  Earlier definitions of capacity for wireless networks, e.g., transport or
transmission capacity, for which exact theoretical results are known, are well
suited for ad hoc networks but are not directly applicable for cellular
wireless networks, where large-scale basestation (BS) coordination is not
possible, and retransmissions/ARQ under the SINR model is a universal feature.
  In this paper, cellular wireless networks, where both BS locations and mobile
user (MU) locations are distributed as independent Poisson point processes are
considered, and each MU connects to its nearest BS. With ARQ, under the SINR
model, the effective downlink rate of packet transmission is the reciprocal of
the expected delay (number of retransmissions needed till success), which we
use as our network capacity definition after scaling it with the BS density.
  Exact characterization of this natural capacity metric for cellular wireless
networks is derived. The capacity is shown to first increase polynomially with
the BS density in the low BS density regime and then scale inverse
exponentially with the increasing BS density. Two distinct upper bounds are
derived that are relevant for the low and the high BS density regimes. A single
power control strategy is shown to achieve the upper bounds in both the
regimes. This result is fundamentally different from the well known capacity
results for ad hoc networks, such as transport and transmission capacity that
scale as the square root of the (high) BS density. Our results show that the
strong temporal correlations of SINRs with PPP distributed BS locations is
limiting, and the realizable capacity in cellular wireless networks in high-BS
density regime is much smaller than previously thought. A byproduct of our
analysis shows that the capacity of the ALOHA strategy with retransmissions is
zero.
