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：本文显式描述了椭圆高斯复向量的包络分布，或等价地，具有一般协方差结构的二元正态随机向量范数的分布。本文显式推导了概率密度函数和累积分布函数，并进一步推导了该分布的某些性质（具体包括矩及矩生成函数），且证明了这些函数的存在性。利用这些函数与表达式，本文还刻画了当二元高斯均值向量和协方差矩阵具有某些简单结构时的特例分布。