## 3 Simulations and Results  
We verified the proposed CP-OOK transmission in simulation. The turbulence channel was emulated by modeling the turbulence-induced scintillation effect with the features of low frequency and lognormal distribution, as shown in Figure 4, and this channel modeling is referred to in research from the National Institute of Information and Communications Technology [6; 7; 15; 16; 17]. The performance of CP-OOK detection was analyzed under various parameters of LA and different levels of cascaded LAs. Furthermore, the MLA-based fixed threshold CP-OOK detection was compared to the CP-OOK with ATD, CP-OOK with FTD, and non-polarized OOK (NP-OOK) with ATD. LA with an ideal amplitude-frequency characteristic and without noises was discussed in the simulation: i.e., the signal distortion from LA was ignored. The data rate was configured into 1 Gb/s. Figure 5 depicts the bit error rate (BER) performance of CP-OOK detection by FTD with a single LA at \(\sigma_{I}^{2}\) of 0.05 and 0.25. A single LA with a base of 2 was used to evaluate the turbulence effect mitigation, and CP-OOK signal ER distortion under different b values. In Figure 5a, initially, the turbulence effect was effectively compensated by nonlinear gains from the LA with low b values. An LA with a larger b value has a higher gain nonlinearity, which can more effectively mitigate the turbulence effect. However, BERs were decreased with the increase of b values due to a serious side effect of CP-OOK signal ER distortion under a high gain nonlinearity of LA. In addition, a single LA with various b values is ineffective as a turbulence channel at \(\sigma_{I}^{2}\) of 0.25, as shown in Figure 5a. This is because the compensation of a higher level turbulence effect requires a high gain in the nonlinearity of the LA, and this high gain nonlinearity causes a significant ER degradation of the CP-OOK signal. Therefore, the b value of LA is set to a low value in order to reduce the ER distortion issue from the high gain nonlinearity of LA during the turbulence effect compensation. Figure 4: Modeled turbulence channel. (**a**) Frequency spectrum, (**b**) Probability distribution. Figure 3: Turbulence caused signal intensity variation. Figure 6 shows the BER performance of CP-OOK detection using FTD with a single LA under various values of a. The b value of LA was set to 1.1 for the sake of the ER distortion reduction. The LA with a base of e (natural logarithm) and 10 (common logarithm) were compared to the LA with a base of 2. In Figure 6a, a similar performance was observed for CP-OOK detection using a single LA with FTD under various base values of the LA at \(\sigma_{l}^{2}\) of 0.05 due to the low intensity variation of turbulence channel. In addition, it has a better BER performance compared to CP-OOK detection with FTD under various average SNRs by reason of the turbulence effect reduction with nonlinear gains from the LA. However, a poor BER performance was obtained compared with CP-OOK detection with ATD due to the ER distortion from the LA. Besides, initially, it performs better than NP-OOK detection with ATD at the lower SNR conditions because of the non-polarized background noise reduction. Nonetheless, a poorer BER is obtained at the higher SNR conditions due to the ER distortion effect. CP-OOK detection with ATD has an improved BER performance compared to NP-OOK detection with ATD due to the filtering of non-polarized background noise. Figure 6b shows the CP-OOK detection using a single LA with FTD at \(\sigma_{l}^{2}\) of 0.25. The FTD method is ineffective with the assistance of a single LA under a higher turbulence effect due to a serious ER distortion of CP-OOK from the LA. Therefore, multi-level LAs are required to improve the performance of CP-OOK detection. Figure 7 shows the BER performance of CP-OOK detection using FTD under different levels of MLAs at \(\sigma_{l}^{2}\) of 0.05. Figure 7a illustrates MLAs-based CP-OOK FTD detection under LA with a base of 2.