  This article explicitly characterizes the distribution of the envelope of an
elliplical Gaussian complex vector, or equivalently, the norm of a bivariate
normal random vector with general covariance structure. The probability density
and cumulative distribution functions are explicitly derived. Some properties
of the distribution, specifically, its moments and moment generating functions,
are also derived and shown to exist. These functions and expressions are
exploited to also characterize the special case distributions where the
bivariate Gaussian mean vector and covariance matrix have some simple
structure.
