Ordered Eigenvalues of a General Class of Hermitian Random Matrices and Performance Analysis of MIMO Systems

In this paper we present a general formulation that unifies the probabilistic characterisation of Hermitian random matrices with a specific structure. Based on a unified expression for the joint pdf, we obtain (i) the joint cdf, (ii) the marginal cdf's, and (iii) the marginal pdf's of the ordered eigenvalues, where (ii) and (iii) follow as simple particularizations of (i). Our formulation is shown to include the distribution of some common MIMO channel models such as the uncorrelated and semicorrelated Rayleigh, and the uncorrelated Rician fading MIMO channel, although it is not restricted only to these. Hence, we provide a solid framework for the simultaneous analytical performance analysis of MIMO systems under different channel models. As an example of application, we obtain the exact outage probability of a spatial multiplexing MIMO system transmitting through the strongest channel eigenmodes.