## 3 Simulations and Results
Initially, BERs were improved with the growth of MLAs levels due to a more effective turbulence effect mitigation, and it has a better BER performance  
Figure 5: BER performance of CP-OOK detection using FTD with single LA under various b values. (a) \(\sigma_{l}^{2}\) of 0.05, (b) \(\sigma_{l}^{2}\) of 0.25. Figure 6: Comparison of CP-OOK detection using FTD with single LA under various a values and SNRs. (a) \(\sigma_{l}^{2}\) of 0.05, (b) \(\sigma_{l}^{2}\) of 0.25. CP-OOK-FTD: CP-OOK detection using FTD, CP-OOK-ATD: CP-OOK detection using ATD, CP-OOK-Base-2: CP-OOK detection using LA with a base of e, CP-OOK-Base-10: CP-OOK detection using LA with a base of 10, NP-OOK-ATD: NP-OOK detection using ATD. than CP-OOK with ATD in the case of four and six levels of MLAs on account of turbulence effect reduction. However, BERs were decreased as to adopting eight and ten levels of MLAs due to the ER degradation of CP-OOK signal from excessive nonlinear gains. With regard to MLAs with a base of e, BERs were enhanced with the increasing of MLAs levels, as shown in Figure 7b. Besides, four, six, eight, and ten levels of MLAs with a base of e-based CP-OOK detection have better BER performance compared to that of MLAs with a base of two because of a more effective turbulence effect compensation. In Figure 7c, a poor BER performance was observed for four, six, eight, and ten levels of MLAs with a base of ten-based CP-OOK detection due to high nonlinearity-induced ER degradation issues. Thus, the CP-OOK signal was effectively detected by MLAs with a of two, and e and n of four and six under \(\sigma_{l}^{2}\) of 0.05. In Figure 8, the proposed technique was discussed in case of a stronger turbulence effect under \(\sigma_{l}^{2}\) of 0.25. The performance of MLAs-based CP-OOK detection was evaluated under different values of a, b, and n as well. Figure 8 shows that the CP-OOK signal was effectively detected by MLAs with a of two and n of six under \(\sigma_{l}^{2}\) of 0.25 since a larger intensity variation can cause a serious ER distortion from MLAs. Therefore, a stronger turbulence effect can be compensated by the MLAs-based CP-OOK detection with lower values of a. Therefore, the turbulence effect was effectively compensated via MLAs-based CP-OOK detection in the case of MLAs optimization. In this work, the proposed technique was evaluated under an ideal LA. However, the signal distortion from bandwidth limitation and amplified noises will limit the available levels of logarithmic amplification. Furthermore, as the parameters of MLAs are determined by the degree of intensity fluctuation, the average power of the received signal, and the gain curve of the LA, comprehensive training is required to determine the parameters of MLA in practical implementations. Figure 7: Comparison of CP-OOK detection using FTD under different levels of MLAs and SNRs at \(\sigma_{l}^{2}\) of 0.05. (a) a = 2, (b) a = e, (c) a = 10. CP-OOK-n = 2: CP-OOK detection using 2-level of MLAs, CP-OOK-n = 4: CP-OOK detection using 4-level of MLAs, CP-OOK-n = 6: CP-OOK detection using 6-level of MLAs, CP-OOK-n = 8: CP-OOK detection using 8-level of MLAs, CP-OOK-n = 10: CP-OOK detection using 10-level of MLAs.