## 4 Experimental Setup and Results  
To experimentally verify the effectiveness of our proposed MFI scheme, a series of proof-of-concept experimental demonstrations were undertaken. The setup for these is shown in Figure 15. In the transmitter, a PRBS with a word length of \(2^{15}-1\) was generated by offline DSP and mapped onto different modulation formats with 2 samples/symbol. A SRRC filter with a roll-off factor of 0.1 was employed to shape the up-sampled signals. In addition, a pre-distortion operation was also applied to compensate for the frequency roll-off effect associated with digital-to-analog converters (DACs). An external cavity laser (ECL) produced a continuous wave optical carrier with a wavelength of \(\sim\)1550 nm and a linewidth of \(\sim\)100 kHz, which was then modulated by an integrated LiNbO\({}_{3}\) polarization-multiplexing I/Q modulator. The DACs, operating at 64 GSa/s and 25 GHz analog bandwidth, drove four branches of the modulator to generate 28 GBaud PDM-QPSK/-8 QAM/-16 QAM and 21.5 GBaud PDM-32 QAM optical signals. The transmission links included back-to-back and long-haul fiber transmissions. The long-haul transmission link was composed of multi-span single mode fiber (SMF), whose dispersion parameter, attenuation, and nonlinear coefficient were \(D=16.9\) ps/nm/km, \(\alpha=0.2\) dB/km, and \(\gamma=1.27\) km\({}^{-1}\cdot\)W\({}^{-1}\), respectively. To completely compensate for the fiber loss, an erbium-doped fiber amplifier (EDFA) with a noise figure of \(\sim\)5 dB was applied in each span. An optical spectrum analyzer (OSA ANRITSU MS9740A) was used before the receiver to measure the OSNR in back-to-back case, and an optical band-pass filter (OBPF), whose bandwidth was 200 GHz, was employed to suppress out-of-band ASE noise. After passing through the link, the received signals were detected by an integrated coherent receiver and then sampled by a real-time digital oscilloscope with 80 GSa/s and 33 GHz electrical bandwidth. Finally, these signals were processed by an offline DSP module, where the proposed MFI scheme was embedded. The frame synchronization was achieved by the auto-correlation detection of synchronization codes. The OSNR dynamic ranges for PDM-QPSK/-8 QAM/-16 QAM/-32 QAM signals in the back-to-back links were 10-17 dB, 15-28 dB, 16-28 dB and 18-35 dB, respectively. The step of variable OSNR is 1 dB. In all of the proof-of-concept experiments, 100 samples of independent data were applied for each OSNR or launch power value. The performance of the proposed MFI scheme was first experimentally verified in back-to-back links. As shown in Figure 16, the proposed scheme achieved a 100% correct identification rate for both QPSK and 8 QAM over all OSNR ranges considered in the experiments. The minimum OSNR values required by 16 QAM and 32 QAM for achieving a correct identification rate of 100% were 19 dB and 20 dB, respectively. Figure 15: Proof-of-concept experimental setup of the proposed scheme. PC: polarization controller, PBS: polarization beam splitter, PBC: polarization beam coupler, VOA: variable optical attenuator, LO: local oscillator. Compared with the numerical simulation results, the minimum required OSNR values for these two modulation formats increased slightly. This could have been due to the unwanted effects associated with the signal generation of high-order modulation formats in the experiments. The four modulation formats could still be identified with a 100% correct identification rate when their OSNR values were higher than the thresholds (indicated by the vertical dash lines), corresponding to the 7% FEC correcting BER of \(3.8\times 10^{-3}\).