## 5 Interference Analysis
### V-Ns Interference
}=e^{\mathcal{Y}}\), we get  
\[L_{I_{V}}^{\sharp}(s)=e^{\left(-2\lambda_{V}\sqrt{z^{2}-y^{2}}\right)}\exp \left(2\lambda_{V}\left(\int_{0}^{\sqrt{z^{2}-y^{2}}}\dfrac{dt_{1}}{1+sP_{V}B \mathcal{G}_{t}\mathcal{G}_{r}\big{(}y^{2}+t_{1}^{2}\big{)}\dfrac{-\alpha_{r} }{2}}\right)\right).\]  
After simplification, the V-Ns' interference located at a single road with \(y\geq z_{V}\) is given as  
\[L_{I_{V}}^{\sharp}(s)=\exp\left(-2\lambda_{V}\int_{0}^{\sqrt{z^{2}-y^{2}}} \left(1-\dfrac{1}{1+sP_{V}B\mathcal{G}_{t}\mathcal{G}_{r}\big{(}y^{2}+t_{1}^{2 }\big{)}\dfrac{-\alpha_{r}}{2}}\right)dt_{1}\right). \tag{26}\]  
For \(\alpha_{r}>1\), the closed-form expression is given as  
\[L_{I_{V}}^{\sharp}(s)=\exp\left(\dfrac{-2\lambda\pi(sP_{V}B\mathcal{G}_{t} \mathcal{G}_{r})^{-\alpha_{r}}\csc\left(\dfrac{\pi}{\alpha_{r}}\right)}{\alpha_{ r}}\right). \tag{27}\]  
Following a similar procedure of (26), the V-Ns interference for a single road with \(y<z_{V}\) can be computed and is given as \[L_{I_{V}}^{i}(s)=\exp\left(-2\lambda_{V}\int_{\sqrt{z_{V}^{2}-y^{2}}}^{\sqrt{z_{V}^ {2}-y^{2}}}\left(1-\frac{1}{1+sP_{V}B\mathcal{G}_{i}\mathcal{G}_{r}\big{(}y^{2}+ t_{1}^{2}\big{)}}\frac{-\alpha_{r}}{2}\right)dt_{1}\right). \tag{28}\]  
The roads are distributed in the given region considering a PPP, and the average number of roads with \(y<z_{V}\) is given as \(2\lambda_{R}\lambda_{V}(z-z_{V})\), and the average number of roads with \(y\geq z_{V}\) is given as \(2\lambda_{R}\lambda_{V}z\). Let \(j_{1}\) and \(j_{2}\) be the number of roads such that \(j_{1}\) has the pdf, \(f(t_{1})=\frac{1}{2z}\) with \(y\geq z\) and \(j_{2}\) has the pdf, \(f(t_{2})=\frac{1}{2(z-z_{V})}\) with \(y<z\). Thus, the V-Ns interference, considering all the roads other than the typical road that passes \(o\), can be expressed as  
\[L_{I_{V}}(s)=\Bigg{\{}\sum_{i_{1}\geq 0}\frac{\exp(-2 \lambda_{R}\lambda_{V}z)(2\lambda_{R}\lambda_{V}z)^{j_{1}}}{j_{1}!}\bigg{(} \int_{-z}^{z}L_{I_{V}}^{z}(s)f(t_{1})dt_{1}\bigg{)}^{j_{1}}\Bigg{\}}\] \[\Bigg{\{}\sum_{h\geq 0}\frac{\exp(-2\lambda_{R}\lambda_{V}(z-z_{V }))(2\lambda_{R}\lambda_{V}(z-z_{V}))^{j_{2}}}{j_{2}!}\bigg{(}\int_{z_{V}}^{z} L_{I_{V}}^{i}(s)f(t_{2})dt_{2}\bigg{)}^{j_{2}}\Bigg{\}}. \tag{29}\]  
Substituting \(f(t_{1})\) and \(f(t_{2})\) in (29) and simplifying the expression, we get  
\[L_{I_{V}}(s)=e^{-2\lambda_{R}\lambda_{V}z}\frac{\sum_{i_{1}\geq 0}\!\Big{(}2\lambda_{R}\lambda_{V}\!\int_{0}^{z}L_{I_{V}}^{i_{1}}(s)dt_{1} \Big{)}^{j_{1}}}{j_{1}!}e^{-2\lambda_{R}\lambda_{V}(z-z_{V})}\frac{\sum_{h \geq 0}\!\Big{(}2\lambda_{R}\lambda_{V}\!\int_{z_{V}}^{z}L_{I_{V}}^{i_{1}}(s) dt_{2}\Big{)}^{j_{2}}}{j_{2}!}. \tag{30}\]  
Employing \(\sum_{i=0}^{\infty}\mathcal{Y}^{i}/i!=e^{y}\), (30) is simplified as  
\[L_{I_{V}}^{\sharp}(s)=\sum_{j\geq 0}\dfrac{e^{\left(-2\lambda_{V}\sqrt{z^{2}-y ^{2}}\right)}\left(2\lambda_{V}\sqrt{z^{2}-y^{2}}\right)^{j}}{j!\left(2\sqrt{ z^{2}-y^{2}}\right)^{j}}\left(\int_{-\sqrt{z^{2}-y^{2}}}^{\sqrt{z^{2}-y^{2}}} \dfrac{dt_{1}}{1+sP_{V}B\mathcal{G}_{t}\mathcal{G}_{r}\big{(}y^{2}+t_{1}^{2} \big{)}\dfrac{-\alpha_{r}}{2}}\right)^{j}. \tag{24}\]0  
The final expression of the V-Ns interference, excluding the typical road passing origin, is expressed as  
\[L_{I_{V}}^{\sharp}(s)=\sum_{j\geq 0}\dfrac{e^{\left(-2\lambda_{V}\sqrt{z^{2}-y ^{2}}\right)}\left(2\lambda_{V}\sqrt{z^{2}-y^{2}}\right)^{j}}{j!\left(2\sqrt{ z^{2}-y^{2}}\right)^{j}}\left(\int_{-\sqrt{z^{2}-y^{2}}}^{\sqrt{z^{2}-y^{2}}} \dfrac{dt_{1}}{1+sP_{V}B\mathcal{G}_{t}\mathcal{G}_{r}\big{(}y^{2}+t_{1}^{2} \big{)}\dfrac{-\alpha_{r}}{2}}\right)^{j}. \tag{24}\]1  
The V-Ns interference from the typical road passing \(o\) is expressed by substituting \(y=0\) in (28).