Optimal MMSE Beamforming for Multiuser Downlink with Delayed CSI Feedback Using Codebooks

This paper investigates the beamforming design for multiuser downlink with limited feedback, where a practical channel state information (CSI) feedback model consisting both feedback delay and CSI quantization error is considered. Under this circumstance, we derive a closed-form multiuser beamforming scheme via minimizing the expected mean square error (MSE) with respect to the feedback imperfection. Compared with conventional MMSE beamforming scheme, we find that not only the regularization factor but the optimal MMSE beamforming structure changes due to the CSI imperfection, especially the feedback delay. Numerical results verify in different cases that the optimized beamforming design outperforms conventional ones in terms of both sum rate and BER performance.