## 4 Simulations and Discussion
Figure 6: (**a**) Average BER versus average irradiance received under different types of noise; (**b**) average capacity versus average irradiance received under different types of noise (\(C_{n}^{2}=0.75\times 10^{-14}\) m\({}^{-2/3}\) for moderate turbulence, \(\lambda=850\) nm, \(R_{\text{p}}=0.155\) Gb/s). correlated with several parameters, including temperature \(T_{e}\), received irradiance \(I_{o}\), and symbol transmission rates \(R_{b}\) based on the expression \(\sigma_{T_{e}}^{2}=\frac{4k_{1}T_{e}R_{b}}{RR_{L}I_{o}^{2}}\). The influence of the temperature on the average BER and average capacity are shown in Figure 7a,b, respectively. It can be observed that the average BER increases and the average capacity decreases with an increase in the temperature. Note that the variation tendency slows down during this period. At \(I_{o}=-20\) dBm, the increase in the average BER is 0.5 and the decrease in the average capacity is 0.24 bps when the temperature is increased from 500 to 700 K. However, the average BER increases by 0.25 and the average capacity decreases by 0.74 bps when the temperature is increased from 100 to 300 K. Theoretically, the influence of temperature on the FSO communication system is reasonable, since the structure function, \(C_{n}^{2}\), of the atmospheric turbulence varies when the temperature fluctuates, which results in fluctuation in the refractive index. From a visual point of view, this fluctuation is reflected in the distortion of the picture. Furthermore, the strength of the atmospheric turbulence is represented by the variance in the refractive index fluctuation. As a result, atmospheric turbulence will lead to changes in the BER and capacity. The analytical and MC simulation results coincide which is clearly seen in the figure about average capacity, however, about average BER the results aloof. In addition to the temperature, the symbol transmission rate also affects the variation in the average BER and average channel capacity. Figure 8 shows the performance in terms of the average BER and average capacity with an increase in the average received irradiance under moderate turbulence at different symbol transmission rates. It is clearly seen that average BER analytical results are not in a perfect agreement with the simulation results while average capacity analytical results are in an agreement with simulation results. It is interesting to observe that the trend is almost the same as in Figure 7. For example, at \(R_{b}=0.155\) Gb/s, when the received irradiance increases from \(-30\) to \(-20\) dBm, the average BER decreases from \(5\times 10^{-2}\) to \(1.6\times 10^{-4}\), and the average capacity increases from 1.9 to 5.4 bps. The average BER decreases from \(1.6\times 10^{-4}\) to \(7.9\times 10^{-8}\), and the average capacity increases from 5.4 to 8.1 bps as the received irradiance increases from \(-20\) to \(-10\) dBm. This can be explained based on the expression \(\sigma_{T_{e}}^{2}=\frac{4k_{1}T_{e}R_{b}}{RR_{L}I_{o}^{2}}\), in which the thermal noise is directly correlated with the symbol transmission speed. Figure 7: **(a)** Average BER at different temperatures under the influence of thermal noise; **(b)** average capacity at different temperatures under the influence of thermal noise (\(C_{n}^{2}=0.75\times 10^{-14}\) m\({}^{-2/3}\) for moderate turbulence, \(\lambda=850\) nm, \(R_{b}=0.155\) Gb/s). The average BER versus the average electrical SNR under the BPSK, On-Off Keying (OOK) and Differential Phase Shift Keying (DPSK) modulation schemes for moderate turbulence is shown in Figure 9. Note that the background noise, thermal noise, and quantum noise are considered in this simulation as the total noise. We can conclude that with DPSK and BPSK modulation the analytical and MC simulation results have a good match validating the accuracy of the derived analytical expression for the average BER, while there is a small departure with OOK modulation. The average BER decreases gradually with an increase in the SNR.