An any order generalization of JADE for complex source signals

In this paper, considering the complex case, we extend some results leading to the popular JADE algorithm to cumulants of any order greater than or equal to three. We first exhibit a new contrast function which constitutes a generalization for the underlying contrast of JADE which thus appears as a particular case. Then we generalize the link between this new contrast and a joint-diagonalization criterion of a set of matrices. Moreover, in the two sources case, we show that the generalized contrast can be written as a simple quadratic form whatever the cumulant order. Finally, some computer simulations illustrate the potential advantage one can take of considering statistics of different orders for the joint-diagonalization of cumulant matrices