Total positivity, spherical series, and hypergeometric functions of matrix argu ment
Journal of Approximation Theory - On Total Positivity and Applications, Part II
Eigenvalues and Condition Numbers of Complex Random Matrices
SIAM Journal on Matrix Analysis and Applications
Characterizing the statistical properties of mutual information in MIMO channels
IEEE Transactions on Signal Processing
Efficient detection algorithms for MIMO channels: a geometrical approach to approximate ML detection
IEEE Transactions on Signal Processing
Design of Optimal High-Rank Line-of-Sight MIMO Channels
IEEE Transactions on Wireless Communications
On the condition number distribution of complex wishart matrices
IEEE Transactions on Communications
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In this paper, we explore the statistical characterization of Multiple-Input Multiple-Output (MIMO) channel correlation matrices with the main focus being on their condition number statistics. More specifically, novel expressions are derived for the probability density function (PDF) and cumulative distribution function (CDF) of the MIMO condition number. Contrary to the majority of related studies, where only the common case of Rayleigh fading was considered, our investigation is extended to account for the generalized case of Ricean fading where a deterministic Line-of-Sight (LoS) component exists in the communication link. The overall analysis is based on the principles of random matrix theory and particularly of dual complex noncentral Wishart matrices; the latter represent a practical class of MIMO systems, namely dual-branch systems which are equipped with two transmit and receive antenna elements. All the derived formulae are validated through extensive simulations with the attained accuracy being remarkably good.