### Scatterer Distribution Models Applied to Optical Communication Systems  
After an in-depth literature review, it can be seen that there are some works that present scatterer distribution models applied to optical communication systems [12; 18; 19; 20; 21; 22; 23]. In [18; 19], a spread spectrum wireless dispersion model based on an NLoS optical component is presented. The paradigm of these works is based on the fact that air molecules and suspended aerosols build NLoS optical communication links caused by scattering when using carriers in the infrared light band. References [20; 21] are the pioneering research by including and modeling the effect of scattering in indoor VLC environments. To model scattering, several particles are randomly placed in a 2D ellipse or ring shape. Finally, the complete VLC channel model is derived by the arithmetic add of the LoS channel component and the channel components produced by scattering. In [22] the authors propose a proposes a 3D Regular-Shaped Geometry-Based Stochastic Model (RS-GBSM) for vehicular VLC Multiple-Input Single-Output (MISO) channels. The distribution proposed combines a two-sphere model and an elliptic-cylinder model. The results of this work demonstrate the relationship between the communication range and the elevation angle in the proposed model on the received optical power. The authors in [12] present a novel channel model that includes in its analysis influential factors in the UM-VLC system. Among the characteristics considered are the random orientation of the LED and PD, irregular walls that produce reflections with random directions, shadowing caused by machinery and scattering caused by suspended dust particles. Although the VLC channel model presented considers important components of the UM environment, the scatterer distribution model implemented is simplistic. This model is based on the assumption that the dust particles are distributed within a two-dimensional disk-shaped area. Therefore, this scheme should be improved to have a more accurate and realistic UM-VLC channel model. Finally, the most recent work on the study of dust particles and their influence on VLC systems applied to underground coal mines is presented in [24]. The focus of this manuscript is based on the influence of coal dust particles and the scattering model. Furthermore, the impact of coal dust particles on visibility and attenuation is analyzed for visible light transmission. Although the work analyzes the effect of scatterers (dust particles) on the performance of the VLC system, the article does not present a specific mathematical and analytical model of scatterer distribution for the tunnel environment. A VLC channel component produced by the interaction of light with scatterers is also not specified. As observed in the state of the art analysis of scatterer models applied to optical communications systems, the consideration and implementation of dust particles distributions that closely emulate their behavior in UM environments and their effect on VLC systems. Neither an exhaustive analysis on the interaction of light bonds with the atmosphere and dust particles in UM tunnels has been made. Based on these premises and opportunities to improve the existing state-of-the-art UM-VLC channel models, the main contributions of this work are presented below:  
1. An in-depth analysis of the absorption and scattering parameters in the UM environment and the interaction of the incident light in the VLC system with the dust particles and the atmosphere of the UM environment was performed. 2. A novel 3D dust particle distribution model based on a hemispherical region, along with its mathematical parameters and its statistics based on the joint distribution of the arrival time and the arrival angle of the scattering down-link were developed and analytically proposed. 3. A more accurate and realistic UM-VLC channel component produced by dust particles (scattering), which enhances the general UM-VLC channel model, was derived and presented. 4.