# DeCGAN: Speech Enhancement Algorithm for Air Traffic Control
## 2 Materials and Methods
### Generator
The dilated convolution module further enhances the ability to capture global contextual features while maintaining a balance between kernel size and computational complexity. The final convolution block compresses \(F\) to reduce computing complexity, denoted as \(F^{\prime}=F/2\). The feature map generated by the Encoder module is represented as \(F_{in}\in\mathbb{R}^{B\times T\times F\times C}\) and subsequently passes into the DeConformer module. DeConformer: As mentioned before, the traditional Conformer model can capture long-range dependencies while extracting local features, making it a popular approach for speech recognition and separation. However, this approach has to address two challenges when applied to speech enhancement: first, the correlations between the inputs of the model will be reduced because of the stage-wise modeling of signals in the time and frequency domains, and capturing global information is difficult because of the lack of modeling of signals in the channel dimension; second, in the modeling of detailed information, the model is over-reliant on the self-attention mechanism for local feature extraction, which is inefficient in terms of computational resource utilization. Furthermore, exploiting the autocorrelation of noisy data to mine local feature correlations may introduce errors, thereby affecting the accuracy of the modeling. To address these issues, the DeConformer module is proposed, as illustrated in Figure 2. This DeConformer module comprises the TFC-SA and DeConv-FFN. The TFC-SA processes the input feature map in three parallel branches along the channel, time, and frequency dimensions. Each branch computes a one-dimensional attention feature via global pooling and a pointwise convolution, then merges them through elementwise multiplication and a final pointwise convolution layer. Next, the output is passed to the DeConv-FFN, which contains two parallel branches of deformable convolution layers. One branch has two deformable convolutions, and the other has four. Each branch produces an output feature map, which is then fed into a channel-attention block. Finally, the outputs from these branches are combined, and a residual connection adds the module's input back to the result, concluding one DeConformer block. The details of the generator architecture are shown below. Specifically, here, we define the input feature to the \((i-1)\) module as \(f_{i-1}\); then, the operation of the DeConformer module is as follows:  
\[\hat{f}_{i}=f_{i-1}+TFC\text{-}SA(LN(f_{i-1}))\, \tag{2}\]  
\[f_{i}=\hat{f}_{i}+DeConv\text{-}FFN\left(LN(\hat{f}_{i})\right)\, \tag{3}\]where \(LN\) represents layer normalization, while \(\hat{f}_{i}\) in the output features of TFC-SA and \(f_{i}\) are those of DeConv-FFN. The structure of TFC-SA is also shown in Figure 2. For a given feature map \(F_{in}\in\mathbb{R}^{B\times T\times F^{\prime}\times C}\), \(C\), \(T\) and \(F^{\prime}\) are the number of channels, time frames, and frequency units, respectively. This module consists of three branches that generate one-dimensional energy features: \(F_{c}\in\mathbb{R}^{C\times 1}\) for the channel dimension, \(F_{i}\in\mathbb{R}^{T\times 1}\) for the time dimension, and \(F_{f}\in\mathbb{R}^{F^{\prime}\times 1}\) for the frequency dimension. Each branch has independence in terms of operation, and computes queries and keys via global pooling and a \(1\times 1\) convolutional layer. The attention feature maps are generated through an activation function: \(M_{c}\in\mathbb{R}^{C\times C}\) is the attention feature map for the channel branch, with \(M_{t}\in\mathbb{R}^{T\times T}\) for the time branch, and \(M_{f}\in\mathbb{R}^{F^{\prime}\times F^{\prime}}\) for the frequency branch. After generation, \(F_{in}\) is processed by a 2D \(1\times 1\) convolutional layer to obtain \(F_{o}\). To generate the final result \(F_{out}\), the feature maps \(F_{o}\), denoted as \(M_{c}\), \(M_{t}\), and \(M_{f}\), are multiplied sequentially.