Fast Implementation of a Subband Adaptive Algorithm for Acoustic Echo Cancellation

The block subband adaptive algorithm in [1] has 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. The Fast Affine Projection (FAP) algorithm [2] also outperforms the NLMS with a slight increase in complexity, but involves the fast calculation of the inverse of a covariance matrix of the input data that could undermine the performance of the algorithm. In this paper, we present a sample-by-sample version of the algorithm in [1] and develop an exact, low complexity implementation of this algorithm. The new fast algorithm does not require matrix inversion thus alleviating the drawbacks of the FAP algorithm. Moreover, we will show that the new sample-by-sample algorithm approximates the affine projection algorithm and possesses a similar property in reducing the coefficient bias that appears in monophonic and stereophonic teleconferencing when the receiving room impulse responses are undermodelled. 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.