Transfer Learning-Based Specific Emitter Identification for ADS-B over Satellite System

Abstract

In future aviation surveillance, the demand for higher real-time updates for global flights can be met by deploying automatic dependent surveillance–broadcast (ADS-B) receivers on low Earth orbit satellites, capitalizing on their global coverage and terrain-independent capabilities for seamless monitoring. Specific emitter identification (SEI) leverages the distinctive features of ADS-B data. High data collection and annotation costs, along with limited dataset size, can lead to overfitting during training and low model recognition accuracy. Transfer learning, which does not require source and target domain data to share the same distribution, significantly reduces the sensitivity of traditional models to data volume and distribution. It can also address issues related to the incompleteness and inadequacy of communication emitter datasets. This paper proposes a distributed sensor system based on transfer learning to address the specific emitter identification. Firstly, signal fingerprint features are extracted using a bispectrum transform (BST) to train a convolutional neural network (CNN) preliminarily. Decision fusion is employed to tackle the challenges of the distributed system. Subsequently, a transfer learning strategy is employed, incorporating frozen model parameters, maximum mean discrepancy (MMD), and classification error measures to reduce the disparity between the target and source domains. A hyperbolic space module is introduced before the output layer to enhance the expressive capacity and data information extraction. After iterative training, the transfer learning model is obtained. Simulation results confirm that this method enhances model generalization, addresses the issue of slow convergence, and leads to improved training accuracy.

1. Introduction

The automatic dependent surveillance–broadcast (ADS-B) over satellite system, serving as the core technology for next-generation air traffic management, broadcasts real-time dynamic flight status and unique identification information. The evolving demands of future aviation require higher standards for surveillance applications, which the ADS-B over satellite system can meet, ensuring efficient global monitoring. In recent years, research on the effective utilization of key information in ADS-B signals has garnered significant attention. Specific emitter identification (SEI) technology utilizes hardware physical characteristics of emitting devices. By analyzing the subtle influence on emitter signals, unique “fingerprint information” is obtained. This information is then compared with a precollected library of known signals to determine the identity of a specific emitter [1,2,3,4,5,6]. Z. Wu et al. implemented SEI using deep learning and addressed the issue of insufficient labeled data through contrastive learning [1]. Y. Zhang et al. proposed a GPU-free SEI method based on a signal-feature-embedded broad learning network using a single-layer forward propagation network on a central processing unit platform [3]. X. Zha et al. demonstrated an SEI method based on complex Fourier neural operators for extracting fingerprint information, incorporating a time and frequency domain attention mechanism [4]. X. Hao et al. discussed a signal contrastive self-supervised clustering method for unsupervised SEI applications [5]. C. Liu et al. introduced a few-shot SEI method based on self-supervised learning and adversarial augmentation [6]. SEI technology has significant applications in cognitive radios, spectrum management, and network security. In traditional methods, emitter signals are usually analyzed, and features are extracted to construct feature templates and generate recognition databases for specific signal identification tasks. As electromagnetic interference levels escalate, precise individual identification becomes increasingly complex and costly. Within distributed sensor networks, the impact of ever-changing propagation and transmission conditions results in distinct signal observations at each receiving sensor, even when transmitters emit identical signals. To address this challenge comprehensively, transferring complete sensor observation data to a central node can effectively capture the signal differences, ultimately leading to the global optimization of SEI. Consequently, SEI within distributed networks offers substantial practical value [7,8,9,10,11,12].

Y. Li et al. presented a feature extraction technique utilizing the short-time Fourier transform. This method extracts the time–frequency distribution for fingerprint recognition and addresses the issue of being unsuitable for handling transient signals in the fast Fourier transform [13,14]. In [15], the empirical mode decomposition method was employed to separate the steady-state signal, extract and remove its data component, and subsequently utilize the entropy as well as the first and second moments of the residual signal as recognition features. This approach yields promising recognition results in both single-hop and relay scenarios. However, it suffers from relatively high computational costs. In [16], dynamic wavelet coefficients were utilized as fingerprint extraction features, and a supervised classification technique was employed for device identification, achieving a high accuracy rate. In [17], a method for extracting radio frequency fingerprint (RFF) features based on the I/Q imbalance of orthogonal modulation signals was proposed. This method utilizes an I/Q modulator model to study the RF fingerprints present in the constellation diagram. Simulation results indicated that this approach outperforms both bispectrum transformation and Hilbert–Huang transform in terms of performance. L. Peng et al. introduced a feature extraction method known as the differential constellation transform feature extraction method. Extracting this feature requires no synchronization or prior information and is of low complexity [18,19]. In [20], specific features were extracted and recognized in the Hilbert–Huang transform domain, and a support vector machine was utilized as the classifier to address the limitations of traditional methods, which relied on expertise and struggled to adapt to waveform variations. A feature extraction method based on bispectrum transform (BST) was proposed in [21,22,23,24]. This method achieves high recognition accuracy and performs well in noise suppression. To address the aforementioned issues, this paper employs bispectrum transform for feature extraction of individual signals, fully exploiting the fingerprint information differences among signals.

Classifiers in SEI are typically divided into two main categories: traditional machine learning algorithms and deep learning algorithms. In traditional machine learning approaches, such as the variational mode decomposition and the spectral features technique proposed by Satija et al., Taylor polynomials are used to model transmitter amplifiers, and the effectiveness of this method was validated in up to four SEI tasks [25]. In [26], radar emitter signals are classified using the relevance vector machine, with robust features obtained against variations in the signal-to-noise ratio (SNR) through transfer learning. However, traditional machine learning methods require manual feature extraction and struggle to adapt to complex electromagnetic environments. In contrast, deep learning algorithms have the capability to automatically extract and learn high-dimensional abstract features, making them widely applicable in fields like image analysis, voice identification, computational linguistics, and more. Therefore, there is immense potential in applying deep learning algorithms to the field of SEI [27,28,29,30,31,32,33]. The convolutional neural network (CNN), a deep neural network specifically designed for processing grid-structured data, is primarily utilized for image and video analysis and recognition tasks. The CNN can automatically extract and learn high-dimensional abstract features without the need for manual feature design. It excels in handling complex and dynamic signal environments due to its ability to learn more robust features. In signal processing tasks, a CNN typically demonstrates higher classification accuracy and reliability. Therefore, this paper employs a CNN for processing signal data.

Due to the high cost of collecting and annotating data from communication emitters, constructing a comprehensive dataset for communication emitters is a formidable challenge. Additionally, a small dataset can lead to overfitting during training, resulting in low model recognition accuracy. Recently, transfer learning has garnered substantial attention in addressing practical issues such as insufficient scenario data and changing data distributions. Transfer learning offers a promising solution to address the generalization shortcomings of individual identification models, as well as the “cold start” and “slow convergence” issues encountered in network training. In [6], to address the constraints of sample dependency, knowledge transfer was employed for refining both the extractor and a classifier using a target dataset comprising limited samples and their associated labels. Z. Yao et al. utilized sufficiently unlabeled training samples to drive the training process of an asymmetric masked autoencoder, obtaining an RFF extractor. Subsequently, the pretrained RFF extractor and classifier were fine-tuned using limited labeled training samples [34]. In [35], a feature fusion transfer learning algorithm was introduced, enhancing detection efficiency for overlapping objects by complementing information from distinct feature maps, thereby elevating the final recognition accuracy. Regarding a different aspect, while reinforcement learning shows great potential in fields like robotics and gaming, transfer learning has emerged to address several issues encountered in reinforcement learning. It leverages knowledge from external sources to enhance the efficiency and efficacy of the learning process [36]. Concurrently, in [37], the idea of domain adaptation was employed. An optimized model was constructed to align the features of signals at different signal-to-noise ratios (SNRs). This alignment enables a neural network trained at a specific SNR to learn fingerprint features independent of channel noise, achieving high-accuracy recognition of signals at other SNRs. Furthermore, in [38], a method for SEI was introduced, employing a deep residual adaptation network. Deep learning techniques are utilized to achieve the transfer identification task, moving from the source domain to the target domain. The optimization process involves integrating distribution disparities between the source and target domains and fine-tuning the loss function iteratively to obtain the ultimate model. This paper proposes an SEI technology based on a distributed network. The fingerprint features of signals are extracted using the BST, known for its effective noise suppression. The combination of the BST and CNN improves feature extraction and classification accuracy for signal recognition. By employing a transfer learning approach, this study extends existing domain adaptation methods and integrates a hyperbolic space module to optimize the network structure. This optimization enhances the information representation and data mining capabilities, thereby further improving the effectiveness of transfer learning.

This paper introduces a distributed transfer learning method based on convolutional neural networks (CNNs) for SEI recognition. The primary contributions are as follows:

• It uses bispectrum transform to extract features from individual signals to thoroughly mine the difference in fingerprint information among signals. The deep learning framework with CNNs is utilized for training, circumventing the issue of poor classifier results arising from insufficient feature information;
• It implements transfer learning by first training the model and storing parameters and then utilizing a well-trained model to train the target model, reusing partial network models and their parameters from the source domain. This approach avoids redundant processes such as data representation, empirical reasoning, and optimization search, focusing on specific performances in the new task, thereby enhancing training efficiency and generalization capability;
• It uses a feature-based domain adaptive transfer learning method to address the challenges of differing source and target domains. Additionally, introducing the hyperbolic space module further augments network expression capability and information mining ability, thus enhancing overall recognition accuracy.

The remaining sections of this paper are as follows. Section 2 presents an overview of the system. Section 3 illustrates the intelligent representation method for signals with fingerprint information. Section 4 provides an in-depth discussion of the transfer learning convolutional neural network. Section 5 analyzes the simulation results. Finally, Section 6 summarizes the entire paper.

Table 1. The main acronyms in this paper.

Acronym	Definition
ADS-B	Automatic dependent surveillance–broadcast
BST	Bispectrum transform
CNN	Convolutional neural network
CNNs	Convolutional neural networks
MMD	Maximum mean discrepancy
RFF	Radio frequency fingerprint
SEI	Specific emitter identification
SNR	Signal-to-noise ratio
SNRs	Signal-to-noise ratios

lists the main acronyms in this paper.

2. System Model

In this paper, we consider a specific emitter identification system based on ADS-B over satellite, as depicted in Figure 1. Each sensor receives ADS-B signals and employs transfer learning for SEI, forming a subrecognition system. Ultimately, the outputs from various sensors are integrated using a decision fusion system. The signal reception process in the system can be described as

$$X\left(t\right)=\mathit{H}S\left(t\right)+N\left(t\right),$$

(1)

where $S\left(t\right)$ represents the ADS-B signal, $\mathit{H}$ denotes the transmission channel, and $N\left(t\right)$ signifies additive Gaussian noise. The signal power is $P_s=1/T{\displaystyle \sum _{t=0}^{T-1}}{\left|S\left(t\right)\right|}^2$, the noise power is $N=1/T{\displaystyle \sum _{t=0}^{T-1}}{\left|N\left(t\right)\right|}^2$, T represents one complete cycle of the signal $S\left(t\right)$, and the signal-to-noise ratio is defined as SNR $=10{log}_{10}(P_s/N)\mathrm{dB}$.

We utilize the BST to extract the “fingerprint information” within the emitter signals to address the received ADS-B signals. Subsequently, a convolutional neural network is employed for feature extraction and classification, resulting in a trained model. To tackle the issue of decreased recognition accuracy in distributed sensor systems, we use a transfer learning approach and leverage decision fusion techniques to process the outputs from various sensors comprehensively.

3. Bispectral Feature Analysis

The bispectrum transform, known as the third-order spectrum, performs Fourier transforms on the third-order cyclic cumulant. This method remains unaffected by temporal interference, allowing for the preservation of fundamental information from the original signal and partial suppression of noise. As a result, the BST has found widespread application in the field of SEI. However, this method comes with a relatively high complexity and is often combined with techniques such as slicing or integration to achieve dimensionality reduction.

Nonparametric techniques are employed to estimate the bispectrum of the received signal, denoted as $r\left(n\right)$. The signal $r\left(n\right)$ is partitioned into $\Gamma$ segments, each comprising $\Delta$ samples. Hence, the third-order cyclic cumulant of the received signal $r\left(n\right)$ can be expressed as [39]

$${\stackrel{⌢}{c}}_{3r}({\tau }_1,{\tau }_2)=\frac{1}{\Gamma }{\displaystyle \sum _{\gamma =1}^{\Gamma }}{\chi }^{\gamma }({\tau }_1,{\tau }_2),$$

(2)

where ${\chi }^{\gamma }({\tau }_1,{\tau }_2)$ represents the third-order cyclic cumulant of each signal segment. The bispectral estimation of $r\left(n\right)$ can be expressed as

$$\stackrel{⌢}{B}(w_1,w_2)={\displaystyle \sum _{{\tau }_1=-\delta }^{\delta }}{\displaystyle \sum _{{\tau }_2=-\delta }^{\delta }}{{\stackrel{⌢}{c}}_{3r}}_{3r}({\tau }_1,{\tau }_2)w({\tau }_1,{\tau }_2)e^{-j(w_1{\tau }_1+w_2{\tau }_2)},$$

(3)

where $\delta <\Delta -1$, and $\omega ({\tau }_1,{\tau }^2)$ is a hexagonal window function. We can define the objective function for bispectral dimensionality reduction as

$$\underset{U_1,\dots ,U_M}{min}\frac{{\sum }_{i,j}\Vert U_i-U_j{\Vert }^2{s}_{ij}}{{\sum }_{i,j}\Vert U_i-U_j{\Vert }^2{d}_{ij}},$$

(4)

where $\{{\mathrm{U}}_1,\dots ,{\mathrm{U}}_{\mathrm{M}}\}$ represents the compressed bispectral projection space of the originally selected bispectral set $\{{\mathrm{V}}_1,\dots {\mathrm{V}}_{\mathrm{M}}\}$, $1\le i\le M$, and $1\le j\le M$. In this context, S and D are bispectral weight matrices originating from different or the same emitter signals. When the emitters are distinct, $s_{ij}=0$, otherwise

$$s_{ij}=\frac{1}{\epsilon }{e}^{-\Vert V_i-V_j{\Vert }^2}.$$

(5)

If the emitters are identical, $d_{ij}=0$, otherwise

$$d_{ij}=\frac{1}{\epsilon }{e}^{-\Vert V_i-V_j{\Vert }^2},$$

(6)

where $\epsilon$ is a positive real value.

Then we can rewrite (4) as

$$\underset{\omega }{min}\frac{{\omega }^{T}V({\phi }_1\otimes I_n)V^T\omega }{{\omega }^{T}V({\phi }_2\otimes I_n)V^T\omega },$$

(7)

where ${\phi }_1=O-S,{\phi }_2=F-D$, $o_{ii}={\sum }_j{s}_{ij},f_{ii}={\sum }_j{d}_{ij}$, ⊗ is the matrix multiplication. Let $w^{T}V({\phi }_2\otimes I_n)V^{T}w=\delta$, where $\delta$ is a nonzero constant, so we can then express the Lagrangian function as

$$G(\omega ,\lambda )={\omega }^{T}V({\phi }_1\otimes I_n)V^T\omega +\lambda (u-{\omega }^{T}V({\phi }_2\otimes I_n)V^T\omega ),$$

(8)

where $\lambda$ serves as a weight coefficient. To achieve the minimization of (7), we establish $\frac{\partial G(\omega ,\lambda )}{\partial w}=0$. Subsequently, we can derive from the Lagrangian function

$$V({\phi }_1\otimes I_n)V^{T}w=\lambda V({\phi }_2\otimes I_n)V^{T}w.$$

(9)

According to the above expression, we can calculate the elements ${\omega }_i$ inside the mapping matrix and consequently obtain the projection matrix $W=[{\omega }_1,\dots ,{\omega }_d]$, from which the compressed bispectrum $U_i$ can be calculated as

$$U_i=V_{i}W.$$

(10)

where $V_i$ is the original selected bispectrum.

Figure 2 illustrates the bispectrum transformation diagram of an ADS-B signal. The x axis and y axis represent the two frequency components of the signal, while the z axis represents the bispectral density, indicating the strength of the interaction between these two frequency components. The lighter the color, the higher the spectral density. We can observe that the bispectral transform features of different ADS-B signals are distinct.

4. Specific Emitter Identification Based on Transfer Learning

Deep learning can leverage latent features more comprehensively, thus relaxing the requirements for feature extraction. CNNs are a deep feed-forward artificial neural network that has demonstrated exceptional performance across various data recognition tasks. In this study, we employ Alex-Net as the recognition architecture, comprising 60 million parameters and 65,000 neurons. The first layer of the network includes five convolutional layers with kernel sizes and quantities of 96 × 11 × 11, 256 × 5 × 5, 384 × 3 × 3, 384 × 3 × 3, and 256 × 3 × 3, respectively. A 3 × 3 pooling layer follows each convolutional layer, facilitating data compression and reduction in computational load. Subsequently, three fully connected layers with 4096, 4096, and 1000 nodes, respectively, are incorporated. As the objective is to classify the number of individual emitters, a soft-max function is added as the output layer with M nodes (M representing the number of emitters to be identified). Additionally, to mitigate overfitting, a dropout layer is introduced following each fully connected layer. The convolutional neural network architecture employed in this paper, designed to accomplish the task of individual emitter identification, is illustrated in Figure 3. The input to the neural network consists of the bispectral density information of the signals described in Figure 2.

In real-world applications, machine learning faces several challenges. For instance, there might need to be more data to support practical training in specific scenarios. For example, acquiring high-quality labeled data could be costly and difficult in medical image processing. Additionally, deep learning models assume that data follow a fixed distribution, yet real-world data distributions can change over time and space, leading to inadequate robustness of deep learning models. Hence, transfer learning emerges as a solution, leveraging pretrained models (source domain models) to enhance the desired models (target domain models) to improve training efficiency, enhance model generalization ability, and address issues like network convergence.

In transfer learning, several key concepts need to be clarified initially. “Domain” refers to the feature space $\mathcal{X}$ and the marginal probability distribution ${\mathit{P}}^X$ (where X represents the input sample set x) of the data. Different domains possess distinct feature spaces and marginal probability distributions. “Task”, on the other hand, pertains to a specific domain $\mathit{D}=\{\mathcal{X},{\mathit{P}}^X\}$ and comprises the label space y and the prediction function $f(·)$, where $f(·)$ is used to predict unknown data. ${\mathcal{D}}_x={\left\{(x_{s_i},y_{s_i})\right\}}_{i=1}^{n_s}$ and ${\mathcal{D}}_y={\left\{(x_{s_i},y_{s_i})\right\}}_{i=1}^{n_s}$ represent labeled data from the source domain and the target domain, respectively, while $x_{s_i}\in {\mathcal{X}}_s,x_{s_i}\in {\mathcal{Y}}_s$, respectively, denote the inputs and outputs of the target domain. The objective is to utilize knowledge acquired from the source domain ${\mathit{D}}_s$ and source task ${\mathit{T}}_s$ to assist in the learning of the $f(·)$ for the target domain ${\mathit{D}}_t$ and target task ${\mathit{T}}_t$, aiming to enhance learning performance. Figure 4 illustrates an example process of transfer learning.

4.1. Model-Based Transfer Learning

Model-based transfer learning assumes that the target domain and source domain share specific parameters or common knowledge at the model level. The source network model encapsulates expertise and experience through its network parameters and architecture. The main objective is to identify the parameter components that embody the learning outcomes. In other words, the aim is to reuse parts of the source network model and its parameters, avoiding redundant processes of data representation, experiential reasoning, and optimization when training the new task. This makes transfer learning more efficient, capturing essential information within the network.

In model-based transfer learning, two key approaches should be noted:

(1) Learning and transfer of source domain model ${\theta }_s$: The source domain model must initially acquire rich knowledge from known data. The pretrained source domain model is then transferred to the target domain model, leveraging the acquired knowledge to initialize and optimize the network. With limited labeled data ${\left\{(x_{s_i},y_{s_i})\right\}}_{i=1}^{n_s}$, a more accurate target domain model ${\theta }_t$ can be obtained while reducing the risk of overfitting.

(2) Determination of shared parameters: When deciding which parameters to retain and which to modify, consideration must be given to different layers of the network structure. Typically, the initial layers of the model, such as convolutional layers, function like Gabor filters, extracting shallow features like color distribution, light intensity, and contours. Conversely, the final layer of the network is often tailored to a specific task, such as animal or ethnicity classification. This suggests that the parameters of the initial layers are generalizable, while those of the final layers are task-specific. When dealing with limited target data, freezing the parameters of the general feature extraction layers while learning only the task-specific components could lead to better performance gains.

The essence of model-based transfer learning can be summarized as follows: acquire the source network model, transfer its parameters to the target network, and train the network on the new dataset. When the target dataset is small, fine-tuning all layers might lead to overfitting. Instead, freezing the parameters of the first N layers and learning only the remaining task-specific layers is recommended. Conversely, joint learning of all parameters is feasible when the target dataset is extensive. Figure 5 illustrates the concept of model-based transfer learning. Algorithm 1 outlines the training procedure for model-based transfer learning.

Algorithm 1 Training procedure of model-based transfer learning.

1: Collect and preprocess 40 classes of civil aviation aircraft signals (1000 signals per class); 2: Extract features using the bi-spectrum transform; 3: Annotate and store the data; 4: Train the source domain model using 32 classes and save the model; 5: Fine-tune the model with the remaining 8 classes; 6: Test the final model on the testing dataset.

4.2. Feature-Based Transfer Learning

In the current landscape of machine learning, specific features may only hold meaning in particular domains. For instance, skin color might only be relevant for classifying different ethnicities but not in the context of fruit classification. Consequently, reusing samples from the old model to achieve transfer learning objectives becomes challenging due to inherent feature differences. To tackle this problem, this study introduces a transfer learning approach that integrates MMD with classification error. The key lies in mapping features from the original input space to an abstract space rather than directly dealing with the raw area. Specifically, we learn a pair of mapping functions, denoted as $\{{\phi }_s(·),{\phi }_t(·)\}$, to transform features from different domains into a shared common mapping space that contains domain-invariant features. Such mapping aids in reducing the disparity between the source and target domains, thereby achieving the objectives of transfer learning.

This paper introduces a feature-based transfer method grounded in domain adaptation theory. Firstly, we define a feature transformation T to align the joint distribution of the target and source domains, enabling them to share a common mapping in feature space. The feature transformation T can be expressed as [40]

$$\begin{array}{c}\underset{T}{min}{∥{\mathbb{E}}_{P({\mathcal{X}}_{\mathit{s}},y_s)}\left[T\left({\mathcal{X}}_{\mathit{s}}\right),y_s\right]-{\mathbb{E}}_{P({\mathcal{X}}_{\mathit{t}},y_t)}\left[T\left({\mathcal{X}}_{\mathit{t}}\right),y_t\right]∥}^2\hfill \\ \approx {∥{\mathbb{E}}_{P_s\left({\mathcal{X}}_{\mathit{s}}\right)}\left[T\left({\mathcal{X}}_{\mathit{s}}\right)\right]-{\mathbb{E}}_{P_t\left({\mathcal{X}}_{\mathit{t}}\right)}\left[T\left({\mathcal{X}}_{\mathit{t}}\right)\right]∥}^2\hfill \\ +{∥{\mathbb{E}}_{Q_s\left(y_s\right|{\mathcal{X}}_{\mathit{s}})}\left[y_s|T\left({\mathcal{X}}_{\mathit{s}}\right)\right]-{\mathbb{E}}_{Q_t\left(y_t\right|{\mathcal{X}}_{\mathit{t}})}\left[y_t|T\left({\mathcal{X}}_{\mathit{t}}\right)\right]∥}^2\hfill \end{array},$$

(11)

where $Q\left(y\right|\mathcal{X})$ represents the conditional probability distribution. This paper employs principal component analysis (PCA) to perform dimensionality reduction and reconstruction of errors. In other words, we seek an orthogonal transformation matrix $\mathit{A}$ to maximize the variance of the embedded data, achieved by optimizing the following expression:

$$tr\left({\mathit{A}}^T\mathit{X}\mathit{H}{\mathit{X}}^T\mathit{A}\right),$$

(12)

where $\mathit{I}$ represents the identity matrix, $\mathit{H}=\mathit{I}-\frac{1}{n}$, $\mathit{X}$ is the input feature matrix, $tr(·)$ denotes the trace of a matrix, and the equation can be optimized as an efficient solution to the eigenvalue decomposition $\mathit{X}\mathit{H}{\mathit{X}}^T\mathit{A}={\mathit{A}}^T\varphi$, with $\varphi$ representing the top k largest eigenvalues.

The distribution discrepancy between domains needs further refinement, and in this paper, the MMD is employed to quantify the distance between domains. MMD is a nonparametric metric, which can be estimated as

$$MMD(X_s,X_t)={∥\frac{1}{n_s}{\displaystyle \sum _{i=1}^{n_s}}\varphi \left(x_i^s\right)-\frac{1}{n_t}{\displaystyle \sum _{j=1}^{n_t}}\varphi \left(x_j^t\right)∥}_{\mathcal{H}},$$

(13)

where $X_s$ denotes the sample set of the source domain, $X_t$ represents the sample set of the target domain, and $\varphi \left(x\right)$ maps each sample to the Hilbert space $\mathcal{H}$ using the kernel $k(x_i,x_j)=\varphi {\left(x_i\right)}^T\varphi \left(x_j\right)$. $n_s{n}_t$, respectively, denote the sizes of the source and target domain sample sets. Substituting this into PCA yields

$$\begin{array}{cc}\hfill MMD(X_s,X_t)& =∥\frac{1}{n_s}{\displaystyle \sum _{i=1}^{n_s}}{\mathit{A}}^T{x}_i-\frac{1}{n_t}{\displaystyle \sum _{j=1}^{n_s+n_t}}{\mathit{A}}^T{x}_j∥\hfill \end{array}$$

(14)

Simplify it through the kernel function

$$MMD(X_s,X_t)=tr\left({\mathit{A}}^T\mathit{X}{\mathit{M}}_{\mathbf{0}}{\mathit{X}}^T\mathit{A}\right),$$

(15)

where ${\mathit{M}}_{\mathbf{0}}$ is defined as

$${\left(M_0\right)}_{ij}=\left\{\begin{array}{c}\frac{1}{n_s^2}{x}_i,x_j\in {\mathit{X}}_s\hfill \\ \frac{n_1{n}_e}{n_s{n}_t}{x}_i,x_j\in {\mathit{X}}_t\hfill \\ -\frac{1}{n_s{n}_t}others\hfill \end{array}\right..$$

(16)

In addition to MMD, this paper also aims for the transfer learning paradigm to contribute to the representation of the classifier. This requires minimizing the loss function as much as possible, i.e.,

$$\mathcal{L}={\mathcal{L}}_c(X_L,y)+\lambda MM{D}^2(X_S,X_T),$$

(17)

where ${\mathcal{L}}_c(X_L,y)$ denotes the classification loss of the model concerning the actual labels y and input data $X_L$. Meanwhile, $MMD(X_S,X_T)$ represents the distance between the source data $X_S$ and the target data $X_T$, with $\lambda$ being a hyperparameter that governs the level of domain confusion. It is imperative to establish $\lambda$. Setting $\lambda$ too low renders the MMD regularizer ineffective on the learned representation, while setting $\lambda$ too high imposes excessive regularization, resulting in a degenerate representation where all points are too close together. For transfer learning methods, we set the regularization hyperparameter to $\lambda =0.25$, which makes the objective primarily weighted towards classification but with sufficient regularization to prevent overfitting [40]. Algorithm 2 outlines the training procedure for feature-based transfer learning.

Algorithm 2 Training procedure of feature-based transfer learning.

1: Preprocess signal data: clean, filter, and reduce noise; 2: Transform signals using bi-spectrum analysis, downsample to n × 1 × 256 × 256 dimensions; 3: Initialize network training on source data, compute loss ${\mathcal{L}}_c(X_L,y)$, preserve source network parameters; 4: Transfer $X_S$ network to $X_T$, freeze first five convolutional layers; 5: Embed adaptation error layer in target network, co-train using limited $X_S$ and $X_T$ data, merge classification and MMD losses for parameter refinement; 6: Refine network parameters iteratively to derive finalized model.

4.3. Domain-Adaptive Transfer Learning in Hyperbolic Space

While we have indeed been able to enhance recognition accuracy through feature-based transfer learning methods, they still fall short of our expectations. We are aware that MMD narrows the gap between different domains by mapping features into an abstract space, where distinct domain spaces are transformed through mapping into a common mapping space composed of domain-invariant features. Nevertheless, we can reconsider delving again into the hierarchical relationship information of training samples, further probing their associations to enhance the expressive capabilities of the model. This endeavor contributes to rendering the source network model more comprehensive, thereby further amplifying the effects of transfer learning. In recent years, hyperbolic space has gradually found its way into deep learning and has been extensively applied. Its unique strengths, such as aiding information mining and enhancing model expressiveness, aptly align with the goal of improving transfer learning outcomes [41].

Hyperbolic geometry, also known as Lobachevskian geometry, departs from the “parallel axiom” of Euclidean geometry and instead employs the distinct “dual-sector plane axiom”, thus constituting a form of non-Euclidean geometry. This study adopts the Poincaré ball model of hyperbolic space as the spatial model, defined by ${\mathit{D}}_{\tau }^d=\left\{\mathbf{x}\in {\mathit{R}}^d:\tau ∥\mathbf{x}∥<1,\tau \ge 0\right\}$, where $\tau$ represents the curvature of the Poincaré ball. In this model, the induced distance between any two points ${\mathbf{z}}_i,{\mathbf{z}}_j\in {\mathit{D}}_{\tau }^d$ can be expressed as

$$d_{\mathit{D}}\left({\mathbf{z}}_i{\mathbf{z}}_j\right)={cosh}^{-1}\left(1+\frac{2{∥{\mathbf{z}}_i-{\mathbf{z}}_j∥}^2}{\left(1-{∥{\mathbf{z}}_i∥}^2\right)\left(1-{∥{\mathbf{z}}_j∥}^2\right)}\right).$$

(18)

By appending a hyperbolic network layer to the end of the original deep learning network [40] and ultimately mapping the Euclidean space ${\mathit{R}}^n$ onto the hyperbolic manifold ${\mathit{D}}_{\tau }^n$, the process can be represented as

$$\mathbf{z}=tanh\left(\sqrt{\tau }∥\mathbf{x}∥\right)\frac{\mathbf{x}}{\sqrt{\tau }∥\mathbf{x}∥}.$$

(19)

Algorithm 3 outlines the training procedure for domain-adaptive transfer learning in hyperbolic space.

Algorithm 3 Training procedure of domain-adaptive transfer learning in hyperbolic space.

1: Preprocess signal data: clean, filter, and reduce noise; 2: Transform signals using bi-spectrum analysis, downsample to n × 1 × 256 × 256 dimensions; 3: Initialize training on the source data with a hyperbolic space layer before the soft-max layer, compute the classification loss, and preserve parameters; 4: Transfer $X_S$ network to $X_T$, freeze first five convolutional layers; 5: Add an MMD layer to the target network and co-train it with limited source and target data. Develop a hybrid loss function that combines classification and MMD losses to refine parameters.; 6: Refine network parameters iteratively to derive finalized model.

5. Numerical Results and Discussion

The S-mode transponder extended squitter message protocol is one of the ADS-B link protocols. We adopt the widely used 1090ES in the extended squitter of mode S transponders as the simulation signal. The operational frequency is 1090 MHz, and the total frame length is 120 μs, with the first 8 μs being the leading pulse and the subsequent 112 μs being the data field. The leading pulse consists of four pulses with a duration of 0.5 μs, starting at times 0 μs, 1 μs, 3.5 μs, and 4.5 μs. The data field comprises 112 bits, where each bit represents a message containing information such as the position, altitude, speed, heading, and identification number of the aircraft. Pulse position modulation and binary amplitude shift keying are employed for data encoding, where a falling edge represents a data signal of “1” and a rising edge represents a data signal of “0”, indicating each message. We sample data of 5 μs length from the leading pulse of the ADS-B signal, using a frequency of 600 MHz, and set the SNR in the range of −8 dB to 8 dB.

The simulation experiments were conducted on an Intel Core i9-9920X desktop computer. The CPU of this machine runs at a speed of 3.50 GHz, with 96 GB of RAM, and is equipped with two RTX2080Ti graphics cards. We conducted our experiments using MATLAB version R2018b (MathWorks, Natick, MA, USA) and PyTorch version 1.10 (Facebook AI Research, Menlo Park, CA, USA).

To assess the reliability of our method, we trained the source model with 1090ES simulated signals at an 8 dB signal-to-noise ratio and the transfer target model at −8 dB. Figure 6 displays the training and testing accuracy of the source model at 8 dB, while Figure 7 shows the corresponding loss values. The prediction outcomes on the test set are depicted in the output confusion matrix in Figure 8. Diagonal values represent prediction accuracy probabilities. Figure 9 depicts the progression of the learning rate across training batches. These figures indicate that at higher SNRs, signals demonstrate strong recognition performance, achieving up to a 96% average accuracy on the validation set.

At a −8 dB SNR without transfer learning, Figure 10 and Figure 11 display the training and testing accuracies alongside the associated loss values. The test set predictions are further illustrated in the output confusion matrix in Figure 12. At a −8 dB SNR, the recognition performance significantly declines, nearly reaching random guessing levels (12.5%). As depicted in Figure 12, the neural network misclassifies all signals. In this situation, the network model becomes meaningless. However, what we need to consider is that regardless of whether it is 8 dB or −8 dB noise, the signals belong to the ADS-B signal. Their dual-spectrum transformations should exhibit the same distribution and retain many standard learning features. Therefore, this study first addresses this performance degradation issue using a model-based transfer learning approach.

Figure 13 and Figure 14 showcase the training accuracy and loss under the transfer learning paradigm. We retain parameters from the 8 dB-trained source model, incorporate them into the −8 dB targeted model and keep the convolutional layer parameters fixed, enabling only standard updates to the fully connected layers. This strategy yields the final recognition model, with its performance depicted in the confusion matrix in Figure 15.

Figure 15 illustrates that using the model parameter sharing-based transfer learning method boosts training accuracy from about 12% to roughly 79% compared to direct training with the target dataset. This illustrates that the method of transferring the source domain model and freezing the convolutional layer parameters is advantageous for initializing and optimizing the network, effectively addressing the issue of difficult convergence. However, the convolutional neural network often misclassifies the sixth-class signal, mistaking it for the eighth-class signal.

Conventionally, in transfer learning, convolutional layers remain untrained while only the fully connected layers adapt to specific tasks. Yet, determining the optimal layer for transitioning from shared to task-specific parameters and whether to freeze initial layers remains open to further exploration. These findings suggest potential enhancements in model parameter-based transfer learning.

Figure 16 and Figure 17 depict the recognition accuracy and loss of the feature-based transfer learning method, incorporating the MMD error loss. Compared to exclusive model parameter-based approaches, recognition accuracy improves by about 10%, nearing 90%. This suggests that integrating the MMD error adaptation term further refines recognition accuracy beyond fixed parameters, aligning with transfer learning goals. The confusion matrix in Figure 18 demonstrates enhanced classification for the sixth-class signal in feature-based transfer learning, indicating progress over model parameter-based methods.

We apply domain-adaptive transfer learning within hyperbolic space to bolster recognition accuracy, as detailed in Figure 19 and Figure 20 for accuracy and loss trends and Figure 21 for the confusion matrix.

Analyzing Figure 19, Figure 20 and Figure 21 reveals the advantages of leveraging hyperbolic space, facilitating enhanced model expressiveness and capturing hierarchical signal relationships. The test dataset yields a recognition accuracy of approximately 92%. This outperforms the MMD error domain adaptation approach by roughly 2% and notably elevates recognition for the sixth-class signal.

We conducted simulation experiments to validate the efficacy of our method, exploring diverse Doppler shifts, SNRs, and ADS-B signal channels. Figure 22 demonstrates consistent recognition accuracy across most signal classes at varied SNRs, highlighting the effectiveness of noise suppression in the method. It can be observed that when the SNR is greater than 0 dB, the recognition rates of various types of signals after transfer learning all exceed 90%. Furthermore, with changes in SNR, the recognition rates of most signals show no significant fluctuations, indicating the high robustness of the proposed method. Specifically, the model trained at an 8 dB SNR undergoes transfer learning to adapt to lower SNR signals.

Figure 23 depicts recognition accuracy fluctuations with varying Doppler shifts. It can be observed that the phenomenon of Doppler shift affects recognition accuracy, with lower Doppler shifts corresponding to higher accuracy rates. Although Doppler shift influences accuracy, transfer learning ensures a recognition accuracy of over 90% at a Doppler shift of 100 Hz, highlighting enhanced robustness. Figure 24 examines average recognition accuracy across Rayleigh flat fading and Gaussian channels. The approach proposed by Zhang, X. et al. [27] is used for comparison. It employs a domain adversarial neural network to generate domain-invariant fingerprint features, thus achieving SEI. By comparison, the recognition accuracy of the proposed CNN network framework for identification surpasses that of the existing literature in both Gaussian and Rayleigh channels. When SNR is above −8 dB, the average recognition accuracy still exceeds 85%; while Rayleigh conditions marginally reduce recognition, the decline remains insignificant, affirming the adaptability of the method to Rayleigh fading.

Lastly, Figure 25 contrasts the recognition accuracy of three transfer learning methods across different SNRs. The approaches proposed by Yang, Z. et al. [26] and Zhang, X. et al. [27] are for comparison. From Figure 25, it can be observed that model-based transfer learning achieves approximately 80% accuracy at an SNR of −8 dB. However, according to Figure 15, its performance on the sixth category of signals remains suboptimal. Feature-based transfer learning further refines the recognition method, elevating the recognition rate to 90% under equivalent conditions. Furthermore, the hyperbolic space domain adaptation in transfer learning enhances performance even further, yielding an ultimate recognition accuracy of about 92% at −8 dB SNR. As a result, hyperbolic space domain adaptation-based transfer learning emerges as an effective learning approach, particularly under low SNR conditions. Furthermore, the three methods proposed in this paper demonstrate higher recognition rates compared to SEI using traditional approaches, and the result indicates that the approach has robustness against SNR variation.

6. Conclusions

This paper proposed an SEI framework based on transfer learning to address individual emitter recognition in an ADS-B over satellite system. Firstly, signal fingerprint information was extracted through a bispectrum transform to capture signal features accurately. Subsequently, these fingerprint details were input into a convolutional neural network to enable intelligent processing, ultimately leading to SEI recognition. A decision fusion approach was employed to tackle the problem of inconsistent identification accuracy in distributed systems. Three transfer learning methods were introduced in this paper to enhance model generalization and address the “cold start” and “slow convergence” issues in network training. Through comprehensive simulation studies, the effectiveness of this approach was confirmed. Simulation results demonstrated that transfer learning can overcome convergence challenges or slow convergence rates in various network models. Even under low SNR conditions (−8 dB), favorable training outcomes can still be achieved. Additionally, this approach exhibited a certain level of robustness in scenarios involving frequency shifts or Rayleigh fading. However, this study only considered typical Gaussian noise as the noise model, while in complex channel environments, such as in the presence of non-Gaussian noise, individual emitter fingerprints are susceptible to disturbance, increasing the difficulty of knowledge transfer. Effectively integrating transfer learning for multidimensional feature extraction in complex signal environments becomes a crucial research direction.