Capacity of cellular wireless network

In cellular networks, under ARQ and SINR model of transmission, the effective downlink rate of packet transmission is the reciprocal of the expected delay (number of retransmissions needed till success). We define the cellular network capacity as the ratio of the basestation (BS) density and the expected delay. Exact characterization of this natural and practical but non-trivial (because of SINR temporal correlations) capacity metric is derived. The capacity is shown to first increase polynomially with the BS density 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 upto constants. Our result is fundamentally different than the transport and transmission capacity for ad hoc networks 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 model for cellular networks is limiting, and the realizable capacity is much smaller than previously thought.