# A Novel and Adaptive Angle Diversity-Based Receiver for 6G Underground Mining VLC Systems
## 3 Adaptive Orientation Receiver
### Adaptive Orientation Receiver Structure  
Basically, an adaptive orientation receptor consists of multiple PDs connected to a single signal processing chain, as shown in Figure 2. We can see that this receiver structure only requires a single Trans-Impedance Amplifier (TIA), which considerably reduces energy consumption in the optical signal reception and processing stage. In order to present a generalized model, we consider the set of PDs \(J\) defined in Section 2.1. For illustrative and demonstrative purposes, these PDs are installed in a hemidodecahedron geometric structure, which is described in detail in Section 4. However, our solution can be applied to any geometric structure (pyramidal, hemispherical, etc). Therefore, initially, the PDs point in different directions according to their position in the receiver of the hemidodecahedral structure that is installed in the helmet of the mining worker, as we can see in Figure 2.  
For ease, we assume that all PDs in the receiver have the same optical characteristics, except for their position and pointing direction. In practice, even though the geometric structure is physically small, there are unavoidable differences between the positions of the PDs in the receiver. This causes variations between the distance from the LEDs to each PD. However, the distances among PDs are significantly small compared to the distance from the LEDs to the receiving geometric structure, so they are not considered. In addition, we consider that the orientation that the receiver takes will be based on the received power of the LoS component of the total UM DC channel gain, because it contributes with the largest magnitude optical power.  
We denote the location of the hemidodecahedric structure as \((x^{H},y^{H},z^{H})\), which according to the assumptions considered will be the common location for all PDs in the receiving structure. Consequently, we can affirm that \((x^{H},y^{H},z^{H})=(x_{j}^{R},y_{j}^{R},z_{j}^{R})\ \forall j\in[1,J]\), \(V_{i-j}\approx V_{i}=(x_{i}^{T},y_{i}^{T},z_{i}^{T})-(x^{H},y^{H},z^{H})\), \(\|V_{i-j}\|=d_{ij}\approx d_{i}\), where \(d_{i}\) is the Euclidean distance from LED \(i\) to the receiving structure. Based on these mathematical considerations, we can approximately rewrite and expand expression (13) as  
\[P_{r,i,j} \approx R_{PD}P_{t}H_{minr,i,j}+N_{j} \tag{14}\] \[\approx R_{PD}P_{t}\Big{[}H_{LoS,i,j}+H_{NLoS,i,j}^{(1)}+H_{sca,i,j} \Big{]}+N_{j}\] \[\approx R_{PD}P_{t}H_{LoS,i,j}+R_{PD}P_{t}H_{NLoS,i,j}^{(1)}+R_{PD}P_{t }H_{sca,i,j}+N_{j}\] \[\approx R_{PD}P_{t}\frac{(m+1)A_{p}}{2\pi d_{i}^{m+3}}\big{(}V_{i} \cdot\mathbf{n}_{i}^{tilt}\big{)}^{m}\big{(}V_{i}\cdot\mathbf{n}_{i}^{tilt}\big{)}G( \theta_{ij}^{tilt})P_{i}+R_{PD}P_{t}H_{NLoS,i}+R_{PD}P_{t}H_{sca,i}+N_{H}\] \[\approx\frac{C}{d_{i}^{m+3}}\Big{(}V_{i}\cdot\mathbf{n}_{i}^{tilt} \big{)}^{m}\big{(}V_{i}\cdot\mathbf{n}_{j}^{tilt}\big{)}P_{i}+R_{PD}P_{t}H_{NLoS, i}^{(1)}+R_{PD}P_{t}H_{sca,i}+N_{H},\]  
where \(C\)=\(\frac{(m+1)A_{p}}{2\pi}R_{PD}P_{t}G(\theta_{ij}^{tilt})\) is a constant, \(P_{t}\) is the weighing function that describes the probability that the LoS link between the LED \(i\) and the entire receiving structure is blocked, \(H_{NLoS,i}^{(1)}\) and \(H_{sca,i}+N_{H}\) are the non-LoS channel and scattering components between the LED \(i\) and the receiver structure, respectively, and \(N_{H}\) is the additive noise in the receiver structure.  
As mentioned in this section, we will focus mainly on the UM LoS channel component, i.e., the former component of \(P_{r,i,j}\). Therefore, our analysis and algorithm that we propose below is based on that assumption.