Signal separation using second and high order statistics

Abstract

This paper presents two methods for signal separation. One is based on second order statistics while the other is based on fourth and higher order statistics. In either method, the fundamental criterion for separation relies on reducing to zero or at least minimizing, either the output cross correlation or cross cumulant functions, respectively. This is achieved through designing a decoupling multi-input multi-output system. The parameters of this system are determined through solving-in a least squares sense-a linearized set of equations describing either the cross correlation or cross cumulant functions when evaluated for different lags. An alternative rapidly convergent adaptive algorithm is also described for the minimization of each respective function. The paper considers also both FIR and IIR representation of the decoupling system. It shows that using IIR functions in the decoupling system does not offer any merit over the FIR case. Illustrative examples are given to show the performance of the proposed algorithms.