## 3 Materials and Methods  
### Chrono-ECAPA-TDNN Network Architecture  
The architecture of the Chrono-ECAPA-TDNN network is shown in Figure 1. The input data consist of the raw digital signals of air-ground communication audio, which are then processed by a feature extractor to generate Filter Bank (Fbank) features. First, the input features are processed through a 1D convolutional layer (Conv1D + ReLU + BN) to capture temporal dependency features in the speech signal. Conv1D refers to a one-dimensional convolutional operation, ReLU denotes the Rectified Linear Unit activation function and BN refers to Batch Normalization. Next, the features are passed through three layers of the Chrono Block module. The Chrono Block module consists of multiple parallel branches designed to capture both global and local features, further extracting the temporal information of the speech. The output of the three layers of the Chrono Block is then fed into a 1D convolutional layer. After multi-layer feature aggregation, the features are further extracted. Subsequently, the features are aggregated through an attentive stat pooling layer, which aggregates all temporal information and generates a fixed-length global feature vector. Finally, after being processed through a fully connected layer and Batch Normalization (FC + BN), a fixed-length speaker embedding is generated, and the inter-class distance and intra-class divergence are computed using the Sub-Center Loss function, outputting the predicted speaker class. The specific computation process is as follows:The raw digital signals of air-ground communication audio are processed by a feature extractor to generate 80-dimensional Fbank features. The shape of the input features is \(X\in R^{B\times D\times T}\), where \(B\) represents the batch size, \(D\) is the feature dimension, and \(T\) is the number of frames. The input features are processed through a 1D convolutional layer (Conv1D + ReLU + BN) to extract temporal dependency features, as shown in Equation (1). The output feature shape is \(X_{Conv1}\in R^{B\times C\times T}\).  
\[X_{Conv1}=\text{BN}(\text{ReLU}(\text{Conv1D}(X))), \tag{1}\]  
where \(C\) represents the number of convolution channels.  
The features are then passed through three layers of the Chrono Block module, as shown in Equation (2). The Chrono Block module consists of multiple parallel branches designed to capture both global and local features, further extracting the temporal information of the speech. The output feature shape is \(X_{chrono}\in R^{B\times C\times T}\).  
\[X_{chrono}^{(l)}=\text{Chnoro Block}(X_{conv1}^{(l-1)})\text{ for }l=1,2,3, \tag{2}\]  
The outputs of the three layers are eventually combined into a single representation, as shown in Equation (3).  
\[X_{chrono\_final}\in R^{B\times 3C\times T}, \tag{3}\]  
Next, the features are passed through a 1D convolutional layer for multi-layer feature aggregation, and the output feature shape is \(X_{agg}\in R^{B\times 3C\times T}\), as shown in Equation (4).  
\[X_{agg}=BN(\text{ReLU}(\text{Conv1D}(X_{chrono\_final}))), \tag{4}\]  
Figure 1: Chrono-ECAPA-TDNN network architecture.  
Then, the features are passed through the Attentive Stat Pooling layer to aggregate all temporal information, generating a fixed-length global feature vector \(X_{pool}\in R^{B\times 3C}\), as shown in Equation (5).  
\[X_{pool}=\text{AttentiveStatPooling}(X_{agg}), \tag{5}\]  
The features are passed through a fully connected layer and Batch Normalization (FC + BN), generating a fixed-length speaker embedding \(X_{embed}\in R^{B\times N}\), where \(N\) represents the output dimension, as shown in Equation (6).  
\[X_{embed}=\text{BN}(\text{FC}(X_{pool})), \tag{6}\]  
Finally, the Sub-Center Loss function is used to compute the inter-class distance and intra-class variance, and the predicted speaker class is output, as shown in Equation (7).  
\[l=\text{SubCenterLoss}(X_{embed},Y), \tag{7}\]  
where \(Y\) represents the true label and \(l\) is the loss function.