Exact ergodic capacity of MIMO channels in correlated Rayleigh fading environments

Using recent results on the moment generating function of mutual information, we derive exact formulas for the calculation of ergodic capacity of a fully correlated MIMO channel with transmit as well as receive correlation in a flat Rayleigh fading environment. The analysis is non-asymptotic, i.e. it is applicable without constraints to systems with a small number of elements. It turns out that the ergodic capacity can be expressed in terms of a sum of determinants with elements that are a combination of polynomials, exponentials, and the exponential integral E₁ solely. Various Monte-Carlo simulations confirm the validity and accuracy of the analysis.