Analysis of conjugate gradient algorithms for adaptive filtering

Author

Chang, Pi Sheng ; Willson, Alan N., Jr.

Author_Institution

Dept. of Electr. Eng., California Univ., Los Angeles, CA, USA

Volume

48

Issue

2

fYear

2000

fDate

2/1/2000 12:00:00 AM

Firstpage

409

Lastpage

418

Abstract

The paper presents and analyzes two approaches to the implementation of the conjugate gradient (CG) algorithm for filtering where several modifications to the original CG method are proposed. The convergence rates and misadjustments for the two approaches are compared. An analysis in the z-domain is used in order to find the asymptotic performance, and stability bounds are established. The behavior of the algorithms in finite word-length computation are described, and dynamic range considerations are discussed. It is shown that in finite word-length computation and close to steady state, the algorithms´ behaviors are similar to the steepest descent algorithm, where the stalling phenomenon is observed. Using 16-bit fixed-point number representation, our simulations show that the algorithms are numerically stable

Keywords

adaptive filters; adaptive signal processing; conjugate gradient methods; digital simulation; filtering theory; fixed point arithmetic; numerical stability; 16 bit; CG method; adaptive filtering; asymptotic performance; conjugate gradient algorithms; convergence rates; dynamic range; finite word-length computation; fixed-point number representation; misadjustments; numerically stable algorithms; simulations; stability bounds; stalling phenomenon; steady state; steepest descent algorithm; z-domain analysis; Adaptive filters; Algorithm design and analysis; Asymptotic stability; Character generation; Convergence; Dynamic range; Filtering algorithms; Performance analysis; Stability analysis; Steady-state;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.823968

Filename

823968