Optimum space-time transmission for a high K factor wireless channel with partial channel knowledge

We study the optimum transmission scheme that maximizes ergodic capacity of a 2×1 multiple-input single-output (MISO) system, when the channel knowledge at the transmitter is characterized by a known gain ratio and a known probability density function of the phase shift between antennas. Such a channel scenario can arise in a forward link at the base station when there is a single direct path propagation. We show that the optimum transmit solution is beamforming on the mean value of the phase shift with unequal power input to the antennas. When the phase is completely unknown, the solution reduces to a single antenna transmission.