MIMO Instantaneous Blind Identification Based on Second-Order Temporal Structure

Blind identification is a crucial subtask in signal processing problems such as blind signal separation (BSS) and direction-of-arrival (DOA) estimation. This paper presents a procedure for multiple-input multiple-output instantaneous blind identification based on second-order temporal properties of the signals, such as coloredness and nonstationarity. The procedure consists of two stages. First, based on assumptions on the second-order temporal structure (SOTS) of the source and noise signals, and using subspace techniques, the problem is reformulated in a particular way such that each column of the unknown mixing matrix satisfies a system of multivariate homogeneous polynomial equations. Then, this nonlinear system of equations is solved by means of a so-called homotopy method, which provides a general tool for solving (possibly nonexact) systems of nonlinear equations by smoothly deforming the known solutions of a simple start system into the desired solutions of the target system. Our blind identification procedure allows to estimate the mixing matrix for scenarios with more sources than sensors without resorting to sparsity assumptions, something that is often believed to be impossible when using only second-order statistics. In addition, since our algorithm does not require any assumption on the mixing matrix, also mixing matrices that are rank-deficient or even have identical columns can be identified. Finally, we give examples and performance results for speech source signals.