On the Global Output SNR of the Parameterized Frequency-Domain Multichannel Noise Reduction Wiener Filter

The parameterized multichannel Wiener filter (PMWF) is known to allow for a flexible tuning of speech distortion and noise reduction. In addition, the output signal-to-noise ratio (SNR) is a natural metric that shows the true effect of such a filter on both residual noise and filtered speech. Earlier contributions have only shown that the output SNR of the Wiener filter is larger than the input SNR (as a proof of its effectiveness). However, the effect of the tuning parameter (denoted as beta following the notation of [1]) on this metric is not yet understood. In this paper, we prove that the global (fullband) output SNR of the PMWF is an increasing function of beta but remains below an asymptotic value. As a byproduct, a very simplified proof of the global output SNR improvement is provided.