Characterization of optimal power allocation at the transmit antennas in MIMO system with covariance feedback

We study the optimal transmission strategy of a single user multiple-input multiple-output (MIMO) wireless communication system. For the case in which the receiver has full channel state information (CSI) and the transmitter has only long-term CSI in terms of the channel covariance feedback, it was recently shown that the transmit directions for achieving capacity correspond with the eigenvectors of the channel covariance matrix, while the optimal power allocation can not be solved in closed form. In this paper, we analyze the ergodic capacity function by exploiting its property of Schur-concavity, and determine a necessary condition for eigenvalues of the optimal transit covariance matrix to characterize the transmit power allocation for achieving capacity. Theoretical result is illustrated by numerical simulation.