## 4 Results and Discussion
the bandwidth efficiency, which leads to an optimization of system performance for a reduction of average BER. Furthermore, the performance of the mixed modulation is affected by both modulations. Therefore, the value of L has a significant effect on the BER performance of hybrid system, the BER decreases as L increases, and the hybrid RF-FSO system achieves better BER performance by using the hybrid PPM-BPSK-SIM scheme only if the length of symbol, L, is greater than eight. Figure 4: Average BER of L-ary pulse position modulation (LPPM) and BPSK against average SNR per hop under strong turbulence and the pointing error parameter is \(\xi=1\). Turbulence parameters are \(\alpha=4.2\) and \(\beta=1.4\), the constant is assumed to be \(C=1\). Figure 5: Average BER of L-ary pulse position modulation–binary phase shift keying–subcarrier intensity modulation (LPPM–BPSK–SIM) and BPSK against average SNR per hop under strong turbulence and the pointing error parameter is \(\xi=1\). Turbulence parameters are \(\alpha=4.2\) and \(\beta=1.4\), the constant is assumed to be \(C=1\). In Figure 7, the average BERs of LPPM-BPSK-SIM, LPPM, and BPSK in the hybrid RF-FSO system are presented under the same channel condition in Figure 4, we conducted studies about \(L=16\) and \(L=64\). It can be observed that when average SNR is fixed, the average BER of hybrid PPM-BPSK-SIM is higher than that of LPPM, and both of them outperform BPSK. For instance, when SNR = 25 dB, the average BER decreases in the order of BPSK, 16 PPM-BPSK-SIM, 16 PPM, 64 PPM-BPSK-SIM, 64 PPM. From another perspective, to achieve a BER of 10-3, 28 dB of SNR is required for 64 PPM-BPSK-SIM and 32 dB is needed for 16 PPM-BPSK-SIM, 33.5 dB is needed for BPSK. It can be noticed that the value of L has a great influence on the average BER of the system when using hybrid modulation, and the larger L, the lower the average BER. Considering the power efficiency and average BER of the hybrid modulation, we have conducted further research on the performance of 16 PPM-BPSK-SIM. Figure 6: Average BER of LPPM–BPSK–SIM and BPSK against average SNR per hop under moderate turbulence and the pointing error parameter is \(\xi=1\). Turbulence parameters are \(\alpha=4.0\) and \(\beta=1.9\). Figure 7: Average BER of hybrid modulation, LPPM, and BPSK against average SNR per hop under strong turbulence and the pointing error parameter is \(\xi=1\). Turbulence parameters are \(\alpha=4.2\) and \(\beta=1.4\), the constant is assumed to be \(C=1\). In Figure 8, simulations of 16 PPM-BPSK-SIM under different turbulence strength and different pointing error conditions have been implemented. What can be observed easily is that pointing error has a significant influence on the average BER of the hybrid system, the average BER increases as the value of \(\xi\) decreases. For example, regardless of the intensity of turbulence, the system with \(\xi=5\) outperforms the system with \(\xi=1\). On the other hand, when \(\xi\) is a fixed value, the average BER increases as the intensity of the turbulence increases, which is in line with our theoretical analysis. However, under moderate and weak turbulence with \(\xi=5\), the average BER of the system suddenly drops and appears to be undulating. After that, we changed the value of L and found that this condition still existed, this phenomenon indicates that the RF-FSO systematic performance is unstable. The adoption of hybrid PPM-BPSK-SIM has a stable improvement on average BER performance, especially under conditions with strong turbulence and severe pointing error. In Figure 9, hybrid RF-FSO systematic average channel capacity against average SNR per hop is depicted with various turbulence intensities and different parameters of pointing error. As shown in Figure 9a, the average capacity of the system decreases with the increase of turbulence intensity regardless of the pointing error. When atmospheric turbulence strength is fixed, the larger the pointing error parameter is, the larger the system capacity will be.