Characteristic function of a quadratic form formed by correlated complex Gaussian variables
M. P. Slichenko · Journal of Communications Technology and Electronics · 2014
An exact closed-form analytical expression is obtained for a one-dimensional characteristic function of an arbitrary quadratic form formed by statistically dependent Gaussian random variables with nonzero means. Necessary and sufficient conditions under which an arbitrary quadratic form has the generalized χ 2 distribution are formulated. Parameters of the distribution of an arbitrary quadratic form are analyzed for particular cases.