Performance limits on beamforming with finite rate feedback for multiple antenna systems

In this work, we address the problem of evaluating the outage performance of beamformers designed for multiple transmit and single receive antenna systems when quantized channel state information is available at the transmitter. We present a tight universal lower bound for the outage probability of an arbitrary beamformer codebook consisting of a finite number of beamforming vectors. We also characterize the loss in outage performance due to the quantized nature of the channel information available at the transmitter. In particular, we show that the outage probability of beamforming baaed on quantized channel information approaches the performance of perfect information beamforming as (t - 1)2^-B/t-1, where B is the number of bits used to quantize the vector channel and t is the number of transmit antennas.