Blind MIMO system estimation based on PARAFAC decomposition of HOS tensors

We present a novel frequency domain approach for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on parallel factorization (PARAFAC) of three-way tensors constructed based on third-order cross-spectra of the system outputs. The main difficulties in frequency domain methods are frequency dependent permutation and filtering ambiguities. We show that the information available in the higher-order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation, and a linear phase ambiguity. The advantages of the proposed approach is that, it does not require exact channel length information, need no phase unwrapping, and unlike the majority of existing methods, need no pre-whitening of the system outputs