A fast exact weighted subband adaptive algorithm and its application to mono and stereo acoustic echo cancellation

The fast affine projection (FAP) algorithm (Gay and Tavathia, Proceedings of the IEEE International Conference on Acoustic, Speech and Signal Processing, 1995, 3023) is known to outperform the NLMS with a slight increase in complexity, but it involves the fast calculation of the inverse of a covariance matrix of the input data that could undermine the performance of the algorithm. The block subband adaptive algorithm in (Courville and Duhamel, IEEE Trans. Signal Processing 46(9) (1998) 2359) has also illustrated significant improvement in performance over the NLMS and other frequency domain adaptive algorithms. However, it is known that block processing algorithms have lower tracking capabilities than the their sample-by-sample counterparts. In this paper, we present a sample-by-sample version of the algorithm in (Courville and Duhamel, IEEE Trans. Signal Processing 46(9) (1998) 2359) and develop a low complexity implementation of this algorithm. As a sample-by-sample algorithm, it avoids the reduced tracking capability of block algorithms. Because it does not use matrix inversion, it avoids the numerical problems of FAP algorithms. We will show that the new sample-by-sample algorithm approximates the affine projection algorithm and possesses a similar property in reducing coefficient bias that appears in monophonic and stereophonic teleconferencing when the receiving room impulse responses are undermodeled. The new fast sample-by-sample algorithm is extended for stereo acoustic echo cancellation. Simulations of echo cancellations in actual rooms are presented to verify our findings.