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Modulation-Domain Multichannel Kalman Filtering for Speech Enhancement

Compared with single-channel speech enhancement methods, multichannel methods can utilize spatial information to design optimal filters. Although some filters adaptively consider second-order signal statistics, the temporal evolution of the speech spectrum is usually neglected. By using linear prediction (LP) to model the inter-frame temporal evolution of speech, single-channel Kalman filtering (KF) based methods have been developed for speech enhancement. In this paper, we derive a multichannel KF (MKF) that jointly uses both interchannel spatial correlation and interframe temporal correlation for speech enhancement. We perform LP in the modulation domain, and by incorporating the spatial information, derive an optimal MKF gain in the short-time Fourier transform domain. We show that the proposed MKF reduces to the conventional multichannel Wiener filter if the LP information is discarded. Furthermore, we show that, under an appropriate assumption, the MKF is equivalent to a concatenation of the minimum variance distortion response beamformer and a single-channel modulation-domain KF and therefore present an alternative implementation of the MKF. Experiments conducted on a public head-related impulse response database demonstrate the effectiveness of the proposed method.