## 3 Simulation and Experiment Results  
### Simulation Results  
As shown in Figure 6, we set up the simulation system using the commercial software Virtual Photonics Inc (Norwood, MA, USA). and the DBSCAN-based joint algorithm is used at the receiver end to identify the MF and estimate OSNR. The wavelength of the laser at transmitter is 1553.6 nm with 100 kHz linewidth. After modulated by an IQ modulator which I and Q branches independently driven by two 30-order PRBS produced by AWG, five widely used MFs are generated. By changing the random seed of PRBS, we can get five different signal patterns. The symbol rate is set to 28 Gbaud and the launched optical power to standard single-mode fiber (SSMF) is 0 dBm. The modulated signal light is amplified by an Erbium Doped Fiber Amplifier (EDFA) and transmitted in 100 km SSMF with CD parameter is \(16 ps/(nm.km)\) every span. The polarization mode dispersion (PMD) parameter is set as \(0.1 ps/\sqrt{km}\). The transmission fiber length is set to 4000 km, 2000 km, 1000 km, 500 km and 500 km for PDM-QPSK, PDM-8 PSK, PDM-16 QAM, PDM-32 QAM, and PDM-64 QAM signals, respectively. A variable optical attenuator (VOA) and an EDFA are used to vary OSNR with transmitted signal light in 3 dB coupler. The linewidth of local oscillator laser is 100 kHz. After analog-to-digital converter (ADC), the DSP blocks described in Section 2.1 are followed.  
Figure 7a shows the cluster number \(N\) varies with different OSNR after using the DBSCAN-based algorithm for QPSK, 8 PSK, and 16 QAM signals with the same neighborhood parameters \(\varepsilon\) = 0.09 and _MinPlts_ = 25. The cluster numbers of three different MFs are represented by different color symbols. There are five different signal patterns for every OSNR condition. With the decision thresholds proposed in Section 2.2, modulation formats of different signal patterns are correctly identified with 100% accuracy. Figure 7b shows the \(\gamma\) value of 32 QAM and 64 QAM signals and these two MFs can be divided with the decision thresholds proposed in Section 2.2. The red/green area in Figure 7a,b represents the OSNR range below/upon the 7% FEC threshold of different MFs.  
Figure 6: Simulation setup to utilize the DBSCAN-based joint algorithm.  
Figure 8 shows the estimated OSNR and mean absolute error of five different signal patterns for five MFs signals. Signal patterns used for fitting fourth-order polynomial are not the same as five different signal patterns above. The estimated OSNR values are represented by different solid points while the mean absolute errors of five different signal patterns for every OSNR condition are represented by different hollow points. It can be seen that the mean absolute errors of all reference OSNR conditions for five MFs are all less than 1 dB. The mean estimated error is 0.3 dB, 0.2 dB, 0.3 dB, 0.5 dB, and 0.6 dB for QPSK, 8 PSK, 16 QAM, 32 QAM, and 64 QAM, respectively. It notes that the OSNR estimation error increases with greater reference OSNR. It can be explained that the ASE noise power is too low and the algorithm cannot extract the change of density information of clusters. As a result, OSNR estimation will have more deviation [45]. Table 1 shows the neighborhood parameters of five different MFs.  
Figure 8: The estimated OSNR and mean absolute error for five MFs. (**a**) QPSK; (**b**) 8 PSK; (**c**) 16 QAM; (**d**) 32 QAM; (**e**) 64 QAM.  
Figure 7: MFI results using the DBSCAN-based algorithm. (**a**) cluster number \(N\) of QPSK, 8 PSK and 16 QAM varies with different OSNR; (**b**) \(\gamma\) value of 32 QAM and 64 QAM varies with different OSNR.