Clock-Offset and Microphone Gain Mismatch Invariant Beamforming

The use of wireless acoustic sensor networks (WASNs) has received increased attention over the last decade. The advantages of WASNs over stand-alone multi-microphone devices are that the microphone array is not anymore limited by the dimensions of a single device, and that microphones can be placed at arbitrary locations. One of the disadvantages, however, is that for many applications, like beamforming, the clocks of all devices in the network need to be synchronised and that the microphone gains need to be equalised. In this paper we will prove that a specific class of beamformers is clock-offset and gain mismatch invariant. The parameters for these beamformers (acoustic transfer function and power spectral density matrices) can be estimated directly from the uncalibrated microphone signals, instead of first synchronising the clocks and equalising the gains and then estimating them. The resulting beamformers are applied to the non-calibrated microphone signals. We will substantiate, by means of computer simulations, that the proposed approach gives identical results compared to the setup where microphone signals are first calibrated, so that clock-offset compensation and microphone gain equalisation becomes unnecessary.