# The Impact of Antenna Height on 3D Channel:
## 3 Results  
### Scenario A: Straight Street in the Center of Paris  
Under the straight street in Figure 2a, the PDFs of EAoD and EAoA are investigated firstly. Due to reflection and diffraction during the signal transmission, each receiver can obtain multiple rays with different path losses, EAoDs and EAoAs. The PDFs of EAoD and EAoA can then be calculated after adding the weighting value (path loss). Two simulation results, antenna heights at 8 m and 12 m, are indicated above. Figure 3 indicates that the PDF values of both the EAoD and EAoA around 0 radians are obviously greater than the values away from 0 degrees, and the sub-curves at the negative and positive are asymmetrical, which have been verified in [18]. The author observed that a double-sided exponential function is more suitable for the PDF of elevation angles which can be represented as:  
\[f_{EAOD}(x)=\left\{ \begin{array}{ll}\lambda_{1 EAOD}e^{-\lambda_{1 EAOD}x},&x<0 \\ \lambda_{2 EAOD}e^{-\lambda_{2 EAOD}x},&x>0\end{array} \right. \tag{1}\]  
\[f_{EAOA}(x)=\left\{ \begin{array}{ll}\lambda_{1 EAOA}e^{-\lambda_{1 EAOA}x},&x<0 \\ \lambda_{2 EAOA}e^{-\lambda_{2 EAOA}x},&x>0\end{array} \right. \tag{2}\]  
Here, the unit of x is degrees. \(\lambda_{1 EAOD}\), \(\lambda_{2 EAOD}\), \(\lambda_{1 EAOA}\), and \(\lambda_{2 EAOA}\) are the rate parameters of these double-sided exponential functions. By logarithm fitting the PDFs of EAoD and EAoA (for example: \(\lambda^{{}^{\prime}}_{1 EAOD}=-10\times\log_{10}e\times\lambda_{1 EAOD}\)), we can finally obtain the values of \(\lambda^{{}^{\prime}}_{1 EAOD}\), \(\lambda^{{}^{\prime}}_{2 EAOD}\), \(\lambda^{{}^{\prime}}_{1 EAOA}\), and \(\lambda^{{}^{\prime}}_{2 EAOA}\). In Figure 3: \(\lambda^{{}^{\prime}}_{1 EAOD}=26.83\), \(\lambda^{{}^{\prime}}_{2 EAOD}=-36.48\), \(\lambda^{{}^{\prime}}_{1 EAOA}=16.43\), \(\lambda^{{}^{\prime}}_{2 EAOA}=-15.69\). Obviously, the \(\lambda^{{}^{\prime}}\) will be different with various antenna heights. In Figure 4, the \(\lambda^{{}^{\prime}}\) with various antenna heights (4-18 m) are listed. This illustrates that the logarithm exponent value are almost linearly correlated with the antenna height. Then, we can derive that: \(\lambda^{{}^{\prime}}_{1 EAOD}=1.64\times\) m + 14.35, \(\lambda^{{}^{\prime}}_{2 EAOD}=1.60\times\) m \(-\) 48.83, \(\lambda^{{}^{\prime}}_{1 EAOA}=-0.63\times\) m + 22.84, \(\lambda^{{}^{\prime}}_{2 EAOA}=-0.76\times\) m \(-\) 9.55, where m is the antenna height which unit is meter. As we can see \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Average Buildings** & **Length of** & **Width of** & **Length of** & **Width of** \\  & **Height** & **Wider Street** & **Wider Street** & **Lower Street** \\ \hline Straight street & 20 m & 80 m & 20 m & 0 m & 0 m \\ Forked road & 25 m & 80 m & 20 m & 40 m & 12 m \\ Crossroad & 22 m & 40 m & 20 m & 40 m & 12 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the three scenarios. Figure 2: Three typical scenarios: (**a**) description of the straight street; (**b**) description of the forked road; and (**c**) description of the crossroad. from Figure 4, the logarithm exponent values \(\lambda^{{}^{\prime}}_{\text{1 EAoD}}\) and \(\lambda^{{}^{\prime}}_{\text{2 EAoD}}\) (as shown in Equation (1)) linearly increase with the antenna height growing, and the exponent values \(\lambda^{{}^{\prime}}_{\text{1 EAoA}}\) and \(\lambda^{{}^{\prime}}_{\text{2 EAoA}}\) (as shown in Equation (2)) linearly decrease with the antenna height growing. Finally, the PDFs of EAoD and EAoA related to antenna height can be represented as:  
\[f_{EAOD}(x)=\left\{ \begin{array}{ll}-(0.38m+3.30)\exp(0.38m+3.30),&x<0\\ -(0.37m-11.24)\exp(0.37m-11.24),&x>0\end{array} \right. \tag{3}\]  
\[f_{EAOA}(x)=\left\{ \begin{array}{ll}-(-0.15m+5.26)\exp(-0.15m+5.26),&x<0\\ -(-0.18m-2.20)\exp(-0.18m-2.20),&x>0\end{array} \right. \tag{4}\]  
Using the PDFs, the AS and the DS, which represent the elevation angle dispersion and the time dispersion of multipath components respectively, can be evaluated [13].