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

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. Solutions for the scalar MIMO case, within scaling and permutation ambiguities, have been proposed in the past, based on the canonical decomposition of tensors constructed from higher-order cross-cumulants of the system output. In this paper, we look at the problem in the frequency domain, where, for each frequency we construct a number of tensors based on cross-polyspectra of the output. These tensors lead to 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. This work was supported by NSF under grant MIP-9553227, and ONR under grant N00014-20-1-0137. L. De Lathauwer is also affiliated with the group SCD (SISTA) of the E.E. Dept. (ESAT) of the K.U.Leuven (http://www.esat.kuleuven.ac.be/sista). Part of this work was supported by the Flemish Government (Research Council K.U.Leuven (GOA-Mefisto-666), FWO (G.0240.99,G.0256.97, Research Communities ICCoS and ANMMM, postdoc grant), Federal State (IUAP IV-02, IUAP V-10-29). March 18, 2002 DRAFT