## 5 Simulation Results and Analysis
It can be seen from Figure 5 that under different atmospheric turbulence intensities and different channel average signal-to-noise ratios, the system bit error rate decreased with the increase of channel asymmetry parameters. Under the average signal-to-noise ratio of the same channel, the BER performance of the system decreased due to the enhancement of atmospheric turbulence intensity. Under the same atmospheric turbulence intensity, such as the atmospheric refractive index structure constant \(C_{n}^{2}=1.2\times 10^{-14}\), the average signal-to-noise ratio of the channel increased from \(SNR=5\) dB to \(SNR=15\) dB, and the BER performance of the system became better and better, which could drop below \(10^{-8}\). The higher the average signal-to-noise ratio of the channel, the more obvious the BER performance drops. When the atmospheric refractive index structure constants \(C_{n}^{2}=2.8\times 10^{-14}\) and \(C_{n}^{2}=7.2\times 10^{-14}\), the scheme also had the same improvement effect on the cooperative FSO communication system. To sum up, the higher the average signal-to-noise ratio of the channel, the more obvious the decrease of the bit error rate of the system using the layered modulation joint physical-layer network coding scheme, which indicates that the scheme has a better improvement effect on the channel with high signal-to-noise ratio. In order to further obtain the improvement of the BER performance of the cooperative FSO communication system by using the layered modulation joint physical-layer network coding scheme under different atmospheric turbulence intensities, the simulation was carried out (Figure 6). In Figure 6, the atmospheric refractive index structure constants are \(C_{n}^{2}=1.2\times 10^{-14}\), \(C_{n}^{2}=2.8\times 10^{-14}\), and \(C_{n}^{2}=7.2\times 10^{-14}\), respectively, and the simulation was carried out with and without the layered modulation-joint physical-layer network coding scheme. It can be seen from Figure 6 that the higher the atmospheric refractive index structure constant, the stronger the atmospheric turbulence intensity, and the lower the BER performance of the cooperative FSO communication system. Under different refractive index structure constants, the BER performance of cooperative FSO communication system  
Figure 5: Comparison of system BER performance under different channel asymmetric parameters. can be improved by using layered modulation, combined with a physical-layer network coding scheme. When the BER of the system is \(10^{-6}\) and the atmospheric refractive index structure constant \(C_{n}^{2}=1.2\times 10^{-14}\), the BER performance of the system was improved by about 0.5 dB, by using the layered modulation-joint physical-layer network coding scheme; when the bit error rate of the system was \(10^{-6}\) and the atmospheric refractive index structure constant \(C_{n}^{2}=2.8\times 10^{-14}\), the bit error rate performance of the system using the layered modulation-joint physical layer network coding scheme was improved by about 1 dB; when the bit error rate of the system was \(10^{-6}\) and the atmospheric refractive index structure constant \(C_{n}^{2}=7.2\times 10^{-14}\), the bit error rate performance of the system using the layered modulation-joint physical-layer network coding scheme was improved by about 1.5 dB. In the strong atmospheric turbulence channel, the higher the BER performance of the cooperative FSO communication system using this scheme, the more it indicates that this scheme is applicable to the strong atmospheric turbulence channel and has higher anti-interference performance to the strong atmospheric turbulence channel. At the same time, in order to further obtain the effect of hierarchical modulation combined with the physical-layer network coding scheme on the average channel capacity (\(C/B\)) of the system, the average channel capacity under different constellation priority parameters \(\lambda\) was studied in this paper.