Performance analysis of the covariance-whitening and the covariance-subtraction methods for estimating the relative transfer function

Estimation of the relative transfer functions (RTFs) vector of a desired speech source is a fundamental problem in the design of data-dependent spatial filters. We present two common estimation methods, namely the covariance-whitening (CW) and the covariance-subtraction (CS) methods. The CW method has been shown in prior work to outperform the CS method. However, thus far its performance has not been analyzed. In this paper, we analyze the performance of the CW and CS methods and show that in the cases of spatially white noise and of uniform powers of desired speech source and coherent interference over all microphones, the CW method is superior. The derivations are validated by comparing them to their empirical counterparts in Monte Carlo experiments. In fact, the CW method outperforms the CS method in all tested scenarios, although there may be rare scenarios for which this is not the case.

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