  Cellular uplink analysis has typically been undertaken by either a simple
approach that lumps all interference into a single deterministic or random
parameter in a Wyner-type model, or via complex system level simulations that
often do not provide insight into why various trends are observed. This paper
proposes a novel middle way using point processes that is both accurate and
also results in easy-to-evaluate integral expressions based on the Laplace
transform of the interference. We assume mobiles and base stations are randomly
placed in the network with each mobile pairing up to its closest base station.
Compared to related recent work on downlink analysis, the proposed uplink model
differs in two key features. First, dependence is considered between user and
base station point processes to make sure each base station serves a single
mobile in the given resource block. Second, per-mobile power control is
included, which further couples the transmission of mobiles due to
location-dependent channel inversion. Nevertheless, we succeed in deriving the
coverage (equivalently outage) probability of a typical link in the network.
This model can be used to address a wide variety of system design questions in
the future. In this paper we focus on the implications for power control and
see that partial channel inversion should be used at low
signal-to-interference-plus-noise ratio (SINR), while full power transmission
is optimal at higher SINR.
