Block conjugate gradient algorithms for adaptive filtering

Abstract

Two adaptive algorithms based on the conjugate gradient method are presented for finite impulse response (FIR) block adaptive filters. First, the block conjugate gradient (BCG) algorithm is derived from minimization of an estimate of the block mean-square error (BMSE). Using the fast convolution technique, the BCG algorithm is then extended to the frequency domain BCG (FBCG) algorithm that yields significant computational savings over the BCG algorithm, especially for a large filter-tap order. Through computer simulations, it is shown that although the adaptation accuracy of the BCG or the FBCG is nearly equal to that of the optimum block adaptive (OBA) algorithm, its convergence property is superior to that of the OBA algorithm under any input conditions. Moreover, it is also shown that their convergence rate is as fast as the recursive least-squares (RLS) algorithms for a relatively small eigenvalue spread.