## 4 Results and Discussion
### Influence of PMD, OSNR, and Nonlinear Effect on the CD Estimation Method  
In order to explore the influence of PMD on the proposed CD estimation method, the range of PMD is changed from 0 to 40 ps by setting the PMD simulator, and the step size of each change is 5 ps. We estimate the CD of the PM-QPSK and PM-16 QAM signals in the range of fiber length from 200 km to 2000 km (step length of 200 km), and their working OSNRs are 20 dB and 25 dB, respectively. Through simulation calculation, the error results of CD estimation of the two types of signals are shown in Figure 10. It can be seen from the figure that in the case of PMD change, although the error rate of the mean and maximum of the estimation error fluctuates, it will not be significantly affected, and the average error value of the two types of signals maintains a stable trend, while the maximum error value is within the range of (\(-\)100, 150) ps/nm, which proves that the proposed CD estimation method has a good tolerance to PMD. In order to measure the resistance of the CD estimation method to OSNR, we calculate the CD estimation results of the PM-QPSK and PM-16 QAM signals while keeping other parameters unchanged and only changing OSNR (12 dB to 30 dB, step size 3 dB), as shown in Figure 11. As shown in the figure, when the OSNR is reduced, that is, the ASE noise is increased, the variation trend of the average and maximum error rate of the two types of signals is not obvious and fluctuates in a limited range. The variation trend of the average error value is also flat, and the maximum error value fluctuates in the range of (\(-\)150, 100) ps/nm. It is proved that the proposed CD estimation method can effectively resist the ASE noise generated in the optical fiber link. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Sampling** & \multicolumn{3}{c}{**0.001**} & \multicolumn{3}{c}{**0.0001**} & \multicolumn{3}{c}{**0.00001**} \\ \hline
**Point** & \(M_{CD}\) & \(\delta_{CD}\) & \(R_{CD}\) & \(M_{CD}\) & \(\delta_{CD}\) & \(R_{CD}\) & \(M_{CD}\) & \(\delta_{CD}\) & \(R_{CD}\) \\ \hline \multicolumn{10}{c}{PM-QPSK Signal} \\
2048 & 122.8 & 182.2 & (\(-\)709,457) & 83.1 & 127.1 & (\(-\)502,418) & 84.8 & 123.9 & (\(-\)461,437) \\
4096 & 67.2 & 99.6 & (\(-\)260,372) & 34.4 & 54.1 & (\(-\)137,204) & 33.6 & 52.8 & (\(-\)123,212) \\  & & & & PM\(-\)16 QAM Signal & & & & & \\
2048 & 149.6 & 225.3 & (\(-\)709,738) & 88.3 & 138 & (\(-\)550,444) & 87.5 & 136.8 & (\(-\)515,439) \\
4096 & 78.6 & 123 & (\(-\)482,409) & 36.9 & 53.2 & (\(-\)188,175) & 36.9 & 51.4 & (\(-\)194,161) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: CD estimation performance under different sampling points and search interval (ps/nm). Similarly, we also study the influence of nonlinear effects in optical fiber links on the proposed CD estimation method. In order to fully show the nonlinear effect, we built two wavelength division multiplexing systems, including 5 \(\times\) 112 Gbps PM-QPSK and PM-16 QAM, with an interval of 50 GHz. The total distance of the optical fiber transmission link is 2000 km, and the cumulative CD is 32,000 ps/nm. Different nonlinear effects are generated by changing the input power of each wavelength channel, and the CD is estimated by using the channel signal of the middle wavelength. According to the characteristics of the wavelength division multiplexing (WDM) system, there is a large channel crosstalk in the middle wavelength, so the result of this channel is more representative. Similarly, the OSNR in the PM-QPSK and PM-16 QAM links are set to 20 dB and 25 dB, respectively, the number of sampling points used is 4096, and the search interval is 0.0001. The CD estimation results of these two types of WDM systems are shown in Figure 12.  
Figure 11: Relationship between (**a**) error rate and (**b**) estimation error with OSNR. Figure 10: Relationship between (**a**) error rate and (**b**) estimation error with PMD.