Blind identification and source separation in 2×3 under-determined mixtures

Under-determined mixtures are characterized by the fact that they have more inputs than outputs, or, with the antenna array processing terminology, more sources than sensors. The problem addressed is that of identifying and inverting the mixture, which obviously does not admit a linear inverse. Identification is carried out with the help of tensor canonical decompositions. On the other hand, the discrete distribution of the sources is utilized for performing the source extraction, the under-determined mixture being either known or unknown. The results presented in this paper are limited to 2-dimensional mixtures of 3 sources. Keywords— Blind Identification, Source Separation and Extraction, Under-Determined Mixtures, Tensor Decomposition, High-Order Statistics