## 4 Simulation Results
### The Convergence Performance  
Choosing the appropriate training sets is very important in a DL training procedure since the channel noise within the training samples affects the learning ability and generalization ability of a customized DL model. Therefore, the favorable SNR of the training set should be investigated first; thus, both the \(\mathcal{S}1\) and \(\mathcal{S}2\) are trained under various training SNR \(\lambda\).  
The training cost of the proposed scheme under the LOS link training is demonstrated in Figure 4, where the \(\lambda\) varies from 5 to 30 dB. In general, all of the five curves tend to be stable gradually as the training epoch increases. The final loss of the proposed scheme for \(\lambda=5\) dB remains around 0.005, which induces the barely satisfactory channel of learning and symbol detection. Moreover, we can find that the curve for \(\lambda\)= 30 dB has a similar final loss result with that of \(\lambda=5\) dB. The main reason is that the samples with high SNR reduce the learning ability of the DL model to channel noise. However, the final loss results for \(\lambda\)= 15, 20, and 25 dB are about \(1.79\times 10^{-4}\), indicating excellent network training since it can meet the requirements of the symbol detection in QAM constellation. In addition, it can be also seen from the figure that the proposed scheme with a large \(\lambda\) converges faster  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline \multicolumn{2}{c}{Dimensions for \(\mathcal{S}1\)} \\ \hline Input & \(\mathcal{M}\) \\ \hline Dense (ReLU) & 256 \\ \hline Dense (Linear) & \(\mathcal{M}\) \\ \hline \multicolumn{2}{c}{Dimensions for \(\mathcal{S}2\)} \\ \hline Input & \(\mathcal{M}\) \\ \hline Dense (ReLU) & 256 \\ \hline Dense (ReLU) & 256 \\ \hline Dense (Sigmod) & \(\mathcal{P}\) \\ \hline Refine & signum function \\ \hline \multicolumn{2}{c}{Training and Testing} \\ \hline Optimizer & Adam \\ \hline Learning Rate & 0.0001–0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters and training of the proposed DL-NPE.  
than the one for a small \(\lambda\), e.g., the curve with \(\lambda=5\) dB takes about 32,000 epochs to achieve convergence, whereas that for \(\lambda=25\) dB undergoes only 14,350 epochs.  
The corresponding loss performance under the NLOS links for training are depicted in Figure 5. Similar conclusions can also be drawn to that of the LOS case. Although the corresponding convergence rate is slightly degraded compared with the one for the LOS case, it still can achieve the final stable state. However, the loss curve for \(\lambda=5\) dB has an apparent fluctuation when it undergoes 35,000 epochs. Generally, the training SNR, which can affect the convergence performance of the proposed scheme to a certain extent, is not as big. Therefore, the size of the required training overheads could be reduced significantly and the learning ability of the proposed scheme can be improved by selecting proper training sets.  
Figure 4: The cost performance comparison for different training SNRs under the LOS case.  
Figure 5: The cost performance comparison for different training SNRs under the NLOS case.