Mutual information of MIMO channels in correlated Rayleigh fading environments - a general solution

We present a novel approach on the calculation of the moment generating function of mutual information, of MIMO channels with correlated Rayleigh fading. For the first time, a concise mathematical formulation of the moment generating function is given in terms of a hypergeometric function of matrix arguments. In contrast to existing literature, our approach is not based on eigenvalue probability density functions but uses a direct integration technique. In principle, via the moment generating function it is possible to calculate exact, i.e. non-asymptotic moments, including e.g. ergodic capacity, for arbitrary array sizes and arbitrary correlation properties at receiver as well as transmitter, thus unifying and completing existing partial solutions for special propagation scenarios. Monte-Carlo simulations of ergodic capacity verify the accuracy of the analysis.