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首页> 外文期刊>IEEE transactions on wireless communications >Joint and Marginal Eigenvalue Distributions of (Non)Central Complex Wishart Matrices and PDF-Based Approach for Characterizing the Capacity Statistics of MIMO Ricean and Rayleigh Fading Channels
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Joint and Marginal Eigenvalue Distributions of (Non)Central Complex Wishart Matrices and PDF-Based Approach for Characterizing the Capacity Statistics of MIMO Ricean and Rayleigh Fading Channels

机译：（非）中心复Wishart矩阵的联合和边际特征值分布以及基于PDF的MIMO Ricean和Rayleigh衰落信道容量统计特性

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摘要

This paper characterizes the eigenvalue distributions of full-rank Hermitian matrices generated from a set of independent (non)zero-mean proper complex Gaussian random vectors with a scaled-identity covariance matrix. More specifically, the joint and marginal cumulative distribution function (CDF) of any subset of unordered eigenvalues of the so-called complex (non)central Wishart matrices, as well as new simple and tractable expressions for their joint probability density function (PDF), are derived in terms of a finite sum of determinants. As corollaries to these new results, explicit expressions for the statistics of the smallest and largest eigenvalues, of (non)central Wishart matrices, can be easily obtained. Moreover, capitalizing on the foregoing distributions, it becomes possible to evaluate exactly the mean, variance, and other higher order statistics such as the skewness and kurtosis of the random channel capacity, in the case of uncorrelated multiple-input multiple-output (MIMO) Ricean and Rayleigh fading channels. Doing so bridges the gap between Telatar's initial approach for evaluating the average MIMO channel capacity (Telatar, 1999), and the subsequently widely adopted moment generating function (MGF) approach, thereby setting the basis for a PDF-based framework for characterizing the capacity statistics of MIMO Ricean and Rayleigh fading channels.
机译：本文描述了从一组具有比例一致协方差矩阵的独立（非）零均值适当复高斯随机向量生成的满秩Hermitian矩阵的特征值分布。更具体地说，所谓的复杂（非）中心Wishart矩阵的无序特征值的任何子集的联合和边际累积分布函数（CDF），以及联合概率密度函数（PDF）的新的简单易处理的表达式，是根据行列式的有限总和得出的。作为这些新结果的推论，可以轻松地获得（非）中心Wishart矩阵的最小和最大特征值统计的明确表达式。此外，在不相关的多输入多输出（MIMO）情况下，利用上述分布，可以精确地评估均值，方差和其他高阶统计量，例如随机信道容量的偏度和峰度。 Ricean和Rayleigh衰落信道。这样做可以弥补Telatar最初用于评估平均MIMO信道容量的方法（Telatar，1999年）与后来被广泛采用的矩量生成函数（MGF）方法之间的差距，从而为基于PDF的框架描述容量统计奠定基础MIMO Ricean和Rayleigh衰落信道。

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