  In this work, we analyze the performance of the uplink (UL) of a massive MIMO
network considering an asymptotically large number of antennas at base stations
(BSs). We model the locations of BSs as a homogeneous Poisson point process
(PPP) and assume that their service regions are limited to their respective
Poisson-Voronoi cells (PVCs). Further, for each PVC, based on a threshold
radius, we model the cell center (CC) region as the Johnson-Mehl (JM) cell of
its BS while rest of the PVC is deemed as the cell edge (CE) region. The CC and
CE users are located uniformly at random independently of each other in the JM
cell and CE region, respectively. In addition, we consider a fractional pilot
reuse (FPR) scheme where two different sets of pilot sequences are used for CC
and CE users with the objective of reducing the interference due to pilot
contamination for CE users. Based on the above system model, we derive
analytical expressions for the UL signal-to-interference-and-noise ratio (SINR)
coverage probability and average spectral efficiency (SE) for randomly selected
CC and CE users. In addition, we present an approximate expression for the
average cell SE. One of the key intermediate results in our analysis is the
approximate but accurate characterization of the distributions of the CC and CE
areas of a typical cell. Another key intermediate step is the accurate
characterization of the pair correlation functions of the point processes
formed by the interfering CC and CE users that subsequently enables the
coverage probability analysis. From our system analysis, we present a
partitioning rule for the number of pilot sequences to be used for CC and CE
users as a function of threshold radius that improves the average CE user SE
while achieving similar CC user SE with respect to unity pilot reuse.
