# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 3 Simulation Results  
This section outlines the VLC system's performance outcomes in the given conditions. The analysis generates matrix components and calculates the incidence and irradiance angles based on a normal distribution. These results are obtained through a computer simulation that focuses on the average power distribution (POW) and the CIR in two positions. In the simulation environment, the NLOS components are modeled as reflections from the surrounding surfaces, assuming that there are no significant obstructions on the propagation paths. This assumption simplifies the analysis by focusing on the impact of reflective surfaces on the system's performance. However, we acknowledge that, in real-world scenarios, objects or obstacles can block NLOS components, leading to signal degradation. This limitation is inherent in our current simulation setup and is considered for future extensions, where dynamic and obstructed environments will be incorporated to provide a more comprehensive evaluation. In addition, the parameters simulate some wall cases to produce reflection coefficients ranging from 0 to 1 in one reflection. Then, dark or light-colored walls can be simulated by adjusting the values in a random distribution. EXPD and GAMD are appropriate for the first case. NORM shows special cases and concentrations of a specific material. UNID exhibits a richness in wall composition. The results are organized into two positions, each positioning the LED in one of  
Figure 2: Representative simulation flow diagram. two arbitrarily selected locations. These positions are detailed in Table 1, along with the parameters used in the simulation. The selected PD and LED parameters are consistent with commercially available components and are used as a reference point for the simulation. The larger PD ensures sufficient signal reception in low-LOS or high-NLOS environments, while the LED semi-angle provides broader beam coverage for improved reach. Furthermore, these values are supported by previous research that has used them as a foundation for simulations [5; 8; 11]. The selection of distribution parameter values is based on the roughness of the wall, which depends on the composition of the material and the geometry of the surface [21; 22; 23]. These factors directly influence the reflection coefficients and angles of incidence and irradiation, which are essential for modeling light propagation in VLC systems. The reflection coefficients were adjusted within a range of 0 to 1, corresponding to different material families. A normal distribution was used to represent moderately reflective surfaces (0.3 to 0.7), while a uniform distribution provided a broader variation. The exponential and gamma distributions modeled darker materials, differentiating them based on their scattering characteristics. The parameters of the probability density function (PDF) are directly related to the roughness of the surface. A higher standard deviation indicates greater texture variability, leading to diffuse reflections, while a lower standard deviation corresponds to smoother surfaces with specular reflections. Although these parameters do not explicitly define material types, they provide realistic approximations of common indoor materials, such as painted walls, glass, and plastic. This modeling approach bridges the gap between theoretical simulations and practical VLC implementations, improving the robustness of system performance predictions in NLOS scenarios.