We have derived new techniques for the blind identification of multiple-input multiple-output (MIMO) finite impulse response (FIR) filters with temporally independent identically distributed and spatially independent non-Gaussian inputs. First we have followed a time-domain approach, and we limited ourselves to the case of 2 outputs and 2 inputs. After a classical prewhitening, the remaining problem is the blind identification of a paraunitary filter. For this task, we have derived a multilinear algebraic algorithm. This procedure is a generalization of the well-known algorithm for independent component analysis (ICA) (i.e., blind identification of a scalar mixture) proposed by Comon. Next, in collaboration with B. Chen and A. Petropulu of Drexel University, Philadelphia, we have proposed a novel frequency domain approach for MIMO systems with at least as many outputs as inputs. The system frequency response is obtained via a singular value decomposition (SVD) of a matrix constructed from the power-spectrum and slices of the polyspectrum of the system output. Since several slices could be used, the SVD can be replaced by a joint diagonalization of a set of matrices. The flexibility to select the polyspectrum slices allows us to bypass the frequency dependent permutation and phase ambiguity problems, which are usually associated with a frequency domain SVD.
Researcher(s): Lieven De Lathauwer