## 5 Analysis of the Hybrid Propagation Channel Model
### Effect of Scattering Angles on the Proposed 3 DFPHDCM  
Second, the trend of path loss at each reception point was investigated for a fixed number of scattered rays when the scattering angle was different. 'A' is denoted as the scattering angle in Figure 8. The variation in path loss with distance at different scattering angles is not obvious. Therefore, it is necessary to study the RMSE and MAE for different numbers of rays. Table 4 shows the RMSE, MAE, and runtime for different scattering angles when the number of scattered rays is nine. There is little difference in the runtime at different scattering angles, indicating that the scattering angle has almost no effect on the runtime. Only when the scattering angle is \(5^{\circ}\) is the RMSE 4.1778 and the MAE 3.4927, which is the only angle among all angles where both RMSE and MAE are less than 10. For the other scattering angles, the RMSE and MAE are greater than 10, which is much larger than the result when the scattering angle is \(5^{\circ}\). The above results indicate that, when the scattering angle increases, not only will the number of scattered rays increase but also the received electric field. Therefore, the difference between the experimental measurement and the theoretical calculation is significant. As a consequence, it is necessary to study the conformity of theoretical calculations and experimental data at a smaller range of angles, for example, approximately \(5^{\circ}\). Figure 7: The trend of path loss with distance for different numbers of rays when the number of the scattered rays is 9 at a scattering angle of \(5^{\circ}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Scattered** & **RMSE (SP)** & **MAE (SP)** & **Running Time (s)** \\
**Rays** & **RMSE (SP)** & **MAE (SP)** & **Running Time (s)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 3: RMSE, MAE, and runtime for approximately 9 scattered rays at a scattering angle of \(5^{\circ}\). Thereafter, the variation in the path loss with distance was investigated near the scattering angle of 5\({}^{\circ}\) when the number of scattered rays was nine. The trend of the path loss with distance between the transmitting and receiving antennas (at each reception point) is shown in Figure 9 when the scattering angles are between 4.1\({}^{\circ}\) and 5.9\({}^{\circ}\). The experimental data and the theoretical calculations are in good agreement when the scattering angle is 5\({}^{\circ}\). The RMSE, MAE, and runtime when the number of scattered rays is nine are shown in Table 5 when the scattering angle is approximately 5\({}^{\circ}\). The difference in runtimes at different scattering angles is minimal and nearly the same as in Table 5, indicating that the scattering angle exhibits no effect on the runtime. The RMSE and MAE are less than 10 for scattering angles of 4.8\({}^{\circ}\), 4.9\({}^{\circ}\), 5\({}^{\circ}\), and 5.1\({}^{\circ}\). The RMSE and MAE are 8.9051 and 7.5535 for scattering angles of 4.8\({}^{\circ}\), 8.8014 and 7.4915 for scattering angles of 4.9\({}^{\circ}\), 5.2127 and 4.3813 for scattering angles of 5.1\({}^{\circ}\), and 4.1778 and 3.4927 for scattering angles of 5\({}^{\circ}\), respectively, which are less than the RMSE and MAE at 4.8\({}^{\circ}\) and 4.9\({}^{\circ}\). Therefore, the scattering angle can be determined as 5\({}^{\circ}\). In conclusion, the experimental data and the theoretical calculations are in good agreement when the number of scattered rays is nine and the scattering angle is 5\({}^{\circ}\) for urban microcellular environments. The scattering angle has no effect on the runtime whereas the number of scattered rays affects the runtime.