Weighted Sum Rate of Multi-Cell MIMO Downlink Channels in the Large System Limit

The optimization of the weighted ergodic sum rate is considered for the downlink of a cellular networks with multiple cells and multi-antenna base stations. We focus on the large system limit where the number of base station antennas and the number of users per cell go to infinity with a fixed ratio. We consider two extreme cases of full inter-cell cooperation (network MIMO) and no inter-cell cooperation (single-cell multiuser MIMO). Using the large random matrix theory and Lagrangian optimization, we obtain a numerical algorithm that exactly computes the maximum weighted sum rate in this asymptotic regime. Numerical results are presented for a simple case of two interfering cells in a linear arrangement.