Massive MIMO Stochastic Geometry and Analysis of Beamforming with Partial CSIT

We consider coordinated beamforming (BF) for the Multi-Input Single-Output (MISO) Interfering Broadcast Channel (IBC) under imperfect channel state information at the transmitter(s) (CSIT). We start from a BF design which optimizes a Massive MISO limit upper bound of the ergodic capacity, termed Expected Signal and Interference Power Weighted Sum Rate (ESIP-WSR). We extend a recently introduced large system analysis (LSA) for beamformers with partial CSIT, by a stochastic geometry inspired randomization of the channel covariance eigen spaces, leading to much simpler analytical results. These depend only on some essential channel characteristics such as the numbers of antennas and users, channel rank and eigenvalue profile, and (channel estimate) signal to noise ratio (SNR). We analyze the spectral efficiency behavior at extreme SNR regions which provide insights (through the SNR offset) into the characteristics of the various channel estimates and suboptimal BFs compared to ESIP-WSR BF with Linear Minimum Mean Squared Error (LMMSE) channel estimates. Furthermore, simulations validate the superior performance of ESIP-WSR BF compared to the suboptimal BFs with different channel estimates and also the accuracy of the large system approximations derived herein. Our analysis is focused on constant channel estimation regime which is indicative of the finite rate feedback channels and pilot contamination regime.