## 1 Introduction  
In the past ten years, the hybrid radio frequency-free space optical (RF-FSO) communication system has attracted great interest due to its advantages compared with FSO system and RF system, respectively. RF system has the advantage of being insensitive to atmospheric turbulence, but the spectrum resource it requires is in shortage. On the contrary, features of the FSO system include license-free transmission, cost-effectiveness, and high security, which meet the demands of modern optical communication, but its communication quality is easily disturbed by the atmosphere [1; 2]. The hybrid RF-FSO system could combine the advantages of the RF system and the FSO system [3]. Inevitably, dynamic weather and complex environment still affect the performance of hybrid RF-FSO system. Therefore, not only should a suitable channel model be chosen for hybrid RF-FSO system but also appropriate modulations could be adopted to improve the performance of the hybrid RF-FSO system. Considering impacts of atmosphere including turbulence, pointing error, and pass fading, many channel models have been used to describe the hybrid RF-FSO system. Such as Nakagami-m/Gamma-Gamma distribution [4], Rayleigh distribution and M-distributed distribution [5], \(\kappa-\mu/\eta-\mu\)distribution and Gamma-Gamma distribution [6], and the Nakagami-m/Exponentiated Weibull (EW) distribution [7]. However, many studies adopted Rayleigh/Gamma-Gamma distribution [8; 9; 10], because the Gamma-Gamma distribution has a good simulation for the atmospheric turbulence from weak to strong of the FSO link, and Rayleigh distribution is close to the condition of the RF channel. As a result, we adopted Rayleigh distribution for the RF link and Gamma-Gamma distribution for the FSO link. On the other hand, many previous researchers have focused on using different modulations to improve the mixed RF-FSO systematic performance for the modulation has a direct relationship with bit error rate (BER), which is a significant indicator to evaluate system performance. In reference [11; 12], various pulse position modulation (PPM), binary phase shift keying (BPSK), and hybrid pulse position modulation-binary phase shift keying-subcarrier intensity modulation (PPM-BPSK-SIM) schemes have been analyzed on the performance over FSO link, the conclusion is that hybrid PPM-BPSK-SIM outperformed BPSK in single FSO link. In literature about the hybrid RF-FSO system [13; 14], most of them adopted various binary modulation when it refers to the average bit error rate, BPSK is the most discussed as the binary modulation for it has the lowest bit error rate. In reference [4], authors investigated various PSK modulation and various quadrature amplitude modulation (QAM) in hybrid RF-FSO system. Unlike the FSO system [15], there are few studies on how to improve the hybrid RF-FSO system performance by adopting hybrid modulation, especially for the research of PPM-BPSK-SIM. Motivated by the aforementioned studies, we investigated end-to-end performance of hybrid RF-FSO system with application of hybrid PPM-BPSK-SIM. The RF link follows Rayleigh distribution, the FSO link obeys Gamma-Gamma distribution, not only atmospheric turbulence but also pointing error is taken into consideration, and the system adopts various hybrid PPM-BPSK-SIM, the receiver employs intensity modulation/direct detection (IM/DD). The unconditional bit error rate (BER) of the PPM-BPSK-SIM is derived, it is noteworthy that the application of hybrid PPM-BPSK-SIM does bring optimization to the hybrid RF-FSO system performance from simulation results. The impact of pointing error on systematic performance is also discussed in detail. The content of the article is arranged as follows. Specific information of the hybrid RF-FSO system and the channel model is described in Section 2. We derived the outage probability, the unconditional BER, and average channel capacity of the hybrid system in Section 3. The simulation is realized by MATLAB, and the results and discussion are shown in Section 4.