in with the MMSE estimate $\hat{{\mathbf{h}}}_{00k}$; that is, $r_{0k} = \nu_{00k}\hat{{\mathbf{h}}}_{00k}^{\Htran}  {\mathbf{y}}_0$ is the received signal after MRC processing with $\nu_{00k} \in \mathbb{C}$ being a scaling factor (see Appendix A). Unfortunately, the ergodic capacity for a network (such as the one under investigation) in which only imperfect CSI is available at the receivers and the inter-cell interference is modeled as a shot-noise process is not known yet [@Weber2010a]. Hence, in this work the SE expression is obtained using classical achievable lower bounds on the ergodic capacity that are particularly common in the massive MIMO literature [@Marzetta2010a; @Yang2013b; @Bjornson2016a]. The following result holds for any given realization of $\Psi_{\lambda}$ and the UE locations.

\[lemma:SINR-ideal\] With MRC processing and any given realization of $\Psi_{\lambda}$ and the UE locations, a lower bound on the ergodic capacity \[bit/symbol/user\] of the typical UE is $$\label{eq:ergodic-capacity}
\Big( 1 - \frac{\beta K}{S} \Big) \log_2 \! \left( 1 + \mathrm{SINR}_{0k}  \right)$$ where the pre-log factor $\big( 1 - \frac{\beta K}{S} \big) $ accounts for pilot overhead and $\mathrm{SINR}_{0k}$, in at the top of the page, is the effective SINR.

The proof is given in Appendix A and proceeds as follows. First, the lower-bounding approach from [@Jose2011b] and [@Medard2000a] 