The uplink of a wireless network with base stations distributed according to
a Poisson Point Process (PPP) is analyzed. The base stations are assumed to
have a large number of antennas and use linear minimum-mean-square-error (MMSE)
spatial processing for multiple access. The number of active mobiles per cell
is limited to permit channel estimation using pilot sequences that are
orthogonal in each cell. The cumulative distribution function (CDF) of a
randomly located link in a typical cell of such a system is derived when
accurate channel estimation is available. A simple bound is provided for the
spectral efficiency when channel estimates suffer from pilot contamination. The
results provide insight into the performance of so-called massive
Multiple-Input-Multiple-Output (MIMO) systems in spatially distributed cellular
networks