## 4 Simulations and Discussion
We can see that the analytical results provide a perfect match to the simulation results on average capacity, while considering average BER there is a deviation. On the other hand, for quantum noise, background noise, thermal noise and total noise, the average BER decreases and the average capacity increases with an increase in the average irradiance received. The influence of the thermal noise on the average BER and average capacity is dominant. For instance, for \(I_{o}=-20\) dBm, the average BER for the total noise is \(2.5\times 10^{-7}\) and the average capacity is 10.5 bps. When only thermal noise is considered, the average BER is \(2\times 10^{-7}\) and the average capacity is 10.4 bps, while with only background noise,  
Figure 4: (**a**) Average BER versus link distance for different wavelengths; (**b**) average capacity versus link distance for different wavelengths (\(C_{n}^{2}=0.75\times 10^{-14}\) m\({}^{-2/3}\) for moderate turbulence, \(T_{e}=300\) K, \(R_{b}=0.155\) Gb/s). Figure 5: (**a**) Average BER versus average irradiance received under different types of noise; (**b**) average capacity versus average irradiance received under different types of noise (\(C_{n}^{2}=0.35\times 10^{-14}\) m\({}^{-2/3}\) for weak turbulence, \(\lambda=850\) nm, \(R_{b}=0.155\) Gb/s). the average BER and average capacity are only \(10^{-13}\) and \(14.7\) bps. Note that the same results can also be obtained in [28], which further certifies our theoretical derivation based on [30]. Besides, the impact of quantum noise is minimal; for example, the average BER and average capacity are only \(7.9\times 10^{-19}\) and \(17.2\) bps when quantum noise is considered. Similar to the analysis of Figure 5, by substituting the expressions of different noises into Equations (16) and (19), the average BER and average channel capacity under moderate turbulence are demonstrated in Figure 6a,b, respectively. Note that the trends and the accuracy between analytical and MC simulation results in these graphs agree with those in Figure 5a,b. The specific values of the average BER and average channel capacity for the FSO communication system under different levels of channel turbulence and various types of noise at \(I_{o}=-20\) dBm are shown in Table 2. It is clear that the average capacity under weak turbulence is about twice that under a moderate regime, and the average BER is far lower than that under a moderate regime, when various types of noise are considered. For example, when only background noise is considered, the average BER and average capacity are \(9.5\times 10^{-14}\) and \(14.72\) bps under weak turbulence, respectively, while under moderate turbulence, the average BER and average capacity are \(1.4\times 10^{-6}\) and \(7.22\) bps. As analyzed above, the thermal noise has a more obvious influence on the average BER and average channel capacity than the background noise and the quantum noise. Therefore, only the influence of the thermal noise on the system performance, including the average BER and average capacity, is further studied. Note that the thermal noise is \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Turbulence** & **Performance** & **Thermal Noise** & **Background Noise** & **Quantum Noise** & **Total Noise** \\ \hline \multirow{4}{*}{Weak} & Average & \(2\times 10^{-7}\) & \(9.5\times 10^{-14}\) & \(8.5\times 10^{-19}\) & \(2.5\times 10^{-7}\) \\  & BER & & & & \\ \cline{1-1}  & Average & & & & \\ \cline{1-1}  & capacity & & & & \\ \cline{1-1}  & (bps) & & & & \\ \cline{1-1}  & Average & & & & \\ \cline{1-1}  & BER & & & & \\ \cline{1-1}  & Average & & & & \\ \cline{1-1}  & capacity & & & & \\ \cline{1-1}  & (bps) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average BER and average channel capacity of an FSO communication system under weak and moderate turbulence conditions with various types of noise (\(I_{o}=-20\) dBm).