Quantifying the Power Loss when Transmit Beamforming Relies on Finite Rate Feedback

Transmit beamforming achieves optimal performance in systems with multiple transmit-antennas and a single receive-antenna, from both the capacity and the received signalto -noise ratio (SNR) perspectives, but ideally requires perfect channel knowledge at the transmitter. In practical systems where the feedback link can only convey a finite number of bits, transmit-beamformer designs have been extensively investigated using either the outage probability, or the average SNR, as the figure of merit. In this paper, we study the symbol error rate (SER) for transmit beamforming with finite-rate feedback, in a multi-input single-output (MISO) setting. We derive a SER lower bound, which is tight for good beamformer designs. Comparing this bound with the SER corresponding to the ideal case, we quantify the power loss due to the finite rate constraint, across the entire SNR range