## 2 Airborne Air-to-Air Channel Laser Communication Link Analysis and Modeling  
According to the information being transmitted from the source to the host of the transmission process, the airborne air-to-air channel laser communication link analysis model can be divided into four parts: laser emission, transmission, pupil reception, and detection and information processing, the specific process is shown in the Figure 1.  
A description of the constructed model is presented below:  
Figure 1: Analytical model of laser communication link for airborne air-to-air channels. At the transmitting end, the actual transmitting antenna aperture size is taken into account not only to constrain the size of the dispersion angle of the outgoing pupil beam but also to control the conditions of the outgoing beam ejection;
2. At the receiving end, taking into account the actual constraints on the field of view of the receiving antenna, one constraint of the simulated pupil reception process is that the transmission angle (stereo angle) of the photon transmitted to the receiving end's face cannot be greater than the actual reception requirements of the receiving antenna's field of view. A photon that fits within the constraints is considered a valid pupil reception photon and enters the subsequent photon counting process. Otherwise, the photon is invalid and does not enter the subsequent photon-counting process;
3. Considering the reception sensitivity power constraints of the actual system, a photon that is recognized as an effective pupil-received photon needs to meet both the low-limit power dimensions of the pupil and the constraints of the three-dimensional transmission angle of the pupil-received photon;
4. The actual ATP (acquisition, tracking, and pointing) error constraints in the airborne communication phase are considered. The airborne ATP channel is a typical atmospheric turbulence channel and the refractive index structure constants of the turbulent channel under different altitude conditions can be described by the Hufnagel-Valley (H-V) correction model as follows [3]:  
\[C_{n}^{2}(h)=1.9\times 10^{-15}\times exp\left(-\frac{h}{100}\right)+8.26\times 10^ {-15}\times h\times exp\left(-\frac{h}{1000}\right)+3.02\times 10^{-17}\times exp \left(-\frac{h}{1500}\right) \tag{1}\]  
In the above equation, \(h\) is the altitude, whose unit is m, and \(C_{n}^{2}\) represents the dimensions in \(m^{-2/3}\). The variance in the refractive index fluctuations, denoted as \(\sigma_{n}^{2}\), is a frequently employed physical parameter for characterizing atmospheric turbulence intensity. This dimensionless quantity exhibits a numerical order of magnitude comparable to the atmospheric refractive index structure constant \(C_{n}^{2}\). Importantly, it is not contingent upon the assumption of turbulence isotropy, making it particularly well-suited for describing the intensity of atmospheric turbulence under general conditions. Here, \(\sigma_{n}^{2}\) is the fluctuation in the refractive index at a single point; \(L_{0}\) has the unit m; \(l_{0}\) is the external scale of turbulence, whose unit is m; and \(r\) is the internal scale of turbulence, whose unit is m, which represents the distance between two points in space. According to [PERSON] turbulence statistical theory, the structure-function \(D_{n}\) should be expressed as follows [8; 9]:  
\[D_{n}(r)=2\sigma_{n}^{2}\left(\frac{r}{L_{0}}\right)^{2/3},\ l_{0}\ll r\ll L_{0} \tag{2}\]  
\[D_{n}(r)=2\sigma_{n}^{2}\left(\frac{l_{0}}{L_{0}}\right)^{2/3}\left(\frac{r}{ l_{0}}\right)^{2},\ r\ll l_{0} \tag{3}\]  
Analytical Modeling of Pulse Time Broadening after Laser Transmission through Airborne Air-to-Air Channels  
The total attenuation and effect of scattering on laser transmission in air-to-air laser communication links are affected by the working wavelength, transmission distance, and altitude of the cloud layer. Around the altitude of 10 km above sea level, laser transmissions in airborne air-to-air channel links will be affected by the scattering effects of various kinds of clouds.