## 4 Simulation and Discussion  
In this section, we numerically evaluate the closed analytical formula obtained in Section 3 to study the performance of a hybrid RF/FSO system modulated by \(L\)-PPM-BPSKSIM under the coronal turbulence. We mainly consider the communication between Earth and Mars. Therefore, the distance between the Earth and the probe is set as \(L_{sp}=1.5L_{se}\), which is suitable for Mars's orbit during superior solar conjunction, where the distance between the Earth and the Sun is \(L_{se}=1.5\times 10^{8}\) km. For simplicity, the SPE angle and relative solar wind density fluctuation factor are set as fixed values, \(\beta=1.2^{\circ}\), \(\eta=10\%\), respectively. According to the experience of NASA deep space exploration [3; 39], we use a 32 GHz radio frequency and consider the transmission power to be 75 W. In addition, the optical wavelengths of \(\lambda=850\), 1064, and 1550 nm are selected. In this paper, unless otherwise specified, the wavelength is selected at 1550 nm, and other parameters used in the calculation are as follows: SEP angle \(0.3^{\circ}<\alpha<0.5^{\circ}\), spectral index \(p=11/3\), outer scale \(l_{o}=5\times 10^{7}\) m, receiver aperture \(D_{m}=0.1\) m. At the same time, for the convenience of calculation, the average SNR of RF link and FSO link is equal in simulation, i.e., \(\overline{\gamma_{1}}=\overline{\gamma_{2}}=\bar{\gamma}\), and the gain constant at the relay is assumed to be \(C=1\)[40]. Figure 5 describes the simulation results of the relationship between SEP angle and scintillation index at different wavelengths. The results indicate that as the SEP angle increases, the scintillation index also increases. The SEP angle will directly affect the heliocentric distance and the smaller the SEP angle, the closer the communication link to the Sun. Therefore, the link will encounter stronger coronal turbulence and the amplitude fluctuation caused by solar scintillation become more severe. In addition, signals with larger wavelengths are more susceptible to coronal turbulence. This phenomenon is reasonable because the spatial coherence length is proportional to the wavelength. Therefore, a smaller wavelength may be considered as an option to improve the quality of deep-space optical communications. Figure 6 depicts the outage probability performance with the scintillation index given by 0.1, 0.3, and 0.5, respectively. As the scintillation index increases, the outage probability also increases. As the overall range is set within the weak scintillation, the increase is not great. As the scintillation boosting, the outage probability may increase significantly and even lead to complete outage of the system. Additionally, the influence of the pointing error is considered. The pointing error of the system will have different effects on the interruption probability under different turbulence intensities. With the increase of the pointing error parameter \(\bar{\zeta}\), the outage probability has been significantly reduced. For example, when average SNR is 15 dB, \(m^{2}=0.1\), the outage probability of \(\bar{\zeta}=1\) is \(4.798\times 10^{-1}\), while the outage probability of the \(\bar{\zeta}=5\) is \(3.439\times 10^{-1}\). Consistent with our theoretical description, the impact of the pointing error on the system will be smaller as \(\bar{\zeta}\) grows larger. Figure 5: The scintillation index against wavelength under different SEP angles. To observe the effect of coronal turbulence on the average BER performance of pure FSO and hybrid RF/FSO systems, we compare two systems by the same modulation technology (16-PPM-BPSK-SIM). Note that the pure FSO system refers to the use of FSO link from terrestrial to deep space detector, i.e., source-destination (S-D), while the hybrid system refers to source-relay-destination (S-R-D). Figure 7 illustrates average BER versus the average SNR under different scintillation indices.