[@Haenggi-2009], wherein the BS locations form a realization of a spatial point process—typically a Poisson point process (PPP). A major advantage of this approach is the ability of providing tractable expressions for key performance metrics such as the coverage probability and the average SE of the network. A few prior works have also derived EE-related performance metrics and showed how these depend on the BS and UE densities; for example, [@Cao2012a] compares the deployment of two types of single-antenna BSs, while [@Li2014a] studies the EE when multi-antenna BSs serve one UE each. In [@Soh2013], the authors focus on the analysis and design of energy-efficient heterogeneous cellular networks (HetNets) through the deployment of small cells and sleeping strategies. The effect of cross-tier BS cooperation and clustering on the EE in the DL is studied in [@Nie2014]. In contrast to the UL analysis in our paper, the vast majority of work on the EE in multi-cell networks using stochastic geometry has focused on the DL. Furthermore, prior work usually aims at deriving closed-form SE and EE expressions, which often turn out to be involved and cumbersome to optimize, thereby providing little or no useful insights on the optimal system design.

Major Contributions
