Optimal power allocation for MISO systems and complete characterization of the impact of correlation on the capacity

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information while the transmitter has only long-term channel state information in regards of the channel covariance matrix. It was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvalues of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We develop a new characterization of the optimum power allocation. Furthermore, we apply this result to develop a simple algorithm which computes the optimum power allocation. In addition to this, we study the impact of correlation on the ergodic capacity of the MISO system with different channel state information (CSI) schemes. We show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave. Additionally, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. Finally, we illustrate all theoretical results by numerical simulations.