# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 3 Simulation Results
### Second VLC Simulation Position
#### 3.2.1 First Case  
In this case, the PD plane (\((X_{l}^{R},Y_{l}^{R},0)\) [m]) is positioned close to the LED in terms of the Euclidean distance, resulting in a more defined POW Figure 10. At both heights, the received power is similar. The analysis of received power (NLOS component) is shown for two distinct transmitter positions, evaluating heights \((X_{l}^{R},Y_{l}^{R},0)\) [m] and \((X_{l}^{R},Y_{l}^{R},1)\) [m] (Figure 3). For the transmitter located in the first position, the maximum power at \((X_{l}^{R},Y_{l}^{R},0)\) [m] (Figure 10) is approximately \(9\times 10^{-7}\) W/m\({}^{2}\), which decreases to \(4\times 10^{-7}\) W/m\({}^{2}\) at \((X_{l}^{R},Y_{l}^{R},1)\) [m], representing a reduction of 55.6%. This change is due to the increased distance between the transmitter and receiver, combined with additional dispersion and absorption caused by the roughness of the walls, reducing the contribution of the reflected components. On the other hand, for the second position transmitter, the maximum power is \(2.5\times 10^{-7}\) W/m\({}^{2}\) at \((X_{l}^{R},Y_{l}^{R},1)\) [m] and decreases to \(1.5\times 10^{-7}\) W/m\({}^{2}\) at \((X_{l}^{R},Y_{l}^{R},1)\) [m] (Figure 10), which corresponds to a reduction of 40%. In this case, the proximity of the transmitter to the receiver plane mitigates the relative power loss with the change in height. Figure 8: Received power distribution for different irradiance and incidence angle distributions. (a) POW using UNID; (b) POW using EXPD; (c) POW using GAMD. In the figures, the analysis of received power (NLOS component) is shown for two distinct transmitter positions, evaluating heights \((X_{l}^{R},Y_{l}^{R},0)\) [m] and \((X_{l}^{R},Y_{l}^{R},1)\) [m] (Figure 3). For the transmitter located in the first position, the maximum power at \((X_{l}^{R},Y_{l}^{R},0)\) [m] (Figure 10) is approximately \(9\times 10^{-7}\) W/m\({}^{2}\), which decreases to \(4\times 10^{-7}\) W/m\({}^{2}\) at \((X_{l}^{R},Y_{l}^{R},1)\) [m], representing a reduction of 55.6%. This change is due to the increased distance between the transmitter and receiver, combined with additional dispersion and absorption caused by the roughness of the walls, reducing the contribution of the reflected components. On the other hand, for the second position transmitter, the maximum power  
Figure 10: Received power distributions for different heights of PD. (**a**) POW at \(Z=0\) m; (**b**) POW at \(Z=1\) m.  
Figure 9: Channel impulse response for different irradiance and incidence angle distributions. (**a**) CIR using UNID; (**b**) CIR using EXPD; (**c**) CIR using GAMD. is \(2.5\times 10^{-7}\) W/m\({}^{2}\) at \((X_{l}^{R},Y_{l}^{R},0)\) [m] (Figure 10) and decreases to \(1.5\times 10^{-7}\) W/m\({}^{2}\) at \((X_{l}^{R},Y_{l}^{R},1)\) [m] (Figure 10), which corresponds to a reduction of 40%. In this case, the proximity of the transmitter to the receiver plane mitigates the relative power loss with the change in height. The general decrease in power with increase in \((X_{l}^{R},Y_{l}^{R},1)\) [m] is explained mainly by the greater direct distance to the transmitter, combined with greater losses in the reflected components due to wall roughness, where the reflection coefficients and the incidence angles are generated with a normal distribution. Additionally, the first position transmitter shows a more uniform vertical propagation reach, resulting in higher initial powers. In contrast, at the second position, the lower position of the transmitter favors a more horizontal distribution of the signal, limiting the overall received power. In conclusion, the power changes between \((X_{l}^{R},Y_{l}^{R},0)\) [m] and \((X_{l}^{R},Y_{l}^{R},1)\) [m] are directly influenced by the transmitter geometry, angular dispersion, and the reflective properties of the environment. The CIR also shows notable differences. The channel gain is higher due to the shorter distance, as shown in Figure 11, and at \((X_{l}^{R},Y_{l}^{R},1)\) [m], the secondary reflections are strong and concentrated around 20 [ns] (Figure 11).