Blind Estimation of a Class of Under-Determined Convolutive MIMO Systems Using Parafac Decomposition of Output Tensors

We consider the problem of frequency domain identification of a convolutive multiple-input multiple-output (MIMO) system driven by white, mutually independent unobservable inputs. In particular, we improve upon a method recently proposed that uses PARAFAC decomposition of a tensor that is formed based on third-order statistics of the system output. The approach utilizes only one slice of the output tensor to recover one row of the system response matrix. We here propose an approach that fully exploits the information in the output tensor. As a result, the proposed method not only achieves lower error values but also becomes applicable to a class of MIMO systems with more inputs than outputs. We also show how by using higher order statistics, i.e., fourth- or sixth-order statistics, or pairs of third or Fourth-order tensors, one can further expand the class of under-determined systems that are identifiable.