## 4 Results and Discussion
For the LP11 mode, the received power is \(-13.81\) dBm, \(-15.82\) dBm, and \(-15.95\) dBm, while for the LP02 mode, the received power values are \(-14.29\) dBm, \(-14.76\) dBm, and \(-16.57\) dBm at the corresponding distances. These results highlight the impact of transmission distance on both SNR and received power, with the performance gradually degrading as the link distance increases. The results indicate that under clear weather conditions, the LP01 mode can extend beyond 14 km, the LP11 mode can reach up to 13 km, and the LP02 mode can transmit up to 12 km, all while maintaining tolerable SNR and maximum received mode power. Additionally, it is observed that the LP11 mode is more susceptible to fading effects compared to both the LP01 and LP02 modes. In summary, while all modes are subject to fading, the specific characteristics of the LP11 mode, its lobular structure, energy distribution, and coupling efficiency render it particularly vulnerable to fading effects, thus distinguishing it from the more stable LP01 and LP02 modes. Figure 9a,b illustrate optimization techniques aimed at enhancing the Q-factor and improving power distribution across mode channels. In Figure 9a, the Q-factor is shown to vary with the bias voltage (V2_22) applied to the second modulator, highlighting the system's sensitivity to performance degradation as this voltage changes. Conversely, Figure 9b demonstrates that power distribution among modes can be equalized to mitigate power penalties, with the received power fluctuating in response to adjustments in the bias voltage of the second LiNbO\({}_{3}\) modulator. Figure 8: (**a**) Transmitter loss against power received per mode; (**b**) the effect of the increase in the transmission distance on signal-to-noise ratio; (**c**) the effect of transmission range on max. power. The Non-Coherent Modified Duobinary Modulation format is utilized. Both figures indicate that optimal performance is achieved at an approximate bias voltage of 3.2 V, where the Q-factor reaches a value of about six. Further analysis underscores the importance of maintaining the bias voltage within this optimal range to ensure consistent signal integrity [29]. Deviations from the 3.2 V threshold lead to a significant decline in the Q-factor, adversely affecting the system's error performance. This situation highlights the necessity for precise control mechanisms within modulation systems to minimize fluctuations caused by environmental or operational factors. Additionally, Figure 9b illustrates the effectiveness of the optimization strategies in achieving a more uniform power distribution across mode channels. By fine-tuning the bias voltage, the system can address discrepancies in power allocation, which is essential for preventing power penalties that could impact overall throughput. The relationship between modulator settings and power distribution emphasizes the delicate balance required to optimize channel performance. The interaction between the Q-factor and power distribution metrics reveals the complex relationship between bias adjustments and performance outcomes, suggesting that a multifaceted approach is necessary for effective system optimization. Future research  
Figure 9: Optimization procedure of (**a**) the Q-factor as a function of bias voltage and (**b**) variation of power shared by modes to a Bias Voltage 2.  
could investigate adaptive bias control techniques that automatically adjust in real time to maintain the Q-factor and power distribution within desired limits, ensuring robust performance under varying operational conditions. The BER for the ASK-FSO, DB NRZ-FSO, MDB RZ-FSO, and MDB NRZ-FSO links is presented in Figure 10, which clearly shows that the DB schemes exhibit similar error performance, with a 0.8 dB error penalty relative to ASK-FSO. Furthermore, as illustrated in Figure 10, the MDB-FSO system based on the NRZ modulation format demonstrates greater resilience to increases in transmission distance.