MIMO channel blind identification in the presence of spatially correlated noise

We address the problem of the second-order blind identification of a multiple-input multiple-output (MIMO) transfer function in the presence of additive noise. The additive noise is assumed to be (temporally) white, i.e., uncorrelated in time, but we do not make any assumption on its spatial correlation. This problem is thus equivalent to the second-order blind identification of a MIMO transfer function in the noiseless case but from a partial auto-covariance function {R_n }_n≠0. Our approach consists of computing the missing central covariance coefficient R₀ from this partial auto-covariance sequence. It can be described simply within the algebraic framework of rational subspaces. We propose an identifiability result that requires very mild assumptions on the transfer function to be estimated. Practical subspace-based identification algorithms are deduced and tested via simulations