A new class of block coordinate algorithms for the joint eigenvalue decomposition of complex matrices

Several signal processing problems can be written as the joint eigenvalue decomposition (JEVD) of a set of noisy matrices. JEVD notably occurs in source separation problems and for the canonical polyadic decomposition of tensors. Most of the existing JEVD algorithms are based on a block coordinate procedure and require significant modifications to deal with complex-valued matrices. These modifications decrease algorithms performances either in terms of estimation accuracy of the eigenvectors or in terms of computational cost. Therefore, we propose a class of algorithms working equally with real- or complex-valued matrices. These algorithms are still based on a block coordinate procedure and multiplicative updates. The originality of the proposed approach lies in the structure of the updating matrix and in the way the optimization problem is solved in CN×N. That structure is parametrized and allows to define up to five different JEVD algorithms. Thanks to numerical simulations, we show that, with respect to the more accurate algorithms of the literature, this approach improves the estimation of the eigenvectors and has a computational cost significantly lower. Finally, as an application example, one of the proposed algorithm is successfully applied to the blind source separation of Direct-Sequence Code Division Multiple Access signals.