Expansions for the multivariate chi-square distribution
Journal of Multivariate Analysis
On Limits of Wireless Communications in a Fading Environment when UsingMultiple Antennas
Wireless Personal Communications: An International Journal
A trivariate chi-squared distribution derived from the complex Wishart distribution
Journal of Multivariate Analysis
An efficient approach to multivariate Nakagami-m distribution using Green's matrix approximation
IEEE Transactions on Wireless Communications
IEEE Transactions on Wireless Communications
Capacity of MIMO Rician channels
IEEE Transactions on Wireless Communications
Infinite series representations of the trivariate and quadrivariate nakagami-m distributions
IEEE Transactions on Wireless Communications
On multivariate Rayleigh and exponential distributions
IEEE Transactions on Information Theory
A simple transmit diversity technique for wireless communications
IEEE Journal on Selected Areas in Communications
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This paper derives a new infinite series representation for the trivariate Non-central chi-squared distribution when the underlying correlated Gaussian variables have a tridiagonal form of an inverse covariance matrix. The joint probability density function is derived using Miller's approach and Dougall's identity. Moreover, the trivariate cumulative distribution function (cdf) and characteristic function (chf) are also derived. Finally, the bivariate non-central chi-squared distribution and some known forms are shown to be special cases of the more general distribution. However, the derivation of non-central chi-squared distribution for an arbitrary covariance matrix seems intractable via Miller's approach. Two applications of the newly derived results are provided for performance analysis of multiple input multiple output (MIMO) systems with transmit antenna selection over a correlated Rician fading environment. Some numerical results are also presented to verify the accuracy of the analytical expressions.