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The LMS Algorithm Under Arbitrary Linearly Filtered Processes

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Executive Summary

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: 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. 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.

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