## 3 Results
### Simulation System and Result Analysis
#### 3.2.2 Analysis of Experimental Results  
Figure 11a illustrates the comparison of the bit error rate (BER) for three algorithms under different input fiber powers, given the same number of SSFM steps (i.e., five steps) and iterations (i.e., four times). The complexity of these algorithms is nearly proportional to the number of iterations, so we compare their compensation performance under similar computational complexity. To ensure a fair comparison, initial values for the nonlinear scaling factor \(k\) and the hyperparameter learning rate \(\mu\) are chosen such that none of the algorithms experience oscillations at the optimal input power. The experimental results demonstrate that, with a limited number of iterations, our proposed method outperforms the GDA and GDAM in terms of compensation performance. The A-DBP-LTM based on RMSProp benefits from an adaptive adjustment of the learning rate \(\mu\), requiring only four iterations to converge to the optimal \(k\). This ensures effective compensation performance across different input powers, enhancing the algorithm's robustness. Compared with the GDA and GDAM, achieving convergence without oscillation in four iterations does not lead to the optimal \(k\). Figure 11a shows that, at the optimal input power of 3.5 dBm, the log10(BER) for both the GDA and GDAM is worse than that of our proposed algorithm. Additionally, it should be noted that the GDA and GDAM have a fixed \(\mu\). This leads to oscillations during the iterative optimization process under varying input powers, resulting in fluctuations in compensation effectiveness. Moreover, their performance at certain power levels is even worse than merely compensating for dispersion alone. Figure 10: Experimental setup for 26-WDM, 63 Gbaud, 16 QAM transmission over 1200 km. Figure 11b depicts the compensation performance of three algorithms across different WDM channels at the optimal input power of 3.5 dBm. The OSNR for channels 1, 7, 13, 19, and 25 are 25.12 dB, 25.07 dB, 25.01 dB, 24.4 dB, and 22.76 dB, respectively. As shown in Figure 11b, as OSNR decreases, the \(\log_{10}\)(BER) of all three algorithms increases, but our proposed method maintains superior compensation performance across all channels. The GDA and GDAM require more iterations to find the optimal \(k\). Under the condition of a fair comparison (i.e., four iterations), their compensation performance is inferior. The GDAM exhibits the worst \(\log_{10}\)(BER) because the introduction of the momentum term \(m\) reduces the robustness of the algorithm during iterations, leading to oscillations and affecting compensation performance. Moreover, due to inter-channel interference, compensation performance varies across different channels. Figure 11c illustrates the compensation performance of the three algorithms in the middle channel under different spans at the optimal input power of 3.5 dBm. Our proposed method maintains excellent compensation performance even with only four iterations. It shows that, as the number of spans increases, the accumulation of nonlinear impairments also increases. A-DBP-LTM based on RMSProp achieves a more significant BER reduction compared to the compensation of dispersion only. In contrast, for the GDA and GDAM, as nonlinear impairments accumulate, it becomes challenging to converge to the optimal \(k\), resulting in poorer compensation performance for both algorithms. To compare the compensation performances of the three algorithms at four iterations, the BER curves versus OSNR are evaluated as shown in Figure 11d. The dashed line represents the FEC threshold value of 2.3 \(\times\) 10\({}^{-2}\). The OSNR difference at the FEC threshold for different algorithms is defined as the OSNR penalty. The OSNR is adjusted by combining the received optical signal with ASE noise whose power is controlled by a variable optical attenuator. As shown in Figure 11d, when switching the algorithm from A-DBP-LTM to the GDA or GDAM, there will emerge a 0.189 dB or 0.3315 dB OSNR penalty, respectively.