## 2 Principle
So \(\mathrm{C_{n}}^{2}\) is selected as \(10^{-13}\)\(\mathrm{m}^{-2/3}\). Therefore, the PDF of irradiance is shown as below, under the conditions where the transmitting angle is 1 mrad, the alignment error \(\mathrm{r}=0\), the transmitting optical power is 1 W and the communication distance \(\mathrm{L}=1\) km:  
\[\mathrm{p}(\mathrm{I})=\frac{1}{1.98\times 1}\exp\left[-\frac{\left(\ln \mathrm{I}+0.089\right)^{2}}{1.25}\right]. \tag{8}\]  
The relationship between the probability distribution function of irradiance and irradiance is shown in Figure 2.  
According to Reference [24], the coherence time of typical weak atmospheric turbulence is 1-10 ms, while the time of sending a single packet of data in the system is less than 1 us, so it can be concluded that there will be no sudden change in the time channel in the process of sending a packet of data. When the receiving area S = 1 cm\({}^{2}\) and the detection sensitivity w = 10 uW, the minimum irradiance that can be detected by the receiving end is  
\[\mathrm{P}(\mathrm{I})=\frac{1}{\mathrm{I}\sigma_{1}(\mathrm{r},\mathrm{L})\sqrt{2 \pi}}\exp\left\{-\frac{\left[\ln\left(\frac{\mathrm{I}}{\mathrm{I}\omega( \mathrm{I}(\mathrm{r},\mathrm{L}))}\right)+\frac{1}{2}\sigma_{1}^{2}(\mathrm{r },\mathrm{L})\right]^{2}}{2\sigma_{1}^{2}(\mathrm{r},\mathrm{L})}\right\}, \tag{1}\]0  
So the communication probability of a single packet is  
\[\mathrm{P}(\mathrm{I})=\frac{1}{\mathrm{I}\sigma_{1}(\mathrm{r},\mathrm{L})\sqrt{2 \pi}}\exp\left\{-\frac{\left[\ln\left(\frac{\mathrm{I}}{\mathrm{I}\omega( \mathrm{I}(\mathrm{r},\mathrm{L}))}\right)+\frac{1}{2}\sigma_{1}^{2}(\mathrm{r },\mathrm{L})\right]^{2}}{2\sigma_{1}^{2}(\mathrm{r},\mathrm{L})}\right\}, \tag{1}\]1  
The relationship between the number of times n that the system sends the same data packet in 1 s and the communication probability of the system in 1 s is as follows:  
\[\mathrm{P}(\mathrm{I})=\frac{1}{\mathrm{I}\sigma_{1}(\mathrm{r},\mathrm{L})\sqrt{2 \pi}}\exp\left\{-\frac{\left[\ln\left(\frac{\mathrm{I}}{\mathrm{I}\omega( \mathrm{I}(\mathrm{r},\mathrm{L}))}\right)+\frac{1}{2}\sigma_{1}^{2}(\mathrm{r },\mathrm{L})\right]^{2}}{2\sigma_{1}^{2}(\mathrm{r},\mathrm{L})}\right\}, \tag{1}\]2  
The function image is shown in \[\mathrm{P}(\mathrm{I})=\frac{1}{\mathrm{I}\sigma_{1}(\mathrm{r},\mathrm{L})\sqrt{2 \pi}}\exp\left\{-\frac{\left[\ln\left(\frac{\mathrm{I}}{\mathrm{I}\omega( \mathrm{I}(\mathrm{r},\mathrm{L}))}\right)+\frac{1}{2}\sigma_{1}^{2}(\mathrm{r },\mathrm{L})\right]^{2}}{2\sigma_{1}^{2}(\mathrm{r},\mathrm{L})}\right\}, \tag{1}\]3  
\[\mathrm{P}(\mathrm{I})=\frac{1}{\mathrm{I}\sigma_{1}(\mathrm{r},\mathrm{L})\sqrt{2 \pi}}\exp\left\{-\frac{\left[\ln\left(\frac{\mathrm{I}}{\mathrm{I}\omega( \mathrm{I}(\mathrm{r},\mathrm{L}))}\right)+\frac{1}{2}\sigma_{1}^{2}(\mathrm{r },\mathrm{L})\right]^{2}}{2\sigma_{1}^{2}(\mathrm{r},\mathrm{L})}\right\}, \tag{1}\]4 The relationship between the communication probability and the number of transmissions in 1 s.  
\[\mathrm{P}(\mathrm{I})=\frac{1}{\mathrm{I}\sigma_{1}(\mathrm{r},\mathrm{L})\sqrt{2 \pi}}\exp\left\{-\frac{\left[\ln\left(\frac{\mathrm{I}}{\mathrm{I}\omega( \mathrm{I}(\mathrm{r},\mathrm{L}))}\right)+\frac{1}{2}\sigma_{1}^{2}(\mathrm{r },\mathrm{L})\right]^{2}}{2\sigma_{1}^{2}(\mathrm{r},\mathrm{L})}\right\}, \tag{1}\]5 Probability distribution function of irradiance. The communication rate of the system is 1 Mbps, and the length of each packet is 1 Kb. So, the same packet can be sent 1000 times in 1 s. The communication probability of the system in 1 s is:  
\[\mathrm{P}(\mathrm{I})=\frac{1}{\mathrm{I}\sigma_{1}(\mathrm{r},\mathrm{L})\sqrt{2 \pi}}\exp\left\{-\frac{\left[\ln\left(\frac{\mathrm{I}}{\mathrm{I}\omega( \mathrm{I}(\mathrm{r},\mathrm{L}))}\right)+\frac{1}{2}\sigma_{1}^{2}(\mathrm{r },\mathrm{L})\right]^{2}}{2\sigma_{1}^{2}(\mathrm{r},\mathrm{L})}\right\}, \tag{1}\]6  
According to the calculation, although the UAV will be affected by the atmospheric turbulence in the flight process, the probability of the UAV receiving the command in 1 s is greater than 99.99%.