Unbiased coherent-to-diffuse ratio estimation for dereverberation

We investigate the estimation of the time- and frequency-dependent coherent-to-diffuse ratio (CDR) from the measured spatial coherence between two omnidirectional microphones. We illustrate the relationship between several known CDR estimators using a geometric interpretation in the complex plane, discuss the problem of estimator bias, and propose unbiased versions of the estimators. Furthermore, we show that knowledge of either the direction of arrival (DOA) of the target source or the coherence of the noise field is sufficient for an unbiased CDR estimation. Finally, we apply the CDR estimators to the problem of dereverberation, using automatic speech recognition word error rate as objective performance measure.