that analyzed the EE, as defined above, have focused on the single-cell case wherein the interference from other cells is neglected. Examples in this context are [@Miao2013a; @Hu2014a; @Bjornson2013e; @Ha2013a; @Yang2013a; @Mohammed2014a; @Bjornson2014b; @Bjornson2015a]. In particular, in [@Miao2013a] the authors consider the UL power allocation of multi-user MIMO systems and show that the EE is maximized when specific UEs are switched off. The UL was studied also in [@Hu2014a], where the EE was shown to be a concave function of the number of BS antennas, $M$, and the UE rates. The DL has been investigated in [@Bjornson2013e; @Ha2013a; @Yang2013a], whereof [@Bjornson2013e] and [@Ha2013a] show that the EE is a concave function of $M$, while a similar result is shown for the number of UEs, $K$, in [@Yang2013a]. Unfortunately, in these works, the system parameters were optimized by means of simulations that (although useful) do not provide a complete picture of how the EE is affected by $M$ and $K$. Recently, [@Mohammed2014a] derived the optimal $M$ and $K$ for a given UL sum rate, while [@Bjornson2015a] derived the optimal $M$, $K$ and UE rates to maximize the EE jointly for the UL and DL. These two works utilize a realistic power 