# The Impact of Antenna Height on 3D Channel:
## 3 Results
### Scenario B: Forked Road in the Center of Paris  
Then, by using the same research steps in Section 3.1, we investigate the PDFs of EAoD and EAoA under the forked road scenario, as shown in Figure 2b. The simulation results when the antenna is located at 8 m and 12 m are indicated in Figure 7.  
After fitting the curves under different antenna heights (4 m, 6 m, 8 m, 10 m, 12 m, 14 m, 16 m and 18 m), the PDFs of EAoD and EAoA can be obtained as indicated in Table 3.  
From Table 3, two conclusions can be reached:  
* For the PDF of EAoD: the logarithm exponent value \(\lambda^{{}^{\prime}}_{1\text{EAoD}}\) is nearly unchangeable when the antenna height is lower than half of the building's height, but has a dramatic increase when the antenna height grows. However, the logarithm exponent value \(\lambda^{{}^{\prime}}_{2\text{EAoD}}\) enhances when the antenna height is lower than half of the building's height and then remains stable. * For the PDF of EAoA: the logarithm exponent value \(\lambda^{{}^{\prime}}_{1\text{EAoA}}\) decreases rapidly when the antenna height is lower than half of the building's height and then varies slightly. However, the logarithm exponent value \(\lambda^{{}^{\prime}}_{2\text{EAoA}}\) is almost stable when the antenna height is lower than half of the building's height, but has a significant drop when the antenna height increases. Finally, the PDFs of EAoD and EAoA related to antenna height can be calculated:  
\[f_{EAOD}(x)=\left\{ \begin{array}{rrrr}-(7.64)\exp(7.64),&x<0,&m\leq 12.5\\ -(0.14m+5.89)\exp(0.14m+5.89),&x<0,&12.5<m<25\\ -(0.07m-8.43)\exp(0.07m-8.43),&x>0,&m\leq 12.5\\ -(-7.58)\exp(-7.58),&x>0,&12.5<m<25\end{array} \right. \tag{10}\]  
Figure 7: PDFs of EAoD and EAoA under the forked road scenario. (**a**) The description of the antenna height at 8 m; and (**b**) the description of the antenna height at 12 m. \begin{table}
\begin{tabular}{c 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 & 40.19 & 32.86 & 32.31 & 33.16 & 33.16 & 33.25 & 34.58 & 36.2 \\ EAoD up & \(-32.49\) & \(-35.89\) & \(-34.23\) & \(-33.67\) & \(-32.63\) & \(-32.99\) & \(-32.93\) & \(-32.94\) \\ EAoA down & 17.4 & 20.92 & 19.11 & 18 & 17.69 & 17.94 & 17.95 & 18.03 \\ EAoA up & \(-18.06\) & \(-16.2\) & \(-15.77\) & \(-16\) & \(-17.06\) & \(-16.64\) & \(-16.45\) & \(-18.68\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: 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 \(\lambda^{{}^{\prime}}_{1\text{EAoD}}\), \(\lambda^{{}^{\prime}}_{2\text{EAoD}}\), \(\lambda^{{}^{\prime}}_{1\text{EAoA}}\), and \(\lambda^{{}^{\prime}}_{2\text{EAoA}}\), respectively. \[f_{EAOA}(x)=\left\{ \begin{array}{rl}-(-0.06m+4.87)\exp(-0.06m+4.87),&x<0,&m\leq 12.5 \\ -(4.13)\exp(4.13),&x<0,&12.5<m<25\\ -(-3.80)\exp(-3.80),&x>0,&m\leq 12.5\\ -(-0.06m-3.01)\exp(-0.06m-3.01),&x>0,&12.5<m<25\end{array} \right. \tag{11}\]  
With the results obtained above, the AS and the DS of EAoD and EAoA can be gained as displayed in Figures 8 and 9. It is obvious from Figure 8 that the ASs of EAoD and EAoA arrive at the peak value when the antenna height (12 m) is half of the building's height. In Figure 9, we can conclude that the minimum value of the DS can be achieved when the antenna height is half of the building's height and the value arises when the antenna is near the ground or the top of the buildings. Finally, the AS and the DS related to antenna height can be represented as:  
\[\sigma_{AS,EAOD}=\left\{ \begin{array}{rl}0.0824m+9.2706,&m\leq 12.5\\ -0.1273m+11.8909,&12.5<&m\leq 25\end{array} \right. \tag{12}\]  
\[\sigma_{AS,EAOA}=\left\{ \begin{array}{rl}0.2412m+22.6853,&m\leq 12.5\\ -0.2m+28.2,&12.5<&m\leq 25\end{array} \right. \tag{13}\]  
Figure 8: The AS under the forked road scenario with various antenna heights (4 m, 6 m, 8 m, 10 m, 12 m, 14 m, 16 m, and 18 m).