Transient weight misadjustment properties for the finite precision LMS algorithm

Implementation of the least mean squares (LMS) algorithm in finite precision (FP) arithmetic introduces degradations in performance compared to the infinite precision (IP) implementation. This paper derives a new and more accurate analytical result for the expected misadjustment in the LMS weight vector due to FP effects. Whereas previous results have been applicable only during steady state, the results of this present paper are applicable to both the transient adaptation period and steady state. Experimental data are then presented which show the new analytical results to be valid for approximating the weight misadjustment during the transient adaptation period over a wide range of filter and data values.