## 2 Analysis of Scattering Models and Channel Characteristics  
### Single-Scattering Channel Model  
In UV NLOS scattering communication, the optical signal from the transmitter undergoes multiple or single scattering before reaching the photodetector at the receiver end. Investigators employ a co-planar geometric single-scattering channel model for analysis.  
As illustrated in Figure 2, the diagram depicts the UV NLOS scattering communication link under the coplanar geometric configuration, where the transmitter (TX) is located at point T and the receiver (RX) is situated at point R. The following parameters are defined: \(\theta_{1}\) and \(\theta_{2}\) represent the angles between the communication devices and the horizontal axis at TX and RX, respectively; \(\phi_{1}\) and \(\phi_{2}\) denote the beam divergence angle at the TX end and the field of view (FOV) at the RX end; \(\theta_{s}\) denotes the scattering angle between the emission direction of the incident light and the reception direction, satisfying the condition \(\theta_{s}=\theta_{1}+\theta_{2}\); \(r\) signifies the straight-line distance between the transmitter and the receiver; and \(r_{1}\) and \(r_{2}\), respectively, represent the distances from the scattering common volume to TX and RX.  
The path loss, designated as \(L\), is defined as the quotient of transmitted signal power (\(E_{t}\)) to received signal power (\(E_{r}\)), which depends on the common volume \(\delta V\), itself being contingent upon the shape of the intersection point. In the case of narrow beam widths, the common scattering region can be approximated as a small truncat  
Figure 2: NLOS single scattering communication geometry.  
for path loss in the truncated cone approximation model is provided by the following equation [8]:  
\[L\approx\frac{96r\sin\theta_{1}\sin^{2}\theta_{2}(1-\cos\frac{\phi_{1}}{2})\exp[ \frac{k_{x}r(\sin\theta_{1}+\sin\theta_{2})}{\sin\theta_{s}}]}{k_{s}P(\mu)A_{r} \phi_{1}{}^{2}\phi_{2}\sin\theta_{s}\left(12\sin^{2}\theta_{2}+\phi_{2}{}^{2} \sin^{2}\theta_{1}\right)} \tag{1}\]  
In this context, let \(k_{e}\) denote the atmospheric extinction coefficient, expressed as \(k_{e}=k_{s}+k_{a}\), derived from the sum of scattering and absorption coefficients. \(A_{r}\) denotes the area of the receiving aperture and \(P(\mu)\) represents the scattering phase function, where \(\mu=\cos\theta_{s}\).  
Based on the corresponding scattering coefficients, the scattering phase function is modeled as a weighted sum of Rayleigh (molecular) and Mie (aerosol) scattering phase functions [8]:  
\[P(\mu)=\frac{k_{s}^{Ray}}{k_{s}}p^{Ray}(\mu)+\frac{k_{s}^{Mie}}{k_{s}}p^{Mie}(\mu) \tag{2}\]  
where \(k_{s}=k_{s}^{Ray}+k_{s}^{Mie}\), with \(k_{s}^{Ray}\) and \(k_{s}^{Mie}\) being the Rayleigh and Mie scattering coefficients, respectively. The associated scattering phase functions follow the generalized Rayleigh model [30] and the generalized Henyey Greenstein function [31]:  
\[p^{Ray}(\mu)=\frac{3[1+3\gamma+(1-\gamma)\mu^{2}]}{16\pi(1+2\gamma)} \tag{3}\]  
\[p^{Mie}(\mu)=\frac{1-g^{2}}{4\pi}[\frac{1}{\left(1+g^{2}-2g\mu\right)^{3/2}}+ f\frac{0.5(3\mu^{2}-1)}{\left(1+g^{2}\right)^{3/2}}] \tag{4}\]  
where \(\gamma,g,\) and \(f\) are model parameters. This closed-form expression facilitates simplified treatment and analysis of the path loss as well as the BER performance of communication systems under various geometric conditions.