Opportunistic random beamforming with optimal precoding for spatially correlated channels

It has been shown recently that dirty paper coding (DPC) achieves optimum sum-rate capacity in a multi-antenna broadcast channel with full channel state (CSI) information at the transmitter. With only partial feedback, random beamforming (RBF) is able to match the sumrate of DPC for large number of users. However, in the presence of spatial correlation, RBF incurs an SNR hit as compared to DPC. In this letter, we explore precoding techniques to reduce the effect of correlation on RBF. We thus derive the optimum precoding matrix that minimizes the rate gap between DPC and RBF. Given the numerical complexity involved in calculating the optimum precoder, we derive approximate precoding matrices that are simple to calculate and close in performance to the optimum precoder.