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

With an abundance of tools based on kernel methods and information theoretic learning, a void still exists in incorporating 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 information of both the distribution and that of the time structure of a stochastic process. It is shown how this measure can be interpreted from a kernel method as well as from an information theoretic learning points of view, demonstrating some relevant properties. To underscore the effectiveness of the new measure, a simple blind equalization problem is considered using a coded signal.