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.

翻译：本文明确刻画了椭圆高斯复向量包络的分布，等价于具有一般协方差结构的二元正态随机向量范数的分布。文中显式推导了其概率密度函数和累积分布函数。同时推导了该分布的若干性质，特别是其矩及矩母函数，并证明了这些量的存在性。利用这些函数与表达式，进一步刻画了二元高斯均值向量与协方差矩阵具有简单结构时的特例分布。