# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 3 Simulation Results
### Second VLC Simulation Position
#### 3.2.2 Second Case  
In UNID, the initial maximum power reaches approximately \(1.4\times 10^{-7}\) W/m\({}^{2}\) (Figure 5), demonstrating a more homogeneous spatial distribution. However, in the second position, this power drops sharply to \(3\times 10^{-8}\) W/m\({}^{2}\) (Figure 12), indicating a significant reduction in the reflection intensity due to increased attenuation on rough surfaces. In EXPD, the initial peak power is around \(9\times 10^{-8}\) W/m\({}^{2}\) (Figure 5), less than UNID, with more concentrated power in specific areas, reflecting the probabilistic nature of the exponential coefficients. This decreases further to \(2\times 10^{-8}\) W/m\({}^{2}\) (Figure 12) in the second case, showing a rapid decline influenced by the distance and incidence angles. GAMD starts with a maximum power of \(2.5\times 10^{-8}\) W/m\({}^{2}\) (Figure 5), the lowest among the three, focusing reflections in limited regions, suggesting less uniformity in reflections. This value reduces further to \(5\times 10^{-9}\) W/m\({}^{2}\) (Figure 12), highlighting weaker reflections influenced by local conditions. The observed reduction in power in all distributions in the second position is attributed to the increase in propagation distance and the cumulative reflection losses on rough surfaces. The normally distributed angles enhance the angular dispersion, decreasing  
Figure 11: Channel impulse responses for different heights of PD. (**a**) CIR at \(Z=0\) m; (**b**) CIR at \(Z=1\) m.  
the concentrated reflected power. The uniform distribution, despite having the highest initial power, experiences a steep decline as a result of the rapid loss of intensity from surface absorption. The exponential distribution shows a less severe drop, consistent with its propensity to concentrate reflections in select areas. In contrast, the gamma distribution exhibits the weakest maximum power in both cases, as its coefficients generate weaker reflections under rough and dispersed angular conditions. The anomalies and reduction in power are driven by angular dispersion from normal distribution angles, surface roughness increasing absorption and scattering, and distance from the transmitter leading to more rapid attenuation in gamma and exponential distributions compared to the uniform distribution. Overall, while the uniform distribution initially exhibits the highest power due to even reflection, the exponential and gamma distributions reflect more dispersed and lower-intensity patterns, influenced by their inherent properties and the environmental conditions of rough surfaces and varied angles. The CIR for UNID (Figure 13) shows a maximum amplitude of approximately \(2\times 10^{-8}\), suggesting moderate temporal dispersion and a balance between coverage and signal quality. On the other hand, the CIR produced by EXPD (Figure 13) has a maximum amplitude of around \(1.59\times 10^{-8}\), indicating a more temporally concentrated response with reduced dispersion and a potentially stronger multipath effect. Finally, the CIR deployed by GAMD (Figure 13) exhibits the lowest channel gain, with a maximum amplitude of approximately \(3.5\times 10^{-9}\). Overall, UNID's CIR suggests the best channel conditions, with a balance between coverage and signal quality. EXPD's CIR indicates a stronger multipath effect, while GAMD's CIR shows the lowest channel gain. Figure 12: Received power distributions for different reflection coefficients statistical distributions. (**a**) POW using UNID; (**b**) POW using EXPD; (**c**) POW using GAMD. Once again, distance plays a key role in distinguishing positions. In the first scenario, the POW has lower received power than in the second. In both uniform and exponential distributions, the smooth pattern is maintained, while GAMD shows distinct peaks. In terms of channel performance, if the PD and LED are closer, the first reflection gains more amplitude. This effect is observed in uniform and exponential distributions, though GAMD behaves oppositely.