# Statistical Modeling of Wall Roughness and Its Influence on NLOS VLC Channels in Underground Mining
## 1 Introduction  
Underground mining (UM) plays a crucial role for nations in resource extraction, and there is a constant pursuit of technological advances within mines in terms of communication systems. In this sense, wireless communications have been implemented based on new technologies, which allow us to solve different UM work activities [1]. Among these tasks are monitoring machines, real-time communication between mine workers, and performing measurement tasks that do not allow a direct human approach. Currently, RF bands along with Zigbee systems facilitate these tasks in a sub-optimal way [2]. It is important to note that wireless communication systems based on RF or Zigbee offer a flexible connection in dynamic environments due to their scalability [3]. This meansthat the devices can communicate redundantly and reliably in the event of failure points. Moreover, they allow for a mobile network without important communication problems. Currently, technological advances have made it possible to mitigate different issues, such as RF interference, and provide improvements in UM [4]. In addition, these upgrades, for example, are made with the Internet of Things, remote telemetry, and autonomous machinery, among others. Moreover, these advances are based on the RF theory [4]. However, these wireless technologies based on RF are not exempt from other issues that directly attack performance. For example, in most UM environments, there exist rough sidewalls that affect signal reflections, representing a factor capable of distorting signal quality. Furthermore, obstructions resulting from machinery, as well as reflections from mine dust, contribute to these challenges [5]. These problems are opportunities for the establishment of emerging technologies such as optical communication, specifically Visible Light Communication (VLC). In this context, VLC emerges as a significant alternative to RF-based technologies utilized in data transmission in UM environments. In contrast to traditional radio-wave technologies, VLC employs light as a medium for communication [6]. This can be achieved by modulating the light intensity emitted for some optoelectronic source (LED) as a transmitter [7]. In recent years, research on UM-VLC has become more important due to its low cost and easy implementation. Moreover, a luminous infrastructure can be repurposed for this application and does not generate electromagnetic interference with other systems that utilize this type of signal. On the other hand, the implementation of optical communication systems within the mining industry is a well-established practice, particularly with the employment of fiber optics [8]. Nevertheless, there is a growing interest in the application of light within an unrestricted medium, which, in turn, has increased the prominence of research into VLC in recent years. In this regard, a pertinent challenge arises concerning tunnel sidewalls, which are characterized by their rough and irregular surfaces, resulting in unpredictable and unconventional reflections. However, existing studies on UM-VLC primarily utilize theoretical and analytical models, which show a depth deficiency in terms of the reflection component [9]. In the existing literature, there is a notable absence of studies on VLC systems that statistically and representatively model walls within UM [10]. In addition, no verifications have been performed using appropriate metrics [11]. Based on a comprehensive survey of reflection components, Non-Line-of-Sight (NLOS) conditions arise due to light reflection off irregularly structured sidewalls [12]. In this context, this research offers an analysis of VLC systems by probabilistic modeling of the reflection coefficients about walls in UM scenarios. The objective is to facilitate a discussion on the impact of these parameters on light signals, specifically concerning conventional wireless communication metrics.