Multichannel noise reduction — Algorithms and theoretical limits

In this contribution we present a theoretical study on the performance of several multichannel noise reduction algorithms. It is known that the magnitude squared coherence (MSC) determines the performance of a class of adaptive algorithms i.e. active noise control or noise reduction with a reference microphone. However, the MSC is not sufficient for performance evaluation of other noise reduction methods like the Generalized Sidelobe Canceller (GSC) or adaptive post-filter techniques. We propose to measure the spatial complex coherence (CC) or normalized cross power spectrum of the sound field and show that it can be used as a much more general tool for performance analysis. First of all, we summarize the results of previous studies and present new results for the performance of the Generalize Sidelobe Canceller (GSC) as a function of the complex coherence. In the second part we examine different noise fields to show theoretical limits of multichannel noise reduction schemes.