Joint Diagonalization of Third Order Complex Symmetric Tensors and Application to Blind Separation of Non-Circular Sources

In this communication, we consider the problem of the joint- diagonalization of square complex tensors through a least- squares approach. In particular, this allows us to show that recent joint-diagonalization criteria used in source separation can be seen as based on a least-squares criterion. Using the proposed criteria, we propose a Jacobi-like algorithm for the decomposition of symmetric third order tensors. The above approach is applied to the problem of the separation of statistically independent complex source signals based on higher order statistics. We show how all possible fourth order cumulants can be considered within a common framework to identify the mixing matrix. A link with contrast functions is established. Finally, computer simulations on digital communication signals illustrate the above results.