\mathcal{A},\mathcal{C}_0,\mathcal{C}_1,\mathcal{D}_0,\mathcal{D}_1$), to find the tuple of parameters $\theta = (\beta, \rho,\lambda,K,M)$ that solves the following constrained EE maximization problem: $$\label{eq:main-optimization-problem}
\begin{split}
{{\underset{{\theta \in \Theta}}{\mathrm{maximize}}}} &\quad \mathrm{EE}(\theta) = \frac{\mathrm{ASE}(\theta)}{\mathrm{APC}(\theta)}\\
\mathrm{subject} \,\, \mathrm{to}  &   \quad \underline{\mathrm{SINR}} = \gamma 
\end{split}$$ where $\Theta$ is the feasible parameter set defined as $$\Theta = \{\theta: \, \rho\geq 0, \lambda \geq 0, \beta \geq 1, (M,K) \in \mathbb{Z}_+, K\beta \leq S\}$$ with $K\beta \leq S$ being the upper limit on the pilot signaling overhead. The parameter $\gamma>0$ in is used to impose an average SE constraint of $\log_2(1+\gamma)$ \[bit/symbol/user\], where the average is computed with respect to both BS and UE locations. This constraint is needed to obtain a network with an acceptable throughput, since unconstrained EE maximization often leads operating points with very low SEs per UE; this is later on illustrated in Fig. \[figureBSdensity\] where the EE increases as $\gamma$ decreases.

In the remainder of this section, we analyze the EE maximization problem in to expose fundamental behaviors and to develop an algorithm for solving it.

Feasibility {#subsec:feasibility}
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Due to the unavoidable inter-cell interference in cellular networks, the optimization problem is only feasible for some values of $\gamma$. This feasible range is obtained as 