Throughput effects of noisy feedback of channel state information in multiple-antenna systems

With a new throughput metric, the impact of noisy feedback of channel state information (CSI) is studied for a multiple-input, single-output (MISO) system. The covariance matrix of the input that maximizes the throughput is obtained. Results show that beamforming can achieve the maximal throughput only if the SNR of the CSI feedback is sufficiently large. With a new throughput metric, a necessary condition for the optimality of beamforming is determined, and the necessary and sufficient condition is numerically found with the Gauss-Chebyshev quadrature method. Analysis of beamforming transmission shows that at a fairly high SNR for CSI feedback the rate allocation needs to be reduced, while at low SNR for CSI feedback, the allocated rate should be increased. When two-mode transmission is adopted, beamforming may be preferred over spatial diversity even when the necessary condition for the optimality of beamforming is not met.