Blind identification of possibly under-determined convolutive MIMO systems

Blind identification of a Linear Time Invariant (LTI) Multiple-Input Multiple-Output (MIMO) system is of great importance in many applications, such as speech processing, multi-access communication, multi-sensor sonar/radar systems, and biomedical applications. The objective of blind identification for a MIMO system is to identify an unknown system, driven by N_i unobservable inputs, based on the N_o system outputs. We first present a novel blind approach for the identification of a over-determined (N_o [greater than or equal to] N_i) MIMO system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on Parallel Factorization (PARAFAC) of three- or four-way tensors constructed respectively based on third- or fourth-order cross-spectra of the system outputs. We show that the information available in the higher-order spectra allows for the system response to be identified up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approaches are that they do not require channel length information, need no phase unwrapping, and unlike the majority of existing methods, need no pre-whitening of the system outputs. While several methods have been proposed to blindly identify over-determined convolutive MIMO systems, very scarce results exist for under-determined (N_o < N_i) case, all of which refer to systems that either have some special structure, or special N_o, N_i values. We propose a novel approach for blind identification of under-determined convolutive MIMO systems of general dimensions. As long as min(N_o,N_i) [greater than or equal to] 2, we can always find the appropriate order of statistics that guarantees identifiability of the system response within trivial ambiguities. We provide the description of the class of identifiable MIMO systems for a certain order of statistics K, and an algorithm to reach the solution. Finally we propose a novel approach for blind identification and symbol recovery of a distributed antenna system with multiple carrier-frequency offsets (CFO), arising due to mismatch between the oscillators of transmitters and receivers. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual MIMO problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently decouple the users and transform the multiple CFOs estimation problem into a set of independent single CFO estimation problems.