Frequency domain blind multiple-input multiple-output system identification

The goal of blind r-input n-output system blind identification is to identify an unknown system, driven by r unobservable inputs, based on the n system outputs. Blind identification of a Multiple-Input Multiple-Output (MIMO) system is of great importance in many applications. For example, in speech enhancement in the presence of competing speakers, an array of microphones is used to obtain multiple recordings, based on which the signal of interest can be estimated. MIMO models arise frequently in digital multiuser/multi-access communications systems, multisensor sonar/radar systems.; Most of the existing approaches for MIMO system blind identification operate in the time domain. They require a priori knowledge of the mixing system length while are sensitive to order mismatch, and their complexity increases rapidly with channel length. This work considers the problem in the frequency domain, and as such, does not suffer from the aforementioned problems.; We proposed three frequency domain methods for the MIMO system blind identification. We first proposed a second order statistics based method for estimating the response of a Two-Input-Two-Output system excited by non-white inputs with unknown statistics. This method provides an analytical solution to the problem based on eigenvalue decomposition of matrices constructed of second order spectra correlations of the system output.; We next propose an extension of this method, which uses second and higher order statistics of the system output, and applies to the case of white inputs. The system frequency response is now obtained based on SVD of a matrix constructed based on the power-spectrum and slices of cross-polyspectra of the system output. The freedom to select the polyspectra slices allows us to bypass the frequency dependent ambiguities.; The derived frequency domain framework also revealed a link between the MIMO problem and that of the separation of instantaneous mixtures. Most of the exiting results for the instantaneous case can now be imported to the MIMO case. That link enabled us to derive the first algorithm for the identification of a MIMO system with more inputs than outputs, which is based on canonical decomposition of tensors constructed of higher-order statistics of the system output.