A relative gradient algorithm for joint decompositions of complex matrices

The problem of joint decomposition of sets of complex matrices arises in many problems in signal processing. In this paper, we address the problem for the general case where the matrices can be Hermitian and/or complex symmetric. As such, complete statistical information in the complex domain can be taken into account for the given signal processing problem. The proposed algorithm is based on an optimal step size relative gradient approach and computer simulations are provided to illustrate the behavior of this algorithm in different contexts and to establish a comparison with other algorithms.