Contrast Functions for Convolutive ICA of Complex-Valued Linear Processes

Complex ICA for convolutive mixtures is a hot subject but is far from theoretically complete. In this paper, contrast functions for convolutive ICA of complex-valued processes, especially circular complex-valued linear processes, are studied and formulated in a general setting. The superadditive functional of class II in complex domain is defined and used to construct the contrast functions for convolutive ICA of circular complex-valued processes. It is also introduced how to construct the superadditive functional of class II for circular complex random variables, and an example is shown based on quadratic entropy. Finally, relevant issues are discussed and analyzed. Because of the lack of the theory of convolutive ICA in complex domain, this paper fills in the blank and indicates the way to design specific algorithms to solve this difficult problem.