Beamforming for correlated broadcast channels with quantized channel state information

The design of channel quantization codebooks for correlated broadcast channels with limited feedback is addressed. A design criterion that effectively exploits the cell statistics is proposed, based on minimizing the average sum-rate distortion in a system with joint linear beamforming and multiuser scheduling. The proposed average distortion function is optimized by generating a set of quantization codebooks through random trials, keeping the codebook that yields the lowest distortion. Comparisons with limited feedback approaches relying on random codebooks are provided, highlighting the importance of matching the codebook design to the cell statistics. Numerical results show a performance gain in scenarios with non-uniform user distributions. Further, we propose a scheme that exploits the limited channel knowledge at the base station to reduce the computational complexity of determining the beamforming vectors and of finding the optimal user set.