant gain; decreasing gain; mean square convergence; normalized error; recursive algorithm; sharp bound; stochastic differential equation; Adaptive arrays; Adaptive control; Adaptive filters; Constraint theory; Convergence; Differential equations; Diffusion processes; Gaussian processes; Signal processing algorithms; Stochastic processes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.32162

Filename

32162