## 5 Numerical Results
### Com  
Because many pre-cursor and post-cursor SBR values are close or equal to zero, MAPE and MRE are not suitable for evaluating the accuracy of SBR predictions, and only RMSE and MAE are used to evaluate the prediction accuracy for the SBR. For the SBR before equalization of the 40 test channels, the RMSE is 7.3 \(\times\) 10\({}^{-4}\) and the MAE is 6.3 \(\times\) 10\({}^{-4}\). For the SBR after equalization, the RMSE is 1.1 \(\times\) 10\({}^{-3}\) and the MAE is 1.6 \(\times\) 10\({}^{-4}\). Below, we use a randomly selected channel (ID: 3) from the test set to illustrate the SBR prediction performance. As depicted in Figure 12, both the pre-equalization and post-equalization SBR can be predicted by the Transformer model with high precision. For the PAM4 signal format, Figure 13 provides a concise demonstration. We selected an equalizer configuration that includes a 3-tags TX FFE, an RX CTLE with dual DC gain, and a 12-taps RX DFE (hereafter referred to as the standard equalizer configuration). As shown in Figure 13, channels No. 7 and No. 30 have large relative errors due to their complex shapes. Some channels with high RL, such as channels No. 7-No. 9, also exhibit significant relative error. The relative error of the predicted COM values for each test channel is within 2%, demonstrating the ability of the DNN-Transformer model to achieve the required prediction accuracy. Here, the influences of different combinations of equalizers on the prediction precision of COM values are analyzed deeply. As shown in Table 5, we configured five different equalizer combinations. The results indicate that our proposed cascaded model achieves the expected prediction performance across various equalizer combinations. However, it is apparent that a reduction in the variety of equalizers weakens the model's generalization capability and decreases its prediction accuracy. When only the DFE was enabled, the RMSE increased to 1.6 \(\times\) 10\({}^{-1}\), and the MRE reached 17.5%. We attribute this to the optimization method of this equalizer within the COM framework and the fact that the cascaded model also takes into account predictions for both the CTLE and FFE. Therefore, we adjusted the network structure by removing unused equalizers in the cascaded model for different \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Eye** & **Modulation** & **RMSE** & **MAE** & **MAPE** & **MRE (\%)** \\ \hline \multirow{2}{*}{EH (mV)} & PAM3 & 4.8 \(\times\) 10\({}^{-1}\) & 3.3 \(\times\) 10\({}^{-1}\) & 5.7 \(\times\) 10\({}^{-3}\) & 2.5 \\ \cline{2-6}  & PAM4 & 4.0 \(\times\) 10\({}^{-1}\) & 2.9 \(\times\) 10\({}^{-1}\) & 8.1 \(\times\) 10\({}^{-3}\) & 2.8 \\ \hline \multirow{2}{*}{EW (UI)} & PAM3 & 4.4 \(\times\) 10\({}^{-3}\) & 3.4 \(\times\) 10\({}^{-3}\) & 9.3 \(\times\) 10\({}^{-3}\) & 2.7 \\ \cline{2-6}  & PAM4 & 4.4 \(\times\) 10\({}^{-3}\) & 3.6 \(\times\) 10\({}^{-3}\) & 1.2 \(\times\) 10\({}^{-2}\) & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction of eye diagrams with the DNN model. Figure 11: Relative errors of eye diagrams for test set channels in the two modulation formats. Below, a test channel (ID: 3) is used to illustrate the prediction capability of the model with the first four taps of the DFE and three taps of the FFE. As shown in Figure 13(a), the cascaded model realizes highly accurate predictions. Furthermore, the prediction results for the main DC gain of the CTLE for the 40 test channels, as presented in Figure 13(b), also indicate a high level of accuracy. The predictive capabilities of different cascaded model combinations were investigated as follows. The equalizer configuration was set as the standard configuration, and the HPO parameters were uniformly configured, with the learning rate search range set from 0.0001 to 0.01, conducting 20 trials for optimization. Given the characteristics of the SBR, we tested the predictive performance of standalone models, including a DNN, an LSTM network, and a Transformer.