Energy Efficiency Evaluation of Multi-Tier Cellular Uplink Transmission Under Maximum Power Constraint

This paper evaluates the energy efficiency of uplink transmission in heterogeneous cellular networks (HetNets), where fractional power control (FPC) is applied at user equipments (UEs) subject to a maximum transmit power constraint. We first consider an arbitrary deterministic HetNet and characterize the properties of energy efficiency for UEs in different path loss regimes, or different access regions. By introducing the notion of transfer path loss, we reveal that, for UE whose path loss is below the transfer path loss, its energy efficiency highly depends on the value of power control coefficient adopted by FPC. In contrast, for UE with path loss above the transfer path loss, the uplink energy efficiency asymptotically decreases inversely with path loss, independent of the adopted power control coefficient. Based on these properties, we characterize the optimal power control coefficients for maximizing the energy efficiency of FPC in different access regions. Next, we extend the analysis to stochastic HetNets where UEs and BSs are distributed as independent Poisson point processes, and investigate the distribution of transmit power for uplink UEs. Moreover, the probability of truncation outage due to constrained maximal transmit power, as well as the average energy efficiency of UEs are analytically derived as functions of the BS and UE densities, power control coefficient, and receiver threshold. Simulation results validate the analytical results, show the consistency between deterministic and stochastic analyses, and suggest suitable power control coefficient for achieving energy efficient uplink transmission by FPC in HetNets.