On the Noise Reduction Performance of a Spherical Harmonic Domain Tradeoff Beamformer

In this letter, we derive an expression for the expected incoherent noise reduction factor of a spherical harmonic domain (SHD) tradeoff beamformer. The tradeoff beamformer attempts to reduce noise while minimizing speech distortion, and includes the minimum variance distortionless response (MVDR) and multichannel Wiener filters as special cases. For the open spherical microphone array, we find a number of analogies between the expressions for the expected noise reduction factor of the SHD and spatial domain MVDR beamformers. In an anechoic environment we find that the performance of the SHD MVDR beamformer with an open array depends almost entirely on the number of microphones, as in the spatial domain.