A subspace-based perspective on spatial filtering performance with distributed and co-located microphone arrays

Commonly used data-dependent spatial filters depend on the acoustic transfer functions and the power spectral density (PSD) matrices of the desired and the undesired signals. Assuming a low-rank model of the spatial PSD matrix of the signals, and a particular spatial filter, the performance in terms of a given objective measure can often be described analytically. In this paper, we propose to use the similarity between the desired and undesired signal subspaces obtained from the sample spatial PSD matrices, as an indicator of the achievable spatial filtering performance. The subspace similarity is expressed as a distance function on the Grassmann manifold, computed using the principal angles between the subspaces. Particularly, subspace distances and spatial filtering performance are compared when using distributed arrays and co-located microphones. Experimental results demonstrate the relation between these two different measures for different array configurations and reverberation levels.