On the Mutual Information Distribution of MIMO Rician Fading Channels

In a fading environment, the statistical distribution of the mutual information of a multiple-input multiple-output (MIMO) system depends on the joint distribution of the eigenvalues of a Wishart matrix, and is quite complex in general. We obtain here simple expressions for the distributions of the determinant and the trace of a Wishart matrix. Based on the obtained distributions, we derive some simple and tight bounds on the complementary cumulative distribution function (CCDF) of the mutual information of a MIMO system in Rician fading environments. The bounds obtained on the CCDF of mutual information provide further insights into the channel mutual information, and show the effects of the system parameters on the mutual information distribution explicitly. In addition, results for the Rayleigh channels are obtained as a special case.