## 2 Airborne Air-to-Air Channel Laser Communication Link Analysis and Modeling
The simulation results show that the effect of the time-domain pulse broadening of the laser pulse due to turbulence effects in the airborne air-to-air channel is much larger than that caused by scattering effects. Studies conducted at home and abroad [19; 20; 21; 22] have shown that turbulence intensity generally decreases with height but that these changes are sporadic and the turbulence increases slightly at the top of the troposphere from 15 km to 18 km. Turbulence has a more obviously stratified structure with increasing height and because turbulence is intermittent in time and space, it is irregularly stratified, with stronger and weaker levels of turbulence throughout. The distribution of \(C_{n}^{2}\), a structural parameter of the atmospheric refractive index, with altitude varies across different seasons in the same region as well as between day and night. In general, the turbulence intensity at high altitudes will be 1-2 orders of magnitude higher during the daytime than at night. In this paper, sounding test data on the daytime and nighttime turbulence of the airborne air-to-air channel collected at an altitude of 10 km over a region in the south of China in the summer [21] were taken as the basis for analysis and inverse derivation was performed to obtain the standard deviation of the fluctuation in the atmospheric refractive index in the analyzed region. The \(\Delta\)n change in \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Transmission Model**} & \multicolumn{4}{c}{**Average (ps)**} & \multicolumn{4}{c}{**Variance (ps\({}^{2}\))**} \\ \cline{2-7}  & **150 km** & **200 km** & **250 km** & **150 km** & **200 km** & **250 km** \\ \hline Scattering & 16 & 21 & 28 & 2.67 & 2 & 0.67 \\ Scattering+Turbulence Bubble & 61 & 72 & 86 & 4.67 & 2.67 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean and variance in laser pulse time-domain broadening for different transmission models (different transmission distances). Figure 5: Time-domain waveform and analysis of time–space channel of laser pulse with/without turbulence under different transmission distances. (**a**) Simulation of laser pulse time-domain waveform (200 km) and (**b**) ratio of pulse broadening to pulse half-width (different transmission distances). the study region is as follows: \(C_{n-day}^{2}=10^{-16}\)m\({}^{-2/3}\), \(C_{n-night}^{2}=10^{-17}\)m\({}^{-2/3}\). The analysis in this paper is based on clear weather scattering channel conditions and also simulates the time-response characteristics of laser signals transmitted via the airborne air-to-air channel under different standard deviations of fluctuation in the atmospheric refractive index and different turbulence channel conditions. The standard deviations of the fluctuation in the atmospheric refractive index, \(\sigma_{n}\), are 97, 74, and 56 for the time-domain pulse spread and 497, 474, and 456 for the pulse half-width (in ps) of the airborne multipath channel in the presence of turbulence for the \(1\times 10^{-7}\)\(1\times 10^{-8}\), and \(1\times 10^{-9}\) conditions, respectively. The simulation and analysis of time-domain waveforms of laser pulses with different standard deviations of atmospheric refractive index fluctuation are shown in Figure 6. The ratios of the time-domain spread of the laser pulses to the pulse half-widths are 19.5%, 15.8%, and 12.3% for the three conditions, respectively. Mean and variance of in laser pulse time-domain broadening under different standard deviations of the fluctuation in atmospheric refractive index are shown in Table 3.  
The simulation results were analyzed and it was found that with the increase in the standard deviation of the fluctuation in the atmospheric refractive index, the time-domain spreading of the laser pulse caused by the airborne multipath channel is characterized by an increasing trend.