## 4 Simulations and Discussion
Note that the log irradiance variance \(\sigma_{x}^{2}\) is thereby related to the average BER and average capacity which have been expressed as Equations (11) and (12). \begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Description** & **Value (Unit)** \\ \hline \(R\) & Photodetector responsivity & 1 \\ \(R_{L}\) & Receiver circuit load resistance & 50 (\(\Omega\)) \\ \(T_{e}\) & Temperature & 300 (K) \\ \(q\) & Elementary charge & \(1.602\times 10^{-19}\) (C) \\ \(k_{1}\) & Boltzmann constant & \(1.38\times 10^{-23}\) (J/K) \\ \(R_{b}\) & Symbol rate & \(1.55\times 10^{8}\) (bps) \\ \(B\) & Bandwidth & \(10^{-3}\) (bit/s) \\ \(I_{bg}\) & Background radiation irradiance & \(\dfrac{4}{\pi}\times 0.6^{2}\times 10^{-6}\)+ \(5.5\times 10^{-5}\) (A) \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters used in the simulations. The average BER becomes smaller with an increase in the wavelength, while the average capacity becomes higher during this period. Note that the average capacity decreases suddenly while that of the average BER becomes slow when the link distance is very large. For instance, for \(\lambda\) = 850 nm, the average BER increases from \(4.3\times 10^{-7}\) to \(10^{-4}\) when the link distance is increased from 3 to 4 km, and the average capacity decreases from 16.1 to 15.0 bps. However, the average BER increases from \(2.7\times 10^{-2}\) to \(6.3\times 10^{-2}\), and average capacity decreases from 8.9 to 7.4 bps when the link distance is increased from 7 to 8 km. Based on Equations (16) and (19), the effects of the wavelength and the link distance on the average BER and average channel capacity under moderate turbulence are presented in Figure 4a,b. The link distance \(L\) is directly correlated with the log irradiance variance \(\sigma_{x}^{2}\), and further results in the variation of the effective turbulence numbers at small scales \(\alpha\) and large scales \(\beta\) in Equation (6). Note that the \(\alpha\) and \(\beta\) are thereby related to the average BER and average capacity which have been expressed as Equations (16) and (19). The wavelengths are 850, 1050 and 1250 nm, respectively, and the overall trend of the change agrees with that shown in Figure 3a,b, although the average BER under moderate turbulence is larger than that under weak turbulence, and the corresponding channel capacity is about three times smaller than for weak turbulence. Besides, the analytical and MC simulation results have an exact match to validate the accuracy. Figure 3: (**a**) Average BER versus link distance for different wavelengths; (**b**) average capacity versus link distance for different wavelengths (\(C_{n}^{2}=0.35\times 10^{-14}\) m\({}^{-2/3}\) for weak turbulence, \(T_{e}=300\) K, \(R_{b}=0.155\) Gb/s). Figure 2: (**a**) Average BER versus normalized SNR for different structure constants; (**b**) average capacity versus normalized SNR for different structure constants (\(\lambda=850\) nm, \(T_{e}=300\) K, \(R_{b}=0.155\) Gb/s). As shown in Figure 5a,b, different types of noise result in significant effects on the average BER and average channel capacity under weak turbulence. We first insert different noises, including total noise, background noise, thermal noise, and quantum noise, which can be expressed as \(\sigma_{bg}^{2}+\sigma_{T_{e}}^{2}+\sigma_{Quantum}^{2}\), \(\sigma_{bg}^{2}\), \(\sigma_{T_{e}}^{2}\), \(\sigma_{Quantum}^{2}\), into normalized SNR \(\gamma\), as \(\gamma=\dfrac{R^{2}A^{2}}{\sigma^{2}}\). Then, substituting \(\gamma\) into Equations (11) and (12), the average BER and average channel capacity are depicted in Figure 5a,b. Note that the above-mentioned forms of noise can also be expressed as, \(\sigma_{bg}^{2}=\dfrac{2 qI_{bg}R_{b}}{RI_{0}^{2}}\), \(\sigma_{T_{e}}^{2}=\dfrac{4k_{1}T_{e}R_{b}}{RR_{L}I_{0}^{2}}\), \(\sigma_{Quantum}^{2}=\dfrac{2 qR_{b}}{RI_{0}}\). According to the expressions of various noises, we aim to discuss the influence of average irradiance received \(I_{o}\).