# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 3 Simulation Results
### Second VLC Simulation Position
#### 3.2.3 Third Case
Regarding temporal spread, UNID and EXPD show multiple reflected paths distributing energy in a more controlled manner, while GAMD presents a broader dispersion with fewer dense echoes, confirming  
Figure 15: Received power distribution for different irradiance and incidence angle distributions. (**a**) POW using UNID; (**b**) POW using EXPD; (**c**) POW using GAMD. that the gamma angles result in a more diffuse propagation pattern compared to the other distributions. The choice of angular distribution significantly affects the behavior of CIR. The uniform distribution provides the highest channel gain and a well-defined echo structure, while the exponential distribution maintains a controlled spread but at a lower amplitude. The gamma distribution results in weaker reflected energy and greater temporal dispersion. These differences highlight that selecting an appropriate angular distribution is essential for accurately modeling NLOS propagation in underground environments, as it directly influences both signal intensity and echo structure. To summarize all our important findings and comparisons, we can look at Tables 2-7. Position 1 experiences greater channel losses compared to Position 2, suggesting that the surrounding geometry and the reflection distribution significantly affect signal propagation. In Position 1, the maximum received power at \((X_{l}^{R},Y_{l}^{R},0)\) [m] is \(7.50\times 10^{-8}\) W/m\({}^{2}\), while at \((X_{l}^{R},Y_{l}^{R},1)\) [m], it decreases to \(4.00\times 10^{-7}\) W/m\({}^{2}\), indicating a substantial reduction. This change is also reflected in the CIR peak, which increases with receiver height from \(6.00\times 10^{-9}\) W/m\({}^{2}\) to \(1.20\times 10^{-7}\) W/m\({}^{2}\), suggesting that higher receiver placement enhances stronger reflected paths. In contrast, in Position 2, the maximum received power at \((X_{l}^{R},Y_{l}^{R},0)\) [m] is \(2.40\times 10^{-7}\) W/m\({}^{2}\) and increases slightly to \(2.45\times 10^{-7}\) W/m\({}^{2}\) at \((X_{l}^{R},Y_{l}^{R},1)\) [m], meaning that height has a much smaller impact on channel loss in this case. The CIR peak follows a different trend, fluctuating between \(1.18\times 10^{-8}\) W/m\({}^{2}\) and \(1.00\times 10^{-7}\) W/m\({}^{2}\), indicating that the height variation affects the channel response less severely in this position. Figure 16: Channel impulse response for different irradiance and incidence angle distributions. (**a**) CIR using UNID; (**b**) CIR using EXPD; (**c**) CIR using GAMD. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Random Distribution** & **Max Received Power (W/m\({}^{2}\))** & **Max CIR Peak** \\ \hline UNID & \(3.0\times 10^{-9}\) & \(2.00\times 10^{-8}\) \\ \hline EXPD & \(2.5\times 10^{-9}\) & \(1.59\times 10^{-8}\) \\ \hline GAMD & \(6.0\times 10^{-9}\) & \(3.50\times 10^{-9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Max power and CIR peak in position 2 results (random reflection coefficient). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Random Distribution** & **Max Received Power (W/m\({}^{2}\))** & **Max CIR Peak** \\ \hline UNID & \(1.5\times 10^{-8}\) & \(8.9\times 10^{-9}\) \\ \hline EXPD & \(1.0\times 10^{-9}\) & \(4.0\times 10^{-9}\) \\ \hline GAMD & \(3.0\times 10^{-9}\) & \(1.79\times 10^{-9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Max power and CIR peak in position 1 results (random incidence and irradiance angles). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Height [m]** & **Max Received Power (W/m\({}^{2}\))** & **Max CIR Peak** \\ \hline UNID & \(3.75\times 10^{-8}\) & \(2.10\times 10^{-8}\) \\ \hline EXPD & \(2.50\times 10^{-9}\) & \(1.49\times 10^{-8}\) \\ \hline GAMD & \(2.51\times 10^{-9}\) & \(1.49\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Max power and CIR peak in position 2 results (random incidence and irradiance angles).