Exact capacity distributions for MIMO systems with small numbers of antennas

It is well known that multiple input multiple output (MIMO) systems offer the promise of achieving very high spectrum efficiencies (many tens of bit/s/Hz) in a mobile environment. The gains in MIMO capacity are sensitive to the presence of spatial correlation introduced by the radio environment. In this letter we consider the capacity outage performance of MIMO systems in correlated environments. For systems with large numbers of antennas Gaussian approximations are very accurate. Hence, we concentrate on systems with small numbers of antennas and derive exact densities and distribution functions for the capacity, which are simple and rapid to compute.