## 4 System Algorithm Simulation Furthermore, Analysis  
According to the control theories and control algorithms discussed above, a simulation system shown in Figure 7 is fabricated based on the Simulink platform. Figure 6: Flow of the variable-step greedy algorithm. Figure 7: Structure of the simulated system. The LO and modulated signal originate from the same laser. The light is split into two branches by a splitter and then one is modulated into a 28 Gbaud, 16 QAM signal for transmission, and the other is transmitted as an LO. The polarization scrambler (PS) is used to simulate the impact of the random polarization disturbance caused by the optical fiber link on LO. The composition of PS consists of three QWPs, one HWP, and three QWPs [24]. The rotation rate of the HWP represents the RSOP of LO. The sampling rate and main frequency clock of the DSP module are 65 MHz and 250 MHz, respectively. The control algorithm takes about 15 cycles of the main frequency, mainly depending on the number of operations. Meanwhile, the waiting loop delay is set to around 80 cycles of the main frequency considering the response of DA, AD, and photoelectric devices. Before the receiver, LO scrambled by the PS is controlled using a PC based on HWP or MZI to produce two output lights with orthogonal polarization states and equal power. The insertion losses of HWP and MZI are set to 2.5 dB and 1 dB, respectively. After PC, the output LO together with modulated optical signal injects into the coherent receiver. Note that the system structure does not consider the transmission mismatch length of the two optical signals. Table 2 gives some simulation parameters. The laser generates light with a linear SOP, and arbitrary SOP change of the LO which has random power attenuation can be obtained after PS. Since LO and the modulated signal originate from the same laser, frequency offset compensation is not required in the DSP process, and the process of phase recovery can also be simplified. The power of these two output lights is equal, but the phase error between the controlled LO and signal changes slowly. Figure 8 shows the constellation plots for RSOP of 10 krad/s and 100 krad/s without carrier phase recovery (CPR), both under the condition that the LO is fully controlled to \(S_{1}=0\). It can be seen that the change rate of phase error increases with the increase in RSOP. To compensate for the tight phase error, we use simplified blind phase search (BPS) for CPR. It uses a fixed phase for phase compensation within a certain period of time. The fixed phase is updated periodically. Considering the mismatch length, the phase error can be compensated together with the phase error caused by the mismatch length. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Modulation format & 16 QAM \\ Polarization & Dual-polarization \\ Baudrate & 28 Gbaud \\ Laser power & 13.8 dBm \\ Laser linewidth & 1 MHz \\ Responsivity of PD & 0.65 \\ Dark current of PD & 10 nA \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Key parameters of PC system simulation. Figure 8: Constellation without CPR under different RSOP (**a**) 10 krad/s (**b**) 100 krad/s. In the case where the feedback signal is not fully controlled, the normalized amplitude of the feedback signal will appear bumpy. To characterize the worst-case communication quality, we measured the bit error rate (BER) at the largest bump, which is called the worst-BER in this paper. Figure 9 shows the worst-BER of the GLD algorithm with different steps in case of different RSOP under the PC based on HWP. In the step variation range of \(2^{\circ}\)-\(5^{\circ}\), a smaller step corresponds to higher control accuracy but weaker control ability, correspondingly a larger step corresponds to poorer control accuracy but stronger control ability. As depicted in Figure 9, even when the feedback signal is fully controlled within the 5 krad/s-50 krad/s range, the worst-BER remains high under the \(5^{\circ}\) step due to poor control precision.