## 2 System Model  
The relay network model based on collaborative FSO communication used in this article is shown in Figure 1, where the four source nodes \(S_{1}\), \(S_{2}\), \(S_{3}\), and \(S_{4}\), with the assistance of the relay node, exchange information with each other. Information is exchanged with each other with the assistance of relay nodes, and all nodes use the half-duplex working mode between them. FSO communication is used between all nodes, and the two source nodes on the diagonal need to exchange information through relay nodes and neighboring source nodes. Due to the increase in atmospheric turbulence intensity caused by the increase in communication distance, the channel condition of the relay channel in the system is better than the channel condition of the direct-pass link between the two adjacent user nodes, which leads to the asymmetric problem of the system. The asymmetric problem will degrade the bit error rate performance of the system, assuming that there is an asymmetric problem between the source nodes \(S_{1}\), \(S_{2}\) and the relay node \(R\). If the collaboration system formed between \(S_{1}\), \(S_{2}\), and \(R\) uses low-order modulation, then the good channel conditions from \(S_{1}\) to \(R\) and \(R\) to \(S_{2}\) will not be fully utilized, resulting in a waste of channel conditions; if the high-order modulation method is used, the direct-pass link between \(S_{1}\) and \(S_{2}\) cannot withstand this high-order modulation method, which will lead to the reliability of the receiving data not being guaranteed, resulting in a decrease in system performance.  
Figure 1: Relay network model with asymmetric channel conditions.  
In the Figure 1 system, FSO communication was used between all nodes, and the communication link obeyed the Gamma-Gamma distribution model. The light intensity distribution of the GG channel model was related to the size scale vortex, the irradiance of the size scale of the light intensity was in line with the gamma distribution, and the probability density functions of the light intensity received by the GG channel model were as follows [14]:  
\[f(h)=\frac{2(\alpha\beta)^{(\alpha+\beta)/2}}{\Gamma(\alpha)\Gamma(\beta)}h^{( \frac{\alpha+\beta}{2})-1}K_{\alpha-\beta}\left(2\sqrt{\alpha\beta h}\right) \tag{1}\]  
In Equation (1), \(h\) is the channel state information of the communication link, \(K_{\alpha-\beta}\) represents the modified second-class Bezier function, and \(\Gamma(\cdot)\) is the gamma function. \(\alpha\) and \(\beta\) represent the effective number of large- and small-scale vortices, respectively, and can be represented by Equations (2) and (3) below:  
\[\alpha=\left[\exp\left(\frac{0.49\sigma_{l}^{2}}{\left(1+1.11\sigma_{l}^{12/5 }\right)^{7/6}}-1\right)\right]^{-1} \tag{2}\]  
\[\beta=\left[\exp\left(\frac{0.51\sigma_{l}^{2}}{\left(1+0.69\sigma_{l}^{12/5 }\right)^{5/6}}-1\right)\right]^{-1} \tag{3}\]  
In the above equation, the Rytov variance is represented and can be defined as:  
\[\sigma_{l}^{2}=1.23C_{n}^{2}K^{7/6}L^{11/6} \tag{4}\]  
where \(C_{n}^{2}\) is the atmospheric refractive index structure constant, \(k=2\pi/\lambda\) is the number of light waves, \(\lambda\) is the laser wavelength, and \(L\) is the transmission distance of the link.