# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 1 Introduction
It is essential to emphasize that this article is based on the research presented in [5], which introduced a UM-VLC channel model that accounts for the roughness of the wall in the NLOS component. The study recognized the influence of wall roughness; however, it depended on hypothesized values without conducting a comprehensive analysis. It lacked a deterministic probability distribution for wall composition and physical form. Consequently, the study addressed various communication phenomena without an adequate random distribution model for the NLOS component. In addition, this can provide an approach to model NLOS channel gain considering irregular walls. It is pertinent to note that the consideration of wall reflections has been a subject of analysis since the advent of radiofrequency studies [13]. In this context, surface roughness affects something called the diffuse radiation component. However, because this involvesthe radio wave spectrum, it does not apply to visible light and the wall distribution is once again assumed. In fact, some methodologies used in other works are useful for working with VLC. For instance, radio waves can be modeled using the ray-tracing method at low frequencies into a tunnel [14]. However, this technique applies to concurrent technologies, such as VLC. In the work reported in [15], a dielectric waveguide of a rectangular section is set with specific conditions to model the roughness of the wall. In addition, the research studies how this affects radio-wave signal propagation at ultra-high frequency. For this, a loss factor is added where the standard deviation of an assumed probability distribution is utilized. This approach introduces a probabilistic element to account for the variability in reflections. The results of this work show that roughness causes another loss in the received power. Additionally, this significantly impacts propagation with a greater effect in larger walls and shorter tunnels. On the other hand, the roughness effect on UM-VLC has not been studied either. Nevertheless, this property is considered to calculate the light reflectance of a tunnel sidewall in [16] using a bidirectional reflection distribution function. For this, the work explains a model of the reflective properties of different side materials and the achievement of prediction increases in illumination with precision. The research describes a five-parameter model and an optimization search algorithm to obtain the best values that describe the optical properties of materials. This work demonstrates that highly diffuse reflective materials are ideal for tunnel sidewalls because of improved energetic efficiency. Nevertheless, this context does not refer to UM-VLC. The assumption of randomness in reflections and its impact on the NLOS channel component is a crucial insight derived from these earlier works. Although this concept has not been directly applied to VLC in the current body of literature, it serves as a valuable foundational framework for analyzing the behavior of light when it reflects off surfaces. It posits that reflections within VLC systems might also demonstrate random characteristics by potentially influencing signal propagation in complex ways. The analysis of the VLC system includes a scenario where wall roughness is modeled by a number of statistical distributions representing random reflections and how this has repercussions for VLC system performance. In fact, this can represent an improvement in the NLOS channel gain model by adding the random component and how it affects signal propagation. In addition, this can be approached to show how materials can change signal behavior. The structure of this article is as follows: Section 2 provides a comprehensive overview of the NLOS system model. Section 3 is devoted to the comparison, evaluation, and numerical analysis of the techniques simulated in the UM-VLC system. Finally, Section 4 presents the study's conclusions and final remarks.