Abstract
We exploit tools from stochastic geometry to develop a tractable analytical approach for modeling uplink cellular networks. The developed model is load aware and accounts for per-user power control as well as the limited transmit power constraint for the users' equipment (UEs). The proposed analytical paradigm is based on a simple per-user power control scheme in which each user inverts his path-loss such that the signal is received at his serving base station (BS) with a certain power threshold.. Due to the limited transmit power of the UEs, users that cannot invert their path-loss to their serving BSs are allowed to transmit with their maximum transmit power. We show that the proposed power control scheme not only provides a balanced cell center and cell edge user performance, it also facilitates the analysis when compared to the state-of-the-art approaches in the literature. To this end, we discuss how to manipulate the design variable. in response to the network parameters to optimize one or more of the performance metrics such as the outage probability, the network capacity, and the energy efficiency.