## 3 Methods
### Data Augmentation Methods for AMR
There were three augmentation methods proposed in the existing work [18], i.e., jitter, rotation, and flip, and five new augmentation methods proposed in this paper, i.e., channel shuffle, inversion, split and permutation, scaling, and flip and channel shuffle. As shown in Figure 1, we randomly selected CPSFK and QPSK from the dataset as examples to demonstrate the effect of eight augmentation transformations. A brief description of each transformation is given below. The Jitter (Jit) method augments the original samples with noise. Deep neural networks typically overfit when they learn high-frequency features that may or may not be useful. Gaussian noise with a zero mean contains data points at almost every frequency, effectively distorting high-frequency features. This also means that lower-frequency components are distorted. Model learning can thus be improved by adding a moderate amount of noise. Unlike previous research, in which Gaussian noise is added with a fixed standard deviation, our augmentation method is sample dependent. In Jit augmentation, the standard deviation \(\sigma^{2}\) of Gaussian noise is 5% of each sample, and the augmented sample \(\bar{x}\) is denoted as follows:  
\[\bar{x}=x+\mathcal{N}(0,\sigma^{2}) \tag{3}\]  
Rotation (Rot) is currently considered to be the most efficient transformation for AMR tasks [18]. Rot rotates the constellation diagram of the signal clockwise by \(\theta\), \(\theta\in\{0,\pi/2,\pi,3\pi/2\}\). In terms of the constellation diagram, the rotation transformation is thus spatially invariant. We can then obtain an augmented signal sample \((\bar{A},\bar{\phi})\)[18]. \[ \begin{bmatrix}\bar{A}\\ \bar{\phi}\end{bmatrix} = \begin{bmatrix}\cos\theta&-\sin\theta\\ \sin\theta&\cos\theta\end{bmatrix}\begin{bmatrix}\bar{A}\\ \phi\end{bmatrix}  \tag{4}\]  
Flip inverts the sign of the IQ component [18], so the transformation exists in four cases: the I component is converted to a negative value, the Q component is converted to a negative value, both the I and Q components are converted to negative values, and both the I and Q components are held constant. This can be expressed mathematically as follows:  
\[ \begin{bmatrix}\bar{I}\\ \bar{Q}\end{bmatrix} = \begin{bmatrix}\alpha I\\ \beta Q\end{bmatrix}  \tag{5}\]  
where \(\alpha,\beta\in\{-1,1\}\). Channel shuffle (CS) swaps the channels of the IQ array. This transformation does not change the correspondence between the I and Q components at each time point, and the values do not change; only the channels are shuffled. Swapping the two channels does not change the labels of the samples, and this transformation reduces the dependence of the  
Figure 1: Example of 8 transforms for CPSFK and QPSK samples. For the raw IQ samples, the blue curve represents the I component, and the orange curve represents the Q component. Despite the inclusion of several possible transformations, such as Rot, Flip, and SP, only one of these forms is shown in the figure. model on the relationship between the locations of the IQ components. The augmented data are represented as follows:  
\[ \begin{bmatrix}\tilde{I}\\ \tilde{Q}\end{bmatrix} = \begin{bmatrix}Q\\ I\end{bmatrix}  \tag{6}\]  
Inversion (Inv) is the process of inverting a time series. This transformation fully utilizes the AMR task, which is required to discover patterns within the IQ signal data cycle that do not change when the sequence is inverted. Inverting the sequence, on the other hand, reduces the model's reliance on the sequence's preceding and following orders and focuses more on the signal's global properties. \[ \begin{bmatrix}\tilde{I}\\ \tilde{Q}\end{bmatrix} = \begin{bmatrix}i_{L},i_{L-1},\ldots,i_{1}\\ q_{L},q_{L-1},\ldots,q_{1}\end{bmatrix}  \tag{7}\]  
Split and permutation (SP) divide the IQ sample into S segments, which are then disrupted, with S ranging from 1 to 8.