## 3 System Design with Simulation and Experimental Results  
### UV Channel Modeling Analysis and Simulation  
#### 3.1.1 LOS Model  
Figure 1 represents the UV line-of-sight communication link model. In LOS communication, the vast majority of UV photons go directly from the transmitter to the receiver without scattering. In Figure 1, \(Tx\) is the position of the transmitter light source, \(Rx\) is the position of the receiver detector, \(\phi_{1}\) is the dispersion angle of the UV light source, and \(\phi_{2}\) is the receiving field of view of the detector.  
Assume the transmitted power of the UV light source at the transmitter is \(P_{t}\). After absorption and scattering in the atmosphere over distance \(r_{1}\), the power becomes \(\frac{P_{t}e^{-K_{e}r_{1}}}{r_{1}{}^{2}}\). Following the distance loss over \(r_{2}\), the remaining power is \(\frac{P_{t}e^{-K_{e}r_{1}}}{r_{1}{}^{2}}\times\left(\frac{\lambda}{4\pi r_{2}} \right)^{2}\). \(e^{-K_{e}r_{2}}\) represents the atmospheric attenuation factor, \(K_{e}\) is the extinction coefficient, \(\lambda\) is UV wavelength, \(A_{r}\) is the receiver aperture area, and \(\frac{4\pi A_{r}}{\lambda^{2}}\) is the detector reception gain.  
The optical power reaching the receiver is as follows:  
\[P_{r,LOS}=P_{t}\bigg{(}\frac{e^{-K_{e}r_{1}}}{r_{1}{}^{2}}\bigg{)}\bigg{(} \frac{\lambda}{4\pi r_{2}}\bigg{)}^{2}e^{-K_{e}r_{2}}=\frac{P_{t}A_{r}}{4\pi r _{1}{}^{2}r_{2}{}^{2}}e^{-K_{e}(r_{1}+r_{2})} \tag{27}\]  
According to the geometric relationship in Figure 1, the following equation can be obtained:  
\[h_{1}=\frac{r\sin(\phi_{2}/2)}{\sin(\phi_{1}/2+\phi_{2}/2)} \tag{28}\]  
\[h_{2}=\frac{r\sin(\phi_{1}/2)}{\sin(\phi_{1}/2+\phi_{2}/2)} \tag{29}\]  
\[r_{1}=h_{1}\cos(\phi_{1}/2)=\frac{r\sin(\phi_{2}/2)\cos(\phi_{1}/2)}{\sin(\phi _{1}/2+\phi_{2}/2)} \tag{30}\]  
\[r_{2}=h_{2}\cos(\phi_{2}/2)=\frac{r\sin(\phi_{1}/2)\cos(\phi_{2}/2)}{\sin(\phi _{1}/2+\phi_{2}/2)} \tag{31}\]  
Therefore, we can obtain the following:  
\[P_{r,LOS}=\frac{P_{t}A_{r}e^{-K_{e}(r_{1}+r_{2})}}{4\pi\Big{(}\frac{r\sin( \phi_{2}/2)\cos(\phi_{1}/2)}{\sin(\phi_{1}/2+\phi_{2}/2)}\Big{)}^{2}\Big{(} \frac{r\sin(\phi_{1}/2)\cos(\phi_{2}/2)}{\sin(\phi_{1}/2+\phi_{2}/2)}\Big{)}^ {2}} \tag{32}\]  
\[L_{LOS}=10\log_{10}\bigg{(}\frac{P_{t}}{P_{r,LOS_{t}}}\bigg{)}=10\log_{10} \bigg{(}\frac{\pi r^{4}\sin^{2}(\phi_{1})\sin^{2}(\phi_{2})}{4A_{r}\sin^{4}( \phi_{1}/2+\phi_{2}/2)e^{-K_{e}r}}\bigg{)} \tag{33}\]  
As shown in Equations (32) and (33), the factors affecting \(P_{r,LOS}\) and \(L_{LOS}\) are the transmission distance \(r\), the divergence angle of the light source \(\phi_{1}\), the receiving field of view angle of the detector \(\phi_{2}\) and so on.  
We simulated the path loss versus distance curve using a computer. In the simulation, the extinction coefficient \(K_{e}=0.9\) km\({}^{-1}\) and \(Ar=5\) cm\({}^{2}\); the results are shown in Figure 2.  
As observed in Figure 2, under identical conditions, path loss exhibits an upward trend with increasing distance. At a fixed distance, as shown in subplot (a), larger transmitter divergence angles result in higher path loss. This phenomenon can be attributed to the reduced energy concentration caused by a more divergent ultraviolet (UV) light source. Conversely, subplot (b) demonstrates that a larger receiver field of view (FOV) corresponds  
Figure 1: UV communication LOS Model.  
to lower path loss at the same distance, as a broader FOV allows the receiver to capture a broader spatial distribution of UV photons.