## 2 Airborne Air-to-Air Channel Laser Communication Link Analysis and Modeling
### Simulation of Laser Transmission Characteristics under Different Visibility Conditions  
In this paper, the time-domain waveforms of the laser pulse after transmission through multipath airborne channels with different visibility conditions are simulated using the MCRT method. The simulation results are shown in Figure 7. As well as the mean and variance in laser pulse time-domain broadening under different atmospheric visibility conditions are shown in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Standard Deviation of Atmospheric Refractive** & **Average (ps)** & **Variance (ps\({}^{2}\))** \\ \hline \(1\times 10^{-7}\) & 56 & 0.67 \\ \(1\times 10^{-8}\) & 72 & 2.67 \\ \(1\times 10^{-9}\) & 96 & 4.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean and variance in laser pulse time-domain broadening under different standard deviations of the fluctuation in atmospheric refractive index. Figure 6: Simulation and analysis of time-domain waveforms of laser pulses with different standard deviations of atmospheric refractive index fluctuation. (**a**) Simulation results of laser pulse time-domain waveform and (**b**) ratio of pulse spread to pulse half-width. The laser pulse broadening of the pulse signal time-domain and the pulse half-width (in ps) after transmission over 200 km is 98, 86, and 74 and 498, 486, and 474, respectively, for the airborne air-to-air channel under visibility conditions (in km) of 5, 20, and 50. The laser pulse time-domain spread to pulse half-width ratios are 20%, 18%, and 15.8%, respectively. The analysis found that the laser beam is less influenced by the multipath effect when it is transmitted in an empty channel with greater visibility (i.e., a smaller number of molecules and particles dispersed in the channel) and that the time-domain spreading of the laser pulse after effective reception at the receiving end is smaller. Simulation of Time-Response Characteristics after Laser Signal Transmission with Different Initial Pulse Widths  
The time-response characteristics of laser signals after transmission with different initial pulse widths are simulated in the paper. The time-response characteristics of the laser pulse signal after transmission over a distance of 200 km corresponding to initial Gaussian pulse half-widths, in ps, of 200, 400, and 800 are shown in Figure 8. The mean and variance in time-domain broadening of laser pulses under different initial pulse half-widths are shown in Table 5.  
Under the conditions in which scattering and turbulence are also considered, the corresponding pulse broadening (received pulse half-width) in ps of laser pulse signals transmitted through the airborne multipath channel with different initial pulse widths of \begin{table}
\begin{tabular}{c c c} \hline \hline
**Atmospheric Visibility (km)** & **Average (ps)** & **Variance (ps\({}^{2}\))** \\ \hline
5 & 99 & 4.67 \\
20 & 87 & 2 \\
50 & 72 & 2.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean and variance in laser pulse time-domain broadening under different atmospheric visibility conditions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Initial Pulse Half Width (ps)** & **Average Percentage (\%)** & **Percentage Variance (\%\({}^{2}\))** \\ \hline
200 & 25 & 1 \\
400 & 15.3 & 0.79 \\
800 & 10 & 0.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean and variance in time-domain broadening of laser pulses under different initial pulse half-widths. Figure 7: Simulation and analysis of time-domain waveforms of effectively received laser pulses under different visibility conditions. (**a**) Simulation results of laser pulse time-domain waveform and (**b**) ratio of pulse spread to pulse half-width. 200, 400, and 800 ps are about 69 (269), 74 (474), and 89 (889). The ratios of the laser pulse time-domain broadening to the pulse half-width are 26%, 15.8%, and 10%, respectively.