Hybrid nonlinear moments in array processing and spectrum analysis

The aim of this paper is to provide a theoretical basis for the use of hybrid nonlinear (HNL) moments in array processing and spectrum analysis. These moments are defined as the expected value of the product of one random variable times a nonlinear function of another random variable. They generalize a class of twofold higher order moments, and their additional flexibility can be exploited for optimization purposes or for computational convenience. A number of properties beyond the classical Bussgang´s (1952) and Price´s (1958) theorems are found for HNL moments and matrices, making these statistics suitable for harmonic analysis and bearing estimation. Covariance based and higher order moments based methods are extended to the HNL moments domain, and a new class of Gaussian noise rejecting statistics is added to cumulants. The properties of some classes of matrices of HNL moments of practical interest are analyzed in detail