antenna branches per BS), which in turn increases the circuit power consumption per BS.

In summary, both densification technologies can improve the area throughput and reduce the radiated power, but at the cost of deploying more hardware infrastructure. Hence, the overall EE of the network can only be improved if these benefits and costs are properly balanced. The main objective of this paper is to develop an analytical framework for designing dense cellular networks for maximal EE, as well as to provide guidelines for practical deployment when (among others) the spectral efficiency (SE), radiated power, BS density, number of antennas and UEs per BS, channel estimation, and the circuit power consumption are taken into account from the outset.

Related Works
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The EE of cellular networks has been defined from different perspectives in the last decade [@Feng2013a; @Li2011a]. One of the most common definitions is a benefit-cost ratio, where the service quality per area unit (a.u.) is compared with the associated energy costs. In this paper, the following general definition is used: $$\begin{aligned}
&\mathrm{EE} = \\ &\frac{\textrm{Area spectral efficiency [bit/symbol/km}^2]}{\textrm{Transmit power + Circuit power per a.u.~[J/symbol/km}^2]}\end{aligned}$$ which yields to an EE metric measured in bit/J.[^2]

Most of the early works 