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M. Rupp:
"The LMS Algorithm Under Arbitrary Linearly Filtered Processes";
Talk: European Signal Processing Conference (EUSIPCO), Barcelona, Spain; 08-29-2011 - 09-02-2011; in: "19th European Signal Processing Conference", (2011), ISSN: 2076-1465; 126 - 130.

In this paper the mean square convergence of the LMS algorithm is
shown for a large class of linearly filtered random driving processes.
In particular this paper contains the following contributions: i) The
parameter error vector covariance matrix can be decomposed into
two parts, a first part that exists in the modal space of the driving
process of the LMS filter and a second part, existing in its orthogonal
complement space, not contributing to the performance measures
(misadjustment, mismatch) of the algorithm. ii) The LMS
updates force the initial values of the parameter error vector covariance
matrix to remain essentially in the modal space of the driving
process and components of the orthogonal complement die out.
iii) The impact of additive noise is shown to contribute only to the
modal space of the driving process independent of the noise statistic
and thus defines the steady-state of the filter. In particular it will be
shown that the joint fourth order moment m(2;2)of the decorrelated
driving process is a more relevant parameter for the step-size bound
and not as often believed the second order moment m(2).

LMS algorithm

http://publik.tuwien.ac.at/files/PubDat_198826.pdf

Project Head Markus Rupp:
Signal and Information Processing in Science and Engineering - Entwicklungsmethodik