Design and Optimization of Superdirective Beamforming and Post-Filtering for Speech Enhancement

Superdirective beamformers, used with small microphone arrays, are highly attractive due to their high directivity and frequency-invariant beampatterns, making them well-suited for processing broadband acoustic and speech signals. However, these beamformers are very sensitive to array imperfections such as sensor mismatches and self-noise. To improve robustness, robust superdirective (RSD) beamformers have been developed, employing techniques such as diagonal loading or white-noise-gain constraints during their derivation. Although RSD beamformers offer enhanced robustness compared to classical superdirective beamformers, they cannot achieve the maximum directivity factor and lose some frequency-invariant properties, resulting in a beamwidth that is wider at low frequencies and narrower at high frequencies. As a result, RSD beamformers do not fully meet the criteria of true superdirective beamformers, providing less effective noise reduction and introducing some speech distortion. Post-filtering methods have been developed to improve noise reduction after RSD beamforming, but they often fail to address the distortion issues, especially when the speech source deviates from the array’s look direction. To overcome this limitation, this paper proposes a joint optimization approach that combines post-filtering with RSD beamformers. By using the output of RSD beamformers as input data and considering various deviations in look directions and array mismatches, we train a post-filtering network to further enhance the beamformer’s output. Experimental results on speech enhancement demonstrate the effectiveness and robustness of the proposed method.