${\mathbf{h}}_{ljk}$ has a constant stochastic realization within a block and takes independent realizations across blocks. Since the number of BS antennas is treated as an optimization variable in this work, we need a channel model that is reasonable for both small and large arrays. For this purpose, we make use of a Rayleigh fading model as it well-matches non-line-of-sight measurements in both cases [@Gao2015a]. Hence, we consider Rayleigh fading channels with ${\mathbf{h}}_{ljk} \sim \mathcal{CN}({\mathbf{0}}, \omega^{-1} d_{ljk}^{-\alpha} {\mathbf{I}}_M)$, where $d_{ljk}$ is the propagation distance (measured in km) and $\alpha> 2$ is the pathloss exponent. The parameter $\omega$ accounts for the pathloss at a reference distance of 1 km and can thus be used to model distance-independent propagation losses (such as wall penetration).

Power control is an essential mechanism in the UL of any multi-user MIMO system; the finite dynamic range of analog-to-digital converters at the BSs otherwise creates near-far blockage where weak signals from distant UEs drown in stronger signals from nearby UEs. Statistical channel inversion is a convenient power-control policy [@Bjornson2016a], where UE $i$ in cell $j$ uses the transmit power $$\label{p_{ji}}
p_{ji} = \rho  \omega d_{jji}^{\alpha}$$ with $\rho \geq 0$ being a power-control coefficient to be designed.[^4] The average 