The distribution of eigenvalues of a Wishart matrix with correlation and application to MIMO capacity

We investigate the capacity distribution of spatially correlated MIMO channels. In particular, we consider MIMO systems with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh fading environments. We derive a simple expression for the distribution of the eigenvalues of a Wishart matrix including correlation, and then a closed-form expression for the characteristic function (CF) of MIMO system capacity. Using the exact expression of the CF, the probability density function and the cumulative distribution function can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels.