A New Algorithm with Low Complexity for Adaptive Filtering

In this paper, we propose a new algorithm M-SMFTF for adaptive filtering with fast convergence and low complexity. It is the result of a simplified FTF type algorithm, where the adaptation gain is obtained only from the forward prediction variables and using a new recursive method to compute the likelihood variable. The computational complexity was reduced from 7L to 6L, where L is the finite impulse response filter length. Furthermore, this computational complexity can be significantly reduced to (2L+4P) when used with a reduced P-size forward predictor. This algorithm presents a certain interest, for the adaptation of very long filters, like those used in the problems of echo acoustic cancellation, due to its reduced complexity, its numerical stability and its convergence in the presence of the speech signal. The proposed algorithm outperforms the classical adaptive algorithms because of its convergence speed which approaches that of the RLS algorithm and its computational complexity which is slightly greater than the one of the normalized LMS algorithm.