to a BS that is called the *typical BS* and is denoted as $\mathrm{BS}_0 \in \Phi_{\lambda}$. Then, the following basic properties hold (see for example [@Weber2010a]):

\[lemma:distance-distribution\] The distance $d_{00k}$ from the typical UE to its serving BS is Rayleigh distributed as $d_{00k} \sim \mathrm{Rayleigh} \big( \frac{1}{\sqrt{2\pi \lambda}} \big)$. The BSs of the other cells form a homogenous PPP $\Psi_{\lambda} = \Phi_{\lambda} \setminus \{ \mathrm{BS}_0 \}$ in $\mathbb{R}^2 \setminus \{ {\mathbf{x}} \in \mathbb{R}^2 : \| {\mathbf{x}} \| < d_{00k} \}$.

Using the notation introduced in Lemma \[lemma:distance-distribution\], each interfering BS, $\mathrm{BS}_j \in \Psi_{\lambda}$, is situated at the geographical position determined by its spatial point $\mathrm{BS}_j \in \mathbb{R}^2$. Since in most cases we are interested only in the index of the interfering BS, the shorter notation $j \in \Psi_{\lambda}$ is used henceforth for $\mathrm{BS}_j \in \Psi_{\lambda}$.

Channel Model and Power-Control Policy
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We consider a UL transmission protocol where the time-frequency resources are divided into blocks of $T_c$ seconds and $W_c$ Hz. This leaves room for a total number of $S = T_c W_c$ transmission symbols for pilot signaling and data. The channel response ${\mathbf{h}}_{ljk} \in \mathbb{C}^M$ between $\mathrm{BS}_l$ and UE $k$ in cell $j$ is modeled as block-fading such that 