Maximizing Predicted Signal-to-Distortion Ratio: A New Microphone Selection Criterion for Beamforming in Acoustic Sensor Networks

This paper addresses the problem of selecting an effective subset of microphones in acoustic sensor networks (ASNs) for speech enhancement applications. A basic approach to this problem is to select a subset of microphones such that the output signal-to-noise ratio (oSNR) of the beamforming output signal is maximized. However, oSNR does not necessarily correlate well with widely used signal quality measures such as the signal-to-distortion ratio (SDR), perceptual evaluation of speech quality (PESQ), and short-time objective intelligibility (STOI). We here introduce a new measure that predicts SDR for beamforming output signals. This measure, termed predicted SDR (pSDR), demonstrates a better correlation with SDR, PESQ, and STOI compared to oSNR. Whereas the original SDR requires an oracle reference signal for measurements, the proposed pSDR is defined in the short-time Fourier transform domain and can be estimated solely from source covariance matrices already used for obtaining beamformers. Therefore, our pSDR can be immediately used as a measure for selecting microphones instead of oSNR. We also extend conventional subset selection methods to jointly select a reference microphone of beamformers in a unified optimization problem. This extension is crucial because the choice of the reference microphone can significantly affect the quality of enhanced signals in ASNs. Numerical experiments suggest that, as a measure for selecting both a microphone subset and a reference microphone, pSDR is generally better than, or at least comparable to, oSNR in terms of SDR, PESQ, and STOI. We also demonstrate the effectiveness of selecting a microphone subset jointly with a reference microphone of beamformers.