Generalized correlation function: Definition, properties and application to blind equalization

Abstract—With an abundance of tools based on kernel methods and information theoretic learning, a void still exists in incorpo-rating both the time structure and the statistical distribution of the time series in the same functional measure. In this paper, a new generalized correlation measure is developed that includes the in-formation of both the distribution and that of the time structure of a stochastic process. It is shown how this measure can be inter-preted from a kernel method as well as from an information theo-retic learning points of view, demonstrating some relevant proper-ties. To underscore the effectiveness of the new measure, a simple blind equalization problem is considered using a coded signal. Index Terms—Blind equalization, entropy, generalized corre-lation kernel, information theoretic learning, reproducing kernel Hilbert space (RKHS). I