## 3 Our Proposed Method
### Sub-Coordinate System  
The realization of the sub-coordinate system is accomplished in the PyTorch environment, utilizing the matplotlib module [18]. First, we establish \(K\) virtual sub-coordinate systems in the planar rectangular coordinate system. After that, \(K\) points are obtained by mapping the \(K\) components of the received signal \(\mathbf{y}_{j}\), both real and imaginary (e.g., \(\mathrm{Re}\left(y_{jk}\right)\) and \(\mathrm{Im}\left(y_{jk}\right)\), respectively, represent the real and imaginary parts of \(y_{jk}\), which is the \(k\)-th component of the received signal \(\mathbf{y}_{j}\)), into the \(K\) sub-coordinate systems, respectively, which can be expressed as  
\[\left(S_{X_{k}},S_{Y_{k}}\right)=\left(\mathrm{Re}\left(y_{jk}\right),\mathrm{ Im}\left(y_{jk}\right)\right), \tag{3}\]  
where \(\left(S_{X_{k}},S_{Y_{k}}\right)\) is the point's coordinate in the \(k\)-th sub-coordinate system. Following that, by establishing a transformation function that express the spatial relationship between each sub-coordinate system and the planar rectangular coordinate system, we can compute the precise coordinates of the \(K\) points in the planar rectangular coordinate system, which can be expressed as  
\[\left(X_{k},Y_{k}\right)=\left(A\cdot S_{X_{k}}+X_{O_{k}},A\cdot S_{Y_{k}}+Y_ {O_{k}}\right), \tag{4}\]  
where \(\left(X_{k},Y_{k}\right)\) represents the coordinate of the \(k\)-th point in the original planar rectangular coordinate system, \(A\) denotes the ratio of the unit distance within the \(k\)-th sub-coordinate system to that of the original planar rectangular coordinate system, and \(\left(X_{O_{k}},Y_{O_{k}}\right)\) is the coordinate of the origin of the \(k\)-th sub-coordinate system in the original plane rectangular coordinate system. Next, for a receiver with perfect channel state information (CSI), during the single communication process, the channel vector \(\mathbf{h}_{j}\) is calculated instantaneously in real-time to evaluate the characteristics of the wireless channel [16]. Floating-point numbers in the 0 to 1 range may be converted to color values using the matplotlib.colors module and colormap class [18]. The following setting is made to the floating-point number that corresponds to the color value of the \(k\)-th point:  
Figure 2: **Left**: Standard convolutional layer with BatchNorm and ReLU. **Right**: Depthwise separable convolutions with depthwise and pointwise layers followed by NatchNorm and ReLU. \[\text{sig}\left(\left|h_{jk}\right|\cdot\frac{\text{Im}\left(h_{jk}\right)}{\text{ Re}\left(h_{jk}\right)}\right), \tag{5}\]  
where \(\left|h_{jk}\right|\) represents the magnitude of \(h_{jk}\); \(\text{Re}\left(h_{jk}\right)\) and \(\text{Im}\left(h_{jk}\right)\), respectively, represent the real and imaginary parts of \(h_{jk}\); and \(\text{sig}(\cdot)\) refers to the sigmoid activation function. Finally, by not displaying the plane rectangular coordinate system and sequentially connecting the \(K\) points, with the connecting lines during this process set to black, we obtain a closed the \(K\)-Polygon diagram for training as shown in Figure 3. It is worth noting that, during the process of handling the output of \(K\)-Polygon diagram, we output only the region of the image corresponding to the x-axis range \(\left[-2s:+2s\right]\) and the y-axis range \(\left[-2s:+2s\right]\). This operation eliminates excessive white space around the output \(K\)-Polygon diagram, thereby facilitating enhanced quantization precision. The output format of the \(K\)-Polygon diagram is set as a grayscale image with dimensions of \(56\times 56\), where \"\(56\times 56\)\" specifies the size of the image in terms of width and height in pixels. The aforementioned illustrates how a specific \(K\)-Polygon diagram is generated. There are a total of \(M^{l}\) different types of \(K\)-Polygon diagrams, which correspond to the \(M^{l}\) types of input symbol combinations, when \(J\) users are taken into account, each having \(M\) kinds of transmission symbols.