A novel anti-Doppler SEI algorithm based on the vector diagram decomposition

In practical applications, communication emitters are often carried by low orbit satellites aircraft, ships, and other moving carriers. Doppler phenomenon usually exists due to the relative motion between the emitter and the receiver, which seriously affects the identiﬁcation performance. Given this situation, a method based on the signal vector decomposition and the multi-feature fusion is proposed. By normalizing and demodulating the target signal, the signal vector diagram is decomposed into four parts. We present a multi-feature fusion model with varying features extracted from each diagram by a deep learning network. Experimental results show that the proposed method is effective in the presence of Doppler effect.

✉ Email: mici0928@163.com In practical applications, communication emitters are often carried by low orbit satellites aircraft, ships, and other moving carriers. Doppler phenomenon usually exists due to the relative motion between the emitter and the receiver, which seriously affects the identification performance. Given this situation, a method based on the signal vector decomposition and the multi-feature fusion is proposed. By normalizing and demodulating the target signal, the signal vector diagram is decomposed into four parts. We present a multi-feature fusion model with varying features extracted from each diagram by a deep learning network. Experimental results show that the proposed method is effective in the presence of Doppler effect.
Introduction: Specific emitter identification(SEI) plays a quite pivotal role in many military and civilian applications. The SEI aims to identify transmitters by extracting radio frequency (RF) fingerprint features present in the emitted signals. Existing schemes can be divided into two categories: approaches based on mathematical expression or on mechanism analysis. Schemes based on mathematical expression extract features by signal mathematical processing, such as fractal [1], timefrequency analysis-based methods [2], and higher order statistics analysis [3,4]. Mechanism analysis schemes extract features by constructing a distortion model of the emitter [5]. Compared with the mathematical expression scheme, features extracted by mechanism analysis are more interpretable. In recent years, deep learning (DL) technology combined with the above two schemes has been widely explored [6]. These algorithms achieve excellent identification performance, which verifies the superiority of the DL technology in SEI.
However, relatively few studies have been done on SEI considering Doppler. In [7], the Doppler effect is regarded as a fixed frequency shift in each transmission. Due to the complexity of the motion state, the Doppler frequency shift is usually time-varying, which is difficult to accurately estimate. To improve SEI performance impacted by Doppler effect, we conceive a SEI framework based on vector decomposition diagram. The major contributions are summarized as follows. (1) The method does not need to estimate the Doppler frequency shift, which avoids unnecessary processing errors. (2) By decomposing the vector diagram, the signal trajectory winding phenomenon is reduced and the anti-noise ability is improved. (3) With the DL and multi-feature fusion technology, the extracted features are effective and robust in the Doppler scenario.
Signal model and vector diagram presentation: Assuming that the ideal RF signal is s 0 (t) and v is the comprehensive representation of the RF fingerprint, the actual transmitted signal can be defined as where f(g) is the transmitter analog circuit system response. The received signal with Doppler effect resulted from the relative motion between emitter and receiver can be expressed as where f c is the carrier frequency, n(t) represent the white Gaussian noise, α(t) represent the Doppler factor. In particular, α(t) can be given as where v denotes the initial radial velocity of their relative motion, a indicates the acceleration, and c is the speed of light. The imperfections of the emitter mainly exist in the following nonlinear front-end components: I/Q modulator, filter, oscillator, and power amplifier [5]. The vector diagram is mainly utilized to show the overall transformation of signal trajectory, which recombine the I-channel and Q-channel waveforms of signal with the corresponding time. Due to the distortion which may be caused by various mechanisms in the transmitter, different emitters will produce different visual characteristics in the vector diagram. Meanwhile, from Figure 1 and Equation (2), it can be demonstrated that the Doppler effect only causes the signal trajectory to rotate clockwise or counter-clockwise, while many useful features remain unaffected, such as amplitude gain, phase angle and the trajectory geometric center etc. Consequently, we utilize the signal vector diagram as the feature representation.
Overall architecture: The model's overall architecture is shown in Figure 2. It can be divided into three stages: vector diagram decomposition based on pre-demodulation, feature extraction based on DL network, and multi-feature fusion based on ensemble learning. Part 1: Vector diagram decomposition. Since the signal symbol sequence is required when decomposing the vector diagram, we demodulate the signal first. Compared with the SEI task, the signal demodulation is less sensitive to SNR so that we can precisely get the signal symbol sequence S. S (p,q), k signifies that the symbol of time k is p and k + 1 is q. Assuming the received signal is QPSK modulated, we can divide S into 3 types based on the relationship between the front and back symbols: symbol retentionS (p,q = p), k , adjacent symbol transfer S (p,q = p ± 1), k and reverse symbol transfer S (p,q = p ± 2), k . With these symbol transition states, we can decompose the vector diagram. The decomposition method is formulated as follows:

Fig. 3 Vector diagram decomposition
where M is over-sampling. From Equation (3), we can get 5 kinds of sequences: S, r 0 (n), r 1 (n), r 2 (n), r(n). Next, we operate on each sequence x(n) to get different feature representations. The operation can be expressed as follows: where H is P × P feature matrix. MAP(g) represents colour-map function. In this letter, we utilize 'parula' colour-map. The matrix H can be calculated as shown in Equation (5) where g represents round up. The overall process of vector diagram decomposition is shown in Figure 3.
Part 2: Feature extraction. For the feature extraction network, we choose the typical convolutional neural networks (VGG16, VGG19, ResNet18, ResNet34, ResNet50), which h2ave been proved to be very effective in the image classification field. To ensure the model adaptation, we adjust the network output nodes number as the emitter number. By comparing each network's performance on the SEI problem, we consider the ResNet34 network as the feature extraction network for the proposed model. In the training step, features are extracted respectively from each diagram for DL. In the feature extraction step, we remove the classification layer of each network and utilize the output of the network maxpool layer as the feature vector for subsequent processing. The dimension of each feature vector is 512.
Part 3: Multi-feature fusion. In this part, we firstly concatenate the feature vectors extracted from each network. To reduce the feature vector's dimension (5 × 512 = 2560), we adopt the principal component analysis (PCA) method to remove the linear correlation among features, and maximize the variance among the base vectors. We set the dimension of the projection space to 50 and the variance as 0.9832, which largely preserves the information of the base vector. For the classifier, we resort to a stacking method which can fuse features. The base classification models include K-nearest neighbour (KNN), support vector machine (SVM), and deep neural network (DNN). The meta classifier is the linear regression (LR) model. The base classifier classifies the reduced features and gets the probability of each class. In the meta classifier, the output probabilities of each base model are weighted.
Experiments: In this letter, we generate 7 emitters based on the distortion model proposed in [5]. Assuming that the orbit height of emitter on LEO satellite is 1000 km, the parameters v in Equation (2) randomly value in the range of [6000, 7000] m/s and a is 250 m/s 2 . Figure 4 illustrates the performance of the single feature and multifeatures. It can be demonstrated that the fused feature has better classification ability than the single feature. With the feature fusion model, the diversity and complementarity between different features can be fully exploited, and the recognition accuracy can be greatly improved. Moreover, the proposed approach is based on the prior demodulation knowledge, which has better anti-noise performance. Figure 5 shows the performance of different DL networks on the Im 0 . It can be demonstrated that the ResNet18, ResNet34, and ResNet50 have similar identification performance, while the VGG16 and VGG19 have relatively low recognition accuracy. It can be validated that when the network parameters reach a certain scale, the identification accuracy rate tends to be stable and fluctuates in a small range. Consequently, we choose ResNet34 as the feature extraction network of our model.
As shown in Figure 6, the identification performance has also been evaluated in the relevant literature (e.g. algorithm1 based on [8], algo- rithm2 based on [9], algorithm3 based on [2], algorithm4 based on [6]). It can be demonstrated that the proposed approach achieves a uniformly better performance than other algorithms. Meanwhile, the algorithm in this paper is insensitive to Doppler, while other algorithms suffer from a severe performance degradation in the Doppler scenario.
To further prove the effectiveness of the fusion model, we visualize the high-dimensional feature vectors before and after fusion as twodimensional points using t-SNE. The visualization results are shown in Figure 7. It can be demonstrated that the feature vector after fusion has a  larger inter-class scatter and a smaller within-class scatter than the feature vector before fusion, which is more conducive to the classification. Table 1 illustrates the performance of the different classifiers. It can be demonstrated that the SVM-based classifier has the worst performance, the KNN-based classifier the second, and the DNN-based classifier the best. Moreover, the performance of the stacking method is better than a single classifier.

Conclusion:
In this letter, we propose a novel SEI algorithm based on the vector diagram decomposition. We utilize the signal vector diagram as the DL network input. In order to improve the performance of the algorithm, we decompose the vector diagram. Compared to the existing schemes, the proposed approach provides higher identification accuracy and is insensitive to Doppler. Furthermore, it is validated that multi-feature fusion can significantly improve SEI performance.