## 4 Results
### Results on Class-Imbalanced Datasets  
On the class-imbalanced datasets, the comparison is divided into two parts: the comparison of the proposed methods with the existing representative class rebalancing methods on the class-imbalanced datasets and the comparison of the representative methods in terms of the recognition accuracy of each modulation class. On the three class-imbalanced datasets, Table 5 compares the performance of the proposed methods to the representative class rebalancing methods and individual transformations. Based on the experimental results in the table, the following discussion and analysis will expand from top to bottom and from left to right. As the degree of imbalance in the dataset increases, so does the performance of the baseline model. SE-MSFN outperforms DAE and LSTM2 in terms of stability. First, we investigate the performance of each model on each dataset. The performance gap between the lightweight model DAE and the other two models is larger than on the balanced dataset. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{3}{c}{**DAE**} & \multicolumn{3}{c}{**SE-MSFN**} & \multicolumn{3}{c}{**LSTM2**} \\ \cline{2-10}  & **Mean** & **Std** & **Gain** & **Mean** & **Std** & **Gain** & **Mean** & **Std** & **Gain** \\ \hline Inv & 77.20 & 1.40 & 3.11 & 82.86 & 0.37 & 3.03 & 82.24 & 0.15 & 2.45 \\ SP & 78.46 & 2.37 & 4.38 & 82.96 & 0.13 & 3.13 & 83.02 & 0.23 & 3.24 \\ Sca & 75.13 & 1.82 & 1.05 & 79.70 & 0.96 & \(-\)0.14 & 80.02 & 0.51 & 0.23 \\ FCS & 78.71 & 2.61 & 4.62 & 82.23 & 0.20 & 2.40 & 83.71 & 0.35 & 3.92 \\ SigAugment-C & 77.68 & 1.27 & 3.59 & **83.81** & 0.29 & **3.98** & **85.29** & 0.05 & **5.50** \\ SigAugment-R & **79.82** & 1.23 & **5.73** & 83.63 & 0.46 & 3.80 & 85.27 & 0.12 & 5.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._In class rebalancing methods, the focal loss is only useful for recognition when training a specific model on a specific dataset, and it is usually comparable to the baseline model, i.e., when using the cross-entropy loss function. The four up-sampling methods performed very differently. When training LSTM2 on the 2016A-20 dataset, the most helpful methods are Polynom_fit_SMOTE_poly and SMOTE_IPF, with accuracy gains of 14.12% and 14.80%, respectively. In most other cases, the gains in recognition accuracy are negligible, and the models frequently struggle to converge when training LSTM2 and DAE. On the three datasets in that order, we calculate the mean accuracy values for each of the four up-sampling methods and then compare them to the baseline method, with gains of 1.74%, 2.58%, \(-\)34.43%, \(-\)1.28%, 1.12%, 3.63%, \(-\)25.66%, \(-\)5.32%, and 17.55%. When training DAE and LSTM2, we can see that the up-sampling methods always result in a significant decrease in accuracy on three datasets. The overall improvement in performance is minor and highly variable. Furthermore, the up-sampling methods generate data offline, which can significantly increase the number of training samples and thus reduce model training efficiency. Our proposed online data augmentation strategies do not explicitly increase the number of samples, but rather transform the original training data at each epoch of training, only increasing the computational cost associated with the transformations. Similarly, we compute the average accuracy of SigAugment-C and SigAugment-R across models and datasets, with gains of 3.70%, 9.78%, 13.24%, 6.65%, 14.01%, 31.46%, 0.62%, 12.60%, and 29.92% on the three datasets in that order. With an average gain of 24.88% across the three datasets, SigAugment had the greatest improvement for the LSTM2 model. Furthermore, the greater the degree of imbalance in the dataset and the smaller the data size, the greater the gain from data augmentation. This is consistent with the expectation that smaller datasets require more regularization.