An LCMV filter for single-channel noise cancellation and reduction in the time domain

In this paper, we consider a recent class of optimal rectangular filtering matrices for single-channel speech enhancement. This class of filters exploits the fact that the dimension of the signal subspace is lower than that of the full space. Then, extra degrees of freedom in the filters, that are otherwise reserved for preserving the signal subspace, can be used for achieving an improved output signal-to-noise ratio (SNR). Interestingly, these filters unify the ideas of optimal filtering and subspace methods. We propose an optimal LCMV filter in this framework with minimum output power that passes the desired signal undistorted and cancels correlated noise. The cancellation was not facilitated by the filters derived so far in this framework. The results show that the proposed filter can achieve output SNRs similar to that of competing filter designs, while having a much higher output signal-to-interference ratio. This is showed for both synthetic and real speech signals.