target per UE must be met with equality, to guarantee good service quality. This problem is solved analytically with respect to the tuple $\theta = (\beta,\lambda, \rho,M,K)$ of optimization variables. The resulting closed-form expressions provide valuable design insights on the interplay between the different system parameters and the various components of the power consumption model. We show analytically and numerically that the radiated power is negligible in most practical cases and that massive MIMO configured BSs appear naturally since this technology can protect the desired signals from inter-cell interference and share the circuit power between many UEs.

Outline and Notation
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The remainder of this paper is organized as follows. Section \[sec:system\] introduces the system model for the network under investigation, including hardware impairments at the UEs and CSI estimation at the BSs. A new and tractable lower bound on the average SE is derived in Section \[sec:ASE\]. It is used in Section \[sec:problem\] to formulate the EE maximization problem and to obtain closed-form expressions for the EE-maximizing pilot reuse factor, BS density, and transmission power as well as the number of UEs and antennas per BS. The theoretical analysis is corroborated by numerical results in Section \[sec:simulations\] while the 