Ordered Eigenvalues of a General Class of Hermitian Random Matrices With Application to the Performance Analysis of MIMO Systems

In this paper, we present a general formulation that unifies the probabilistic characterization of Hermitian random matrices with a specific structure. Based on a general expression for the joint pdf of the ordered eigenvalues, we obtain i) the joint cdf; ii) the marginal cdfs; and iii) the marginal pdfs 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, semicorrelated, and double-correlated Rayleigh MIMO fading channel and the uncorrelated Rician MIMO fading channel, although it is not restricted only to these. Hence, the proposed formulation and derived results provide a solid framework for the simultaneous analytical performance analysis of MIMO systems under different channel models. As an illustrative application, we obtain the exact outage probability of a spatial multiplexing MIMO system transmitting through the strongest channel eigenmodes.