## 5 Analysis of the Hybrid Propagation Channel Model
### Effect of the Number of Scattered Rays on the Proposed 3 DFPHPCM  
The path loss variation with the number of scattered rays at each reception point was first studied for a fixed scattering angle in this study. The trend of the path loss at each reception point with the horizontal distance between the transmitting and receiving antennas for a scattering angle of \(5^{\circ}\) and different numbers of scattered rays is shown in Figure 6. 'P_mea' indicates the measured value, 'SP' indicates the sum-of-individual-ray-powers (SP) method, and 'N' indicates the number of scattered rays. The curves are more consistent with the experimental data when the number of ray bars is 9 and 29. The RMSE, MAE, and runtime for different numbers of scattered rays at a scattering angle of \(5^{\circ}\) are shown in Table 2. As the number of scattered rays increases, the runtime of the procedure increases accordingly, as shown in Table 2. The two sets of data with the smallest RMSE and MAE can be found in Table 2. When the number of scattered rays is 29, the RMSE is 5.6016, the MAE is 4.9940, and the runtime is 94.56 s. When the number of scattered rays is nine, the RMSE is 4.1778, the MAE is 3.4927, and the runtime is 199.29 s. Therefore, the theoretical calculation and the experimental data are in good agreement, and the runtime is short when the number of scattered rays is nine. Moreover, the number of scattered rays affects the runtime. The conformity of the theoretical calculations and experimental data is examined in the following section when the number of scattered rays is approximately nine.  
Figure 5: Measurement in the urban microcellular environment.  
As shown in Figure 7, the consistency between the theoretical calculations and experimental data was examined when the scattering angle was \(5^{\circ}\) and the number of scattered rays was approximately nine in this study. The theoretical calculation and experimental data are more consistent when the number of scattered rays is 9 and 15, as shown in the figure. The RMSE, MAE, and runtime when the number of scattered rays is nine at a scattering angle of \(5^{\circ}\) are shown in Table 3. As above, the runtime increases as the number of scattered rays increases; however, the increase is not obvious. When the number of scattered rays is 15, the RMSE is 5.941 and the MAE is 4.6944, both of which are greater than the RMSE and the MAE when the number of scattered ray bars is nine. The RMSE and MAE of the other number of scattered rays are also larger than those when the number of scattered rays is nine. The above findings indicate that the theoretical calculation and experimental data are in good agreement when the number of scattered rays is nine; therefore, the number of scattered rays was set to nine in the subsequent study.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number of Scattered** & **RMSE (SP)** & **MAE (SP)** & **Running Time (s)** \\
**Rays** & & & \\ \hline
9 & 4.1778 & 3.4927 & 94.56 \\
19 & 14.8409 & 9.5007 & 148.482 \\
29 & 5.6016 & 4.9940 & 199.29 \\
39 & 9.8880 & 8.3241 & 252.172 \\
49 & 16.2592 & 11.4766 & 305.003 \\
59 & 20.9067 & 18.4632 & 359.282 \\
69 & 10.3565 & 8.0150 & 408.97 \\
79 & 11.3172 & 8.9271 & 462.32 \\
89 & 10.2659 & 8.2918 & 515.726 \\ \hline \hline \end{tabular}
\end{table}
Table 2: RMSE, MAE, and runtime for different numbers of scattered rays at a scattering angle of \(5^{\circ}\).  
Figure 6: The trend of path loss with distance for different numbers of scattered rays when the scattering angle is \(5^{\circ}\).