i.e. daughter points of the same parent point; and ii) other transmitters. Let us denote the Laplace functional of interference from the former and latter transmitters as $\mathcal L_{I_{\Psi}}^{\dag}(s)$ and $\mathcal L_{I_{\Psi}}^{\ddag}(s)$ respectively. Then, we have: $$\label{taj}\mathcal L_{I_{\Psi}}(s)=\mathcal L_{I_{\Psi}}^{\ddag}(s)\mathcal L_{I_{\Psi}}^{\dag}(s).$$ Using equation (18) in [@math], and by conditioning on $\Theta_{k}$ and $\theta_{\bf y}^{(j)}$, one has: $$\begin{aligned}
 &\mathcal L_{I_{\Psi}}^{\ddag}(s)\label{li}\\
&  =  \prod\nolimits_{j,k}\mathbb E_{y}\bigg[  \prod\limits_{{\bf y}\in \Theta_{k}}\big\{\exp\big(\text{-}\hat \upsilon_{k,j}  \int\nolimits_{\mathbb R^2} [1\text{-}{u({\bf x},{\bf y})}]\text{f}({\bf x})d {\bf x}\big)\big\} \bigg]\nonumber,\\
 &  =\exp\big( \text{-} {\textstyle \sum\limits_{j,k}}\lambda_k \int\limits_{\mathbb R^2}\big\{1\text{-}\exp\big(\text{-}\hat\upsilon_{k,j} \int\limits_{\mathbb R^2}[1\text{-} {u({\bf x},{\bf y})}]\text{f}({\bf x})d {\bf x} \big)\big\}d {\bf y}\big).\nonumber
 \end{aligned}$$ Also, in the average numbers of interfering type-$k$ devices in each cluster for $j\in\{1,2\}$ are denoted as $\hat \upsilon_{k,1}=\upsilon_k\frac{n_k\tau_k}{T_k} \frac{w_k}{W}\frac{1}{|\varpi| }$ and $\hat \upsilon_{k,2}=\upsilon_k\frac{n_k\tau_k}{T_k} \frac{w_k}{W}\frac{|\varpi| -1}{|\varpi| }$ for $k\in\phi$. In these two expressions, the first fraction represents the percentage of time in which device is active, i.e. the time activity factor, the second fraction represents the ratio of bandwidth that device occupies in each transmission, i.e. the frequency activity-factor, and the third fraction represents the code-domain activity factor, i.e. the probability that two devices select the same code, i.e. $\frac{1}{|\varpi| }$, or different codes $\frac{|\varpi| -1}{|\varpi| }$. Then, for $k\notin \phi$, in which devices don’t share 