Covariance of finite-sample cumulants in array-processing

Abstract

In this paper we provide explicit formulas for the covariances of second-third-, and fourth-order sample cumulants as used in narrowband array processing. These covariances provide a basis for analysing the performance of cumulant based algorithms for finite-sample length, which is in contrast to usual asymptotic performance analyses. The use of these formulas, which consist of several thousand terms, will be demonstrated, and a rough idea of their applicability to a performance analysis for finite numbers of samples will be given.