Large multi-antenna stochastic geometry

We consider coordinated beamforming (BF) for the Multi-Input Single-Output (MISO) Interfering Broadcast Channel (IBC). The beamformers are optimized for the Ergodic Weighted Sum Rate (EWSR) or various approximations and bounds thereof, for the case of Partial Channel State Information at the Transmitters (CSIT). Gaussian (posterior) partial CSIT can optimally combine channel estimate and channel covariance information. With Gaussian partial CSIT, the beamformers only depend on the means (estimates) and (error) covariances of the channels. We extend a recently introduced large system analysis for optimized beamformers with partial CSIT, by a stochastic geometry inspired randomization of the channel covariance eigen spaces, leading to much simpler analytical results, which depend only on some essential channel characteristics. In the Massive MISO (MaMISO) limit, we obtain deterministic approximations of the signal and interference plus noise powers at the receivers, which are tight as the number of BS antennas and the total user subspace dimension tend to infinity at fixed ratio. Simulation results exhibit the correctness of the large system results and the performance superiority of optimal BF designs based on both the MaMISO limit of the EWSR and using Linear Minimum Mean Squared Error (LMMSE) channel estimates.