Does Beamforming achieve Outage Capacity with Direction Feedback?

We explore the outage capacity of an isotropic fading vector channel with multiple transmit antennas at the base station and a single antenna at the mobile receiver. Perfect channel knowledge is assumed to be available at the receiver while the transmitter has only partial knowledge of the direction of the user’s channel vector based on quantized feedback. We provide a proof technique to determine whether transmit beamforming is optimal in terms of outage capacity for a quantized channel direction feedback system. The technique is used to establish the optimality of beamforming for several cases, e.g for a two antenna system with any number of feedback bits. Extensions to more than two transmit antennas are also provided.