Recursive Bayesian Control of Multichannel Acoustic Echo Cancellation

We present a novel recursive Bayesian method in the DFT-domain to address the multichannel acoustic echo cancellation problem. We model the echo paths between the loudspeakers and the near-end microphone as a multichannel random variable with a first-order Markov property. The incorporation of the near-end observation noise, in conjunction with the multichannel Markov model, leads to a multichannel state-space model. We derive a recursive Bayesian solution to the multichannel state-space model, which turns out to be well suited for input signals that are not only auto-correlated but also cross-correlated. We show that the resulting multichannel state-space frequency-domain adaptive filter (MCSSFDAF) can be efficiently implemented due to the submatrix-diagonality of the state-error covariance. The filter offers optimal tracking and robust adaptation in the presence of near-end noise and echo path variability.