PARAFAC-Based Blind Estimation Of Possibly Underdetermined Convolutive MIMO Systems

In this paper, we consider the problem of blind identification of a convolutive multiple-input-multiple-output (MIMO) system with No outputs and Ni inputs. While many methods have been proposed to blindly identify convolutive MIMO systems with No ges Ni (overdetermined), very scarce results exist for the case of (underdetermined), all of which refer to systems that either have some special structure or special and values. In this paper, we show that, as long as , independent of whether the system is overdetermined or underdetermined, we can always find the appropriate order of statistics that guarantees identifiability of the system response within trivial ambiguities. We also propose an algorithm to reach the solution, that consists of parallel factorization (PARAFAC) of a -way tensor containing th-order statistics of the system outputs, followed by an iterative scheme. For a certain order of statistics , we provide the description of the class of identifiable MIMO systems. We also show that this class can be expanded by applying PARAFAC decomposition to a pair of tensors instead of one tensor. The proposed approach constitutes a novel scheme for estimation of underdetermined systems, and improves over existing approaches for overdetermined systems.