# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 4 Conclusions  
In this work, we have investigated the impact of the roughness of the wall on NLOS in the VLC channels within underground mining environments (UM-VLC). Through statistical modeling and Monte Carlo-based simulations, we analyzed how different wall compositions and surface irregularities influence the received power, CIR, and reflection coefficients. The study considered multiple probabilistic distributions (uniform, normal, exponential, and gamma) to model the wall roughness and its effects on the performance of the VLC system. In fact, two positions are analyzed in two different positions of the LED transmitter. For each position, three cases are investigated that change the height of the PD, the distributions to generate reflection coefficients, and the incidence and irradiance angles. The choice of each distribution depends on the tone of color of the wall material and the rough geometry. GAMD and EXPD satisfy a tendency to low values on reflection coefficients and higher values on angles. For UNID, the interval determined can define the variation in these parameters. NORM allows a greater tendency to higher values but without exempting the minority (lower or higher). The results indicate that wall roughness significantly affects light propagation, with different statistical distributions leading to varying levels of signal dispersion, power loss, and multipath effects. In particular, highly diffuse reflective surfaces, modeled using uniform and normal distributions, tend to enhance multipath contributions, increasing CIR delay spread but also improving power distribution uniformity. In contrast, walls with lower reflectivity and greater roughness, modeled by gamma and exponential distributions, result in greater signal attenuation, leading to greater losses in received power and reduced channel gain. Our findings highlight the need for statistically driven channel models that account for random variations in surface geometry and material composition. These insights can aid in the design and optimization of VLC systems for underground environments, where reflections play a crucial role in system reliability. Although the results presented in this study are based on rigorous Monte Carlo simulations and well-established probabilistic modeling techniques, future work should focus on experimental validation to further confirm the precision and applicability of the proposed approach. A controlled laboratory setup will be developed to replicate key environmental factors affecting VLC in underground mining, including surface roughness, material reflectivity, and multipath propagation effects. This will involve using adjustable LED sources, high-precision photodetectors, and tunable reflective surfaces to measure the real-world impact of light scattering and diffusion. In addition, field measurements in underground mining environments will be considered to analyze the influence of dynamic conditions, such as dust, humidity, and human or machinery obstructions. These experiments will al low for more precise calibration of the proposed statistical models and contribute to refining the design of the VLC system for real-world applications in harsh industrial settings. Conceptualization, S.C. and P.P.J. ; methodology, S.C.; software, S.C.; validation, P.P.J., C.A.M. and I.S. ; formal analysis, S.C.; investigation, S.C.; resources, P.P.J., C.A.M. and I.S. ; data curation, S.C.; writing--original draft preparation, S.C.; writing--review and editing, P.P.J., C.A.M. and I.S. ; supervision, P.P.J., C.A.M. and I.S. ; project administration, P.P.J., C.A.M. and I.S. ; funding acquisition, P.P.J., C.A.M. and I.S. All authors have read and agreed to the published version of the manuscript. This research was funded by ANID/FONDECYT Iniciacion No. 11240799, ANID FONDECYT Regular 1211132, ANID/FONDECYT Iniciacion No. 11230129, SENESCYT \"Convocatoria abierta 2014-primera fase, Acta CIBAE-023-2014\" and Faculty of Engineering and Applied Sciences, Networking and Telecommunications Engineering, UDLA. Not applicable.