Performance analysis of transform domain normalized LMS algorithm

The performance of the transform domain normalized least mean square (LMS) algorithm is studied. The discussion is limited to the systems that employ an orthogonal transform to convert the incoming samples to a set of partially uncorrelated components, to be used as input to an adaptive linear combiner. To obtain an effective mathematical tool for analysis of the LMS-type algorithms a new performance index is proposed. The proposed index is used to derive many useful results. It is shown that a thorough understanding of the filtering concept results in many rules of thumb that can be readily used for choosing near-optimum transformations in the cases when partial information of input statistics is available. It is shown that the KLT (Karhunen-Loeve transform) implements a set of parallel filters which is optimal in the sense that it fulfils the conditions imposed by the filtering concept