On the capacity of doubly correlated MIMO channels

In this paper, we analyze the capacity of multiple-input multiple-output (MIMO) Rayleigh-fading channels in the presence of spatial fading correlation at both the transmitter and the receiver, assuming the channel is unknown at the transmitter and perfectly known at the receiver. We first derive the determinant representation for the exact characteristic function of the capacity, which is then used to determine the trace representations for the mean, variance, skewness, kurtosis, and other higher-order statistics (HOS). These results allow us to exactly evaluate two relevant information-theoretic capacity measures - ergodic capacity and outage capacity - and the HOS of the capacity for such a MIMO channel. The analytical framework presented in the paper is valid for arbitrary numbers of antennas, and generalizes the previously known results for independent and identically distributed or one-sided correlated MIMO channels to the case when fading correlation exists on both sides. We verify our analytical results by comparing them with Monte Carlo simulations for a correlation model based on realistic channel measurements as well as a classical exponential correlation model