Blind Identification of Convolutive MIMO System with 3 Sources and 2 Sensors

摘要

We address the problem of blind identification of a convolutive Multiple-Input Multiple-Output (MIMO) system with more inputs than outputs, and in particular, the 3-input 2-output case. We assume that the inputs are temporally white, non-Gaussian distributed, spatially independent, and the system has real impulse response. Solutions for the scalar MIMO case, within scaling and permutation ambiguities, have been proposed in the past, based on canonical decomposition of tensors constructed from higher-order cross-cumulants of the system output. We here look at the problem in the frequency domain, where, for each frequency we construct two tensors based on cross-polyspectra of the output. Canonical decomposition of these tensors yields the system frequency response within frequency dependent scaling and permutation ambiguities. We propose ways to resolve these ambiguities, and show that it is possible to obtain the system response within a scalar and a linear phase.