Non-orthogonal Simultaneous Diagonalization of K-Order Complex Tensors for Source Separation

Source separation in the statistical framework is usually managed using tensor decompositions or matrix joint diagonalization. In this letter, we propose one of the first coordinate algorithms for non-orthogonal simultaneous diagonalization of any order complex tensors. It relies on the optimization of an inverse criterion and on a particular decomposition allowing to derive each parameter in an independent way. In the framework of digital telecommunication source separation, computer simulations show the interest of using sets of high-order tensors. They also illustrate the overall interesting performances of the proposed algorithm in comparison to a Jacobi-like algorithm of matrix joint diagonalization and to a canonical polyadic decomposition algorithm.