Title :
A unifying view of error nonlinearities in LMS adaptation
Author :
Al-Naffouri, Tareq Y. ; Zerguine, Azzedine ; Bettayeb, Maamar
Author_Institution :
Sch. of Electr. & Comput. Eng., Georgia Inst. of Technol., Atlanta, GA, USA
Abstract :
This paper presents a unifying view of various error nonlinearities that are used in least mean square (LMS) adaptation such as the least mean fourth (LMF) algorithm and its family and the least-mean mixed-norm algorithm. Specifically, it is shown that the LMS algorithm and its error-modified variants are approximations of two previously developed optimum nonlinearities which are expressed in terms of the additive noise probability density function (PDF). This is demonstrated through an approximation of the optimum nonlinearities by expanding the noise PDF in a Gram-Charlier series. Thus a link is established between intuitively proposed and theoretically justified variants of the LMS algorithm. The approximation has also a practical advantage in that it provides a trade-off between simplicity and more accurate realization of the optimum nonlinearities
Keywords :
adaptive filters; adaptive signal processing; error analysis; filtering theory; least mean squares methods; probability; series (mathematics); Gram-Charlier series; LMS adaptation; LMS algorithm; PDF; adaptive filter; additive noise; approximations; error nonlinearities; least mean fourth algorithm; least mean square; least-mean mixed-norm algorithm; optimum nonlinearities; probability density function; Adaptive filters; Additive noise; Algorithm design and analysis; Approximation algorithms; Computer errors; Density functional theory; Least squares approximation; Numerical stability; Physics; Robust stability;
Conference_Titel :
Acoustics, Speech and Signal Processing, 1998. Proceedings of the 1998 IEEE International Conference on
Conference_Location :
Seattle, WA
Print_ISBN :
0-7803-4428-6
DOI :
10.1109/ICASSP.1998.681783
