Robustness of Parametric Source Demixing in Echoic Environments

Blind source separation (BSS) of audio signals in echoic environments such as an office room is still a very challenging problem. Here we approach the problem from a practical perspective and shed light on how robust a two channel echoic parametric demixing can get. We assume that an oracle (i.e. a perfect estimator) provides a truncated estimate of the mixing FIR filters for a given source configuration. This way we can study the properties of a parametric demixer using the adjoint of the truncated mixing matrix. For several degrees of truncation, we compute how the separation SNR varies as a function of the uncertainty of the true source position. The true source position is uniformly distributed within a sphere of radius R around an assumed position, to reflect the fact that parameters of interest are imprecisely estimated. Simulations of artificial echoic mixings show that the higher order demixing filters have little robustness to position uncertainties (and therefore to errors of estimation) while the overall performance remains almost constant beyond the second order approximation. This should represent a guideline for what is practically achievable with a class of BSS techniques in echoic environments.