Multi-channel post-filtering based on spatial coherence measure

• A spatial coherence measure on microphone array for signal field similarity.
• A post-filtering algorithm considering multi-rank signal models.
• A bias-compensated post-filtering algorithm is further proposed.
• The superiority of the proposed method across different types of noise fields.

A multi-channel post-filtering algorithm using the proposed spatial coherence measure is derived. The spatial coherence measure evaluates the similarity between the measured signal fields using power spectral density matrices. In the proposed post-filter, the assumption of homogeneous sound fields is relaxed. Besides, multi-rank signal models can be easily adopted. Under this measure, the bias term due to the similarity of the desired signal field and the noise field is further investigated and a solution based on bias compensation is proposed. It can be shown that the compensated solution is equivalent to the optimal Wiener filter if the bias or the noise power spectral density matrix is perfectly measured. Simulations with incoherent, diffuse, and coherent noise fields and a local scattered desired source were conducted to evaluate the algorithms. The results demonstrate the superiority of the proposed bias compensated post-filter across different types of noise fields with a more accurate signal model.