Under-determined source separation based on power spectral density estimated using cylindrical mode beamforming

Sound source signals can be separated using Wiener post-filters calculated by estimating the power spectral densities (PSDs) of sources from the outputs of a set of beamformers. This approach has been shown effective in the under-determined case where the number of sources to be separated exceeds the number of microphones. In this paper, a limit on the maximum number of separable sources is derived beyond which the problem becomes rank deficient. This study reveals the number of sources that can be separated simultaneously is related to the order of the beam patterns. Further, using the principles of cylindrical mode beamforming, the performance can be predicted as a function of frequency. The result is consistent with simulations in which the performance of separating music and speech sound sources was quantified.