IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
On the monotonicity of the generalized Marcum and Nuttall Q-functions
IEEE Transactions on Information Theory
On the condition number distribution of complex wishart matrices
IEEE Transactions on Communications
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Mutual information statistics and beamforming performance analysis of optimized LoS MIMO systems
IEEE Transactions on Communications
On marginal distributions of the ordered eigenvalues of certain random matrices
EURASIP Journal on Advances in Signal Processing
Journal of Multivariate Analysis
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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.