# A Long Time Span-Specific Emitter Identification Method Based on Unsupervised Domain Adaptation
## 3 Methodology
### Classifier  
The classifier is used to integrate the shallow RFFs extracted by the feature extractor into deep features and predict labels. In the LTS-SEI framework, the classifier comprises several fully connected layers and a Softmax activation layer, as shown in Figure 4. The number of neurons of the last fully connected layer of the classifier equals the number of specific emitters. The deep feature \(\textbf{f}_{i}\) extracted from this layer can be represented as  
\[f_{c}:F_{i}\in\mathbb{R}^{1\times fi}\overset{\theta_{c}}{\rightarrow}\textbf {f}_{i}\in\mathbb{R}^{1\times N} \tag{5}\]  
where \(f_{c}\) represents the mapping function that the classifier needs to learn. \(\theta_{c}\) represents the variable parameters of \(f_{c}\). Each neuron of the last fully connected layer corresponds  
Figure 3: Structure of feature extractor: (**a**) Dataset A and (**b**) Dataset B.  
to a specific emitter, and the Softmax activation layer is used to calculate the classification probability \(\mathbf{p}_{i}\) of sample \(i\) as \[\mathbf{p}_{i}=\frac{\exp(\mathbf{f}_{i})}{\sum_{j=1}^{N}\exp(\mathbf{f}_{j})}\] (6) where \(\exp(\cdot)\) is used to calculate the exponent of the feature vector. The index value that corresponds to the greatest element of \(\mathbf{p}_{i}\) is the classifier's prediction label \(\hat{y}_{i}\) for sample \(i\). \(\hat{y}_{i}\) can be described as \[\hat{y}_{i}=\text{argmax}\left\{\mathbf{p}_{i}\right\}\] (7) where \(\text{argmax}\{\cdot\}\) represents the index that corresponds to the maximum element value. The loss function should be reasonably designed at the label output end in a bid to use the chain rule and backpropagation algorithm to update the parameter \(\theta_{f}\) of the feature extractor and the parameter \(\theta_{c}\) of the classifier. More importantly, sample features should be interclass separated, domain invariant, and intraclass consistent. We designed an effective deep-feature learning method for the feature extractor and classifier. The method uses a hybrid metric of Softmax Loss [5; 17; 18; 19], Center Loss [46], and HOMM3 Loss [40] to calculate gradient information. It can effectively reduce the distance of samples from the same specific emitters and also expand the distance of samples from different specific emitters in the feature space. Additionally, it can learn stable deep RFFs from specific emitter signals at different time periods. 1. Softmax Loss: Softmax Loss is often used for classification or recognition tasks in the field of signal processing. This is because its original intention is to enhance the interclass separation of features in a bid to identify different individuals. Without loss of generality, we also expect to minimize Softmax Loss to enhance the recognition performance of source domain samples. Softmax Loss can be expressed as \[L_{SL}=-\frac{1}{M}\sum_{i=1}^{M}\sum_{j=1}^{N}y_{S}^{ij}\log(\mathbf{p}_{S}^{ ij})\] (8) where \(M\) represents the number of source domain samples, and \(y_{S}\in Y_{S}\) denotes the true labels of the source domain samples and is represented as a one-hot vector. 2. Center Loss: Center Loss was first proposed for face recognition. It can map data with intraclass diversity into feature spaces that are close to each other. Center Loss has been applied in the fields of image classification and modulation recognition to learn discriminative features. By continuously optimizing the distance between features and their clustering centers, similar samples become more compact after being mapped to the feature space. For the classifier we designed (shown in Figure 4), the source domain sample features output by the last fully connected layer are used to calculate the Center loss \(L_{CL}\). Noteworthily, \(L_{CL}\) comprises two parts. The first part  
Figure 4: Structure of the Classifier of LTS-SEI. can reduce the distance between sample features and their class centers to enhance intraclass compactness of features.