# DeCGAN: Speech Enhancement Algorithm for Air Traffic Control
## 2 Materials and Methods
### Generator
Subsequently, another 2D \(1\times 1\) convolutional layer processes the multiplication results to yield the output \(F_{out}\in\mathbb{R}^{B\times T\times F^{\prime}\times C}\). In this manner, a global relationship is calculated by TFC-SA, based on the features of each dimension. The DeConv-FFN module, inspired by [15], introduces a channel attention mechanism to facilitate adaptive channel selection while enhancing feature modeling capabilities through local processing with varying receptive field sizes. The module's architecture is also available in Figure 2. In DeConv-FFN, there are two parallel branches, each of which has a varied number of deformable convolutional layers to produce feature maps with distinct receptive field sizes. The outputs of these branches are independently processed using the channel attention mechanism. For the input feature \(I\), the two branches have two and four deformable convolution layers, respectively, which concurrently generate the outputs \(f_{2}\) and \(f_{4}\):  
\[\left\{ \begin{array}{l}f_{2}=H_{2}(I)\\ f_{4}=H_{4}(I)\end{array} \right. \tag{4}\]  
Specifically, input feature \(I\) is fed into each branch separately. \(H_{2}(\cdot)\) applies two deformable convolution blocks in sequence, while \(H_{4}(\cdot)\) applies four. Each block expands the sampling grid via learned offsets, enabling the network to capture more flexible local patterns. After passing through these respective blocks, the two branches output their feature maps as \(f_{2}\) and \(f_{4}\). Figure 2: Network architecture of DeConformer. After calculating \(f_{2}\) and \(f_{4}\), we follow the steps specified in Equation (5) to compute the output \(S\):  
\[\left\{ \begin{array}{l}v=Global\ Pooling(Concat(f_{2},f_{4}))\\ w_{2},w_{4}=sigmoid\big{(}[H^{1}_{FC}(v),H^{2}_{FC}(v)]\big{)}\\ S=f_{2}\cdot w_{2}+f_{4}\cdot w_{4}\end{array} \right., \tag{5}\]  
where \(H^{1}_{FC}(\cdot)\) and \(H^{2}_{FC}(\cdot)\) represent two different fully connected layers. Therefore, we use two separate fully connected layers to produce two scalar values, \(w_{2}\) and \(w_{4}\). Then, the sigmoid function is applied to each scalar individually. Unlike conventional and dilated convolution using standard or zero-padding sampling grids, deformable convolution enhances the sampling grid through trainable offsets, which are learned by additional convolutional layers from the input feature maps to enable the capturing of information beyond regular local neighborhoods. Through this mechanism, the receptive field is expanded, and the speech features can be modeled more flexibly. Decoder: Using the DeConformer module, both local and global time-frequency features are deeply extracted for input into the mask decoder and complex decoder, respectively. The former predicts a mask to enhance the magnitude feature of speech signals. Specifically, the mask is applied to the time-frequency points of the input spectrum to augment effective information while suppressing background noises in the speech signals. The complex decoder, while also considering phase information recovery to ensure the integrity of the recovered spectrum, focuses on processing the real and imaginary parts of the complex spectrum. Although the two decoders serve different functions, they share a similar structure, as shown in Figure 1. Both decoders have four dilated convolution blocks, with \(\{1,2,4,8\}\) as the dilation factors, respectively; they use convolutional layers to upsample the frequency dimension, restoring it to the original frequency size \(F\). In the last convolutional layer of the mask decoder, the output channel is defined as \(1\), and a convolutional layer with a parametric rectified linear unit (PReLU) activation function is used to generate the final amplitude mask.