By considering the multi-frame signal model, speech correlation between different time-frames can be exploited. Based on this signal model, the multi-frame minimum variance distortionless response (MFMVDR) filter for single-channel speech enhancement has been derived, which minimizes the total signal output power while avoiding speech distortion. It has been shown that the MFMVDR filter is very sensitive to estimation errors in the speech correlation vector resulting in correlated speech components being mistakenly suppressed. Inspired by robust beamforming approaches, in this paper we propose a robust constrained MFMVDR filter for single-channel speech enhancement by estimating the speech correlation vector that maximizes the total signal output power within a spherical uncertainty set. For the upper bound of the spherical uncertainty set, we propose to use a trained mapping function that depends on the a-priori signal-to-noise ratio (SNR). Experimental results for different noise types and SNRs show that the proposed robust approach yields a more accurate estimate of the speech correlation vector. A perceptual evaluation shows that the robust constrained MFMVDR filter leads to an improved speech quality but a lower noise reduction than the original non-robust MFMVDR filter, while still being preferred in overall quality.
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