ULV AND GENERALIZED ULV SUBSPACE TRACKING ADAPTIVE ALGORITHMS

Traditional adaptive filters assume that the effective rank of the imp art: signal is the same as the input covariance matrix or the filter l ength N, Therefore, if the input signal lives in a subspace of dimensi on less than N, these filters fail to perform satisfactorily, lin this paper, we present two new algorithms for adapting only in the dominan t signal subspace, The first of these is a low-rank recursive-least-sq uares (RLS) algorithm that uses a ULV decomposition to track and adapt int the signal subspace. The? second adaptive algorithm is a subspace tracking least-mean-squares (LMS) algorithm that uses a generalized U LV (GULV) decomposition, developed in this paper, to track and adapt i n subspaces corresponding to several well-conditioned singular value c lusters, The algorithm also has an improved convergence speed compared with that of the LMS algorithm, Bounds on the quality of subspaces is olated using the GULV decomposition are derived, and the performance o f the adaptive algorithms are analyzed.