Convergence analysis of block orthogonal projection and affine projection algorithms

The affine projection (AP) and the block orthogonal projection (BOP) algorithms are known to have good convergence properties even when the input signal is correlated. However, their convergence rates are not elucidated yet, since they are based on orthogonal projection. and are too complicated to be analyzed. In this paper, we first consider their geometrical view and derive their convergence rates for white signals. Moreover, we provide an approximation method to evaluate the convergence rate for cot-related signals and show the results which are confirmed by computer simulations. The results imply that the convergence rate of the BOP algorithm gets saturated as the block size increases. (C) 2002 Elsevier Science B.V. All rights reserved.