SAVING COMPLEXITY OF MODIFIED FILTERED-X-LMS AND DELAYED UPDATE LMS ALGORITHMS

In some applications, like in active noise control, the error signal c annot be obtained directly but only a filtered version of it, A gradie nt adaptive algorithm that solves the identification problem under thi s condition is the well known Filtered-x Least-Mean-Squares (FxLMS) al gorithm. If only one coefficient of this error-filter function is nonz ero, a special case of the FxLMS algorithm, the Delayed-update Least-M ean-Squares (DLMS) algorithm is obtained. The drawback of these algori thms is the increased dynamic order which, in turn, decreases the conv ergence rate. Recently, some modifications for these algorithms have b een proposed, overcoming the drawbacks by additional computations of t he same filter order as the filter length M. In this contribution, an improvement is shown yielding reduced complexity if the error path fil ter order P is much smaller than the filter order M, which is the case for many applications. Especially for the DLMS algorithm a strong sav ing can be obtained.