## 5 Simulations
### Convolution Networks with SSTM  
We apply the module proposed in Section 2 to the baseline CNN network. Using the same training and test scenarios as the baseline, we get typical results shown in Figure 7 for the CFO1 and SRO1 datasets. In Figure 7a, it is shown that our method achieves a classification accuracy improvement of 5% to 30% over the absolute value of the frequency offset from 0.1% to 0.4%. For smaller frequency offsets, the classification performance is improved more. The proposed method achieves a broader performance gain over a larger range of training offsets. The increase in classification accuracy arises within the entire test dataset. For the performance decline caused by sample rate offset, our method shows better results. In Figure 7b, the optimization of classification performance is demonstrated in two aspects: Firstly, due to the introduction of SSTM, higher classification accuracy is obtained in the sample rate within the range of training datasets. Then, a consistent classification accuracy improvement is produced at sample rates outside the range of the training dataset. When the test sample rate range exceeds the training dataset, the classification accuracy of our method will not drop drastically. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenarios** & **SNR** & **Low Offset** & **Medium Offset** & **High Offset** \\ \hline \multirow{3}{*}{SRO1} & High & 0.89 & 0.29 & 0.18 \\  & Medium & 0.80 & 0.24 & 0.17 \\  & Low & 0.25 & 0.18 & 0.15 \\ \hline \multirow{3}{*}{SRO2} & High & 0.88 & 0.71 & 0.34 \\  & Medium & 0.80 & 0.62 & 0.31 \\  & Low & 0.32 & 0.27 & 0.17 \\ \hline \multirow{3}{*}{CFO1} & High & 0.85 & 0.41 & 0.31 \\  & Medium & 0.79 & 0.39 & 0.28 \\ \cline{1-1}  & Low & 0.52 & 0.25 & 0.17 \\ \hline \multirow{3}{*}{CFO2} & High & 0.82 & 0.53 & 0.37 \\ \cline{1-1}  & Medium & 0.78 & 0.48 & 0.30 \\ \cline{1-1}  & Low & 0.47 & 0.28 & 0.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison for different training scenarios in typical SNR. Figure 6: Overall classification accuracy for various offsets in Ideal, SRO1, SRO2, CFO1, CFO2, with SNR fixed at 20 dB (**a**) frequency offsets in Ideal, CFO1, CFO2; (**b**) sample rate offsets in Ideal, SRO1, SRO2. In Figure 8, we plot a cross-sectional view of overall accuracy versus frequency offset or symbol rate at a fixed 20 dB SNR. According to the different processing steps of the received signals, the signal models can be divided into the following three types: model of radio frequency signals (MRF), model of baseband signals (MBB), and model of the output of the matched filter at receiver (MMF). According to the preprocessing requirement, the AMR method can be divided into three types: environment of ideal synchronization (EIS) algorithm, environment of nonideal synchronization (ENIS) algorithm, and environment of no synchronization (ENS) algorithm. Our method is an ENS method under the MBB signal model. Therefore, we compare our method with the DL-based method of different synchronization requirements under MBB model. For ENS and ENIS methods, we compare the methods with RTN, which is proposed by [PERSON] [23]. For EIS methods, we compare with the CNN method with the best performance in the DL-based method, namely the baseline method in this article. Besides, the effects of different signal parameterized estimation network structures on classification performance are evaluated, including multilayer perceptrons and CNN. We represent these frameworks as SSTM_Dense and SSTM_CNN. The compared networks have undergone the same optimal hyperparametric search to achieve optimal performance. It is shown in Figure 8a that, for the frequency offset, the methods based on our network model provide a certain performance improvement. The Bi-LSTM method provides the best results, followed by CNN and multilayer perceptrons [32]. It is shown in Figure 8b that for the symbol rate, Bi-LSTM in our network model yields an increase in accuracy overall test ranges.