## 4 System Algorithm Simulation Furthermore, Analysis
Conversely, the LO is out of control at 30 krad/s under the \(3^{\circ}\) step due to weak control ability. Figure 9 shows that the \(4^{\circ}\) step offers the best overall performance in terms of the worst-BER. Therefore, we selected a step of \(4^{\circ}\) for the GLD algorithm. The fluctuation of a fully controlled normalized signal will not exceed \(-0.348\) dB. Therefore, when the normalized feedback signal exceeds \(-0.348\) dB, a larger step size is selected in variable-step GLD algorithms for tracking. Additionally, we chose a \(2^{\circ}\) step and a \(5^{\circ}\) step for the variable-step GLD algorithm to ensure both control accuracy and control ability. Similarly, in the MZI structure, the GLD algorithm uses a step of \(5^{\circ}\), and the steps of the variable-step GLD algorithm vary between \(4^{\circ}\) and \(8^{\circ}\), respectively. We also give the tracking process of the MZI structure employing the GD algorithm, GLD algorithm, and variable-step GLD algorithm under 18 krad/s. The azimuth of scrambled LO and the phase changes of the phase shifter under three algorithms are visual in Figure 10. Figure 11 accordingly expresses the tracking process of the feedback signal with these algorithms. From these figures, it is evident that the phase of MZI varies with the azimuth of input LO as in Equation (12), and the feedback signal remains stable. When the azimuth of LO changes rapidly, the variable phase cannot keep up with it. Furthermore, the updating direction is misjudged, leading to the bumpy of the feedback signal. The above situation is more probable to happen with GD and GLD algorithms. It can be seen that the feedback signal controlled by the variable-step GLD algorithm experiences the smallest bumpy, and the angle of the feedback signal tracks LO with higher accuracy. This observation suggests that the variable-step GLD algorithm exhibits the best tracking ability among the three algorithms. Figure 9: The worst\(-\)BER versus RSOP with different steps. Figure 12 presents the measured worst-BER under different RSOP in different algorithms of HWP polarization control structure. The BER threshold before 7% overhead hard-decision forward error correction (HD-FEC) is used. As shown in the figure, the GD algorithm and GLD algorithm can control RSOP up to 30 krad/s, while the variable-step GLD algorithm can control the RSOP up to 50 krad/s under the pre-FEC BER threshold. Compared with the first two algorithms, the variable-step GLD algorithm effectively improves the tracking speed. It should be noted that phase drift and power fluctuations may slightly affect the tracking results. Figure 11: Feedback signal tracking process under different algorithms. Figure 10: Angle tracking process under different algorithms. Figure 13 displays the schematic diagram of the Poincare sphere and feedback signal normalized amplitude after the scrambled and controlled LO of the variable-step GLD algorithm under the HWP structure at different RSOP. As the RSOP increases, the azimuth of input LO near the pole changes faster than other areas of the Poincare sphere, resulting in the HWP or phase update rate fail to keep up with the azimuth angle change, and the feedback signal is more likely to fall into an uncontrolled area. The situation that the PC output LO is away from \(S_{1}=0\) will exacerbate on the pole of the Poincare sphere. In order to accurately analyze the effectiveness of the polarization tracking scheme in the optical fiber transmission scenario, the 28G baud, 16 QAM standard single-mode fiber (SSMF) transmission system is established. The transmission length of the fiber is 40 km, and its loss is \(0.2\times 10^{-3}\) dB/m. The dispersion and polarization mode dispersion (PMD) coefficients of the fiber are \(16\times 10^{-6}\) ps/nm and \(0.1\times 10^{-12}/31.62\) s/\(\sqrt{\text{m}}\), respectively.