On optimum transmission power strategy in MIMO systems with covariance feedback

We study the optimum transmission power strategy in a multiple-input multiple-output (MIMO) system with perfect channel state information (CSI) at the receiver and channel covariance matrix at the transmitter. A necessary and sufficient condition is derived for the optimum power allocation at the transmitter to maximize the average mutual information. Furthermore, we apply this result to extend the discussion on optimality of beamforming to general cases of transmitting in m directions for achieving capacity.