# The Impact of Antenna Height on 3D Channel:
## 3 Results
### Scenario C: Crossroad in the Center of Paris  
Finally, we research the PDFs of EAoD and EAoA under cross road scenario as shown in Figure 2c. The simulation results are obtained when the antenna located at 8 m and 12 m as shown in Figure 10.  
The logarithm exponent values of EAoD and EAoA can be obtained by fitting the curves through different antenna heights (4 m, 6 m, 8 m, 10 m, 12 m, 14 m, 16 m, and 18 m) which are exhibited in Table 4.  
From Table 4, we can conclude that:  
* For the PDF of EAoD: the logarithm exponent value \(\lambda^{{}^{\prime}}_{\rm 1 EAoD}\) reduces rapidly when the antenna height is lower than half of the building's height, and gains the minimum value at 14 m, and then the value remains the same. In contrast, the logarithm exponent value \(\lambda^{{}^{\prime}}_{\rm 2 EAoD}\) is nearly unchangeable when the antenna height is lower than half of the building's height, but has a dramatic decrease when the antenna height grows. * For the PDF of EAoA: the exponent value decreases \(\lambda^{{}^{\prime}}_{\rm 1 EAoA}\) as the antenna height rises. In contrast, the exponent value \(\lambda^{{}^{\prime}}_{\rm 2 EAoA}\) is nearly unchanged when the antenna height is lower than half of the building's height, but has a significantly drop when the antenna height increases. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **4 m** & **6 m** & **8 m** & **10 m** & **12 m** & **14 m** & **16 m** & **18 m** \\ \hline EAoD down & 199 & 149.8 & 118.3 & 110.5 & 88.88 & 79.08 & 85.5 & 79.05 \\ EAoD up & \(-\)79.57 & \(-\)87.87 & \(-\)76.54 & \(-\)85.21 & \(-\)103 & \(-\)113.1 & \(-\)131.2 & \(-\)172.7 \\ EAoA down & 19.52 & 17.72 & 14.08 & 12.08 & 12.87 & 10.91 & 9.77 & 11.1 \\ EAoA up & \(-\)9.556 & \(-\)12.86 & \(-\)10.7 & \(-\)11.25 & \(-\)13.12 & \(-\)13.46 & \(-\)15.32 & \(-\)19.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The statistic results of logarithm exponent values under fork road scenario with various antenna heights (4 m, 6 m, 8 m, 10 m, 12 m, 14 m, 16 m, and 18 m). Here, EAoD down, EAoD up, EAoA down, and EAoA up represent \(\lambda^{{}^{\prime}}_{\rm 1 EAoD}\), \(\lambda^{{}^{\prime}}_{\rm 2 EAoD}\), \(\lambda^{{}^{\prime}}_{\rm 1 EAoA}\), and \(\lambda^{{}^{\prime}}_{\rm 2 EAoA}\), respectively. Figure 10: PDFs of EAoD and EAoA under the crossroad scenario. (**a**) The description of the antenna height at 8 m; and (**b**) the description of the antenna height at 12 m.  
Then, the PDFs of EAoD and EAoA can be represented as:  
\[f_{EAOD}(x)=\left\{ \begin{array}{c}-(-2.95m+52.22)\exp(-2.95m+52.22),\;\;x<0,\;m \leq 11\\ -(19.80)\exp(19.80),\;\;x<0,\;11<m<22\\ -(-20.72)\exp(-20.72),\;\;x>0,\;m\leq 11\\ -(-1.90m+0.15)\exp(-1.90m+0.15),\;\;x>0,\;11<m<22\\ \end{array} \right. \tag{15}\]  
\[f_{EAOA}(x)=\left\{ \begin{array}{c}-(-0.17m+5.15)\exp(5.15),\;\;x<0,\;0<m<22 \\ -(-2.76)\exp(-2.76),\;\;x>0,\;m<11\\ -(-0.15m-1.08)\exp(-0.15m-1.08),\;\;x>0,\;11<m<22\\ \end{array} \right.. \tag{16}\]  
The AS and the DS of EAoD and EAoA can be gained by the above results. Figure 11a shows that the AS of EAoD remains almost stable with different antenna heights. Figure 11b illustrates the AS of EAoA gains its maximum value when the antenna height is half of the building's height (11 m) and drops gradually to the ground or the top of the buildings. The DS shows a similar phenomenon as that described in Sections 3.1 and 3.2 and as shown in Figure 12.  
Finally, the AS and the DS related to antenna height can be represented as:  
\[\sigma_{AS,EAOD}=4.05 \tag{17}\]  
Figure 11: The AS under the crossroad scenario with various antenna heights (4 m, 6 m, 8 m, 10 m, 12 m, 14 m, 16 m, and 18 m). (**a**) Description of the AS of EAoD; and (**b**) a description of the AS of EAoA. Figure 12: The DS under the crossroad scenario with various antenna heights (4 m, 6 m, 8 m, 10 m, 12 m, 12 m, 14 m, 16 m, and 18 m). \[\sigma_{AS,EAOA}=\left\{ \begin{array}{cc}0.9857m+17.7571,&m\leq 11\\ -0.9m+23,&11<\ m\leq 22\end{array} \right. \tag{18}\]  
\[\sigma_{DS}=\left\{