Optimum step-size control for a variable step-size stereo acoustic echo canceller in the frequency domain

The frequency-domain adaptive filter (FDAF) is a competitive candidate for stereo acoustic echo cancellation (SAEC) because of its good convergence and computational efficiency. However, there is a conflict between the convergence rate and the steady-state misalignment when using a constant step size. In this paper, a variable step-size approach is proposed for the stereo echo canceller in the frequency domain. The proposed method uses a first-order Markov model to describe the time-varying echo paths between the loudspeakers and the microphone. Following a statistical convergence analysis of the two-channel FDAF algorithm, the state recursion of the system distance in each frequency bin is given. The optimal step size is then derived by minimizing the system distance. Several practical problems, including noise power spectral density estimation and echo paths change detection, are discussed in details. Moreover, a close link between the proposed optimum step-size control method and the multichannel state–space frequency-domain adaptive filter is established. We show that the proposed variable step-size approach can also be incorporated into the block extended least-mean-square algorithm to fully exploit their benefits. Finally, computer simulations demonstrate that the proposed algorithm exhibits an excellent convergence performance and is very robust to the double talk.