Frequency-domain adaptive filtering revisited, generalization to the multi-channel case, and application to acoustic echo cancellation

We derive a new frequency-domain adaptive algorithm by using a frequency-domain recursive least squares criterion, minimizing an error signal in the frequency-domain. We then derive an exact adaptive algorithm from the so-called normal equation. It is shown that the obtained algorithm is complex to implement, and to reduce the complexity we need to remove a constraint resulting in the unconstrained frequency-domain LMS (UFLMS) algorithm. Most importantly, we generalize all this to the multi-channel case, thereby exploiting the cross-power spectra among all the channels which is very important (for a fast convergence rate) in multichannel acoustic echo cancellation (AEC), where the input signals are highly correlated