A Probability Distribution Model for the Relative Transfer Function in a Reverberant Environment

The relative transfer function (RTF) is a generalization of the delay-based array manifold, which is applicable to reverberant environments with multiple reflections. Beamformers that utilize RTF are known to outperform the simpler beamforming techniques that use delay-based steering vectors. Adopting established models of the acoustic transfer functions and utilizing recent contributions which derive the probability distribution of the ratio of independent complex-Gaussian random variables, we derive a probability distribution model for the RTF. The model is verified and compared to the empirical distribution in multiple Monte-Carlo experiments.