## 3 Simulation Setup  
In order to verify the feasibility of the CD estimation method based on FrFT, we use Matlab and Optisystem to jointly simulate and build optical fiber signal transmission systems with single carriers of 28 GBaud PM-QPSK and 14 GBaud PM-16 QAM, respectively, as shown in Figure 6. At the system transmitter, the IQ modulator is driven by an uncorrelated pseudo-random sequence to generate signals with different rates and modulation formats. The signal is input into the optical fiber link for transmission after passing through the polarization multiplexing module and preamplifier. The optical fiber link is composed of the set standard single-mode fiber (SSMF) through the loop. After each section of optical fiber transmission, the power loss of optical signal will be compensated by an erbium-doped fiber amplifier (EDFA). The noise index of EDFA module is set to 0 dB, that is, it is assumed that EDFA will not introduce amplified spontaneous emission (AES) noise to reduce OSNR, so we add a SetOSNR module at the end of the whole optical fiber link to change the OSNR of the received signal by directly adding AES noise. The incident optical power of the optical fiber link is 0 dBm, the single span length of SSMF is initially set as 100 km, the CD coefficient is 16 ps/nm/km, the CD slope is 0.075 ps/(nm\({}^{2}\cdot\)km), the polarization mode dispersion (PMD) coefficient is 0.1 ps/km\({}^{1/2}\), and the nonlinear coefficient is 2.6 W\({}^{-1}\cdot\)km\({}^{-1}\). We change the final cumulative CD by changing the length of each transmission fiber, and control the CD range from 1600 ps/nm to 32,000 ps/nm. Set the OSNR in the range of 12 dB to 30 dB (in steps of 3 dB) by setting the SetOSNR module, and set the PMD in the  
Figure 5: Optimal order search flow chart.  
system in the range of 0 ps to 40 ps (in steps of 5 ps) by adding a PMD simulator. After link transmission and coherent detection, the output signal is saved and input to Matlab for offline processing. Phase noise (a kind of nonlinear effect) will be introduced in the simulation process. The existence of CD suppresses the nonlinear phase noise, and the larger the CD value, the smaller the nonlinear noise of the system.  
In the off-line processing module, the data output by the receiver are sampled and extracted with appropriate length, firstly, and the extracted data are input to the storage unit to provide a data source for subsequent CD estimation. Secondly, the extracted four channels of data are combined into two channels of polarization data through the complex field calculation unit. Then, the FrFT processing unit is used to calculate the EC function \(EC(Q)\) after FrFT of different orders. Through the preset CD and the search range of transform order, and using the mathematical relationship between transform order and CD in the formula, the order in \(EC(Q)\) is replaced by the CD value \(EC(Q)\). Finally, the CD value corresponding to the peak position is found through the distribution characteristics analyzed by the CD calculation unit, which is the estimated value. In order to measure the effect of CD estimation, the average dispersion estimation error \(M_{CD}\), standard deviation \(\delta_{CD}\) and the range of dispersion estimation error \(R_{CD}\) are used to evaluate.