MIMO broadcast channels with Gaussian CSIT and application to location based CSIT

Channel State Information at the Transmitter (CSIT), which is crucial in multi-user systems, is always imperfect in practice. In this paper we focus on the optimization of beamformers for the expected weighted sum rate (EWSR) in the MIMO Broadcast Channel (BC) (multi-user MIMO downlink). We first review some beamformer (BF) designs for the perfect CSIT case, such as Weighted Sum MSE (WSMSE) and we introduce the Weighted Sum SINR (WSSINR) point of view, an optimal form of the Signal to Leakage plus Noise Ratio (SLNR) or Signal to Jamming plus Noise Ratio (SJNR) approaches. The discussion then turns to mean and covariance Gaussian CSIT. We review an exact Monte Carlo based approach and a variety of approximate techniques and bounds that all reduce to problems of the (deterministic) form of perfect CSIT. Other simplified exact solutions can be obtained through massive MIMO asymptotics, or the more precise large MIMO asymptotics. Whereas in the perfect CSI case, all reviewed approaches are equivalent, they differ in the partial CSIT case. In particular the expected WSSINR approach is significantly better than expected WSMSE, with large MIMO asymptotics introducing some further tweaking weights that yield a deterministic approach that becomes exact when the number of antennas increases. The complexity and relative performance of the in the end many possible approaches and approximations are then compared.