Unmanned aerial vehicle radio frequency signal open set small sample identification method based on cyclic claw printing graph

Abstract

The invention discloses an unmanned aerial vehicle radio frequency signal open set small sample identification method based on a cyclic claw printing graph, and relates to the field of unmanned aerial vehicle radio frequency signal identification. According to the invention, by combining the time domain and frequency domain features, the signal segment with the highest discrimination capability is accurately identified, and the accuracy and robustness of signal identification are significantly improved. Compared with other common characteristics, the method has the advantages that higher robustness and robustness are shown. Particularly, under the condition of low signal-to-noise ratio (SNR), the key information of the target signal can be extracted more effectively by the CPP feature. The performance of the method in unmanned aerial vehicle radio frequency signal identification shows more excellent classification performance especially in the face of novel unmanned aerial vehicle signals or scarce samples, and the stability and reliability of an identification system are ensured; according to the method, a Transform-enhanced SE (Square-and-Excitation) module and a Gaussian mixture model (GMM) are ingeniously fused and are embedded into a residual network, so that the advantages of each component are fully exerted in the feature extraction and classification process.

Description

Technical Field

[0001] The present invention relates to the field of UAV radio frequency signal recognition. Background Art

[0002] With the wide application of unmanned aerial vehicles (UAVs) in various fields, especially in logistics, agriculture, surveillance and other fields, their influence in daily life has gradually increased. However, the unauthorized use of UAVs also poses a significant threat to personal privacy, public safety and aviation safety. Due to the characteristics of low-altitude flight, low-speed movement and miniaturization of UAVs, there are great challenges in their detection and recognition. Therefore, the development of high-precision UAV detection and recognition technologies has become a research hotspot in recent years.

[0003] UAV identification methods based on radio frequency (RF) features have received extensive attention and are considered to have great application potential because they can work efficiently in both line-of-sight (LOS) and non-line-of-sight (NLOS) environments. In recent years, deep learning methods have also been widely applied to the field of UAV sensing, further promoting the development of this technology. For example, the lightweight multi-scale convolutional block network proposed in the literature Z. Cai, Y. Wang, Q. Jiang, G. Gui, and J. Sha, “Toward intelligent lightweight and efficient UAV identification with RF fingerprinting,” IEEE Internet of Things Journal, vol. 11, no. 15, pp. 26329–26339, August 2024 is used for UAV RF fingerprint identification; the dynamic shrinkage learning network (DSLN) proposed in the literature W. Wu, S. Hu, D. Lin, and Z. Liu, “DSLN: Securing internet of things through RF fingerprint recognition in low-SNR settings,” IEEE Internet of Things Journal, vol. 9, no. 5, pp. 3838–3849, March 2022 helps to improve the identification accuracy in the case of low signal-to-noise ratio (SNR) while reducing the computational complexity; the literature Q. Wang, P. Yang, X. Yan, H.-C. Wu, and L. He, “Radio frequency-based UAV sensing using novel hybrid lightweight learning network,” IEEE Sensors Journal, vol. 24, no. 4, pp. 4841–4850, February 2024 uses wavelet scattering transform (WST) to convert the received UAV RF signal into a scatter plot, and then uses CNN for UAV type identification and achieves good results. However, existing UAV sensing methods generally rely on a predefined UAV candidate set and usually require a sufficiently large training data set. In practical applications, new UAV types not included in the training set are often encountered, or the training samples for each type are very scarce. The former problem is called the “open set problem,” while the latter is the “few-shot problem.”

[0004] Open Set Recognition refers to the ability to make decision-making when faced with unknown classes. To address this issue, the paper "Towards open set deep networks" by A. Bendale and T. E. Boult in the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2016, pp. 1563–1572 proposed the "OpenMax" layer to estimate the probability that the input belongs to an unknown class. In addition, the enhanced open set recognizer proposed in the paper "Transmitter identification with contrastive learning in incremental open-set recognition" by X. Zhang, Y. Huang, M. Lin, Y. Tian, and J. An, IEEE Internet of Things Journal, vol. 11, no. 3, pp. 4693–4711, February 2024 improves the accuracy and computational efficiency of open set radio frequency fingerprint recognition by optimizing the decision boundary. For the few-shot open set modulation classification problem, the paper "Meta supervised contrastive learning for few-shot open-set modulation classification with signal constellation" by J. Zhao, H. Wang, S. Peng, and Y. Yao, IEEE Communications Letters, vol. 28, no. 4, pp. 837–841, April 2024 proposed a meta-supervised contrastive learning (MSCL) scheme to address the few-shot problem by enhancing the discrimination between classes and the compactness within classes. Although most existing open set recognition methods have been successfully applied to the field of image recognition, there are still great challenges in extending these methods to the field of unmanned aerial vehicle (UAV) radio signal perception. Therefore, combining open set recognition with few-shot learning to design a more efficient UAV radio signal recognition algorithm, especially for effective recognition under low-resource conditions, has important research significance.

[0005] Meanwhile, few-shot learning, as a long-standing research hotspot, has achieved some breakthroughs. For example, the literature H. Zhang, F. Zhou, Q. Wu, and N. Al-Dhahir, "SSwsrNet: A semi-supervised few-shot learning framework for wireless signal recognition," IEEE Transactions on Communications, vol. 72, no. 9, pp. 5823–5836, September 2024 proposed an SSwsrNet framework using a deep residual shrinkage network (DRSN) and a semi-supervised learning paradigm for identifying dynamic wireless communication signals with a small number of training samples. The literature X. Ding, Y. Zhang, G. Li, X. Gao, N. Ye, D. Niyato, and K. Yang, "Few-shot recognition and classification framework for jamming signal: A CGAN-Based fusion CNN approach," 2024. [Online]. Available: https: / / arxiv.org / abs / 2311.05273 also proposed a hybrid deep learning model combining a conditional generative adversarial network (CGAN) and a convolutional neural network (CNN) for few-shot signal recognition. However, the few-shot learning technology for UAV radio frequency signals is still relatively scarce, especially the joint challenge of combining the open-set problem with the few-shot problem. Therefore, the research and proposal of an effective open-set few-shot recognition method in this invention have important scientific significance and engineering value for improving the accuracy, robustness, and practicality of UAV radio frequency signal recognition. Specifically, the prior art has the following deficiencies:

[0006] 1) Open-set problem: Existing UAV recognition methods lack a rejection decision mechanism and cannot effectively handle UAV data that does not appear in the training set, resulting in the inability to correctly identify unseen UAV types in practical applications;

[0007] 2) Few-shot problem: In the face of scarce samples of each UAV type, traditional deep learning methods are prone to overfitting, leading to unstable recognition effects. Especially in a low-sample training environment, the generalization ability and robustness of the model are poor. Summary of the Invention

[0008] Existing UAV radio frequency signal recognition methods mainly rely on a predefined candidate set of UAV types and usually rely on large-scale training datasets to support model learning. However, there are often two major challenges in practical applications: one is the unknown UAV types not included in the training dataset (i.e., the open-set problem), and the other is the insufficient training samples for each UAV type (i.e., the small-sample problem). Existing radio frequency feature-based recognition methods perform poorly in dealing with these two problems. Especially when facing new or unseen UAV signals, it is easy to produce recognition errors, resulting in a decline in recognition accuracy.

[0009] Therefore, the present invention aims to propose a UAV radio frequency signal recognition method that can maintain high-efficiency and accurate recognition performance in the face of unknown UAV types and scarce training samples by combining open-set recognition and small-sample learning techniques. This method will effectively improve the recognition accuracy and robustness of UAV radio frequency signals, especially in dealing with challenges in complex dynamic environments in practical applications. The present invention proposes an open-set small-sample recognition method for UAV radio frequency signals based on circular pawprint diagrams, and this method includes:

[0010] Step 1: Selection of effective UAV segments;

[0011] Let the captured discrete-time radio frequency signal sequence of M samples be r(t), where t = 0, 1,..., M - 1. This signal is continuously and seamlessly segmented using a sliding window, and the sliding window contains consecutive sampling points; now, r(t) is divided into windows, where the signal sample of the i-th frame is denoted as

[0012]

[0013] where the signal sample of the i-th frame is represented by the discrete Fourier transform sequence as:

[0014]

[0015] Then, the amplitude spectrum sequence of the i-th frame is calculated as |U i (m)|, where Now, construct the spectral probability sequence P i (m) of the i-th frame such that:

[0016]

[0017] Therefore, the corresponding spectral entropy of the i-th frame is represented as:

[0018]

[0019] Define the ratio e of the short-time energy to the spectral entropy of the i-th frame i as:

[0020]

[0021] All The set of ratios of the short-time energy to the spectral entropy of all frames can form a set When e i is greater than the set threshold, it is considered that there is indeed a UAV signal in the i-th frame; the random variable corresponding to e i is denoted as E i , where Let be independent and identically distributed, and the corresponding probability density function is expressed as:

[0022]

[0023] Therefore, the smallest, the second smallest, the third smallest,..., and the largest ratios of the short-time energy to the spectral entropy are represented by random variables: Satisfying

[0024] The empirical cumulative distribution function of the probability density function given by formula (6) is estimated by the corresponding sample histogram of e i ; the cumulative distribution function P[E E(i) is estimated according to the empirical cumulative distribution function as P[E (i) ≤e], where E(i) represents the ratio of the short-time energy to the spectral entropy of all statistics less than the i-th element in

[0025]

[0026] where and ! represents the factorial. For a given confidence level and a given threshold of the ratio of the short-time energy to the spectral entropy the appropriate i is determined by solving the following equation:

[0027]

[0028] The captured sequence r(t) of M sampled discrete-time RF signals, where t = 0, 1,..., M - 1, will be segmented into frame signal samples, that is For Then, the frame signal samples corresponding to the φ largest short-time energy-to-spectral entropy ratios will be retained. These φ frame signal samples are indexed by π(1), π(2), π(3), ……, π(φ), where

[0029]

[0030] so that the retained signal samples form a new signal sequence x(n), where Its expression is:

[0031]

[0032] where and represents the floor operation;

[0033] Step 2: Cyclic Pseudo-Print (CPP) feature extraction;

[0034] Second-order cyclic spectral analysis is introduced to characterize the sequence x(n) given in Equation (10), where For a given frequency f and cyclic frequency α, its time-smoothed cyclic periodogram

[0035]

[0036] where g′(n) represents a unit area weighting function with a width of Δt = NT s seconds, N represents the number of samples in each fast Fourier transform window, T s represents the sampling period, f1 and f2 represent the center frequencies of the filters used in the summation method, i.e., f1 = f + α / 2, f2 = f + α / 2, and is the complex demodulation of x(n), i.e.:

[0037]

[0038] where λ represents the discrete time variable, represents a data windowing function with a duration of T = N′T s seconds, N′ is the window length, and its bandwidth is consistent with the frequency resolution Δf = f s / N′ of the second-order cyclic spectrum; it should be noted that f s represents the sampling frequency; the second-order cyclic spectrum is obtained from the time-smoothed cyclic periodogram by an unbiased estimate, specifically:

[0039]

[0040] The second-order cyclic spectrum contains N′ + 1 spectral frequencies f q, where \(q = -N' / 2, -N' / 2 + 1, \ldots, N' / 2\), and there are \(2N + 1\) cyclic frequencies \(\alpha\) p , where \(p = -N, -N + 1, \ldots, N\), and it is a three-dimensional spectrum with non-negative amplitudes; thus, the NSCS is calculated as:

[0041]

[0042] NSCS represents the normalized second-order cyclic spectrum, and its top view is represented as a \(P\times Q\) matrix

[0043]

[0044] where \(P = 2N + 1\), \(Q = N' + 1\); the elements in the matrix are is the non-negative normalized amplitude at the cyclic frequency \(\alpha\) p and the spectral frequency \(f\) q for \(p = p + N\), \(q = q + N' / 2\); then, the top view of the NSCS is converted into a grayscale image by a \(b\)-bit quantizer such that:

[0045]

[0046] where \(b\) is a positive integer;

[0047] The grayscale image is reshaped into a square matrix of \(\Lambda\times\Lambda\) denotes the conjugate transpose. By reducing the \(N' + 1\) elements in each column vector to \(\Lambda\) elements and expanding the \(2N + 1\) elements in each row vector to \(\Lambda\) elements, satisfying \(P\lt\Lambda\lt Q\); then, the square grayscale color map matrix is further converted into a pseudo-color square image, represented as:

[0048]

[0049] According to formula (16), the square pseudo-color image is represented as the following third-order tensor:

[0050]

[0051] where, and denote the three square matrices of the red \(R\), green \(G\), and blue \(B\) channels respectively, satisfying:

[0052]

[0053] Step 3: Construct a deep learning network, which includes: a convolutional input layer, residual units, a classification unit, and an unknown detection unit; the convolutional input layer, residual units, and classification unit are connected in series in sequence, and the input of the unknown detection unit is the intermediate calculation data of the classification unit;

[0054] The convolutional input layer sequentially includes: a convolutional layer, a batch normalization layer, a rectified linear unit activation layer, and a max pooling layer;

[0055] The residual unit is sequentially composed of 8 residual blocks with the same structure;

[0056] The classification unit sequentially includes: an adaptive average pooling layer, a flattening layer, a fully connected layer, and an activation function layer; the activation function layer outputs the recognition result;

[0057] The input of the unknown detection unit is the output of the flattening layer in the classification unit, and the unknown detection unit is used to determine whether the received UAV radio frequency signal type belongs to the training candidate set

[0058] Further, the specific process of the convolutional input layer in Step 3 is as follows:

[0059]

[0060] Among them, W c and B c respectively represent the convolution kernel and bias term of the convolutional layer; then, Z c will be normalized in the subsequent batch normalization layer according to its mean μ c and variance , and then the ReLU activation function is applied to the normalized result to accelerate convergence and improve classification accuracy; finally, the spatial dimension of the output of ReLU is downsampled through the max pooling layer, and the output Z c of the convolutional unit will be sent to the subsequent residual unit.

[0061] Further, each residual block in the residual unit sequentially includes: a first convolutional layer Conv1, a first batch normalization layer BN1, a ReLU layer, a second convolutional layer Conv2, a second batch normalization layer BN2, and an SE module;

[0062] The input and output of the l-th residual block are respectively denoted as Z RBI,l and Z RBO,l ;

[0063] The input data first passes through the first convolutional layer Conv1, the first batch normalization layer BN1, and the ReLU layer; for the first residual block l = 1, Z RBI,1 = Zc, for l = 2, 3,..., 8, Z RBI,l = ZRBO,l-1 , the normalized and activated output in the l-th residual block is:

[0064]

[0065] Among them, W RBC1,l and B RBC1,l respectively represent the convolution kernel and bias of the first convolutional layer Conv1 in the l-th residual block, and Z RBC1,l further passes through the second convolutional layer Conv2 and the second batch normalization layer BN2 to generate the corresponding output:

[0066]

[0067] Among them, W RBC2,l and B RBC2,l respectively represent the convolution kernel and bias of the second convolutional layer Conv2 in the l-th residual block;

[0068] Next, Z RBC2,l is input into the SE module. The l-th residual block uses B RBC2,l as the input of the SE module to generate the output Z SE,l , where l = 1, 2,..., 8; the final output Z RBO,l of the l-th residual block is given by the following formula:

[0069] Z RBO,l = Z RBI,l + Z SE,l , l = 1, 2,..., 8 (24)

[0070] The output of the eighth residual block, that is, Z RBO,8 .

[0071] Further, the input of the classification unit is Z RBO,8 , and finally a feature vector is generated, where K represents the total number of known types of UAV radio frequency signal candidates and satisfies Calculate the probability that the feature vector matches the k-th type of known UAV radio frequency signal in the candidate set , which is estimated by the softmax activation function as follows:

[0072]

[0073] Finally, the type of the received radio frequency signal, denoted as is identified by the following method:

[0074]

[0075] Among them,

[0076]

[0077] Further, the input of the unknown category detection unit is the output of the flattening layer in the classification unit, that is used to determine whether the received UAV RF signal type belongs to the training candidate set is regarded as a random vector with a K-modal Gaussian mixture probability density function, where K represents the total number of known UAV RF signals used for training, and the probability density function is:

[0078]

[0079] where ξ k represents the weight coefficient of the k-th Gaussian mode, satisfying 0 ≤ ξ k ≤ 1, and

[0080]

[0081] Estimate the parameter set from the training data, and then the Gaussian mixture probability density function of the K-modal can be characterized, where is the parameter related to the k-th Gaussian mode, and ξ k , respectively represent the mixing coefficient, mean, and covariance matrix of the k-th Gaussian mode, k = 1, 2,..., K. Assume that for each training candidate set k, ζ output samples are collected, which are respectively k = 1, 2,..., K, and these samples come from the flattening layer in the classification unit;

[0082] During testing, the output of the flattening layer from the received UAV RF signal in the classification unit is expressed as Calculate [[ID=Z4]]and the Mahalanobis distance between the mean feature vector of each UAV RF signal candidate in

[0083]

[0084] Assume that the UAV RF signal type generating the test feature vector is Set the threshold according to the actual situation, so that the rejection rule is:

[0085]

[0086] where represents that the feature vector is not generated by Any candidate signal generation therein indicates that it is an unknown UAV radio frequency signal.

[0087] Furthermore, the Expectation-Maximization algorithm is used to estimate Θ as follows:

[0088] First, perform initialization: estimate ξ for each k = 1, 2,..., K k , and such that:

[0089]

[0090] where k = 1, 2,..., K, represents the training set sample feature vector;

[0091] E-step: Re-estimate ξ in the current iteration k as such that:

[0092]

[0093] where k, ε = 1, 2,..., K; l = 1, 2,..., ζ,

[0094]

[0095] M-step: Re-estimate and in the current iteration as and respectively, where k = 1, 2,..., K, such that:

[0096]

[0097] where k, ε = 1, 2,..., K;

[0098] Update the parameters:

[0099]

[0100] where k, ε = 1, 2,..., K; return to the E-step until all parameter estimates converge. The final parameter estimate set is denoted as

[0101] Furthermore, in formula 8 of step 1, the confidence level is set to 0.95, and the spectral entropy ratio threshold is set to the mode of the short-time energy to spectral entropy ratio.

[0102] Furthermore, in formula 15 of step 2, b is set to 16.

[0103] Furthermore, the SE module in the residual unit consists of an adaptive average pooling layer, a flattening layer, a first fully connected layer FC1, a multi-head attention layer MHA, a second fully connected layer FC2, and a Sigmoid activation function in sequence.

[0104] (1) The present invention proposes a novel segment selection mechanism based on the Short-Time Energy-to-Spectral-Entropy Ratio, aiming to effectively capture the key effective segments in UAV signals. By combining time-domain and frequency-domain features, this mechanism accurately identifies the most discriminative signal segments, significantly improving the accuracy and robustness of signal recognition. In the face of complex environmental noise and signal interference, this mechanism can screen out the most representative effective segments from a large number of RF signals, thereby reducing the impact of redundant data on the performance of the recognition system.

[0105] (2) The CPP features proposed by the present invention demonstrate stronger robustness and stability compared to other common features. Especially in the case of low signal-to-noise ratio (SNR), the CPP features can more effectively extract the key information of the target signal. Its performance in UAV RF signal recognition, especially in the face of new UAV signals or scarce samples, shows more excellent classification performance, ensuring the stability and reliability of the recognition system.

[0106] (3) The novel deep learning network TASE-Net proposed by the present invention cleverly integrates the Transformer-enhanced SE (Squeeze-and-Excitation) module and the Gaussian mixture model (GMM), and embeds them into the residual network, thereby giving full play to the advantages of each component in the feature extraction and classification process. The Transformer-enhanced SE module helps capture long-range dependencies and improve the accuracy of feature representation. Especially in complex UAV RF signal recognition tasks, it can effectively improve the attention allocation to key signal features. At the same time, the introduction of the Gaussian mixture model GMM can model the complex distribution of signal features, thereby enhancing the robustness in open-set recognition. Therefore, TASE-Net can achieve efficient classification of UAV RF signals with extremely few samples and effectively handle the open-set problem, identifying new UAV signals that do not appear in the training dataset. Description of the Drawings

[0107] Figure 1 It is a block diagram of an unmanned open-set few-shot recognition system.

[0108] Figure 2 It is an example of segmenting a UAV RF signal sequence.

[0109] Figure 3They are the second-order cyclic spectra of two UAV signals and the corresponding top views.

[0110] Figure 4 It is the network structure of the TASE-Net open-set few-shot recognition network. Detailed implementation manners

[0111] To solve the problems of low accuracy and poor robustness in the prior art when identifying unseen types of UAV signals (open-set problem) and scarce training samples (few-shot problem). This technical solution mainly realizes efficient and accurate UAV radio frequency signal recognition through the following several core technical measures; the specific implementation manners of the present invention will be described in detail below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the present invention. The overall framework of the UAV radio frequency signal recognition system is as shown in the accompanying Figure 1 drawing, and mainly includes three components: 1) Selection of effective segments of UAV radio frequency signals; 2) CPP feature extraction; 3) Construction of the TASE-Net network. The following will elaborate on these three parts in detail:

[0112] Selection of effective segments of UAV radio frequency signals

[0113] According to the accompanying Figure 2 drawing, the obtained radio frequency signal waveforms can be divided into "data transmission interval (DTI)", "frequency hopping interval (FHI)" and "silent interval (SI)", where DTI and FHI usually correspond to digital data transmission (DDT) signals and flight control signals respectively. It should be noted that only features need to be extracted from DTI and FHI for UAV identification. Therefore, the present invention designs a complex mechanism for detecting and segmenting the captured radio frequency signals.

[0114] Let the captured M-sampled discrete-time radio frequency signal sequence be r(t), where t = 0, 1,..., M - 1. This signal can be continuously and seamlessly segmented using a sliding window, and the sliding window contains continuous sampling points. Now, r(t) is divided into frames (windows), as shown in Figure 2 the drawing, where the signal sample of the i-th frame can be expressed as

[0115]

[0116] where the signal sample of the i-th frame The discrete Fourier transform (DFT) sequence of can be expressed as:

[0117]

[0118] Then, the magnitude spectrum sequence of the i-th frame can be calculated as |U i (m)|, where Now, construct the spectral probability sequence P i (m) of the i-th frame such that:

[0119]

[0120] Therefore, the corresponding spectral entropy of the i-th frame can be expressed as:

[0121]

[0122] Define the ratio of the short-time energy to the spectral entropy of the i-th frame (short-time energy to spectral entropy ratio) e i as:

[0123]

[0124] All the set of short-time energy to spectral entropy ratios of the frames can form a set Note that in the presence of a drone signal, e i >> 1; the larger the short-time energy to spectral entropy ratio e i , the more confident one can be that there is indeed a drone signal in the i-th frame. Denote the random variable corresponding to e i as E i , where Without loss of generality, further assume that are independent and identically distributed (i.i.d.), so that the corresponding probability density functions (PDFs) can be expressed as:

[0125]

[0126] Therefore, the smallest, second smallest, third smallest,..., and the largest short-time energy to spectral entropy ratios can be represented by random variables: Satisfying

[0127] Therefore, the empirical cumulative distribution function (ECDF) of the probability density function (PDF) given by formula (6) can be estimated by the corresponding sample histogram of e i . According to the ECDF estimate (using the sample histogram), the cumulative distribution function (CDF) of E(ι) (the i-th order statistic or the i-th smallest short-time energy to spectral entropy ratio in

[0128]

[0129] in and For a given confidence level, e.g. (expressed as a percentage) and a given short-time energy to spectral entropy ratio threshold The appropriate ι can be determined by solving the following equation:

[0130]

[0131] Without loss of generality, the confidence level Set to 0.95, the threshold Set to the most likely ratio of short-time energy to spectral entropy (i.e., the mode of the ratio of short-time energy to spectral entropy).

[0132] As mentioned above, the captured M-sample discrete-time RF signal sequence r(t), where t=0,1,...,M-1, will be divided into Frame signal samples, i.e. for Then, the φ frame signal samples corresponding to the φ maximum short-time energy to spectral entropy ratios (indexed by i=π(1),π(2),π(3),π(φ)) will be retained (selected).

[0133]

[0134] The retained signal samples form a new signal sequence x(n), where Its expression is:

[0135]

[0136] in, and Indicates a floor operation.

[0137] CPP feature extraction

[0138] In order to obtain robustness characteristics, the present invention introduces the second-order cyclic spectrum (SCS) analysis to the UAV RF signal to characterize the sequence x(n) given in equation (10), where The second-order cyclic autocorrelation function of x(n) can be derived by using the FFT (Fast Fourier Transform) accumulation method (FAM). For a given frequency f and periodic frequency α, its time-smoothed cyclic periodogram is for:

[0139]

[0140] Where g′(n) represents the width Δt=NT sThe unit - area weighted function in seconds, N represents the number of samples in each FFT window, T s represents the sampling period, f1 and f2 represent the center frequencies of the filters used in the FAM, i.e., f1 = f + α / 2, f2 = f + α / 2, and is the complex demodulation of x(n), i.e.:

[0141]

[0142] where, represents a data windowing function with a duration of T = N′T s seconds, whose bandwidth is consistent with the frequency resolution Δf = f s / N′ of the SCS. It should be noted that f s represents the sampling frequency. The SCS can be obtained from the time - smoothed cyclic periodogram through an unbiased estimator specifically:

[0143]

[0144] contains N′ + 1 spectral frequencies f = f q , where q = -N′ / 2, -N′ / 2 + 1,..., N′ / 2, and 2N + 1 cyclic frequencies α = α p , where p = -N, -N + 1,..., N, and it is a three - dimensional spectrum with non - negative amplitudes. Therefore, the normalized SCS (NSCS) can be calculated as:

[0145]

[0146] The normalized SCS (NSCS) of a typical UAV RF signal and the corresponding top - view are presented. Figure 3 Examples of the second - order cyclic spectra of two UAV signals and their top - views are shown in the appendix.

[0147] According to the appendix Figure 3 , the top - view of the NSCS of the UAV RF signal usually concentrates on four symmetric regions in the α - f plane, and the corresponding scatter plot is similar to the paw print of an animal. Therefore, this scatter plot is called the cyclic paw print (CPP). It can be clearly seen from the appendix Figure 3 that the CPPs generated by different UAV RF signals have significant distinguishability and can thus be used as robust features for UAV identification. The top - view of the NSCS can be represented as a P×Q matrix where P = 2N + 1 and Q = N′ + 1. The element in the matrix is at the cyclic frequency α p and the spectral frequency fq The non - negative normalized magnitude at, for p = p + N, q = q + N' / 2. Then, the top - view of the NSCS can be regarded as a grayscale color map (black - and - white image), and is further converted into a "quantized" image matrix by a b - bit quantizer such that:

[0148]

[0149] where b is a positive integer. For simplicity of discussion, b can be set to 16 in this study.

[0150] Reshape the grayscale image into a square matrix of Λ×Λ by down - sampling each column vector (reducing N'+1 elements in each column to Λ elements) and interpolating each row vector (expanding 2N + 1 elements in each row to Λ elements), satisfying P < Λ < Q. Then, the square grayscale color map matrix can be further converted into a pseudo - color square image, which can be expressed as:

[0151]

[0152] According to formula (16), the CPP (i.e., the square pseudo - color image) can be expressed as the following third - order tensor:

[0153]

[0154] where, and represent three square matrices of the red (R), green (G), and blue (B) channels respectively, satisfying:

[0155]

[0156] Construction of the TASE - Net open - set few - shot recognition network

[0157] Once the CPP tensor of the UAV RF signal is constructed according to formulas (17) - (19) in Section 2 the proposed new TASE - Net can use it as input for training to identify UAV RF signals. The TASE - Net integrates the Transformer - based SE model into ResNet, and also introduces a new unknown class detection mechanism, which uses the Gaussian mixture model (GMM) to achieve open - set recognition. The TASE - Net proposed in this invention can not only provide excellent classification performance in open - set few - shot scenarios, but also has a low computational complexity. The overall architecture of the TASE - Net is as shown in the appendix Figure 4As shown, it includes a convolutional input layer, a residual unit, a classification unit, and an unknown class detection unit.

[0158] Convolutional input layer

[0159] In the convolutional input layer shown in the appendix Figure 4 a convolutional layer with 64 filters (convolution kernels) of size 7×7 is adopted. The stride of this layer is 2 and the padding is 3, which is used to extract key features from the CPP image (tensor). Then there is a batch normalization (BN) layer, a rectified linear unit (ReLU) activation layer, and a max pooling layer. The third-order CPP tensor of the captured drone RF signal (i.e., ) is directly input into this convolutional unit, and the corresponding output results are:

[0160]

[0161] where, W c and B c represent the convolution kernel and the bias term of the convolutional layer respectively. Then, Z c will be normalized in the subsequent batch normalization (BN) layer according to its mean μ c and variance . Then the ReLU activation function is applied to the normalized result to accelerate convergence and improve classification accuracy. Finally, the spatial dimension of the ReLU output is downsampled by the max pooling layer, and the output Z c of the convolutional unit will be sent to the subsequent residual unit.

[0162] Residual unit

[0163] The residual unit consists of eight residual blocks, which have the same structure, as shown in the appendix Figure 4 . Each residual block consists of two convolutional layers (labeled "Conv1" and "Conv2" respectively), two batch normalization layers (labeled "BN1" and "BN2" respectively), a ReLU layer, and an SE module. Among them, an SE module enhanced by Transfomer is embedded in each residual block to promote the recognition of feature maps. The input and output of the l-th residual block are denoted as Z RBI,l and Z RBO,l respectively. First, they are processed by the first convolutional layer (Conv1), the first batch normalization layer (BN1), and the ReLU activation function. For the first residual block (l = 1), Z RBI,1 = Zc. For l = 2, 3,..., 8, Z RBI,l = Z RBO,l-1 . Therefore, according to the appendix Figure 4 , the normalized and activated output in the l-th residual block can be expressed as:

[0164]

[0165] Among them, W RBC1,l and B RBC1,l respectively represent the convolution kernel and bias of the "Conv1" convolutional layer in the l-th residual block. Then, Z RBC1,l will further pass through the second convolutional layer ("Conv2") and the second batch normalization layer ("BN2") to generate the corresponding output:

[0166]

[0167] Among them, W RBC2,l and B RBC2,l respectively represent the convolution kernel and bias of the "Conv2" convolutional layer in the l-th residual block. Next, Z RBC2,l is input into the proposed transformer-enhanced SE module, which consists of an adaptive average pooling layer, a flattening layer, two fully connected layers (FC1 and FC2), a multi-head attention layer (MHA), and a Sigmoid activation function, as Figure 4 shown. At the same time, the l-th residual block takes B RBC2,l as the input of the SE module to generate the output Z SE,l , where l = 1, 2,..., 8. As shown in the attached Figure 4 figure, the final output Z RBO,l of the l-th residual block is given by the following formula:

[0168] Z RBO,l = Z RBI,l + Z SE,l , l = 1, 2,..., 8. (63)

[0169] According to the attached Figure 4 figure, the output of the eighth residual block, that is, Z RBO,8 , is simultaneously transmitted to the classification unit and the unknown class rejection unit based on the Gaussian mixture model (GMM) to identify or reject the received UAV RF signal.

[0170] Classification unit

[0171] As shown in the attached Figure 4 figure, the output Z RBO,8 of the last (eighth) residual block is fed into the classification unit, which consists of an adaptive average pooling layer, a flattening layer, and a fully connected layer in sequence, and finally generates a feature vector where K represents the total number of known UAV RF signal candidate types and satisfies Then, the received signal and the candidate set The probability of matching the k-th type of known UAV RF signals in can be estimated by the softmax activation function as follows:

[0172]

[0173] Finally, the type of the received RF signal, denoted as can be identified by the following method:

[0174]

[0175] where

[0176]

[0177] unknown class detection unit

[0178] In addition, referring to Figure 4 , the output of the flatten layer in the classification unit, i.e., will also be sent to the unknown class detection unit based on GMM (Gaussian Mixture Model) to determine whether the type of the received UAV RF signal belongs to the training candidate set The proposed unknown class rejection unit will measure the difference between the feature tensor extracted from the received UAV RF signal and the features extracted from each known candidate signal in by the Mahalanobis distance. This Mahalanobis distance will be compared with an appropriate threshold to determine whether to reject a certain candidate signal type. Without loss of generality, can be regarded as a random vector with a K-modal Gaussian mixture probability density function (PDF), where K represents the total number of known UAV RF signals used for training.

[0179] This probability density function is expressed as:

[0180]

[0181] where ξ k represents the weight coefficient of the k-th Gaussian mode, satisfying 0 ≤ ξ k ≤ 1, and It should be noted that:

[0182]

[0183] Estimating the parameter set from the training data can characterize the K-modal Gaussian mixture probability density function (PDF), where is the parameter related to the k-th Gaussian mode, k = 1, 2,..., K. Assume that for each training candidate set k th, for k = 1, 2, ..., K, ζ output samples can be collected, which are respectively These samples come from the flattened layer in the classification unit. The present invention uses the Expectation-Maximization (EM) algorithm to estimate Θ, specifically as follows:

[0184] Initialization: Estimate ξ for each k = 1, 2, ..., K k , and such that:

[0185]

[0186] where k = 1, 2, ..., K.

[0187] E-step: Re-estimate ξ in the current iteration k as such that:

[0188]

[0189] where k, ε = 1, 2, ..., K; l = 1, 2, ..., ζ,

[0190]

[0191] M-step: Re-estimate and in the current (new) iteration, which are respectively and where k = 1, 2, ..., K, such that:

[0192]

[0193] where k, ε = 1, 2, ..., K.

[0194] Update parameters:

[0195]

[0196] where k, ε = 1, 2, ..., K. Return to the E-step until all parameter estimates converge. The final (converged) set of parameter estimates is denoted as

[0197] During the testing process, the output of the flattened layer from the received UAV RF signal in the classification unit can be expressed as The and Mahalanobis distances between the mean feature vectors of each UAV RF signal candidate in can be calculated as follows:

[0198]

[0199] Assume to generate test feature vectors The UAV RF signal type of A suitable threshold can be selected such that the rejection rule is:

[0200]

[0201] where represents the feature vector is not generated by any of the candidate signals in. In other words, it is an unknown UAV RF signal.

[0202] The present invention designs a brand-new key segment selection mechanism based on the Short-Time Energy-to-Spectral-Entropy Ratio. This mechanism captures the key effective segments by jointly analyzing the time-domain and frequency-domain features of the received UAV RF signal. This mechanism can accurately extract the core information of the UAV RF signal in a complex interference environment, thereby improving the recognition accuracy and enhancing the robustness of the system. Through this mechanism, the recognition system can still effectively identify the target UAV signal at low signal-to-noise ratio (SNR).

[0203] The present invention proposes a new type of CPP (Cyclic-Paw-Print) feature, which can effectively characterize the periodic power distribution of the UAV RF signal. Compared with other features, the CPP feature has stronger robustness and stability, and can cope with signal changes in different environments.

[0204] To more effectively handle the open-set problem and small-sample problem, the present invention proposes a deep learning network TASE-Net that combines a Transformer-enhanced SE module and a Gaussian mixture model (GMM). TASE-Net can significantly enhance the model's attention to important features through the Transformer-enhanced SE module, enabling the network to focus on the key signal features when the number of samples is insufficient. At the same time, the GMM model is embedded in the network to model the distribution of RF signals, and finally the Mahalanobis distance is used to measure the difference between known UAV signals and unknown UAV signals for more accurate open-set recognition. By combining these two technical modules, TASE-Net can effectively identify unknown UAV signals and reject signals of unseen types, solving the open-set recognition problem in traditional deep learning methods.

Claims

1. A small-sample recognition method for UAV radio frequency signal open set based on cyclic paw print diagram, the method comprising: Step 1: Selection of effective UAV segments; Let the captured M-sample discrete-time RF signal sequence be r(t), where t = 0, 1,..., M - 1, and the signal is continuously and seamlessly segmented using a sliding window, and the sliding window contains consecutive sampling points; now, r(t) is divided into windows, where the signal samples of the i-th frame are denoted as Among them The discrete Fourier transform sequence of the i-th frame signal sample is expressed as: Then, the amplitude spectrum sequence of the i-th frame is calculated as |U i (m)|, where Now, construct the spectral probability sequence P i (m) such that: Therefore, the spectral entropy corresponding to the i-th frame is expressed as: Define the ratio e of the short-time energy to the spectral entropy of the i-th frame i as follows: All The set of the short - time energy to spectral entropy ratios of all frames can form a set When e i is greater than the set threshold, it is considered that there is indeed a UAV signal in the i - th frame; the random variable corresponding to e i is denoted as E i , where Let be independent and identically distributed, and the corresponding probability density function is expressed as: Therefore, the smallest, second smallest, third smallest, …, and the largest short-time energy to spectral entropy ratios are represented by random variables: Satisfying The empirical cumulative distribution function of the probability density function given by formula (6) is estimated by the corresponding sample histogram of e i ; the cumulative distribution function of E(i) is estimated according to the empirical cumulative distribution function P[E (i) ≤ e] is, where E(i) represents the ratio of the short-time energy to the spectral entropy of all statistics less than the i-th element in where and ! represents factorial. For a given confidence level and a given short-time energy and spectral entropy ratio threshold determine the appropriate i by solving the following equation: The captured sequence of M sampled discrete-time radio frequency signals r(t), where t = 0, 1,..., M - 1, will be segmented into frame signal samples, i.e., For Then, the frame signal samples corresponding to the φ largest short-time energy-to-spectral entropy ratios will be retained. These φ frame signal samples are indexed by π(1), π(2), π(3), ……, π(φ), where Make the retained signal samples form a new signal sequence x(n), where Its expression is: Among them, and represents the floor operation; Step 2: Feature extraction of cyclic paw print diagram (CPP); Second-order cyclic spectral analysis is introduced to characterize the sequence x(n) given in Equation (10), where for a given frequency f and cyclic frequency α, its time-smoothed cyclic periodogram is given by: where g′(n) represents the unit area weighting function with a width of Δt = NT s seconds, N represents the number of samples in each fast Fourier transform window, and T s represents the sampling period, f1 and f2 represent the center frequencies of the filters used in the accumulation method, i.e., f1 = f + α / 2, f2 = f + α / 2, and is the complex demodulation of x(n), i.e.: where λ represents the discrete-time variable, denotes a data windowing function with a duration of T = N′T s seconds, where N′ is the window length and its bandwidth is consistent with the frequency resolution Δf = f s / N′ of the second-order cyclic spectrum; it should be noted that f s represents the sampling frequency; the second-order cyclic spectrum is obtained from the time-smoothed cyclic periodogram through an unbiased estimate specifically as follows: Second-order cyclic spectrum comprises N′ + 1 spectral frequencies f q , where q = -N′ / 2, -N′ / 2 + 1,..., N′ / 2, and 2N + 1 cyclic frequencies α p , where p = -N, -N + 1,..., N, and it is a three-dimensional spectrum with non-negative amplitudes; thus, the NSCS is calculated as: NSCS represents the normalized second-order cyclic spectrum, and its top view is represented as a P×Q matrix Sx: x = x(p,q)] 0≤p≤P-1, 0≤q≤Q where P = 2N + 1, Q = N′ + 1; the matrix elements in are non - negative normalized magnitudes at the cyclic frequency α p and the spectral frequency f q for p = p + N, q = q + N′ / 2; then, the top view of the NSCS is converted to a grayscale image by a b - bit quantizer such that: where b is a positive integer; Reshape the grayscale image into a square matrix of Λ×Λ denotes conjugate transpose. By reducing the N′ + 1 elements in each column vector to Λ elements and expanding the 2N + 1 elements in each row vector to Λ elements, where P < Λ < Q; then, the square grayscale color map matrix is further transformed into a pseudo-color square image, expressed as: According to formula (16), the square pseudo-color image is represented as the following third-order tensor: Among them, and respectively represent three square matrices of the red R, green G, and blue B channels, satisfying: Step 3: Construct a deep learning network, which includes: a convolutional input layer, a residual unit, a classification unit, and an unknown detection unit; the convolutional input layer, the residual unit, and the classification unit are connected in series in sequence, and the input of the unknown detection unit is the intermediate calculation data of the classification unit; The convolutional input layer sequentially includes: a convolutional layer, a batch normalization layer, a rectified linear unit activation layer, and a max pooling layer; The residual unit is sequentially composed of 8 residual blocks with the same structure; The classification unit sequentially includes: an adaptive average pooling layer, a flattening layer, a fully connected layer, and an activation function layer; the activation function layer outputs the recognition result; The input of the unknown detection unit is the output of the flattening layer in the classification unit, and the unknown detection unit is used to determine whether the received UAV radio frequency signal type belongs to the training candidate set 2. The method for small-sample recognition of the open set of UAV radio frequency signals based on the cyclic claw print diagram according to claim 1, wherein The specific process of the convolutional input layer in Step 3 is as follows: Among them, W c and B c represent the convolution kernel and the bias term of the convolutional layer respectively; then, Z c will be normalized according to its mean value μ c and variance in the subsequent batch normalization layer, and then the ReLU activation function is applied to the normalized result to accelerate convergence and improve classification accuracy; finally, the spatial dimension of the output of ReLU is downsampled by the max pooling layer, and the output Z c of the convolutional unit will be sent to the subsequent residual unit.

3. The method for identifying a small sample of an open set of UAV radio frequency signals based on a cyclic claw print diagram according to claim 1, wherein Each residual block in the residual unit in Step 3 sequentially includes: a first convolutional layer Conv1, a first batch normalization layer BN1, a ReLU layer, a second convolutional layer Conv2, a second batch normalization layer BN2, and an SE module; The input and output of the l-th residual block are denoted as Z RBI,l and Z RBO,l ; The input data first passes through the first convolutional layer Conv1, the first batch normalization layer BN1, and the ReLU layer; for the first residual block where l = 1, Z RBI,1 = Zc, and for l = 2, 3,..., 8, Z RBI, l = Z RBO,l-1 , and the normalized and activated output in the l-th residual block is: Among them, W RBC1,l and B RBC1,l respectively represent the convolution kernel and bias of the first convolutional layer Conv1 in the l-th residual block. Z RBC1,l further passes through the second convolutional layer Conv2 and the second batch normalization layer BN2 to generate corresponding outputs: Among them, W RBC2,l and B RBC2,l respectively represent the convolution kernel and bias of the second convolutional layer Conv2 in the l-th residual block; Next, Z RBC2,l is input into the SE module, and the l-th residual block takes B RBC2,l as the input of the SE module and generates the output Z SE,l , where l = 1, 2,..., 8; the final output Z RBO,l of the l-th residual block is given by the following formula: Z RBO,l = Z RBI,l + Z SE, , l = 1, 2, ..., 8 (24) The output of the eighth residual block, namely Z RBO,8 .

4. The small-sample recognition method for UAV radio frequency signal open set based on cyclic claw print diagram according to claim 1, wherein The input of the taxonomic unit in step 3 is Z RBO,8 , and finally a feature vector is generated where K represents the total number of known candidate types of UAV RF signals and satisfies Calculate the probability that the feature vector matches the k-th type of known UAV RF signal in the candidate set , which is estimated by the softmax activation function as follows: Finally, the type of received radio frequency signal, denoted as is identified by the following method: where 5. The method for identifying small samples of an open set of UAV radio frequency signals based on a cyclic claw print diagram according to claim 1, characterized in that, The input of the unknown class detection unit in Step 3 is the output of the flattening layer in the classification unit, that is: Used to determine whether the received UAV radio frequency signal type belongs to the training candidate set is regarded as a random vector with a K-modal Gaussian mixture probability density function, where K represents the total number of known UAV radio frequency signals used for training, and the probability density function is: Among them, ξ k represents the weight coefficient of the k-th Gaussian mode, satisfying 0 ≤ ξ k ≤ 1, and Estimate the parameter set from the training data which can represent the Gaussian mixture probability density function of K modes, where is the parameter related to the k-th Gaussian mode, ξ k , respectively represent the mixing coefficient, mean, and covariance matrix of the k-th Gaussian mode, where k = 1, 2,..., K. Assume that ζ output samples are collected for each training candidate set k, which are respectively k = 1, 2,..., K, and these samples are from the flattened layer in the classification unit; During testing, the flattened layer output from the received UAV RF signals in the taxonomic unit is represented as Calculate with the Mahalanobis distance between the mean feature vectors of each UAV RF signal candidate, as follows: Assume to generate test feature vectors The UAV RF signal type Set the threshold according to the actual situation So that the rejection rule is: Among them represents the eigenvector not generated by any of the candidate signals in, indicating that it is an unknown UAV RF signal.

6. The method for identifying small samples of UAV radio frequency signal open sets based on a cyclic claw print diagram according to claim 1, characterized in that The confidence level in Formula 8 of Step 1 is set to 0.95, and the spectral entropy ratio threshold e is set to the mode of the short-time energy and the spectral entropy ratio.

7. A small-sample recognition method for UAV radio frequency signal open set based on cyclic claw print diagram according to claim 1, characterized in that Set b to 16 in formula 15 of Step 2.

8. The method for identifying a small sample of an open set of UAV radio frequency signals based on a cyclic claw print diagram according to claim 3, wherein, The SE module in the residual unit is sequentially composed of an adaptive average pooling layer, a flattening layer, a first fully connected layer FC1, a multi-head attention layer MHA, a second fully connected layer FC2, and a Sigmoid activation function.

9. The small sample recognition method for the open set of UAV radio frequency signals based on the cyclic claw print diagram according to claim 5, wherein The expectation-maximization algorithm is used to estimate Θ, specifically as follows: First, perform initialization: estimate ξ for each k = 1, 2,..., K k , and such that: where k = 1, 2, ..., K, Represents the feature vector of the training set samples; Step E: Re-estimate ξ in the current iteration k For such that: where k, ε = 1, 2,..., K; l = 1, 2,..., ζ, Step M: Re-estimate and respectively as and where k = 1, 2, ..., K, such that: where k, ε = 1, 2,..., K; Update parameters: where k, ε = 1, 2, ..., K; return to the E-step until all parameter estimates converge, and the final parameter estimate set is denoted as

Images