The optimality of beamforming: a unified view

We explore the optimality of transmit beamforming for a vector channel with multiple transmit antennas and a single receive antenna. Perfect channel information is assumed to be available at the receiver while the transmitter only has partial/limited knowledge of the user's channel vector based on feedback. Without limiting the kind of partial/limited feedback or the type of channel distribution, we derive a general necessary and sufficient condition for the optimality of beamforming in such channels. The condition we obtain is universal - applicable to all partial/limited feedback scenarios in all ergodic fading channel distributions regardless of the number of transmit antennas or transmit power. Considering different types of partial/limited feedback, we show how our conditions can be employed to obtain previous results on the optimality of beamforming. With Monte Carlo simulations, we provide numerical results comparing different partial/limited feedback schemes.