New series representation for the trivariate non-central chi-squared distribution

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.