hardware impairments is included in the system under investigation. We concentrate on UE impairments, which is expected to be the dominating effect since small BS arrays can use high-grade hardware and massive arrays are resilient to hardware impairments [@Bjornson2014a].

Denote by $s_{ji} \in \mathbb{C}$ an arbitrary symbol transmitted by UE $i$ in cell $j$ and assume that it is normalized to unit power (i.e., $\mathbb{E}\{ | s_{ji}|^2 \}=1$). Similar to [@wenk2010mimo; @Zhang2012a; @Bjornson2013c], the hardware impairments are modeled as a reduction of the desired signal power by a factor of $1-\epsilon^2$, with $0 \leq \epsilon < 1$, and by adding Gaussian distortion noise that carries the removed power. More precisely, $s_{ji} $ is replaced with $\sqrt{1-\epsilon^2}s_{ji} + e_{ji}$, where $e_{ji} \sim \mathcal{CN}(0,\epsilon^2)$ is the additive UL distortion noise caused at UE $i$ in cell $j$. In these circumstances, the received signal ${\mathbf{y}}_0 \in \mathbb{C}^{M}$ at $\mathrm{BS}_0$ takes the form $$\label{eq:system-model-received}
\begin{split}
{\mathbf{y}}_0 &= \sum_{i=1}^{K} \sqrt{p_{0i}} (\sqrt{1-\epsilon^2}s_{0i} + e_{0i}) {\mathbf{h}}_{00i}  \\ &+ \sum_{j \in \Psi_{\lambda}}
\sum_{i=1}^{K} \sqrt{p_{ji}} (\sqrt{1-\epsilon^2}s_{ji} + e_{ji})  {\mathbf{h}}_{0ji}  + {\mathbf{n}}_{0}
\end{split}$$ where ${\mathbf{n}}_{0} \sim \mathcal{CN}(0,\sigma^2 {\mathbf{I}}_M)$ models receiver noise with variance $\sigma^2$. The parameter $\epsilon$ is referred to as the *level of impairments* and is tightly connected to 