Multicarrier Beamforming With Limited Feedback: A Rate Distortion Approach

This paper studies the optimal use of limited-rate feedback of channel state information (CSI) in the case of a wideband multicarrier channel with multiple transmit antennas and a single receive antenna. With full knowledge of the CSI, the receiver should compute the optimal beamforming vectors, jointly quantize them, and feed them back to the transmitter. The achievable forward data rate depends on the rate of the feedback link. The optimal tradeoff between the forward and feedback rates is characterized using rate distortion theory in the limit of infinite number of subcarriers with fixed amount of feedback per subcarrier. The distortion metric is the difference between the forward rate achieved with limited feedback and the capacity with perfect CSI at the transmitter. The rate distortion function gives the forward rate as a function of the feedback rate. Numerical results show that to achieve a target forward rate, the required feedback rate can be substantially reduced by joint quantization of the beamformers across subcarriers. A simple quantizer amenable to practical implementation is shown to approach the rate distortion bound with near-linear computational complexity.