  Employing multi-tier networks is among the most promising approaches to
address the rapid growth of the data demand in cellular networks. In this
paper, we study a two-tier uplink cellular network consisting of femtocells and
a macrocell. Femto base stations, and femto and macro users are assumed to be
spatially deployed based on independent Poisson point processes. We consider an
open access assignment policy, where each macro user based on the ratio between
its distances from its nearest femto access point (FAP) and from the macro base
station (MBS) is assigned to either of them. By tuning the threshold, this
policy allows controlling the coverage areas of FAPs. For a fixed threshold,
femtocells coverage areas depend on their distances from the MBS; Those closest
to the fringes will have the largest coverage areas. Under this open-access
policy, ignoring the additive noise, we derive analytical upper and lower
bounds on the outage probabilities of femto users and macro users that are
subject to fading and path loss. We also study the effect of the distance from
the MBS on the outage probability experienced by the users of a femtocell. In
all cases, our simulation results comply with our analytical bounds.
