# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
###### Abstract  
This study investigates the impact of wall roughness on the performance of the Non-Line-of-Sight (NLOS) component in Visible Light Communication (VLC) systems designed for underground mining environments, adhering to safety and communication standards such as IEC 60079-28(intrinsic safety in explosive atmospheres) and IEEE 802.15.7 (VLC parameters). Using probabilistic models aligned with the ITU-R P.1238 propagation guidelines, the research evaluates how wall materials (e.g., coal, shale, limestone) and their irregular geometries, characterized by surface roughness profiles compliant with ISO 8503-2,influence reflection coefficients (0.05-0.85 range), incidence angles (0\({}^{\circ}\)-90\({}^{\circ}\)), and irradiance angles (5\({}^{\circ}\)-180\({}^{\circ}\)), which are critical for signal propagation. Simulation scenarios, parameterized with material reflectivity data from ASTM E423, explore the effects of statistical distributions (uniform, normal with \(\mu\) = 0.3, \(\sigma\) = 0.2; exponential \(\lambda\) = 2; gamma \(\alpha\) = 0.5, \(\beta\) = 0.2) on power distribution, channel impulse response, and reflection coefficients. The results indicate variations in maximum received power: a decrease of 80% for uniform distribution, an increase of 150% for exponential distribution, and a 100% increase for gamma distribution in reflection conditions. Under incidence and irradiance conditions, uniform distribution exhibited a 158.62% increase, whereas exponential distribution and gamma distribution experienced reductions of 72.22% and 7.04%, respectively. These variations align with IEC 62973-1 EMI limits and emphasize the role of roughness (Ra = 0.8-12.5 \(\upmu\)m per ASME B46.1).  
chapter 2024  
###### Abstract  
This study investigates the impact of wall roughness on the performance of the Non-Line-of-Sight (NLOS) component in Visible Light Communication (VLC) systems designed for underground mining environments, adhering to safety and communication standards such as IEC 60079-28(intrinsic safety in explosive atmospheres) and IEEE 802.15.7 (VLC parameters). Using probabilistic models aligned with the ITU-R P.1238 propagation guidelines, the research evaluates how wall materials (e.g., coal, shale, limestone) and their irregular geometries, characterized by surface roughness profiles compliant with ISO 8503-2,influence reflection coefficients (0.05-0.85 range), incidence angles (0\({}^{\circ}\)-90\({}^{\circ}\)), and irradiance angles (5\({}^{\circ}\)-180\({}^{\circ}\)), which are critical for signal propagation. Simulation scenarios, parameterized with material reflectivity data from ASTM E423, explore the effects of statistical distributions (uniform, normal with \(\mu\) = 0.3, \(\sigma\) = 0.2; exponential \(\lambda\) = 2; gamma \(\alpha\) = 0.5, \(\beta\) = 0.2) on power distribution, channel impulse response, and reflection coefficients. The results indicate variations in maximum received power: a decrease of 80% for uniform distribution, an increase of 150% for exponential distribution, and a 100% increase for gamma distribution in reflection conditions. Under incidence and irradiance conditions, uniform distribution exhibited a 158.62% increase, whereas exponential distribution and gamma distribution experienced reductions of 72.22% and 7.04%, respectively. These variations align with IEC 62973-1 EMI limits and emphasize the role of roughness (Ra = 0.8-12.5 \(\upmu\)m per ASME B46.1).  
Keywords:channel modeling; visible light communication (VLC); reflections channel components; underground mining; underground mining visible light communication (UM-VLC) +
Footnote †: journal: Applied Sciences