# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 3 Simulation Results
### First VLC Simulation Position
#### 3.1.1 First Case  
When comparing the radiation patterns at both heights, significant differences in the distribution of the received power are observed in Figure 3. For \((X_{I}^{R},Y_{I}^{R},0)\) [m], the maximum power reached is around \(7.5\times 10^{-8}\), W/m\({}^{2}\), with a more dispersed energy distribution throughout the XY plane. This suggests that, at ground level, the PD captures a greater amount of power because of diffuse reflections from multiple directions.  
When the PD height leverages to \((X_{I}^{R},Y_{I}^{R},1)\) [m] (Figure 3), the maximum received power increases significantly to approximately \(4.0\times 10^{-7}\) W/m\({}^{2}\). In addition, the radiation pattern becomes more concentrated in the area surrounding the source, indicating that as the PD increases, the amount of reflected power it can capture decreases. This may be due to the reduced angle of incidence of the reflected rays. In summary, increasing the height of the PD results in a reduction in the captured NLOS power and a greater concentration of energy in specific areas.  
Regarding the channel impulse response (Figure 4), for \((X_{I}^{R},Y_{I}^{R},0)\) [m], a main peak appears around 35 ns with an amplitude of approximately \(6\times 10^{-9}\). This peak is followed by several secondary peaks of lower amplitude, indicating a greater dispersion of temporal reflections. The presence of these secondary peaks suggests a higher number of reflected paths reaching the detector at different times because of the lower height. There is a significant increase in the maximum amplitude when the receiver is elevated to \((X_{I}^{R},Y_{I}^{R},1)\) [m]. At \((X_{I}^{R},Y_{I}^{R},0)\), the peak amplitude is approximately \(6\times 10^{-9}\), while at \((X_{I}^{R},Y_{I}^{R},0)\) (Figure 4), it increases to \(1.2\times 10^{-7}\), indicating a notable improvement. This increase occurs because the higher receiver position reduces signal attenuation and aligns with more efficient reflection paths. Furthermore, the CIR at \((X_{I}^{R},Y_{I}^{R},1)\) [m] exhibits less temporal dispersion, with a dominant echo that arrives sharply, whereas at \((X_{I}^{R},Y_{I}^{R},0)\), the echoes are more spread out, reflecting greater variability in the reflection trajectories.  
Figure 3: Received power distributions for different heights of PD. (**a**) POW at \(Z=0\) m; (**b**) POW at \(Z=1\) m.  
The difference between \((X_{l}^{R},Y_{l}^{R},0)\) and \((X_{l}^{R},Y_{l}^{R},1)\) [m] is much less pronounced. The maximum amplitude remains around \(1.2\times 10^{-8}\) (Figure 4) in both cases, suggesting that the elevation has a limited effect. Here, the temporal dispersion is similar across heights, with the reflected energy distributed more uniformly over time. This stability indicates that the environment supports consistent multipath propagation, minimizing the impact of receiver height.  
The difference in channel gain highlights the role of geometry and propagation paths. In the first position, the higher receiver position improves alignment with high-energy reflections, increasing the gain. In contrast, in the second position, the propagation paths appear less sensitive to height, resulting in similar channel responses. In general, height influences the CIR, depending on the reflective properties of the environment, where it can enhance gain and reduce dispersion or maintain a stable response with little variation.  
Increasing the receiver height results in a higher received power due to a greater contribution from NLOS reflections. This behavior is evident in Figure 3, where the received power increases with receiver height. Furthermore, Figure 4 shows that these reflections contribute to the CIR by extending the delay spread and increasing the amplitude of the impulse response. This confirms the strong spatial dependence between the received power and CIR, demonstrating how tunnel geometry and wall reflectivity significantly impact NLOS propagation.