## 4 Results and Discussion
### Equalization Performance  
We compared the performance of the teacher model (biGRU), student model (1D-CNN) and 1D-CNN without KD but with the same structure with different experimental parameters (VPP, baud rate and RoP) and used the Q-factor to measure the performance. As shown in Figure 7, for the VPP, all three achieved the best performance at 400 mv, and the 1D-CNN network with KD had a 0.46 dB improvement in the Q-factor compared with the network without KD, and also had a 0.71 dB gap compared with the teacher network biGRU. In addition, at 500 mv, no KD had the most significant effect on the 1D-CNN. Here, KD produced a 0.57 dB improvement to the 1D-CNN and only a 0.46 dB  
Figure 6: (**a**) Comparison of the weight distributions of 1D-CNN and 1D-CNN with KD. (**b**) Intuitional comparison of the weight distributions of 1D-CNN and 1D-CNN with KD. difference compared to the teacher network. When the VPP is small, the difference between the three was not so obvious, which may be caused by the small influence of the timing information on the equilibrium. However, in the process of the continuous improvement of the VPP, KD maintained the improvement of the effect on the 1D-CNN. For the HD-FEC (BER = 1 \(\times\) 10\({}^{-3}\)) threshold [21], the 1D-CNN without KD only exceeded the threshold at 400 mv, while the 1D-CNN after KD crossed the threshold in the range of 250-550 mv, showing the significant improvement brought by KD. In addition, we compared the NN algorithm with the LMS algorithm, and we verified the ability of the neural network to function as a nonlinear equalizer. The baud rate results are shown in Figure 8; it is obvious that the lower the baud rate, the better the performance of each network. However, it is worth noting that when the baud rate was 2 GBaud, the Q-factor for the 1D-CNN with KD increased by 0.32 dB, and the Q-factor difference between the student network and the teacher network after KD was only 0.23 dB. Importantly, only with KD could the 1D-CNN exceed the threshold when the baud rate was 2 GBaud. When the baud rate was lower than 3 GBaud, KD always brought about performance gains for the student model, but there was no effect of KD on the teacher model. It is speculated that the network of the student model at this time cannot always absorb knowledge from the teacher model in the KD, and it may be necessary to change the network architecture to continue learning. In addition, we show the spectrum diagram of the signal at 3 GBaud for all the algorithms in Figure 8, which shows the equalization performance in a bandwidth-limited system in our experiment. Finally, for the receiving optical power RoP (shown in Figure 9), when the RoP is low (less than \(-\)15.8 dB), the performances of the student model, teacher model and student model without KD were almost the same, which may be because the time series information had little effect on the signal recovery at this time. In the process of the gradual increase in RoP later on, KD again manifested its role, and when the RoP reached its maximum, KD brought about a Q-factor improvement for the student model 1D-CNN (up to 1.2 dB), which was the largest improvement among all the experiments. At this time, the gap between the student model and the teacher model after KD was 0.84 dB. Most importantly, KD increased the RoP of the 1D-CNN by 0.89 dB on the HD-FEC threshold, which is enough to show that the role of KD is very significant. The eye diagrams of the in-phase signal before and after equalization demonstrate the existence of inter symbol interference and its suppression after equalization. These experiments verified that KD does improve the equalization performance of the student model. Although there were still some gaps between the student model and the teacher model, we will analyze the huge improvement in time of the student model in  
Figure 7: Q-factor comparison and constellation diagram of the LMS, biGRU, 1D-CNN and 1D-CNN with KD with a changing VPP. the next section.