MMSE optimal feedback of correlated CSI for multi-user precoding

For the separation of the signals for multiple users in the vector broadcast channel (BC), channel state information (CSI) is necessary at the transmitter. Since the transmitter has no access to this information in many cases, the CSI must be fed back from the receivers to the transmitter. Before the feedback, the receivers estimate the CSI and apply a rank reduction possible due to the channel correlations. We propose a joint optimization of the estimation, the rank reduction, and the codebook used for the feedback. Interestingly, the estimator and the rank reduction resulting from this monolithic formulation are independent of the used codebook which can be computed with the generalized Lloyd algorithm. Applying the proposed feedback design to a system with multi-user precoding based on CSI feedback shows the clear superiority of the optimized codebook compared to previous designs.