Weighted sum rate maximization in the MIMO MAC with linear transceivers: Asymptotic results

We present asymptotic results for the weighted sum rate maximization in a MIMO multiple access channel with individual power constraints when the noise power at the receiver becomes small and linear filtering is applied at the transceivers. The key parameter that determines the optimum signaling strategy is the number of antennas at the base station. If there are more antennas than the user terminals have in sum, the asymptotically optimum transmit covariance matrices are scaled identities, whereas scaled rank-deficient projectors have to be chosen when the base station does not have enough degrees of freedom. We derive the optimum transmit covariance matrices for both antenna configurations and shed some light on the impact of the solutions on the underlying rate region structure. In addition, the impact of the optimum transmission strategy on the convex hull of the underlying rate region is demonstrated.