# A Novel and Adaptive Angle Diversity-Based Receiver for 6G Underground Mining VLC Systems
## 3 Adaptive Orientation Receiver
### Adaptive Receptor Orientation Scenario  
In the proposed algorithm, we assume that there are at least two LEDs within the hemidodecahedral geometric arrangement FoV, which consists of six PDs, five on its lateral faces and one on its upper face, as we can see in Figure 2. However, to generalize with any geometric arrangement, we need at least three PDs, that is, \(I\geq 2\) and \(J\geq 3\). We also consider that the FOV of the receiving structure is the intersection of the FoV of all the PDs that compose it. We also assume that each LED takes turns transmitting its \((x_{i}^{T},y_{i}^{T},z_{i}^{T})\) and \(\mathbf{n}_{i}^{tilt}\) in its assigned time slot through visible light; when the optical signal emitted by  
Figure 2: General structure of the hemi-dodecahedron ADR with adaptive orientation PDs. (**a**) Top view and (**b**) side view. the LED is within the FoV of the PD, the PD receives the signal and also measures the corresponding received signal power. As we noted in expression (14), the position, rotation and tilt of the LEDs and PDs directly affect the UM-VLC channel and therefore the received power. However, since the LEDs are fixedly installed, we will focus on the positioning of the PDs in the receiver structure. This positioning affects the incidence angle, as we observe in expression (4), with the \(\alpha_{j}\) and \(\beta_{j}\) angles. Therefore, in the algorithm that we propose, we will first estimate the \(\theta_{ij}^{tilt}\), to then obtain the \(\alpha_{j}\) and \(\beta_{j}\) values, and finally estimate the orientation that the receiving structure must follow. As illustrated in Figure 1, we employ a Cartesian coordinate system with respect to the tunnel to specify positions of the elements of the system. On the other hand, to estimate \(\theta_{ij}^{tilt}\), we need to know the relationships among the different orientations that PDs can take in the receiving structure. However, these orientations are random and unknown if based on the coordinate system with respect to the tunnel. This problem occurs because the receiving structure can rotate and tilt randomly by the movement of the mining worker's head. In contrast, PDs are initially fixed with respect to the hemidodecahedral receptor structure. Thus, it is necessary to introduce a secondary Cartesian coordinate system with respect to the receiving structure to specify the PDs orientations. Based on the system distribution in Figures 1 and 2, the origin point of the secondary coordinate system, \(O^{H}\), is the center of the hemidodecahedron. The \(x^{H}-y^{H}\) plane coincides with the bottom plane of the hemidodecahedron and the positive axis \(x^{H}\) coincides with the normal direction of the hemidodecahedron. By convention, the inclination angles of the PDs in the geometric structure start from zero. To distinguish and differentiate the vector and position notations with respect to the main coordinate system, in the secondary coordinate system, we use the superscript \"\(H\)\" for the respective representation. Therefore, the positions \((x_{i}^{T},y_{i}^{T},z_{i}^{T})\), \((x_{j}^{R},y_{j}^{R},z_{j}^{R})\), and \((x^{H},y^{H},z^{H})\), and the vectors \(\mathbf{n}_{i}^{tilt},\mathbf{n}_{i}^{tilt}\), and \(d_{ij}\) in the main coordinate system are represents by the positions \((x_{i}^{H},y_{i}^{H},z_{i}^{H})\), \((x_{j}^{H},y_{j}^{H},z_{j}^{H})\), and \((x^{H},y^{H},z^{H})\), and the vectors \(\mathbf{n}_{i}^{tilt(H)}\), \(\mathbf{n}_{j}^{tilt(H)}\), and \(d_{ij}^{H}\) in the secondary coordinate system.