On the Asymptotic Capacity of the Rayleigh Fading Amplify-and-Forward MIMO Relay Channel

In this paper the ergodic mutual information of the i.i.d. Rayleigh fading amplify-and-forward MIMO relay channel without direct link between source and destination is derived in the large array limit. By means of the replica method an expression is obtained, whose parameters are determined by a nonlinear equation system. This system can be solved in closed form. Comparisons with Monte Carlo simulations show that the asymptotic expression serves as an excellent approximation for systems with only very few antennas at each node.