# A Long Time Span-Specific Emitter Identification Method Based on Unsupervised Domain Adaptation
## 2 Problem Formulation and Solution  
This section describes the long time span SEI problem and explores ideas for a reasonable solution to the problem. Owing to several factors such as changes in space environment, inaccurate antenna pointing, and external interference, the trained model may not achieve satisfactory results in identifying new data collected at different time periods in the future. Additionally, new data often lack labels, so the model cannot adopt a supervised learning mechanism. Overall, our goal is to construct an SEI model with adaptive and predictive capabilities using limited data. The real received space-specific emitter signal \(x(t)\) can be represented as  
\[x(t)=[s(t)*h(t)+n(t)]\cdot e^{-\beta\pi f_{m}t} \tag{1}\]  
where \(s(t)\) represents the signal containing useful information, \(h(t)\) represents the pulse response of the space channel, and \(n(t)\) represents the noise and interference during transmission. Additionally, \(f_{m}\) represents the frequency generated by the mixer to convert a radiofrequency signal into an intermediate frequency signal. Inspired by domain adaptive learning, we consider the specific emitter signals collected at different time periods as data from different domains. We assume that the initial collected signal \(\mathbf{X}_{S}=\{\mathbf{x}_{1},\mathbf{x}_{2},\mathbf{x}_{3},\ldots,\mathbf{x }_{N}\}\in\mathcal{X}_{S}\) originates from source domain \(S_{D}\) and \(\mathbf{x}=\{x(t_{1}),x(t_{2}),x(t_{3}),\ldots,x(t_{L})\}\), as shown in Figure 1. \(L\) represents the length of each signal vector. \(\mathbf{X}_{S}\) can obtain its label set \(\mathbf{Y}_{S}=\{\mathbf{y}_{1},\mathbf{y}_{2},\mathbf{y}_{3},\ldots,\mathbf{ y}_{N}\}\in\mathcal{Y}_{S}\) through the feature extraction function \(f(x;\theta)\) and Softmax classification function. \(\theta\) and \(N\) represent the learnable parameters of \(f(x;\theta)\) and the number of categories of specific emitters, respectively. We assume that the new data \(\mathbf{X}_{T}=\left\{\mathbf{x}_{1}^{\prime},\mathbf{x}_{2}^{\prime},\mathbf{ x}_{3}^{\prime},\ldots,\mathbf{x}_{n}^{\prime}\right\}\in\mathcal{X}_{T}\) collected after time interval \(\Delta T\) come from the target domain \(T_{D}\) and \(\mathbf{x}=\left\{x(t_{1}^{\prime}),x(t_{2}^{\prime}),x(t_{3}^{\prime}),\ldots,x(t_{L}^{\prime})\right\}\). Additionally, the label set of \(\mathbf{X}_{T}\) is unknown. The pretrained source domain classification model \(f(\mathbf{X}_{S};\theta_{S})\) may not effectively perform to predict \(\mathbf{Y}_{T}\) owing to various factors. This is because \(S_{D}\) and \(T_{D}\) have a relative deviation (\(S_{D}\
eq T_{D}\)), which makes it difficult for \(f(\mathbf{X}_{S};\theta_{S})\) to transfer the domain knowledge learned from \(S_{D}\) to \(T_{D}\). Therefore, when \(S_{D}\) and \(T_{D}\) are not aligned, the hyperplane learned by \(f(\mathbf{X}_{S};\theta_{S})\) may not be appropriate for \(T_{D}\), which results in confusion regarding the sample attributes. As previously mentioned, the labels prediction problem of specific emitter signals collected at different time periods is transformed into an unsupervised domain adaptation problem. We expect to align \(S_{D}\) and \(T_{D}(S_{D}=T_{D}\) or \(S_{D}\approx T_{D})\) through domain adaptation to achieve the same feature distribution for \(\mathbf{X}_{S}\) and \(\mathbf{X}_{T}\). If this is achieved, the source domain hyperplane can correctly predict \(\mathbf{Y}_{T}\). Owing to the inability of domain alignment in completely eliminating the domain offset, when some samples of \(T_{D}\) are close to the source domain classification boundary or far from the source domain feature centers, \(f(\mathbf{X}_{S};\theta_{S})\) may experience misclassification. This problem can be alleviated using some regularization techniques to make \(\mathbf{X}_{S}\) and \(\mathbf{X}_{T}\) closer to their feature centers.