An analytical closed-form lower-bound on ergodic capacity of correlated Rayleigh-fading MIMO channels

In this paper, the ergodic capacity of multiple antenna systems over spatially correlated Rayleigh-fading channels is investigated under the assumption that the channel state information (CSI) is unknown at the transmitter and perfectly known at the receiver. We derive a lower-bound expression, in closed form, for the ergodic capacity through the use of majorization theory and the probability density function (PDF) of the sum of Gamma random variables, which is represented by an infinite series. Furthermore, we also obtain other lower-bounds from the truncation of such series, and we associate truncation errors. Finally, the proposal of the paper is compared with a lower-bound reported in the literature.