\frac{ 2}{\beta( \alpha-2)}  + \frac{\sigma^2}{\rho} \Big) \! + \!
 \frac{ 2K}{\alpha-2} \! \left(  1  + \frac{\sigma^2}{\rho} \right) \! + \!
\frac{K}{\beta} \! \left( \frac{4}{(\alpha-2)^2 } +
\frac{1 }{ \alpha-1} \right) \!
+  M (1-\epsilon^2) \Big( \frac{ 1}{\beta( \alpha-1)} \!+\! \epsilon^2 \Big)  }\end{aligned}$$

The MMSE estimate of the typical UE’s channel to its serving $\mathrm{BS}_0$ is $$\label{eq:MMSE-estimator}
  \hat{{\mathbf{h}}}_{00k} = 
\frac{  \sqrt{ \frac{1-\epsilon^2}{\rho \omega d_{00k}^{\alpha}} }}{ 1   +  \sum_{j \in \Psi_{\lambda} }    \chi_{0kj}    \frac{d_{jjk}^{\alpha}}{ d_{0jk}^{\alpha} } + \frac{\sigma^2}{ \rho} } {\mathbf{z}}_{0k}.$$ The estimation error $\Delta{\mathbf{h}}_{00k} = {\mathbf{h}}_{00k}  - \hat{{\mathbf{h}}}_{00k}$ is distributed as $\Delta{\mathbf{h}}_{00k}  \sim\mathcal{CN}({\mathbf{0}},{\mathbf{C}}_{00k})$, where the estimation error covariance matrix ${\mathbf{C}}_{00k} \in \mathbb{C}^{M \times M}$ is given by $$\label{eq:MMSE-error-cov}
{\mathbf{C}}_{00k} = \frac{1}{\omega d_{00k}^{\alpha}}  \left(1 - \frac{  1-\epsilon^2 }{ 1   +  \sum_{j \in \Psi_{\lambda} }    \chi_{0kj}   \frac{d_{jjk}^{\alpha}}{ d_{0jk}^{\alpha} } + \frac{\sigma^2}{\rho} }  \right) {\mathbf{I}}_M.$$

This follows from standard results on MMSE estimation; see [@Kay1993a Chapter 15.8].

Average Spectral Efficiency {#sec:ASE}
===========================

We assume that MRC processing is used at the BSs for data recovery, since MRC is computationally efficient and performs well in both small cells (with $K=1$) and massive MIMO (with $M \gg K$). In particular, the symbol transmitted by the typical UE is detected at $\mathrm{BS}_0$ by correlating the received signal 