A novel structure for adaptive LS FIR filtering based on QR decomposition

A very powerful technique for computing the LS (least squares) estimates of an FIR (finite impulse response) filter´s impulse response is described. It is based on the QR factorization of the input data matrix. The method consists of two parts. First the input matrix is factorized into an orthogonal Q part and an upper triangular R part. The unknown coefficients are then obtained from a triangular linear system of equations. An algorithm for solving the above linear system, which is appropriate for adaptive processing, is proposed. This is achieved via a set of Givens rotations and a modified Faddeeva scheme