ON THE LEAST-SQUARES TAP ADJUSTMENT ALGORITHM IN ADAPTIVE DIGITAL ECHO CANCELERS

Fast recursive algorithms for updating coefficients in digital echo cancellers can be derived from the well-known method of least squares. Unless zero initial conditions are assumed, the exact initialization of these algorithms is yet unknown. We prove here that for random data of more than twice the order of the filter, there exists a unique least squares solution with very high probability. We then derive a constructive recursive procedure in time and order for computing the pseudoinverse solution for the initial steps. Since the data matrix is composed of integers, this technique facilitates the implementation of stable tap-update algorithms. © 1990 IEEE