## Appendix B
The average path loss of the NLOS link formed by \(M\) from Tx2 can be calculated as follows:  
\[h_{NLOS\_M,2}^{PL\_ap} =\frac{{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}e}^{\frac{-c_{E}D_{R}}{ \xi}}}{2^{1+2/\varepsilon}(L_{w}-v_{w})\xi^{4}}\Bigg{\{}\frac{\bigg{\{}Beta \Bigg{[}\frac{4I_{V_{1}-PD}^{2}}{(4v_{w}+2v_{w})^{2}+4I_{V_{1}-PD}^{2}},\frac{ 3}{2}+\frac{2}{\varepsilon},\frac{1}{2}\Bigg{]}-Beta\Bigg{[}\frac{I_{V_{1}- PD}^{2}}{L_{w}^{2}+I_{V_{1}-PD}^{2}},\frac{3}{2}+\frac{2}{\varepsilon}, \frac{1}{2}\Bigg{]}\Bigg{\}}}} \tag{15}\] \[+\frac{\bigg{\{}Beta\Bigg{[}\frac{I_{V_{1}-PD}^{2}}{L_{w}^{2}+I_{V_ {1}-PD}^{2}},\frac{3}{2}+\frac{2}{\varepsilon},\frac{1}{2}\Bigg{]}-Beta\Bigg{[} \frac{I_{V_{1}-PD}^{2}}{L_{w}^{2}+I_{V_{1}-PD}^{2}},\frac{3}{2}+\frac{2}{ \varepsilon},\frac{1}{2}\Bigg{]}\bigg{\}}}{\big{(}I_{V_{1}-M,1,cas2}I_{M-PD,1, cas2}\big{)}^{2}}\Bigg{\}}.\]  
Based on (14) and (15), the overall average path loss closure expression for the NLOS link formed by \(M\) is as follows:  
\[h_{NLOS\_M}^{PL\_ap} =\frac{{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}e}^{\frac{-c_{E}D_{R}}{ \xi}}}{2(L_{w}-v_{w})\xi^{4}}\Bigg{\{}\frac{\bigg{\{}Beta\Bigg{[}\frac{4I_{V_{1} -PD}^{2}}{L_{w}^{2}+4I_{V_{1}-PD}^{2}},\frac{3}{2}+\frac{2}{\varepsilon}, \frac{1}{2}\Bigg{]}-Beta\Bigg{[}\frac{I_{V_{1}-PD}^{2}}{L_{w  
As shown in Figure 5, it is known that Tx has the same height as Rx and \(\delta_{i,rs}=\delta_{r,rs}\). Therefore, it can be obtained that \(D_{NLOS,1,case1}^{V_{1}-RS}=D_{NLOS,1,case1}^{RS-PD}\), as well as \(I_{V_{1}-RS,1}=I_{RS-PD,1}\). Thus, \(D_{NLOS,1,case1}^{V_{1}-RS}\) and \(D_{NLOS,1,case1}^{RS-PD}\) can be expressed as follows:  
\[D_{NLOS,1,case1}^{V_{1}-RS}=D_{NLOS,1,case1}^{RS-PD}\triangleq X=\sqrt{\left( \frac{L_{h_{1}}}{2}\right)^{2}+\left(\frac{I_{V_{1}-PD}}{2}\right)^{2}+L_{PD} \ ^{2}}. \tag{101}\]  
Based on \(L_{h_{1}}{\sim}u\left(0,\frac{L_{w}}{2}\right)\) and (101), the PDF of \(X\) can be obtained according to the probability density transformation:  
\[D_{NLOS,1,case1}^{V_{1}-RS}=X\sim f_{X}(x)=\frac{8x}{L_{w}\sqrt{4x^{2}-\left(I_ {V_{1}-PD}\ ^{2}+4L_{PD}\ ^{2}\right)}}, \tag{102}\]  
where \(x_{1}=\sqrt{\left(\frac{I_{V_{1}-PD}}{2}\right)^{2}+L_{PD}\ ^{2}}\leq x\leq x_{2}=\sqrt{ \left(\frac{L_{w}}{4}\right)^{2}+\left(\frac{I_{V_{1}-PD}}{2}\right)^{2}+L_{PD }\ ^{2}}\). Case 2 of Tx1: Tx1 is located to the right of the center axis of the PD  
Similarly, in this case, \(D_{NLOS,1,case2}^{V_{1}-RS}\) and \(D_{NLOS,1,case2}^{RS-PD}\) can be expressed as follows:  
\[D_{NLOS,1,case2}^{V_{1}-RS}=D_{NLOS,1,case2}^{RS-PD}\triangleq Y=\sqrt{\left( \frac{L_{h_{1}}}{2}\right)^{2}+\left(\frac{I_{V_{1}-PD}}{2}\right)^{2}+L_{PD }\ ^{2}}. \tag{103}\]  
Based on \(L_{h_{1}}{\sim}u\left(0,\frac{L_{w}}{2}-v_{w}\right)\) and (103), the PDF of \(Y\) can be obtained from the probability density transformation as follows:  
\[=\frac{p_{cas2}\times 2{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}e}^{ \frac{-c_{E}D_{R}}{\xi}}}{(L_{w}-2v_{w})\xi^{4}\big{(}I_{V_{1}-M,1,cas2}I_{M-PD, 1,case2}\big{)}^{2}}\]0  
where \(y_{1}=\sqrt{\left(\frac{I_{V_{1}-PD}}{2}\right)^{2}+L_{PD}\ ^{2}}\leq y\leq y_{2}=\sqrt{ \left(\frac{L_{w}-2v_{w}}{4}\right)^{2}+\left(\frac{I_{V_{1}-PD}}{2}\right)^{ 2}+L_{PD}\ ^{2}}\). According to (11), (102) and (104), the average path loss of the NLOS link formed by \(RS\) from Tx1, can be expressed as follows:  
\[=\frac{p_{cas2}\times 2{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}e}^{ \frac{-c_{E}D_{R}}{\xi}}}{(L_{w}-2v_{w})\xi^{4}\big{(}I_{V_{1}-M,1,cas2}I_{M-PD, 1,case2}\big{)}^{2}}\]1 (A24)  
and  
\[=\frac{p_{cas2}\times 2{A_{M}}^{2}{D_{R}}^{2}{I_{V_{1}-PD}e}^{ \frac{-c_{E}D_{R}}{\xi}}}{(L_{w}-2v_{w})\xi^{4}\big{(}I_{V_{1}-M,1,cas2}I_{M-PD, 1,case2}\big{)}^{2}}\]2 (A25)  
where \(P=I_{V_{1}-PD}\,^{2}+4L_{PD}\,^{2}\). According to (A21), as well as the integration results (A24) and (A25), the average path loss of the NLOS link formed by \(RS\) from Tx1, can be obtained as follows:  
\[