Multiple subspace ULV algorithm and LMS tracking

ABSTRACT. The LMS adaptive algorithm is the most popular algorithm for adaptive ltering because of its simplicity and robustness. However, its main drawback is slow convergence whenever the adaptive lter input auto-correlation matrix is ill-conditioned i.e. the eigenvalue spread of this matrix is large [2, 4]. Our goal in this paper is to develop an adaptive signal transformation which can be used to speed up the convergence rate of the LMS algorithm, and at the same time provide a way of adapting only to the strong signal modes, in order to decrease the excess Mean Squared Error (MSE). It uses a data dependent signal transformation. The algorithm tracks the subspaces corresponding to clusters of eigenvalues of the auto-correlation matrix of the input to the adaptive lter, which have the same order of magnitude. The algorithm up-dates the projection of the tap weights of the adaptive lter onto each subspace using LMS algorithms with dierent step sizes. The technique also permits adaptation only in those subspaces, which contain strong signal components leading to a lower excess Mean Squared Error (MSE) as compared to traditional algorithms. The transform should also be able to track the signal behavior in a non-stationary environment. We develop such a data adaptive transform domain LMS algorithm, using a generalization of the rank reveal-ing ULV decomposition, rst introduced by Stewart [5]. We generalize the two-subspace ULV updating procedure to track subspaces corresponding to three or more singular value clusters