Identification of linear systems with adaptive control of the cross-multiplicative transfer function approximation

In this paper, we extend the cross-multiplicative transfer function (CMTF) approach for improved system identification in the short- time Fourier transform (STFT) domain. The proposed algorithm adaptively controls the number of cross-terms in the CMTF approximation to achieve the minimum mean-square error (mmse) at each iteration. A small number of cross-terms is initially used to achieve fast convergence, and as the adaptation process proceeds, the algorithm gradually increases this number to enhance the steady-state performance. When compared to the conventional multiplicative transfer function (MTF) approach, the resulting algorithm achieves a substantial improvement in steady-state performance, without compromising for slower convergence. Experimental results validate the theoretical derivations and demonstrate the advantage of the proposed approach to acoustic echo cancellation.