A fast least squares algorithm for constrained adaptive filtering

A fast least squares algorithm is proposed for adaptive filtering with linear constraints. The algorithm is exact, with a computational complexity proportional to NK+K²+N+K where N is the number of the filter coefficients and K is the number of constraints. The approach consists of obtaining the adaptation gain by means of a fast least squares (FLS) algorithm and using this gain in the recursive calculations of the parameters related to the constraints. The recursive procedures are carried out by using the matrix inversion lemma. The good performance of the proposed method is illustrated by some simulation results. The algorithm can be used in several applications such as array processing, adaptive beamforming, spectral analysis and telecommunications