## 4 Results and Discussions
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Term** & **1D-DNN** & **1D-CNN** & **2D-CNN** \\ \hline Layers & 3 FCL & 2 Conv + 2 FCL & 2 Conv (3 \(\times\) 2, 3 \(\times\) 1) + 2 FCL \\ Kernel size & Not used & (3), (3) & (3, 2), (3, 1) \\ Activation & ReLU & ReLU & ReLU \\ Epoch & 100 & 100 & 100 \\ Batch Size & 512 & 512 & 512 \\ Loss function & MSELoss & MSELoss + L1 & MSELoss + L1 \\ Optimizer & AdamW & AdamW & AdamW \\ Pooling size & Not used & (2) & (2, 1) \\ Total Parameters & 239,042 & 139,802 & 139,702 \\ MACC & 236,160 & 229,440 & 229,440 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values in 2D-CNN, 1D-CNN, and 1D-DNN. and optimal performance. At an optical power of 8 dBm, the BER was 5.3 \(\times\) 10\({}^{-3}\), which was below the threshold for soft-decision forward error correction of 1.56 \(\times\) 10\({}^{-2}\) with a 15% overhead. It could precisely process communication signals and diminish the error rate. The BER of the 1D-CNN was marginally superior to that of the 2D-CNN, varying between 2.2 \(\times\) 10\({}^{-2}\) and 6.3 \(\times\) 10\({}^{-3}\). Due to its processing of one-dimensional data, it inadequately leveraged the correlation of two-dimensional spatial signals, leading to marginally diminished performance. The BER of the 1D-DNN ranged from 1.3 \(\times\) 10\({}^{-2}\) to 4.6 \(\times\) 10\({}^{-2}\). The structure was susceptible to overfitting, resulting in inadequate generalization capability and a comparatively elevated BER. The conventional VNE approach exhibited the greatest BER, ranging from 1.4 \(\times\) 10\({}^{-2}\) to 4.9 \(\times\) 10\({}^{-2}\). It possessed constraints in addressing intricate issues, and its efficacy was subpar compared to neural networks. We looked at the constellation diagrams of the VNE, 1D-DNN, 1D-CNN, and 2D-CNN to better understand how well they communicate and process signals. The constellation diagram illustrates signal quality and interference resilience. Figure 5 shows that the traditional VNE's constellation diagram had a lot of spread and unclear points, meaning it struggled to reduce nonlinear distortion and noise interference, resulting in poor signal quality and a higher BER. The 1D-DNN constellation diagram exhibited dispersion and indistinct points, indicating overfitting and insufficient adaptability. The 1D-CNN constellation points were spread out and not grouped together well, which shows that it struggled to pick out important features and can't effectively handle interference from nonlinearity and phase noise, possibly leading to signal distortion and a higher BER. In contrast, the 2D-CNN constellation diagram exhibited closely clustered points with little dispersion, facilitating separation. The figure shows that the 2D-CNN could adjust phase settings using convolutional network weights to rebuild the phase with very few errors. The constellations focused on standard QPSK constellation points, minimizing nonlinear and phase noise interference. The more concentrated and prominent constellation points exhibited superior signal quality and resilience to interference. Figure 4: Curve of the BER performance for 2D-CNN, 1D-CNN, 1D-DNN, and VNE. To see how the number of trainable parameters affects the performance of 2D-CNN, we ran tests with four different amounts of trainable parameters: 100,000, 150,000, 200,000, and 350,000. During the tests, we kept everything the same, including the network design, activation function (ReLU), loss function (MSE), optimizer (AdamW), convolution kernel size, pooling method, and the datasets used for training and testing, with the only change being the number of trainable parameters. As shown in Figure 6, increasing the number of trainable parameters from 100,000 to 150,000 lowered the system's BER from 5.9 \(\times\) 10\({}^{-3}\) to 5.6 \(\times\) 10\({}^{-3}\), which means that adding a moderate number of parameters helped the model learn complex signal details better and improved its ability to handle nonlinearity and phase noise.