Optimum transmission scheme for a MISO wireless system with partial channel knowledge and infinite K factor

The optimum transmission scheme that maximizes ergodic capacity in a K→∞ regime for 2×1 MISO systems is studied when the channel knowledge at the transmitter is characterized by a known gain imbalance and a known PDF 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 beam-forming 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.