## 3 Results
### Simulation System and Result Analysis
#### 3.1.2 Analysis and Discussion of Simulation Results
The conventional DBP deteriorates significantly with inaccurate \(\gamma\) values and may underperform LE at certain launching powers. In contrast, our proposed method delivers reliable performance under sufficient convergence across different \(\gamma\) values. It outperforms the conventional DBP with accurate \(\gamma\), as it optimizes \(k\) dynamically for varying launch powers, unlike the fixed \(k\) in the conventional DBP. It is difficult to compensate the Gordon-Mollenauer noise arising from the interaction between the nonlinearity effect and the amplified spontaneous emission (ASE) noise [17] employing an abnormal nonlinear scaling factor. The compensation performance gap narrows in higher launching powers because the Gordon-Mollenauer noise does not dominate in this situation, as the nonlinearity effect is not dominant. In Figure 7, log10(BER) results as a function of the launching power for different numbers of steps per span. It is obvious that the proposed method takes fewer SSFM steps than the conventional DBP. There is only one step for our proposed method to reach the FEC threshold, while the conventional DBP takes six steps. It is worth noting that the increase in the compensation performance is weakened with the augmentation of SSFM steps, which signifies that the same complexity effort yields lower effectiveness. It is hence necessary to balance the complexity resulting from the increase in SSFM steps with the improvement of the compensation performance. As shown in Figure 8, our proposed method achieves better effectiveness than A-DBP based on the GDA and A-DBP based on the GDAM at four iterations with five SSFM steps, even when using their best hyperparameters. This is attributed to the fast convergence of our proposed method. It should be noted that, due to the slow convergence speeds of the GDA and GDAM, the updated \(\gamma\) is still far away from optimum values when RMSProp has completed convergence. Consequently, the additional nonlinear impairment to the signal would be introduced during the processing of the SSFM because of the nonideal \(\gamma\), resulting in performances of the GDA and GDAM being even worse than that of the case with linear equalization only. It can be seen that different initializations of \(\gamma\), \(\mu\), \(m\) affect the compensation performance of the algorithm, which consequently leads to a different result for compensation with four iterations in Figure 4 compared to Figure 8.  
Figure 6: log10(BER) vs. the launching power for LE, the conventional DBP, and the proposed method with different values of \(\gamma\) with SSFM steps of 5. For further investigating the feasibility of our proposed method, LE, the conventional DBP, and the proposed method are implemented on the heterogeneous links which are described in Section 3.1.1 and are shown in Figure 3. Figures 9a and 9b show log\({}_{10}\)(BER) as functions of sweeping launching powers in the link of heterogeneous fiber lengths and types, respectively, with five SSFM steps. Compared with Link B, Link A has a shorter span length of 80 km from the 11 th to 20 th span, which results in a loss reduction of 4 dB. Thus, the performance of Link A is better than that of Link B. In the link of heterogeneous fiber lengths, \(\xi\) should be adjusted according to the length and \(\xi\) is smaller when being applied in shorter spans (\(\xi_{2}\)) with lower nonlinearity effect than in longer spans (\(\xi_{1}\)). The conventional DBP employing \(\xi_{1}\) for all spans results in overcompensation and is worse than employing \(\xi_{2}\) which is undercompensation in some launching powers. The ideal situation of the conventional DBP with \(\xi_{1}\) and \(\xi_{2}\) for different spans also performs worse than our proposed method for the reason that the Gordon-Mollenauer noise cannot be compensated well by the inaccurate \(k\).