A Promising Technique for Blind Identification: The Generic Statistics

Abstract

The generic statistics, related to lower-order derivatives of the log characteristic function (CAF) evaluating at the processing points located away from the origin, are frequently used in multivariate statistical signal processing. In comparison with the conventional statistics, e.g., cumulants, the generic statistics have the following advantages: (a) they can offer the structural simplicity and controllable statistical stability of lower-order statistics, and retain higher-order statistical information; (b) if the derivatives of the log CAF were evaluated at all (infinitely many) possible processing-points, a complete description of the joint CAF would be obtained. Furthermore, we show in this paper that even if a random process is symmetrically distributed, the odd-order generic statistics are not equal to zero, while in such a case the odd-order cumulants are equal to zero. For these reasons, a family of blind identification (BI) methods, in which the mixing matrix is obtained by decomposing the tensor constructed by the higher order derivatives of the log CAF of the observations, is proposed to achieve BI of underdetermined mixtures. Simulation results show that the BI methods based on generic statistics have superior performance to the existing cumulant-based method, such as FOOBI method, especially, when the SNR of the observations is high and/or the data block is short.