Ergodic capacity of MIMO channels with statistical channel state information at the transmitter

It is well known that with the availability of statistical channel state information at the transmitter, the capacity-achieving transmission strategy is transmission on the long-term eigen-modes of the transmit correlation matrix with adequate power allocation. However, the optimum power allocation strategy is not known in general. Using recent analytical results on mean mutual information of MIMO channels with transmit as well as receive correlation, in this paper we study the behavior of the capacity-achieving power allocation strategy. To this end, we also make use of asymptotical results for a large number of transmit or receive antennas and the high as well as low SNR regime, which in certain cases allows for a closed-form analysis. Furthermore, we investigate two low complexity power allocation schemes, which are based on certain upper bounds on mean mutual information.