semi-orthogonal codes for communications, it is clear that $\hat \upsilon_{k,1}=0$, and $\hat \upsilon_{k,2}=\upsilon_k\frac{n_k\tau_k}{T_k} \frac{w_k}{W}$. Following the same procedure used for deriving $\mathcal L_{I_\Psi}^{\ddag}(s)$, one can derive $\mathcal L_{I_\Psi}^{\dag}(s)$ as: $$\begin{aligned}
\mathcal L_{I_\Psi}^{\dag}(s)\text{=}&\prod\nolimits_{j\in\{1,2\}}\mathbb E_y \big[\mathbb E_x [  \prod\nolimits_{{\bf x}\in \theta_{\bf y}^{(j)}}u({\bf x},{\bf y}) ]\big]\label{lik}\\
\text{=}& \int\nolimits_{\mathbb R^2}\exp\big(\text{-}{\textstyle\sum_j}\hat \upsilon_{i,j}  \int\nolimits_{\mathbb R^2} \big(1\text{-}{u({\bf x},{\bf y})}\big)\text{f}({\bf x})d {\bf x}\bigg)\text{f}({\bf y}) d {\bf y}\nonumber.\end{aligned}$$

### Probability of Success in Transmission {#su1}

Let $N$ denote the additive noise at the receiver. Using the interference model, probability of success in packet transmission of a type-$i$ device, located at $\bf z$, to the AP, located at the origin, is: $$\begin{aligned}
\text{p}_{\text{s}}(i,{\bf z})&=\text{Pr}({  P_ih \text{g}({\bf z})}\ge[{N+I_{\Psi}}] \gamma_{\text{th}})\label{suc}\\
&\buildrel (\text{a}) \over =   \sum\limits_{\nu=0}^{m\text{-}1}\frac{1}{{\nu}!}\int\nolimits_{0}^{\infty}\exp({-}\frac{\gamma_{\text{th}}m q}{\Omega   P_i \text{g}({\bf z})}) q^{\nu}  d \text{Pr}(I_\Psi\text{+}N\ge q)\nonumber\\
&\buildrel (\text{b}) \over =  \sum\nolimits_{{\nu}=0}^{m\text{-}1}\frac{(-1)^{\nu}}{{\nu}!}[\mathcal L_{I_{\Psi}}(s)\mathcal L_{N}(s)]^{({\nu})} \big|_{s=\frac{\gamma_{\text{th}}m}{\Omega   P_i \text{g}({\bf z})}}, \nonumber\end{aligned}$$ where $[F(s)]^{({\nu})}=\frac{\partial^{\nu}}{\partial s^{\nu}}F(s)$, (a) follows from [@adhoc Appendix C] and equation in which $\text{p}_h(q)$ has been defined, and finally (b) follows from [@alm Lemma 3.1] and the fact that $\mathcal L (t^n \text{f}(t))=(-1)^n\frac{\partial^n}{\partial s^n}F(s)$. Furthermore, $L_{I_{\Psi}}$ has been characterized in and , and $\mathcal L_N(s)$ is the Laplace transform of noise. In order to get insights on how coexisting services affect each other, in the following we 