On the ergodic capacity as a function of the correlation properties in systems with multiple transmit antennas without CSI at the transmitter

In this letter, the impact of correlation of the transmit antennas of a multiple-input single-output (MISO) system, with no channel state information (CSI) at the transmitter and perfect CSI at the receiver is analyzed. We show that the ergodic capacity for the single-user MISO system is Schur-concave with respect to the vector with eigenvalues of the channel covariance matrix, i.e., the more correlation that exists between the transmit antennas, the less is the achievable capacity. Furthermore, the capacity loss for fully correlated transmit antennas in comparison with the uncorrelated case is derived. The results for the ergodic capacity are compared with the impact of correlation on the outage probability. The relationship between correlation properties and outage probability is more complicated than the relationship between the correlation properties and the ergodic capacity. It is shown that the outage probability is Schur-convex in the high signal-to-noise ratio (SNR) regime, and Schur-concave in the low SNR regime.