## 4 Proposed Method
### Optimized Feature Extraction Module for Radar Spectrograms: TG2  
The simplicity of radar image backgrounds determines that the complexity of the recognition model will not be very high. Therefore, through-wall radar human activity recognition is highly compatible with lightweight network models. Inspired by lightweight  
Figure 4: Overall framework diagram of TG2-CAFNet. The content enclosed by the dashed line represents the CAF module, which performs nonlinear feature fusion. Figure 3: Comparison of TDM results using MTI and exponential weighting methods. model construction ideas in the literature [18], we noticed that GhostNet [27] generates redundant intermediate features using inexpensive operations, significantly improving the performance compared to other lightweight models, with only a slight increase in the number of parameters and FLOPs. A radar human activity recognition model will actually be much smaller than an image recognition model, making this slight increase in computational overhead for improved performance entirely acceptable. The core idea of GhostNet is that, in a well-trained deep neural network, rich and even redundant information in the feature maps often ensures a comprehensive understanding of the input data. Therefore, a ghost convolution can be completed in two steps. First, a \(1\times 1\) convolution is used to generate the intrinsic features [27]:  
\[Y^{\prime}=X*F_{1\times 1}, \tag{8}\]  
where \(X\) represents the input features and \(F_{1\times 1}\) is the pointwise convolution. Then, using depthwise separable convolution, this operation generates multiple ghost features from the intrinsic features. By concatenating these ghost features with the intrinsic features, the ghost convolution is completed:  
\[Y=\text{Concat}([Y^{\prime},Y^{\prime}*F_{dw}])=\text{Concat}([Y^{\prime},Y_{g1 },Y_{g2},\ldots]), \tag{9}\]  
where \(F_{dw}\) represents the depthwise separable convolution operation. Figure 5 illustrates how a ghost convolution is performed. Radar spectrograms contain rich physical significance in their spatial distribution, but ghost convolution's ability to capture spatial information is limited, due to the presence of pointwise convolution. Therefore, we chose GhostV2 to enhance this capability. In fact, the powerful spatial-capture ability of GhostV2 mainly comes from the introduction of DFC (decoupled fully connected) attention, which is a lightweight improvement of fully connected attention and can be specifically represented as  
\[ \begin{split} a^{\prime}_{hw}&=\sum_{h^{\prime}=1}^ {H}f_{H}\odot x_{h^{\prime}w},\quad h^{\prime}=1,2,\ldots,H,\\ a_{hw}&=\sum_{w=1}^{W}f_{W}\odot a^{\prime}_{hw}, \quad w=1,2,\ldots,W,\end{split}  \tag{10}\]  
where \(x_{hw}\) is the element at the \(h\)-th row and \(w\)-th column of \(X\), \(f_{H}\) and \(f_{W}\) are the weights of the horizontal FC and vertical FC, respectively; \(\odot\) denotes element-wise multiplication; and \(a_{hw}\) is the attention map obtained through DFC. We use GhostV2 convolution to construct a feature extraction module and name it Tiny GhostV2 (TG2). The structure of a single TG2 is shown in Figure 6, and Table 1 provides the number of channels for each block of TG2. This design is inspired by the structure of  
Figure 5: Ghost convolution. First, the input feature \(X\) is processed through a \(1\times 1\) convolution to generate intrinsic features \(Y^{\prime}\). Then, \(Y^{\prime}\) is used to produce ghost features \(Y_{g}\) through a cheaper operation. Finally, \(Y^{\prime}\) and \(Y_{g}\) are concatenated to form the output of the ghost convolution. ResNet18 and considers the appropriate number of feature channels for radar spectrograms, enabling TG2 to achieve the maximum performance with minimal parameters and FLOPs. In Section 6.2, we experimentally verify that even slight changes to this structure reduce the performance of the feature extraction module for radar spectrograms. It should be noted that we place an SE [28] module in the last bottleneck block of TG2.