## 4 Simulations and Discussion  
In this section, the effects of the system parameters and channel parameters on the performance of the FSO communication system are analyzed. The relevant parameters used for the simulation are shown in Table 1. Note that the value of background radiation \(I_{bg}\) in Table 1 is considered, including sky irradiation and Sun irradiation with a wavelength of 850 nm and an optical filter bandwidth of \(10^{-3}\) um, which are selected from [13; 28]. The results of the simulations for both the average BER and the average channel capacity of the FSO communication system are given below. Meanwhile, the accuracy of the analytical expressions is corroborated by Monte Carlo (MC) simulations using over \(10^{6}\) independent runs. The simulation and analytical results of the system performance in terms of the average BER and average channel capacity, as influenced by the structure constant and average electrical SNR, is shown in Figure 2a,b, respectively. Note that the average BER in Figure 2a is based on Equations (11) and (16) for the case of both weak turbulence and moderate-to-strong turbulence, while the average capacity in Figure 2b is based on Equations (12) and (19). Note that similar simulation also has been conducted in [13; 28] but without considering the effect of the total noise. To fill this gap, the total noise, which is comprised by the background noise, thermal noise, and quantum noise as shown in (2), is considered in the following simulation unless otherwise specified. The accuracy of the derived analytical channel model which depends on average electrical SNR can be observed. The structure constants were \(0.35\times 10^{-14}\), \(0.75\times 10^{-14}\) and \(1.15\times 10^{-14}\) m\({}^{-2/3}\), corresponding to weak, moderate and strong turbulence, respectively. The transmission channel under weak turbulence was simulated using a lognormal model, while the Gamma-Gamma model was used to describe the transmission channel under moderate-to-strong turbulence. With an increase in the average electrical SNR, a lower average BER and higher average capacity can be achieved. For a larger structure constant representing a stronger turbulence regime, the average BER is higher and the average capacity is smaller. This phenomenon can be explained by the fact that the strength of the atmospheric turbulence is directly determined by the structure constant. The Rytov variance for the propagation of an optical wave in atmospheric turbulence becomes larger with an increase in the structure constant, and finally results in larger average BER and smaller average channel capacity for the PSO communication system. These effects change slowly with an increase in the turbulence condition. For instance, the average BER decreases from \(2.5\times 10^{-3}\) to \(5\times 10^{-6}\) under weak turbulence, and the average capacity increases from 3.2 to 6.3 bps when the SNR is increased from 20 to 30 dB. However, the average BER decreases from \(1.6\times 10^{-2}\) to \(1.6\times 10^{-3}\) and average capacity increases from 1.3 to 2.9 bps under strong turbulence. Figure 3a,b demonstrate the effects of wavelength and link distance on the average BER and average channel capacity, respectively, under weak turbulence, for wavelengths of 850, 1050 and 1250 nm. Note that the average BER and average channel capacity in Figure 3a,b, respectively, are based on Equations (11) and (12) for the case of weak turbulence. It can be observed that the analytical and MC simulation results have a small deviation but can also validate the accuracy of the derived analytical expression for the average BER and average capacity. With an increase in the link distance \(L\), the average BER increases and the average capacity decreases. This can be explained that based on the expression \(\sigma_{x}^{2}=1.23C_{x}^{2}k^{\frac{7}{6}}L^{\frac{11}{6}}\), in which the link distance \(L\) is directly correlated with the log irradiance variance \(\sigma_{x}^{2}\).