Uplink Massive MIMO SIR Analysis: How Do Antennas Scale with Users?

Massive multiple-input multiple-output (MIMO) is a potential physical layer technology for 5G cellular networks. This paper leverages stochastic geometry to derive the uplink signal-to- interference (SIR) distribution in massive MIMO networks. Based on the derived expressions, a scaling law between the number of base station antennas and scheduled users per cell is provided to preserve the uplink SIR distribution, where the impacts of correlation in small-scale fading and power control in the form of fractional path loss compensation are taken account. Numerical results verify the analysis, and show that fractional power control with a compensation fraction of 0.5 is nearly optimal for the average achievable rate in certain cases.