A FAST PROJECTION ALGORITHM FOR ADAPTIVE FILTERING

This paper proposes a new algorithm called the fast Projection algorit hm, which reduces the computational complexity of the Projection algor ithm from (p+1)L+O(p(3)) to 2L+20p (where L is the length of the estim ation filter and p is the projection order.) This algorithm has proper ties that lie between those of NLMS and RLS, i.e. less computational c omplexity than RLS but much faster convergence than NLMS for input sig nals like speech. The reduction of computation consists of two parts. One concerns calculating the pre-filtering vector which originally too k O(p(3)) operations. Our new algorithm computes the pre-filtering vec tor recursively with about 15p operations. The other reduction is acco mplished by introducing an approximation vector of the estimation filt er. Experimental results for speech input show that the convergence sp eed of the Projection algorithm approaches that of RLS as the projecti on order increases with only a slight extra calculation complexity bey ond that of NLMS, which indicates the efficiency of the proposed fast Projection algorithm.