On the Estimation of the Mixing Matrix for Underdetermined Blind Source Separation in an Arbitrary Number of Dimensions

Blind Source Separation consists of estimating n sources from the measurements provided by m sensors. In this paper we deal with the underdetermined case, m < n, where the solution can be implemented in two stages: first estimate the mixing matrix from the measurements and then estimate the best solution to the underdetermined linear problem. Instead of being restricted to the conventional two-measurements scenario, in this paper we propose a technique that is able to deal with this underdetermined linear problem at an arbitrary number of dimensions. The key points of our procedure are: to parametrize the mixing matrix in spherical coordinates, to estimate the projections of the maxima of the multidimensional PDF that describes the mixing angles through the marginals, and to reconstruct the maxima in the multidimensional space from the projections. The results presented compare the proposed approach with estimation using multidimensional ESPRIT.