Circulant-preconditioned block adaptive filtering algorithms based on the nested iteration technique

In this paper, three circulant-preconditioned adaptive algorithms are prese nted based on the nested iteration technique for block adaptive FIR filters . The circulant-preconditioned block conjugate gradient (CBCG) algorithm is derived using the conjugate direction vectors for updating the tap weights . The CBCG algorithm is then modified to two reduced versions employing the unconstrained condition in computation of convolutions and deconvolutions and using the gradient vectors instead of the conjugate gradient vectors, r espectively. The proposed algorithms are formulated from minimization of an estimate of the block mean-square error (BMSE) and efficiently implemented with order of O(N log N) operations in the frequency domain. Through compu ter simulations, it is shown that the proposed algorithms are superior in t he convergence properties to the preconditioned conjugate gradient algorith ms using the preconditioners studied earlier, and the algorithms are robust to the changes of the eigenvalue spread. It is also shown that the conjuga te gradient vectors are more effective in the rate of convergence than the gradient vectors. (C) 2000 Elsevier Science B.V. All rights reserved.