## 4 Results and Discussion  
According to the above analysis of chirp signal parameter estimation, using different sampling points and transform order search intervals will bring different parameter estimation effects. By changing different sampling points, we perform FrFT on PM-QPSK and PM-16 QAM signals to obtain the EC distribution diagram, as shown in Figure 7.  
It can be seen from the figure that the two types of signals have downward peaks under different sampling points, and their extreme points correspond to different transform orders. Therefore, different sampling points combined with a different transform order and search interval will have different effects on the estimation accuracy of CD. However, more sampling points and a smaller search interval will lead to a higher computational complexity. It is worth mentioning that the reason why Figure 3 is smooth compared with Figures 4 and 7 is that Figure 3 is only for chirped signals, and Gaussian white noise has little effect on FrFT. Figures 4 and 7 show the performance of specific signals in complex optical fiber links, and the corresponding results will be affected by complex factors such as cumulative CD, link noise, nonlinearity, and so on.  
Figure 6: System simulation block diagram of the CD estimation method based on FrFT.  
Next, we use different sampling points (2048, 4096) and different order search intervals (0.001, 0.0001, 0.00001) for the two modulation format signals to simulate and compare the dispersion estimation of optical fiber links with an optical fiber length of 100 km to 2000 km (step length of 20 km). For each combination of different sampling points and search intervals, we can obtain the CD estimation error distribution histogram under different fiber lengths, as shown in Figures 8 and 9. Table 3 shows the mean value, standard deviation, and error range of CD estimation error of two types of signals under different sampling points and search intervals.  
Figure 8: \(Cont\).  
Figure 7: EC distribution of (**a**) PM-QPSK and (**b**) PM-16 QAM signals under different sampling points.  
Figure 8: CD estimation error distribution of PM-QPSK signal corresponding to different search intervals when the sampling points are (**a**) 2048 and (**b**) 4096.  
Figure 9: CD estimation error distribution of PM-16 QAM signal corresponding to different search intervals when the sampling points are (**a**) 2048 and (**b**) 4096.  
From the above distribution histogram and the results in Table 3, it can be intuitively analyzed that under the same search interval, the more sampling points, the higher the accuracy of the CD estimation error and the gradual reduction of error range. Under the same sampling number, the smaller the search interval, the more the CD estimation error will gradually increase. It can be seen that using more sampling points and a smaller search interval can get more accurate CD estimation results, but it will increase the computational complexity of the whole system to some extent. Therefore, in a practical application, the number of sampling points and the search interval can be set according to the demand, that is, if the limitation on the computational complexity is relatively strong, it is necessary to reduce the number of sampling points or increase the search interval, and if it is only necessary to improve the estimation accuracy as much as possible without considering the computational complexity, we can use as many sampling points as possible or as small a search interval as possible. Through the above analysis and considering the specific estimation accuracy, this paper only needs 4096 sampling points and a 0.0001 search interval to meet most of the actual needs.