Inverse eigenvalue statistics for Rayleigh and Rician MIMO channels

Recently reclaimed importance of the empirical distribution function of the eigenvalues of Wishart matrices was attached to the analysis of MIMO systems in Hochwald et al. (2001). But for the analysis of MIMO systems with signal processing at the transmitter (Jungnickel et al. (2001)) it is necessary to know the empirical distribution function of the inverse eigenvalues and the first and second moment of these distributions. We extend the results on the eigenvalue distribution and develop a method for computing the moments of the inverse eigenvalues. We show the impact of these results on MIMO system design with examples and verify our results with numerical simulations.