# Unified Performance Analysis of Direct Air-to-Underwater RF/UWOC Systems
## 2 System and Channel Models
 \tag{9}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \((m,n,p,q)\) & \((a_{r},A_{i})_{i-1}^{p}\) & \((b_{r},B_{i})_{i-1}^{q}\) & \(b_{0}\) & \(\lambda\) \\ \hline a \(-\mu\) & \((1,0,0,1)\) & \(-\) & \((\mu-1/a)\) & \(\mu^{1/a}/\Omega(\mu)\) & \(\mu^{1/a}/\Gamma(\mu)\) \\ \(where \(B=2\sqrt{\frac{1}{\pi\alpha_{\alpha}}}\frac{\mathcal{R}_{0}\exp^{k}}{A_{0}^{2}-a^{2 }\Gamma(k)}\frac{\xi^{2}}{A_{0}^{2}}\exp(-\frac{2\pi a^{2}c^{2}}{2\omega_{\alpha} ^{2}})\). **Theory 1**. : _Under the influence of atmospheric turbulence, fog conditions, and a pointing error of nonzero mean single-sided, the PDF expression of the new channel gain under the combined channel fading effect was obtained. The PDF expression for the channel gain of the RF link can be represented by Equation (9)._  
**Proof**: See Appendix A. \(\square\)  
To analyze the air-to-water interface, we rely on the BS distribution. The BS distribution has been applied in various works, including environmental, health indicators, and neural spikes. Applying mathematical concepts to different fields is a meaningful approach. The probability density function of the BS distribution can be expressed as follows [27]:  
\[\begin{array}{l}f_{h_{w}}(h_{w})=\frac{1}{2\sqrt{2\pi a_{0}}\beta}\frac{1}{ \sum\limits_{i=0}^{1}}(\frac{\beta}{h_{w}})^{\frac{1}{2}+i}\\ \exp(\frac{1}{\alpha_{0}})  
\[ \begin{array}{ll}f_{2h_{4}}(h_{4})=\frac{(1-w)cBh_{4}}{2\sqrt{2\pi a_{0}}\beta^{2 }\Gamma(4)^{2}}\sum\limits_{i=0}^{1}{(\frac{1}{2a_{0}^{2}})}^{-i-3/2}\exp(\frac{ 1}{a_{0}^{2}})\\ \times H^{0,1,0,1;m+k+2,m}_{1,0;1,0;p+k+1,d+k+2}[\frac{1}{4a_{0}^{2}}\frac{(2a_ {0}^{2})^{2}}{\lambda\beta^{2}A_{0}^{2}}|^{(-1/2-j;1,2)}|^{(1,1)}_{-}|^{\chi_{i }(\epsilon^{2}-1,1)}_{\beta_{i}(\epsilon^{2}-2,1),(-2,2)}]\end{array}  \tag{15}\]  
**Proof**: See Appendix B. \(\square\)  
We assume that all average signal-to-noise ratios \(\overline{r}\) are equal. The PDF of the signal-to-noise ratio can be obtained based on the relationship between the signal-to-noise ratio and the channel gain, \(\overline{r}h_{4}^{2}=r_{4}\). The signal-to-noise ratio of the combined channel is represented by the sum of Equations (16) and (17). \[\begin{array}{ll}f_{1r_{4}}(r_{4})=&\frac{wB}{2  
The higher the concentration of fog, the greater the absorption and scattering effect of the signal, which weakens the strength of the signal and reduces the performance of the system. We assume that all average signal-to-noise ratios are equal \(\overline{r_{1}}=\overline{r_{2}}=\overline{r}\) and that the parameter \(c\) of EGG is a positive integer. Figure 2 compares the outage probability of the system under light and moderate fog conditions, \(w=0.098\). Set the value for moderate fog to 6.37 and for mild fog to 4.70. When the signal-to-noise ratio is 20 dB and under light fog conditions, the outage probability of the \(\mathcal{F}\) distribution is \(10^{-6}\), the outage probability of the EGK distribution is \(10^{-4}\), the outage probability of the \(\alpha-\mu\) distribution is \(10^{-2}\), and \(\mathcal{F}<\) EGK \(<\alpha-\mu\). It can be seen from the figure that light fog has a better performance compared to moderate fog. From the graph, it can also be seen that the higher the turbulence intensity, the greater the OP. Compared to moderate fog, light fog has a lower concentration of  
Figure 3: The relationship between system parameters \(\alpha\) and \(\beta\) and outage probability. Figure 2: The relationship between outage probability values under different fog conditions. substances in the air, which reduces the probability of signal absorption and scattering, resulting in higher reliability and stability of signal arrival at the receiving end. Therefore, the performance of the outage probability under light fog conditions is superior. From the results of numerical analysis and Monte Carlo analysis, it can be seen that the two curves have good agreement, indicating that the correctness of the numerical simulation results is verified through Monte Carlo simulation.