# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 3 Simulation Results
### First VLC Simulation Position
#### 3.1.2 Second Case  
When comparing the radiation patterns, we observe that the three distributions show significant differences in the dispersion and amplitude of the received power (NLOS). With UNID (Figure 5), to generate reflection coefficients, the maximum power reaches approximately \(1.5\times 10^{-7}\) W/m\({}^{2}\). The distribution has peaks caused by random values, possibly due to different materials creating this effect in specific areas of the wall. In EXPD (Figure 5), to generate reflection coefficients, a similar concentration of reflected power is observed, with a slight decrease in dispersion and a lower maximum power, around \(1\times 10^{-7}\) W/m\({}^{2}\). This pattern appears smoother and more regular than other distributions, suggesting a more uniform composition and wall diversity. On the other hand, the GAMD to generate reflection coefficients (Figure 5) has the lowest maximum power among the three, with a value of \(3\times 10^{-8}\) W/m\({}^{2}\). In this case, GAMD produces a more concentrated reflection pattern, with the reflected energy weakening more rapidly. Although the channel loss is significant, reaching \(8.4\times 10^{-9}\), this distribution shows the highest peak gain among the three analyzed. This behavior reflects the interaction between the reflection coefficients and the angular variations. The rough surface of the  
Figure 4: Channel impulse responses for different heights of PD. (**a**) CIR at \(Z=0\) m; (**b**) CIR at \(Z=1\) m.  
tunnel plays a key role. Even under substantial loss, certain distributions can effectively concentrate power. The CIR values for uniform, exponential, and gamma distributions highlight distinct behaviors. UNID (Figure 6a) exhibits the highest amplitude, showing efficient power concentration in specific time intervals. Its peak amplitude is \(8.4\times 10^{-9}\). However, it shows significant dispersion, leading to prolonged echoes. These echoes may affect the performance of the system. EXPD (Figure 6b) shows a lower peak amplitude of \(3.5\times 10^{-9}\). This reflects a greater attenuation caused by its variable reflection coefficients. The CIR has a broader temporal spread, suggesting weaker but more evenly distributed echoes. These characteristics indicate a lower but more uniform intensity environment. GAMD (Figure 6c) balances the characteristics of the other two. Its peak amplitude is moderate, reaching \(1.8\times 10^{-9}\). The CIR combines reasonable power concentration with controlled temporal dispersion. This makes it suitable for scenarios requiring a trade-off between loss and echo propagation. In the uniform distribution, the strongest echoes are intense and close in time. This results in focused power with fewer dominant echoes, which is beneficial for certain receiver designs. In the exponential distribution, the strongest echoes are weaker and more spread out. This creates a uniform but less intense environment. The gamma distribution offers intermediate behavior, with echoes that are neither as strong as UNID nor as scattered as EXPD. This balance makes GAMD a versatile choice for different scenarios. It is important to mention that the coefficients follow the designated distribution. In Figure 7, the uniform behavior is not trivial. However, it follows the form of the function  
Figure 5: Received power distributions for different reflection coefficients statistical distributions. (**a**) POW using UNID; (**b**) POW using EXPD; (**c**) POW using GAMD. and shows a wide variety of materials. An illustrative example includes a mine side wall that exhibits discoloration, with sections composed of minerals such as quartz or copper [21, 23]. The aforementioned materials possess values ranging from 0.5 to 0.55 and 0.7 to 0.75, respectively. In Figure 7, values are concentrated on the low side, confirming that the coefficients are generated with GAMD. This can be seen in walls constructed with coal, obsidian, or similar tonality materials, with a minority proportion of lighter materials [22, 23].