On the beamforming capacity of MISO channels

This letter addresses the calculation of the ergodic beamforming capacity of a multiple-input single-output (MISO) communication channel in the presence of additive Gaussian noise and known channel distribution information at the transmitter (CDIT). Necessary conditions to achieve the ergodic beamforming capacity are presented in the general case and derived explicitly when the CDIT is Gaussian. This case is commonly addressed in the literature as the joint channel mean information (CMI) and channel covariance information (CCI) case. An iterative algorithm based on the projected gradient approach is derived in order to find the beamforming capacity and the corresponding capacity-achieving beamforming vector.