Virtually increasing microphone array elements by interpolation in complex-logarithmic domain

In this paper, we propose a new array signal processing technique for an underdetermined condition by increasing the number of observation channels. We introduce virtual observation as an estimate of the observed signals at positions where real microphones are not placed. Such signals at virtual observation channels are generated by the complex logarithmic interpolation of real observed signals. With the increased number of observation channels, conventional linear array signal processing methods can be applied to underdetermined conditions. As an example of the proposed array signal processing framework, we show experimental results of speech enhancement obtained with maximum SNR beamformers modified using the virtual observation.