## 3 System Design with Simulation and Experimental Results
### UV Channel Modeling Analysis and Simulation
#### 3.1.2 NLOS Single Scattering Model  
The single scattering model is a simplified model that considers a photon emitted from a transmitter to arrive at the receiving end after only one scattering. [PERSON] proposed that when the optical depth \(\tau<0.1\), the single scattering transmission dominates the main aspect [6]. Therefore, for UV NLOS communication over short distances, the energy received at the receiving end is mainly the energy after the single scattering of photons. Figure 3 shows a single scattering schematic of UV NLOS communication, TX and RX are the transmitting and receiving ends of the system, respectively, \(\phi_{1}\) is the dispersion angle of the UV light source, \(\phi_{2}\) is the receiving field of view angle of the detector, and \(\theta_{1}\) and \(\theta_{2}\) are the transmitting elevation angle and the receiving elevation angle of the system, respectively. Assuming that the output power at the transmitting end is \(P_{t}\), the power per unit of stereo angle is \(\frac{P_{t}}{\Omega_{T}}\); considering the path loss and attenuation, the power becomes \(\frac{P_{t}}{\Omega_{T}}\times\frac{e^{-K_{\tau}\tau_{1}}}{r_{1}{}^{2}}\) after the path \(r_{1}\). There is a secondary light source at the intersection of \(r_{1}\) and \(r_{2}\), and the optical power from the secondary light source is \(\frac{P_{t}}{\Omega_{T}}\times\frac{e^{-K_{\tau}\tau_{1}}}{r_{1}{}^{2}}\times \frac{K_{S}P_{S}V}{4\pi}\). \(V\) is the volume of the effective scatterer and \(P_{S}\) is the phase function of the scattering angle \(\theta_{S}\). The path from the secondary light source to the receiving end can be equated to the LOS model. Therefore, the optical power detected at the receiving end can be obtained as follows:  
\[P_{r,NLOS}=\frac{P_{t}}{\Omega_{T}}\times\frac{e^{-K_{\tau}r_{1}}}{r_{1}{}^{2} }\times\frac{K_{S}P_{S}V}{4\pi}\times\left(\frac{\lambda}{4\pi r_{2}}\right)^{ 2}e^{-K_{\tau}r_{2}}\frac{4\pi A_{r}}{\lambda^{2}} \tag{34}\]  
where \(\left(\frac{\lambda}{4\pi r_{2}}\right)^{2}\) is the free space path loss factor, \(e^{-K_{\tau}r_{2}}\) is the atmospheric attenuation factor, and \(\frac{4\pi A_{r}}{\lambda^{2}}\) is the detector reception gain. Figure 3: NLOS single scattering model. Figure 2: Relationship between path loss and distance: **(a)** different divergence angle; **(b)** different receiving angle. Moreover, according to the geometric relations, it can be obtained as follows:  
\[\Omega_{T}=2\pi[1-\cos(\phi_{1}/2)] \tag{35}\]  
\[r_{1}=r\sin\theta_{2}/\sin\theta_{S} \tag{36}\]  
\[r_{2}=r\sin\theta_{1}/\sin\theta_{S} \tag{37}\]  
\[\theta_{S}=\theta_{1}+\theta_{2} \tag{38}\]  
\[V=r_{2}\phi_{2}(r_{1}\phi_{1})^{2} \tag{39}\]  
\[P_{r,NLOS}=\frac{P_{1}A_{r}K_{S}P_{S}\phi_{2}\phi_{1}^{2}\sin(\theta_{1}+ \theta_{2})}{32\pi^{3}r\sin\theta_{1}(1-\cos\phi_{1}/2)}e^{-\frac{K_{S}r(\sin \theta_{1}+\sin\theta_{2})}{\sin(\theta_{1}+\theta_{2})}} \tag{40}\]  
\[L_{NLOS}=10\log_{10}\biggl{(}\frac{32\pi^{3}r\sin\theta_{1}(1-\cos\phi_{1}/2) }{A_{r}K_{S}P_{S}\phi_{2}\phi_{1}^{2}\sin(\theta_{1}+\theta_{2})}e^{\frac{K _{S}r(\sin\theta_{1}+\sin\theta_{2})}{\sin(\theta_{1}+\theta_{2})}}\biggr{)} \tag{41}\]  
\(r\) represents the direct line-of-sight distance between the transmitter and receiver, \(K_{e}=K_{a}+K_{S}\), \(K_{a}\) is the absorption coefficient, and \(K_{S}\) is the scattering coefficient. In atmospheric channel propagation, UV photons undergo both Rayleigh scattering and Mie scattering processes. Consequently, the scattering phase function can be mathematically formulated as a weighted sum of these two scattering mechanisms. Figure 3:0  
\(K_{SR}\) and \(K_{SM}\) are the Rayleigh and Mie scattering coefficients, respectively, \(P_{R}(\theta_{S})\) is the Rayleigh scattering phase function, and \(P_{M}(\theta_{S},g)\) is the Mie scattering phase function, which can be expressed as follows [25]:  
Figure 3:1  
Figure 3:2  
where \(\gamma,g,f\) are the model parameters. As shown in Equations (40) and (41), \(P_{r,NLOS}\) and \(L_{NLOS}\) are influenced by \(K_{e}\), \(\theta_{1}\), \(\theta_{2}\).