Unifying analysis of ergodic MIMO capacity in correlated Rayleigh fading environments

We present a novel mathematical approach that for the first time allows for calculating the moment generating function of mutual information of Rayleigh fading MIMO channels with arbitrary fading correlation at transmitter and receiver. Specifically, we make use of certain hypergeometric functions of matrix argument, which are frequently used in multivariate statistics. This allows for a concise general expression for the moment generating function and we specialize the general result to scenarios with one-side correlated and uncorrelated channels. Using the moment generating functions, we derive exact formulas of the ergodic capacity, thus unifying the capacity analysis of correlated Rayleigh fading MIMO channels. It turns out that the ergodic capacity in all cases 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. The analysis is verified by Monte-Carlo simulations and shows a perfect match.