RF Fingerprint Feature Extraction Method and System Based on Hybrid Fractional Domain Wavelet Scattering Network

Abstract

A radio frequency fingerprint feature extraction method and system based on a hybrid fractional domain wavelet scattering network includes the following steps: first, constructing a fractional domain wavelet transform scattering network through a multi-layer network cascade; second, using the fractional domain wavelet transform scattering network, the input signal is subjected to feature decomposition based on a multi-scale fractional domain wavelet filter to obtain the low-frequency and high-frequency features corresponding to the input signal. The feature parameters contain the key information of the input signal and the data volume is much smaller than the original signal, thereby removing some unnecessary redundant information; the obtained feature signal is then fed into the corresponding convolutional neural network as input for feature fusion perception, and accurate identification of large-scale radiation source equipment is achieved through a large-scale network. The present invention efficiently completes signal feature information extraction and enhances network interpretability while minimizing redundant information in the input residual network, thereby improving the learning efficiency of the network model and the accuracy of large-scale device identification.

Description

Technical Field

[0001] The present invention belongs to the technical field of radiation source device feature recognition, and in particular relates to a radio frequency fingerprint feature extraction method and system based on a fractional domain wavelet transform scattering network. Background Art

[0002] With the continuous advancement of wireless communication technology, large-scale intelligent IoT and edge computing devices are being deployed in wireless systems. This brings with it significant challenges for traditional upper-layer key and protocol security models, which are often vulnerable to network attacks, man-in-the-middle attacks, and information leaks. Traditional encryption and decryption models not only consume significant computing resources but also place higher demands on the communication payload of lightweight devices, requiring significant communication resources to ensure the proper operation of legitimate user authentication and access protocols. Furthermore, with the rapid development of communications and electronic warfare in the defense and military fields, various types of communications and radar equipment are being used in military competition and confrontation. Specific Emitter Identification (SEI) technology is a key technology in this field. As early as the last century, the United States proposed this technology to identify and track different communication emitters. Later, it evolved and was applied to electronic warfare systems to identify battlefield targets. In scenarios where various network types and emitter devices coexist, how to quickly and accurately identify targets has become a pressing issue. Radio frequency fingerprints are unique characteristics present in radio frequency devices. These characteristics are generated by non-ideal factors such as the manufacturing and processing of various components within the device. The accumulated characteristics of these components form a unique fingerprint for each device. Research institutions both domestically and internationally have conducted extensive and in-depth research on this issue, including on traditional Wi-Fi, GSM, LTE, as well as specialized devices such as communication radios and radars. Traditional computational methods such as statistics, transform domain analysis, and fractal transformations are used to classify different types of devices. However, these traditional computational approaches are often limited by computational complexity and accuracy, hindering their widespread adoption. This is primarily because these characteristics are often formed by the cascade of nonlinear features from different modules, making it difficult to accurately mathematically describe the device's RF signature. Furthermore, these traditional approaches fail to account for the characteristics of various devices. Consequently, as the number of devices increases, accuracy declines and robustness and generalization are lost. In recent years, with the continuous development of deep learning, significant progress has been made in the field of artificial intelligence (AI) in distributed feature extraction and data representation. Since 2016, industry and academia have been actively conducting research on the perception, extraction, and application of subtle RF features, attempting to overcome the difficulties in extracting and applying subtle RF features, and thereby ensure the smooth implementation of practical applications in areas such as large-scale Internet of Things, precise identification of military targets, and key perception of spectrum content.China Mobile recently released a white paper on next-generation wireless communication networks, titled "2030+ Vision and Demand Report." The report emphasizes that 6G should build on 5G to fully support the digitalization of the entire world and, combined with the development of technologies like artificial intelligence, achieve ubiquitous intelligence and fully empower everything. Achieving these goals requires robust and flexible future networks, requiring highly reliable security measures and effective resource scheduling strategies. RF subtle signatures are unique and highly stable device characteristics. Effective spectrum sensing and anomaly detection are prerequisites for resource scheduling and efficient utilization. Deep learning solutions can fully learn the characteristics of specific devices using large datasets. Using a data-driven approach, they can perceive and extract complex RF fingerprints hidden within devices, enabling high-precision identification of large-scale devices. However, deep learning solutions also suffer from limited interpretability and excessive data requirements, often resulting in significant computational and data resource consumption during network training. In 2012, Professor S. Malla proposed Deep Scattering Networks (DSNs) based on traditional wavelet transforms. These networks are simplified convolutional neural networks that replace the linear filters in convolutional neural networks with multi-scale wavelet transform filters to achieve deep decomposition of input signal features. However, deep scattering networks based on traditional wavelet transforms cannot effectively analyze non-stationary signals. Summary of the Invention

[0003] The purpose of the present invention is to provide a radio frequency fingerprint feature extraction method and system based on fractional domain wavelet scattering network to solve the above problems.

[0004] To achieve the above object, the present invention adopts the following technical solutions:

[0005] The radio frequency fingerprint feature extraction method based on mixed fractional domain wavelet scattering network is characterized by comprising the following steps:

[0006] Firstly, a fractional domain wavelet transform scattering network is constructed by cascading multiple layers of networks;

[0007] Secondly, the fractional domain wavelet transform scattering network is used to perform feature decomposition on the input signal based on the multi-scale fractional domain wavelet filter to obtain the low-frequency and high-frequency features corresponding to the input signal. Compared with the amount of original signal data, unnecessary redundant information is removed and the amount of feature data is greatly reduced.

[0008] The characteristic signal obtained after removing unnecessary redundant information is then sent as input to the corresponding residual convolutional neural network for feature fusion perception and classification, thereby achieving accurate identification of large-scale radiation source equipment.

[0009] Furthermore, a fractional domain wavelet transform scattering network is constructed by cascading multiple layers of networks:

[0010] For any input signal f(t), it is combined with the kernel function Perform convolution calculations to obtain the signal overview information of each layer:

[0011]

[0012] Among them, the kernel function The purpose of is to extract the low-frequency feature information in the signal and is equivalent to the following expression:

[0013]

[0014] The high-frequency feature information of the signal is obtained by comparing the input signal with the kernel function Performing convolution operation yields:

[0015]

[0016] Among them, the kernel function It is a filter with high-frequency feature information filtering characteristics. The above formula can be further expressed as:

[0017]

[0018] The fractional domain wavelet scattering network is composed of two operations: linear convolution and nonlinear modulo. The scattering coefficient of any layer of the scattering network is expressed as S α [l (m) ]f(t), the scattering network coefficient of each layer is mainly composed of two parts, where the first part of the first layer is the low-frequency feature information corresponding to the input signal:

[0019]

[0020] High-frequency information corresponding to the second part of the first layer of the scattering network:

[0021]

[0022] Due to the structural characteristics of the network, the corresponding scattering coefficient of the m-th layer fractional domain wavelet scattering network can be calculated by the output information of the first (m-1) layer. Therefore, the above expression can be further generalized to obtain the high and low frequency characteristic scattering coefficients corresponding to the m-th layer scattering network as follows:

[0023]

[0024]

[0025] Among them Iα with C α They represent the high-frequency and low-frequency characteristic information scattering coefficients calculated from the input signal respectively.

[0026] Furthermore, the input signal x(t) is subjected to feature decomposition based on a multi-scale fractional domain wavelet, specifically including:

[0027] By transforming the collected signal using the Fourier transform window, the time-frequency transform result of the signal is obtained:

[0028]

[0029] Among them, h(n) corresponds to the Fourier transform window function, and n and k represent the discrete time domain and frequency domain respectively.

[0030] The scattering network decomposes the transformed signal f(t) layer by layer to obtain the corresponding scattering network coefficients as the characteristic coefficients of the input signal. For any d-dimensional input signal, the corresponding fractional domain Fourier transform is expressed as follows:

[0031]

[0032] in And there is,

[0033] where α i represents the rotation angle of the fractional Fourier transform.

[0034] Furthermore, the fractional domain wavelet transform is used to further enhance the decomposition of the input signal. The fractional domain wavelet transform corresponding to the input signal f(t) is expressed as:

[0035]

[0036] In the above formula, the fractional domain wavelet kernel function satisfies the following conditions:

[0037]

[0038] Where λ and t represent the scaling factor and time factor, respectively. When the rotation factor α in the above expression is equal to π / 2, the fractional domain wavelet transform degenerates into the classic wavelet transform. By setting the fractional domain rotation angle factor, the input signal is decomposed into low-frequency information and high-frequency information using a multi-scale fractional domain wavelet.

[0039] Furthermore, the low-frequency and high-frequency feature information corresponding to the input signal is calculated by the following formula:

[0040]

[0041] The fractional domain wavelet scaling function is expressed as:

[0042]

[0043] The high-frequency feature information corresponding to the input signal is expressed as:

[0044]

[0045] Furthermore, compared with the original data signal, the characteristic information of the input signal greatly reduces unnecessary redundant information, which can further improve the learning and training cost and performance of the system.

[0046] Furthermore, the mixed fractional domain wavelet scattering convolutional neural network radio frequency fingerprint recognition maintains stable invariance to the signal feature information in non-stationary environments.

[0047] The deformation of a non-stationary signal in the fractional domain can be defined as:

[0048]

[0049] Furthermore, the fractional domain deformation error satisfies the following conditions:

[0050]

[0051] in:

[0052]

[0053] For non-stationary characteristic signals that meet the above conditions, the fractional domain wavelet scattering transform ensures that the signal characteristics in the non-stationary noise remain unchanged in the fractional domain scattering transform, thereby retaining the prominent signal characteristics and completing the accurate identification of large-scale equipment.

[0054] Furthermore, the radio frequency fingerprint feature extraction system based on wavelet transform scattering network is characterized by the following different component modules:

[0055] Eigendecomposition Network Module: First, a fractional-domain wavelet transform scattering network is implemented by constructing a multi-layer network cascade. The fractional-domain wavelet transform scattering network then performs eigendecomposition of the input signal based on multi-scale fractional-domain wavelets to obtain the low-frequency and high-frequency feature information corresponding to the input signal. Due to the corresponding feature information extraction network, the presence of redundant information is significantly reduced compared to the original signal.

[0056] Feature recognition and classification module: It is used to input the signal feature information obtained after removing unnecessary redundant information into the corresponding residual convolutional neural network for feature fusion perception, so as to achieve accurate identification of large-scale radiation source equipment.

[0057] Compared with the prior art, the present invention has the following technical effects:

[0058] The present invention aims to extract subtle characteristic information of communication radiation sources and identify individuals. It uses a convolutional neural network composed of a mixture of a fractional domain wavelet scattering network and a one-dimensional residual network. While efficiently extracting signal characteristic information and enhancing network interpretability, it also minimizes redundant information in the input supervision network, thereby improving the learning efficiency of the network model and the accuracy of large-scale device recognition. In fact, in this hybrid network model, since a fractional domain wavelet scattering network is used to extract characteristic information of the input signal, and the excellent characteristics such as the non-stationary stability of the fractional domain wavelet scattering coefficient are utilized, the slow model convergence speed and poor large-scale device recognition accuracy caused by the non-stationary characteristics of the channel can be minimized. Therefore, while improving accuracy, the amount of data for network model learning is minimized, thereby improving learning efficiency. It has the following advantages:

[0059] First: The fractional domain wavelet scattering network can deeply decompose the input signal, greatly improving the interpretability of the hybrid network;

[0060] Second: The fractional domain wavelet scattering network can maximize the removal of redundant information of the input signal in the process of extracting characteristic coefficients, thereby reducing the amount of network learning data;

[0061] Third: The hybrid network maintains fractional domain invariance to the feature information fluctuations caused by non-stationary characteristics, which can make the hybrid network have better robustness and recognition performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a diagram of the system structure;

[0063] Figure 2 It is a fractional domain wavelet scattering network structure;

[0064] Figure 3 Second-order wavelet scattering coefficient of non-stationary signal;

[0065] Figure 4 Mixed fractional domain wavelet scattering convolutional neural network architecture;

[0066] Figure 5 Data acquisition system;

[0067] Figure 6 Recognition accuracy of different network models under different training sample sizes;

[0068] Figure 7 Clustering of normalized RF features of different radiation source devices. DETAILED DESCRIPTION

[0069] The present invention will be further described below with reference to the accompanying drawings:

[0070] See also Figures 1 to 7 The present invention provides a radio frequency fingerprint feature extraction scheme based on a hybrid convolutional neural network of a fractional domain wavelet transform scattering network. This scheme first uses a fractional domain wavelet transform scattering network to perform feature decomposition of the input signal based on a multi-scale fractional domain wavelet basis to obtain the low-frequency and high-frequency features corresponding to the input signal, while removing a large amount of unnecessary redundant information. The obtained feature signal is then fed as input into the corresponding convolutional neural network for feature fusion perception, thereby achieving accurate identification of large-scale equipment. The detailed technical solutions involved in the present invention are as follows:

[0071] 1. RF fingerprint generation mechanism

[0072] like Figure 1 (a) shows a typical wireless transceiver communication system, which includes a universal LTE base station that communicates with various types of mobile terminals. Figure 1 (b) shows the basic signal processing flow of a mobile terminal. After completing the source and channel coding of the transmitted information, the corresponding transmission bit sequence is obtained. This bit sequence passes through the modulation and demodulation, filter, power amplifier and other related modules and then transmits the signal through the antenna. During the signal processing process of the above-mentioned different modules, the non-ideal characteristics of the module components will produce a nonlinear transformation effect on the input signal. Therefore, the uniqueness and uniqueness of the non-ideal characteristics of the device will produce a unique nonlinear operation on the input signal, which mainly includes: IQ imbalance, frequency deviation, amplifier nonlinearity and antenna non-ideal characteristics. Among them, IQ imbalance mainly includes the different modulation amplitude difference and phase difference of the two IQ paths:

[0073] s(t)=I(t)cos(2πf I t+ζ(t) / 2)-Q(t)sin(2πf I t-ζ(t) / 2)

[0074] Among them, f I represents the intermediate frequency of the system, I(t) and Q(t) represent two different orthogonal modulation signals, and ζ(t) represents the orthogonal modulation error of the baseband signal. The RF bandpass filter is an important component of the intermediate frequency wireless communication system. The main function of this filter is to filter the signal in a specific frequency band. The main characteristic parameters include Q value, passband cutoff frequency, passband ripple, and filter delay. The relevant characteristics can be modeled and expressed as follows:

[0075]

[0076] Among them, H(f) represents the ideal filter, φ Ψ (f,t) and A Ψ(f, t) represent the phase and amplitude distortion of the filter, respectively. Different devices have different G(f, t) characteristics, forming a unique filter RF fingerprint. High-power amplifiers are the main component that causes nonlinear distortion in wireless communication systems. After being amplified by the high-power amplifier, the signal propagates through the antenna in the wireless channel.

[0077]

[0078] Where ρ(t) represents the high power amplifier input, f c represents the carrier frequency of the wireless system, and y(t) represents the output of the high-power amplifier. The wireless signal y(t) incorporates the nonlinear characteristics of each module in the entire system, forming a unique device fingerprint. Therefore, the RF fingerprint of the transmitting device can be obtained by analyzing the wireless signal propagating in space. However, in actual wireless channels, signals carrying RF fingerprints are often affected by the non-stationary characteristics of the channel, making it difficult to accurately obtain the RF signature hidden in the signal, thereby affecting the identification accuracy of large-scale devices.

[0079] 2. Deep Scattering Network Based on Fractional Domain Wavelet Transform

[0080] Machine learning involves combining lower-level features to form more abstract higher-level representations (attribute categories or features) in order to discover distributed feature representations of data. In recent years, machine learning has achieved remarkable results in signal processing, image processing, speech processing, and text processing. Deep learning, a key branch of machine learning, constructs complex network models using multi-layer convolutional neural networks. Each layer uses filters of varying scales and characteristics to extract characteristic parameters of the input signal, which serve as input to the next layer. The final fully connected layer classifies devices with different RF fingerprint characteristics. This type of convolutional neural network is a feedback-based learning network, requiring a large amount of training data for network optimization. Furthermore, the complex network parameters require extensive computing resources to aid convergence. Furthermore, convolutional neural networks currently lack interpretability. In 2012, Professor Mallat proposed a wavelet scattering convolutional network based on wavelet transforms. This network replaces linear filters with wavelet filters to achieve non-feedback signal feature decomposition. By calculating semi-discrete wavelet transform coefficients and performing nonlinear modulo operations, the network's signal decomposition process exhibits translational invariance and deformation stability. Many academic institutions at home and abroad have conducted extensive research on this. Relevant researchers have combined wavelet transform, time-frequency analysis, Gabor transform, etc. with scattering networks and applied them to various scenarios. Fractional domain wavelet is a fractional domain transform based on wavelet transform. Different fractional domain transforms can be achieved through different rotation angles to highlight different fractional domain features. In the actual wireless channel transmission process, the collected time series signals often need to be analyzed in time and frequency due to the non-stationary characteristics of the channel. Short-time Fourier transform (STFT) is an effective time-frequency transform tool. In essence, it transforms the collected signal through the Fourier transform window to obtain the time-frequency transform result of the signal:

[0081]

[0082] Among them, h(n) corresponds to the Fourier transform window function, n and k represent the discrete time domain and frequency domain respectively. Figure 2 As shown in Figure 1, the scattering network based on the fractional domain wavelet transform completes the layer-by-layer decomposition of the input signal f(t). The output of each layer of the scattering network is the characteristic coefficient of the corresponding input signal. In order to obtain an accurate mathematical expression of the fractional domain wavelet transform, we know from the definition that for any d-dimensional input signal, the fractional domain Fourier transform can be expressed as follows:

[0083]

[0084] where α i Represents the rotation angle of the fractional Fourier transform, especially if α i =π / 2, then the above transformation will degenerate into the classic Fourier transform, which shows that the fractional domain Fourier transform is a more generalized transform. Therefore, the fractional domain Fourier transform not only has the properties of the traditional Fourier transform, but also has other properties under different rotation angles in the fractional domain. In the fractional domain Fourier transform domain, the non-stationary characteristics of the signal can be characterized by the fractional domain frequency and phase, but the transform cannot obtain the local characteristics of the signal. Therefore, it is necessary to further complete the deep decomposition of the input signal through the fractional domain wavelet transform. The fractional domain wavelet transform corresponding to the input signal f(t) can be expressed as:

[0085]

[0086] in represents the fractional domain wavelet kernel function, represents the signal scattering coefficient calculated by the scattering network, where the fractional domain wavelet kernel function in the above formula satisfies the following conditions:

[0087]

[0088] Among them, λ and t represent the scale factor and time factor respectively. Similarly, when the rotation factor α in the above expression is π / 2, the fractional domain wavelet transform degenerates into the classic wavelet transform. Therefore, by setting a reasonable fractional domain rotation angle factor, the input signal can be decomposed into low-frequency information (signal overview information) and high-frequency information (signal detail information) through the multi-scale fractional domain wavelet basis, corresponding to Figure 2 There are two different nodes in . The low-frequency information features corresponding to the input signal can be calculated by the following formula:

[0089]

[0090] in, Represents the low-frequency characteristic coefficient of the signal, J represents the corresponding scaling function, and the corresponding fractional domain wavelet scaling function can be expressed as:

[0091]

[0092] The high-frequency information characteristics corresponding to the input signal can be calculated by the following expression:

[0093]

[0094] in, represents the calculated high-frequency characteristic information of the signal, and Represents the corresponding high-frequency feature information extraction kernel function;

[0095] The classical wavelet scattering convolutional network can be constructed by cascading multiple layers of networks, so we also adopt the same construction method for the fractional domain wavelet scattering network. The specific composition is as follows: Figure 2 As shown. Where the scale factor J = 4, the network depth m = 3, for any input signal f(t), it can be obtained by the kernel function Perform convolution calculations to obtain the signal overview information of each layer:

[0096]

[0097] Among them, the kernel function The low-frequency feature information in the signal can be extracted and is equivalent to the following expression:

[0098]

[0099] The high-frequency feature information of the signal can be obtained by comparing the input signal with the kernel function Perform convolution operation to obtain,

[0100]

[0101] Among them, the kernel function It has the characteristics of high-frequency feature information filtering, which can be further expressed as:

[0102]

[0103] In summary, it can be seen that for any input signal fractional domain wavelet scattering network, it is composed of two operations: linear convolution and nonlinear modulo, such as Figure 2 As shown, we can get the scattering coefficient of any layer of the scattering network can be expressed as S α [l (m) ]f(t), the scattering network coefficient of each layer is mainly composed of two parts, where the first part of the first layer is the low-frequency feature information corresponding to the input signal:

[0104]

[0105] Scattering network first layer high frequency information:

[0106]

[0107] Therefore, we can calculate the scattering coefficient of the corresponding m-th layer network through the output information of (m-1). After further generalizing the above expression, we can get the high and low frequency scattering coefficients corresponding to the m-th layer scattering network as follows:

[0108]

[0109]

[0110] Among them I α with C α Represent the high-frequency and low-frequency feature information coefficients of the input signal respectively.

[0111] 3. Mixed Fractional Domain Wavelet Scattering Convolutional Neural Network for RF Fingerprint Recognition

[0112] like Figure 3 Shown are the fractional domain wavelet scattering coefficients corresponding to the time-frequency feature images of two different devices. The image on the left shows the non-stationary characteristics of the signal as it transforms over time. The middle part is the first-order scattering coefficient of the fractional domain wavelet scattering network, and the right is the corresponding second-order scattering coefficient. From the figure, we can see that there are obvious differences between the two different devices in terms of both the first-order coefficient and the second-order coefficient. In addition, from the difference between the two, we can see that there is almost no obvious manifestation of the non-stationary characteristics in the time-frequency domain, and more differences are reflected in the existence of frequency bands within the working frequency band. The main reason is that the fractional domain wavelet scattering network is stable and invariant to certain scale deformations in the fractional domain. It is precisely because of the network's invariance to non-stationary characteristics that the network is more suitable for extracting the device's RF fingerprint information from non-stationary signals related to wireless channels. The deformation of a signal in the fractional domain is defined as:

[0113]

[0114] Furthermore, the fractional domain deformation error must satisfy the following conditions:

[0115]

[0116] in,

[0117]

[0118] Therefore, for non-stationary characteristic signals that meet the above conditions, the fractional domain wavelet scattering transform can ensure that this type of non-stationary noise remains unchanged in the fractional domain scattering transform, while only retaining the prominent signal features, thereby completing the accurate identification of large-scale equipment.

[0119] like Figure 4The figure shows the structure of the mixed fractional domain scattering convolutional neural network, where (a) shows the first part of the entire mixed network, which is mainly used to complete the calculation of the fractional domain wavelet scattering coefficient of the input signal, and combine all the coefficients calculated in different layers into a new coefficient vector as the input of the subsequent convolutional neural network. The main function of the first part of the scattering network is to complete the feature information extraction of the input signal, which can further reduce the redundant information input to the convolutional network. At the same time, the scattering coefficients of the input signal at all levels can be obtained through fractional domain wavelet scattering to clarify the various features of the input signal, thereby enhancing the interpretability of the mixed convolutional neural network. For the convolutional neural network, the ResNet network is selected as a reference to implement the one-dimensional signal residual network adaptation, such as Figure 4 As shown in (b), the entire network consists of the input layer, IDblock, ConvBlock, and the final fully connected layer Fc. After obtaining the scattering coefficient, subsequent supervised learning is completed through the ResNet1D network to achieve accurate device identification.

[0120] The present invention aims to extract subtle feature information of communication radiation sources and identify individuals. It uses a fractional domain wavelet scattering network and a one-dimensional residual network to form a hybrid convolutional neural network. While efficiently extracting signal feature information and enhancing network interpretability, it also minimizes redundant information in the input residual network, thereby improving the learning efficiency of the network model and the recognition accuracy of large-scale devices.

Claims

1. A radio frequency fingerprint feature extraction method based on a mixed fractional domain wavelet scattering network, characterized in that: The following steps are involved: Firstly, a fractional domain wavelet transform scattering network is constructed by cascading multiple layers of networks; Secondly, the input signal is decomposed based on the multi-scale fractional domain wavelet filter through the fractional domain wavelet transform scattering network to obtain the low-frequency and high-frequency features corresponding to the input signal. Compared with the original signal data volume, unnecessary redundant information is removed. The characteristic signal obtained after removing unnecessary redundant information is then fed into the corresponding residual convolutional neural network for feature fusion perception and classification, thus achieving accurate classification and identification of large-scale radiation source equipment. Construct a fractional domain wavelet transform scattering network by cascading multiple layers of networks: For any input signal f(t), it is combined with the kernel function Perform convolution calculations to obtain the signal overview information of each layer: Among them, the kernel function The purpose of is to extract the low-frequency feature information in the signal and is equivalent to the following expression: The high-frequency feature information of the signal is obtained by comparing the input signal with the kernel function Performing convolution operation yields: Among them, the kernel function It is a filter with high-frequency feature information filtering characteristics. The above formula can be further expressed as: The fractional domain wavelet scattering network is composed of two operations: linear convolution and nonlinear modulo. The scattering coefficient of any layer of the scattering network is expressed as S α [l (m) ]f(t), the scattering network coefficient of each layer is mainly composed of two parts, where the first part of the first layer is the low-frequency feature information corresponding to the input signal: High-frequency information corresponding to the second part of the first layer of the scattering network: Due to the structural characteristics of the network, the corresponding scattering coefficient of the m-th layer fractional domain wavelet scattering network can be calculated by the output information of the first (m-1) layer. Therefore, the above expression can be further generalized to obtain the high and low frequency characteristic scattering coefficients corresponding to the m-th layer scattering network as follows: Among them I α with C α They represent the high-frequency and low-frequency characteristic information scattering coefficients calculated from the input signal respectively.

2. The radio frequency fingerprint feature extraction method based on mixed fractional domain wavelet scattering network according to claim 1 is characterized in that: The characteristic decomposition of the input signal x(t) based on the multi-scale fractional domain wavelet specifically includes: By transforming the collected signal using the Fourier transform window, the time-frequency transform result of the signal is obtained: Among them, h(n) corresponds to the Fourier transform window function, n and k represent the discrete time domain and frequency domain respectively; The scattering network decomposes the transformed signal f(t) layer by layer to obtain the corresponding scattering network coefficients as the characteristic coefficients of the input signal. For any d-dimensional input signal, the corresponding fractional domain Fourier transform is expressed as follows: in And there is, where α i represents the rotation angle of the fractional Fourier transform.

3. The radio frequency fingerprint feature extraction method based on mixed fractional domain wavelet scattering network according to claim 2 is characterized in that: The fractional domain wavelet transform is used to further enhance the decomposition of the input signal. The fractional domain wavelet transform corresponding to the input signal f(t) is expressed as: In the above formula, the fractional domain wavelet kernel function satisfies the following conditions: Among them, λ and t represent the scale scaling factor and time factor respectively. When the rotation factor α in the above expression is π / 2, the fractional domain wavelet transform degenerates into the classic wavelet transform. By setting the fractional domain rotation angle factor, the input signal is decomposed into low-frequency information and high-frequency information through multi-scale fractional domain wavelet.

4. The radio frequency fingerprint feature extraction method based on mixed fractional domain wavelet scattering network according to claim 3 is characterized in that: The low-frequency and high-frequency feature information corresponding to the input signal is calculated by the following formula: The fractional domain wavelet scaling function is expressed as: The high-frequency feature information corresponding to the input signal is expressed as:

5. The radio frequency fingerprint feature extraction method based on mixed fractional domain wavelet scattering network according to claim 1 is characterized in that: Compared with the original data signal, the characteristic information of the input signal greatly reduces unnecessary redundant information, which can further improve the learning and training cost and performance of the system.

6. The radio frequency fingerprint feature extraction method based on mixed fractional domain wavelet scattering network according to claim 1 is characterized in that: Mixed fractional domain wavelet scattering convolutional neural network radio frequency fingerprint recognition maintains stable invariance to signal feature information in non-stationary environments: The deformation of a non-stationary signal in the fractional domain can be defined as: Furthermore, the fractional domain deformation error satisfies the following conditions: in, For non-stationary characteristic signals that meet the above conditions, the fractional domain wavelet scattering transform ensures that the signal characteristics in the non-stationary noise remain unchanged in the fractional domain scattering transform, thereby retaining the prominent signal characteristics and completing the accurate identification of large-scale equipment.

7. Radio frequency fingerprint feature extraction system based on mixed fractional domain wavelet scattering network, characterized by The following different components: Eigendecomposition network module: First, a fractional domain wavelet transform scattering network is implemented by constructing a multi-layer network cascade. Then, the fractional domain wavelet transform scattering network performs eigendecomposition of the input signal based on multi-scale fractional domain wavelets to obtain the low-frequency and high-frequency feature information corresponding to the input signal. Feature recognition and classification module: It is used to input the signal feature information obtained after removing unnecessary redundant information into the corresponding residual convolutional neural network for feature fusion perception, thereby achieving accurate identification of large-scale radiation source equipment; Construct a fractional domain wavelet transform scattering network by cascading multiple layers of networks: For any input signal f(t), it is combined with the kernel function Perform convolution calculations to obtain the signal overview information of each layer: Among them, the kernel function The purpose of is to extract the low-frequency feature information in the signal and is equivalent to the following expression: The high-frequency feature information of the signal is obtained by comparing the input signal with the kernel function Performing convolution operation yields: Among them, the kernel function It is a filter with high-frequency feature information filtering characteristics. The above formula can be further expressed as: The fractional domain wavelet scattering network is composed of two operations: linear convolution and nonlinear modulo. The scattering coefficient of any layer of the scattering network is expressed as S α [l (m) ]f(t), the scattering network coefficient of each layer is mainly composed of two parts, where the first part of the first layer is the low-frequency feature information corresponding to the input signal: High-frequency information corresponding to the second part of the first layer of the scattering network: Due to the structural characteristics of the network, the corresponding scattering coefficient of the m-th layer fractional domain wavelet scattering network can be calculated by the output information of the first (m-1) layer. Therefore, the above expression can be further generalized to obtain the high and low frequency characteristic scattering coefficients corresponding to the m-th layer scattering network as follows: Among them I α with C α They represent the high-frequency and low-frequency characteristic information scattering coefficients calculated from the input signal respectively.

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