Eigenvalue statistics of finite-dimensional random matrices for MIMO wireless communications

This paper characterizes the marginal probability density function of an unordered eigenvalue of finite-dimensional random matrices of particular interest in MIMO (multiple-input multiple-output) wireless communications. Specifically, a technique is presented for deriving the eigenvalue statistics in one-side correlated Rayleigh-faded channels and in Ricean-faded channels, with or without cochannel interferers. The exact expressions found turn out to be extremely useful in calculating information-theoretic quantities. As an application, we calculate the ergodic mutual information for all the abovementioned channel fading conditions, obtaining a closed form formula for the Rayleigh case and, in turn, a series expression for the Ricean faded one.