The eigenvalue distributions from a complex noncentral Wishart matrix S=XHX has been the subject of interest in various real world applications, where X is assumed to be complex matrix variate normally distributed with nonzero mean M and covariance Σ. This paper focuses on a weighted analytical representation of S to alleviate the restriction of normality; thereby allowing the choice of X to be complex matrix variate elliptically distributed for the practitioner. New results for eigenvalue distributions of more generalised forms are derived under this elliptical assumption, and investigated for certain members of the complex elliptical class. The distribution of the minimum eigenvalue enjoys particular attention. This theoretical investigation has proposed impact in communications systems (where massive datasets can be conveniently formulated in matrix terms), in particular the case where the noncentral matrix has rank one which is useful in practice.

中文翻译：

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受大规模MIMO系统启发的统一，复杂的非中心Wishart类型分布

复杂的非中心Wishart矩阵S = XHX的特征值分布已成为各种现实应用中的关注对象，其中X被假定为具有非零均值M和协方差Σ的正态分布的复杂矩阵变量。本文着重于S的加权分析表示，以减轻正态性的限制。从而使X的选择可以是从业者椭圆形分布的复杂矩阵变量。在此椭圆假设下，得出了更广义形式的特征值分布的新结果，并对复椭圆类的某些成员进行了研究。最小特征值的分布受到特别关注。