RTF based LCMV beamformer with multiple reference microphones

Microphone arrays are widely used for speech enhancement applications. We consider the enhancement of multiple desired speakers in a noisy environment while utilizing the Relative Transfer Function (RTF) approach for the beamformer realization. When beamforming operation relies on an estimated RTF, it produces a signal with reduced noise compared to the signal received by some reference microphone associated with the RTF, while maintaining its speech component undistorted. The reference microphone is usually chosen as the microphone with the highest Signal-to-Noise Ratio (SNR). For large arrays, in a multiple desired speaker environment, there is no single reference microphone which maximizes SNR for all desired speakers. The commonly used RTF technique may result in compromised performance for one or more desired speakers. Here, we propose an alternative scheme that considers multiple reference microphones. Each reference microphone is associated with a single desired speaker such that it maximizes its input SNR, in comparison to other array microphones. We show that by this technique, the beamformer maintains the desired noise reduction without compromising SNR for any of the desired speakers. We present analytical analysis for a 2 microphone array in free-field propagation for far-field sources. Based on this analysis some design criteria are derived and finally evaluated both in synthetic and recorded room environments.