  This paper proposes a stochastic geometry framework to analyze the SINR and
rate performance in a large-scale uplink massive MIMO network. Based on the
model, expressions are derived for spatial average SINR distributions over user
and base station distributions with maximum ratio combining (MRC) and
zero-forcing (ZF) receivers. We show that using massive MIMO, the uplink SINR
in certain urban marco-cell scenarios is limited by interference. In the
interference-limited regime, the results reveal that for MRC receivers, a
super-linear (polynomial) scaling law between the number of base station
antennas and scheduled users per cell preserves the uplink SIR distribution,
while a linear scaling applies to ZF receivers. ZF receivers are shown to
outperform MRC receivers in the SIR coverage, and the performance gap is
quantified in terms of the difference in the number of antennas to achieve the
same SIR distribution. Numerical results verify the analysis. It is found that
the optimal compensation fraction in fractional power control to optimize rate
is generally different for MRC and ZF receivers. Besides, simulations show that
the scaling results derived from the proposed framework apply to the networks
where base stations are distributed according to a hexagonal lattice.
