A radiation source identification algorithm based on amplitude probability distribution difference

Abstract

The present invention belongs to the field of specific radiation source identification technology, specifically an algorithm for radiation source identification based on differences in amplitude probability distributions. This algorithm addresses the problems of existing common algorithms, such as their limited targeting of amplitude distortion and high complexity, low recognition rates under small sample sizes, and sensitivity to prior information on the signal-to-noise ratio. The proposed scheme includes the following steps: S1: performing amplitude mean normalization preprocessing on the real signal, evenly dividing the real signal amplitude into intervals, and calculating the probability distribution of the sample points in each amplitude interval; S2: performing a Hilbert transform on the real signal to obtain an analytic signal, performing amplitude mean normalization preprocessing on the analytic signal, evenly dividing the analytic signal constellation into circular intervals, and calculating the probability distribution of the sample points in each circular interval. The algorithm is insensitive to prior information on the signal-to-noise ratio and can achieve a high recognition rate without requiring an estimation of the signal-to-noise ratio. Furthermore, compared with comparable algorithms, the proposed algorithm has lower computational complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of specific radiation source identification, and in particular relates to a radiation source identification algorithm based on amplitude probability distribution differences. Background Art

[0002] Individual identification of communication emitters is also known as user signal sorting. In communications reconnaissance, investigators typically focus solely on the valid information conveyed by the signal. With the recent advancement of communications technology, the hardware differences between transmitters embedded in signals have become a research hotspot. Extracting subtle features from hardware differences can be used to identify individual emitters. In military operations and defense, this technology can distinguish friendly and enemy emitters, enabling better strategic deployment. In commercial and civilian applications, emitter identification technology can protect user communications and deter unauthorized users.

[0003] Radiator identification primarily exploits subtle features derived from transmitter hardware variations. Common hardware variations include I / Q modulator distortion, oscillator distortion, filter distortion, and power amplifier (PA) nonlinearity. In recent years, a growing body of research has explored subtle feature extraction based on PA nonlinear distortion, with most using Taylor series modeling to model PA nonlinearity. Common algorithms for subtle feature extraction include those based on bispectrum, time-frequency transform, and spurious signatures.

[0004] When using bispectral analysis to identify radiation sources, the bispectral image is a two-dimensional plane with high complexity, thus requiring dimensionality reduction. Common improved algorithms include radially integrated bispectral (RIB), axially integrated bispectral (AIB), circularly integrated bispectral (CIB), and selected bispectral. However, these algorithms do not fully preserve bispectral amplitude and phase information. Xu Shuhua (2008) chose to use rectangular integrated bispectral (SIB) for radiation source identification, which avoids the omission of bispectral information and achieves high recognition rates even at low signal-to-noise ratios. However, the dimensionality reduction process can easily lead to the loss of some features, and recognition performance is easily affected by the feature dimension. Furthermore, this algorithm has high computational complexity, resulting in low recognition rates when training with small sample sets or short sample lengths.

[0005] There are many algorithms for identifying radiation sources using time-frequency transforms. Among them, Hilbert-Huang transform (HHT) is a classic algorithm for obtaining time-frequency spectra. Based on HHT, Zhang Jingwen (2015) extracted the entropy, mean, and variance of the time-frequency spectrum and combined them into a feature vector to identify radiation sources with nonlinear distortion of power amplifiers, which is called EM. 2The empirical mode decomposition (EMD) step in HHT suffers from severe endpoint effects. To avoid EMD decomposition, Ren (2017) used intrinsic time-scale decomposition (ITD), converted the time-frequency spectrum into an image, and used the gray-level co-occurrence matrix to extract image texture features. However, the algorithm was complex and the recognition performance was still low.

[0006] Using the spurious features of the signal to identify the radiation source is a relatively effective algorithm. Its characteristic is that it requires manual analysis of the feature generation mechanism and the extraction of the spurious features manifested in the transmitted signal. Pan Yiwei (2019) used the nonlinear distortion of the power amplifier to extract a 9-dimensional feature based on the peak-to-average power ratio (PAPR). Its recognition rate is higher than that of Ren Dongfang's algorithm, but it is more sensitive to the prior information of the signal-to-noise ratio. Tang Zhiling (2011) identified the radiation source by extracting nonlinear model parameters, but it is limited by the monotonicity of the relationship between the input and output of the power amplifier and is not applicable to the case where the nonlinear function of the power amplifier is non-monotonic. Y.Lin (2021) used the constellation diagram of the radiation source signal as an image and used a neural network to learn the image and then identify the radiation source. The integrity of the image features was retained, but the interpretation of the image extraction features by the neural network algorithm was poor and relied on a large number of sample training.

[0007] Most of these algorithms extract features from the overall transform spectrum, ignoring subtle local features. However, the radiation source signal exhibits significant local characteristics due to the nonlinear distortion of the power amplifier. For example, the distortion varies at different amplitudes, approaching linearity at smaller amplitudes and becoming more severe with larger amplitudes. However, these common algorithms are not well-suited to amplitude distortion and are complex. This leads to low recognition rates with small sample sizes and high sensitivity to prior information about the signal-to-noise ratio, which urgently needs to be addressed. Summary of the Invention

[0008] To address the problem of identifying individual communication radiation sources, the present invention proposes a new algorithm based on the differences in power amplifier nonlinear distortion between radiation sources. This algorithm is low-complexity, suitable for small training sample sets and short sample lengths, and insensitive to prior information on the signal-to-noise ratio. This algorithm is called a radiation source identification algorithm based on differences in amplitude probability distribution. The technical solution adopted to achieve this goal is as follows:

[0009] A radiation source identification algorithm based on amplitude probability distribution difference includes the following steps:

[0010] S1: Perform amplitude mean normalization preprocessing on the real signal, evenly divide the real signal amplitude interval, and obtain the probability distribution of the sample points in each amplitude interval;

[0011] S2: Perform Hilbert transform on the real signal to obtain the analytical signal, perform amplitude mean normalization preprocessing on the analytical signal, evenly divide the circular intervals of the constellation diagram of the analytical signal, and calculate the probability distribution of the sample points in each circular interval;

[0012] S3: Combine the feature vectors proposed by S1 and S2 into one feature vector and use the support vector machine classifier to identify the radiation source.

[0013] Preferably, the S1 specifically includes the following steps:

[0014] A1: In non-cooperative communication, the power amplification factor of the received signal is unknown. Therefore, it is necessary to perform instantaneous amplitude mean normalization preprocessing on the received real signal after the power amplifier nonlinear distortion.

[0015] A2: Get the amplitude of the pre-processed signal The range of is [0, L1], which is divided into k amplitude intervals, and the probability of the number of sample points in each amplitude interval is calculated to obtain the feature vector.

[0016] Preferably, A1 specifically includes the following:

[0017] The instantaneous amplitude mean normalization preprocessing of the real signal y(n) received after the power amplifier nonlinear distortion is:

[0018]

[0019] Substituting y(n) in the Taylor model into the above formula is:

[0020]

[0021] make but

[0022]

[0023] In the above formula, is the amplitude of the amplitude mean normalized signal, j represents the jth radiation source individual, Re is the real part, s(n) is the shaping filter signal, f c is the carrier frequency of the signal, f s is the signal sampling frequency, is the coefficient of the Taylor series, i represents the Taylor order, and it is known from the formula When the value is fixed, the x of different radiation source signals abs and related.

[0024] Preferably, A2 specifically includes the following:

[0025] After preprocessing, the amplitude range of the real signal is mainly in [0,2], so L1 is set to 2. The ratio of the number of samples in each interval to the total number of samples is calculated, that is, the probability that the sample falls in each interval, and the eigenvector A=[A1,A2,…,A k ], A i is the amplitude of the preprocessed signal The probability of falling in the i-th amplitude interval, the interval range is as follows:

[0026]

[0027] when When x is the signal of different radiation sources before distortion abs Interval and At this time, we can use the signal distortion The probability distribution falling in each interval extracts the nonlinear distortion characteristics of the power amplifier of the radiation source.

[0028] Preferably, the S2 specifically includes the following steps:

[0029] B1: The real signal received after the power amplifier distortion is converted into an analytical signal by Hilbert transform, the instantaneous amplitude mean of the analytical signal is normalized, and a constellation diagram is drawn from the signal;

[0030] B2: Take the constellation radius range of the preprocessed analytical signal as [0, L2], and divide it into k concentric ring intervals. Calculate the probability of the number of sample points in each ring interval to obtain the feature vector.

[0031] Preferably, B1 specifically includes the following:

[0032] The Hilbert transform of y(t) is:

[0033]

[0034] For a discrete analytic signal, its amplitude is:

[0035]

[0036] The amplitude mean normalized analytical signal is:

[0037]

[0038] The amplitude of the analytical signal after preprocessing is:

[0039]

[0040] Where, is the analytical signal normalized by the mean amplitude, and j represents the jth radiation source individual.

[0041] Preferably, B2 specifically includes the following:

[0042] After preprocessing, the amplitude range of the analytical signal is mainly [0,1.5]. At this time, the radius L2 is set to 1.5. The ratio of the number of sample points in each circular interval to the total number of sample points is calculated, that is, the probability that the sample point falls in each circular interval, and the eigenvector B=[B1,B2,…,B k ], B i is the amplitude mean normalized analytical signal The probability of falling within the i-th concentric ring interval, the ring range is shown as follows:

[0043]

[0044] Preferably, the S3 specifically includes the following steps:

[0045] C1: In actual communication, the received signal is a real signal. The nonlinear distortion of the power amplifier is directly reflected in the amplitude compression of the real signal. The amplitude interval probability distribution algorithm is used to extract a feature vector A from the real signal. The signal has rich nonlinear distortion information at large amplitudes. Analyzing the signal amplitude can better highlight the nonlinear distortion of the signal at large amplitudes. The constellation diagram ring interval probability distribution algorithm can be used to extract a feature vector B. The two feature vectors are combined into a feature vector [A1, A2, ..., A k ,B1,B2,…,B k ] as the final extracted features;

[0046] C2: Send the sample feature vector and label into the support vector machine (SVM) classifier for training and recognition.

[0047] Preferably, C2 specifically includes the following:

[0048] Set the input data samples and learning labels as follows:

[0049] X={x1,x2,…,x N}

[0050] y={y1,y2,…,y N}

[0051] Where x n =[A1,A2,…,A k ,B1,B2,…,B k ]∈X, where n represents the nth sample;

[0052] It is sent to the support vector machine (SVM) classifier for training. The radial basis Gaussian kernel function is selected in the support vector machine, and a 5-fold cross validation is set to find the optimal parameters. The features are mapped to a high-dimensional space through the kernel function, and the optimal segmentation plane is found in the high-dimensional space to obtain the learning model. The joint feature vector x in the test sample is nIt is sent to the learned model classifier for test identification to achieve the purpose of individual radiation source identification.

[0053] The beneficial effects of the present invention are as follows: the present invention is sensitive to the amplitude distortion caused by the nonlinearity of the power amplifier, retains the local subtle features of the amplitude, and has a high recognition rate for the radiation source. When the signal-to-noise ratio is 10dB, the recognition rate of the algorithm of the present invention is improved by more than 30% compared with the common algorithm. In addition, the proposed algorithm has high robustness to the size of the training sample set and the sample length. When the signal-to-noise ratio is 20dB, as the training sample set or the sample length decreases, the recognition rate of the common algorithm drops to below 65%, while the algorithm of the present invention can still maintain a recognition rate of more than 99%. At the same time, the algorithm of the present invention is not sensitive to the prior information of the signal-to-noise ratio, and a high recognition rate can be achieved without estimating the signal-to-noise ratio. In addition, compared with the comparative algorithm, the proposed algorithm has lower computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of the radiation source identification algorithm of the present invention;

[0055] Figure 2 Schematic diagram of the effect of nonlinear distortion of power amplifier on the amplitude of real signals from different radiation sources;

[0056] Figure 3 Schematic diagram of the probability distribution of different radiation source signals in various amplitude intervals;

[0057] Figure 4 Schematic diagram showing the effect of the number of intervals k on the recognition rate of the algorithm of the present invention;

[0058] Figure 5 Schematic diagram comparing the recognition performance of AIPD, CIPD and APD;

[0059] Figure 6 This is a schematic diagram comparing the recognition rates of the algorithm of the present invention and common algorithms;

[0060] Figure 7 This is a schematic diagram comparing the recognition rates of different algorithms with a small number of training samples;

[0061] Figure 8 Schematic diagram showing the effect of the number of training samples M on the recognition performance of the algorithm of the present invention;

[0062] Figure 9 This is a schematic diagram comparing the recognition rates of different algorithms under short sample length;

[0063] Figure 10 Schematic diagram showing the effect of sample length N on the recognition performance of the algorithm of the present invention;

[0064] Figure 11 Schematic diagram of the impact of prior information SNR on the recognition performance of different algorithms. DETAILED DESCRIPTION

[0065] The technical solutions in the embodiments of the present invention will be described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0066] Reference Figure 1 , a radiation source identification algorithm based on amplitude probability distribution difference, including the following steps:

[0067] S1: Perform amplitude mean normalization preprocessing on the real signal, evenly divide the real signal amplitude interval, and obtain the probability distribution of the sample points in each amplitude interval;

[0068] S2: Perform Hilbert transform on the real signal to obtain the analytical signal, perform amplitude mean normalization preprocessing on the analytical signal, evenly divide the circular intervals of the constellation diagram of the analytical signal, and calculate the probability distribution of the sample points in each circular interval;

[0069] S3: Combine the feature vectors proposed by S1 and S2 into one feature vector and use the support vector machine classifier to identify the radiation source.

[0070] In the present invention, the S1 specifically includes the following steps:

[0071] A1: In non-cooperative communication, the power amplification factor of the received signal is unknown. Therefore, it is necessary to perform instantaneous amplitude mean normalization preprocessing on the received real signal after the power amplifier nonlinear distortion.

[0072] A2: Get the amplitude of the pre-processed signal The range of is [0, L1], which is divided into k amplitude intervals, and the probability of the number of sample points in each amplitude interval is calculated to obtain the feature vector.

[0073] In the present invention, A1 specifically includes the following:

[0074] The instantaneous amplitude mean normalization preprocessing of the real signal y(n) received after the power amplifier nonlinear distortion is:

[0075]

[0076] Substituting y(n) in the Taylor model into the above formula is:

[0077]

[0078] make but

[0079]

[0080] In the above formula, is the amplitude of the amplitude mean normalized signal, j represents the jth radiation source individual, Re is the real part, s(n) is the shaping filter signal, f c is the carrier frequency of the signal, f s is the signal sampling frequency, is the coefficient of the Taylor series, i represents the Taylor order, and it is known from the formula When the value is fixed, the x of different radiation source signals abs and related.

[0081] Reference Figure 2 , the amplitude of the mean normalized output signal of the power amplifier The amplitude x normalized to the mean value of the amplifier input signal abs / mean(x abs ); differences in power amplifier hardware are the primary source of subtle signal characteristics. At the transmitter, the input and output exhibit nonlinearity, which can be represented by nonlinear functions. Here, the radiation source transmits a QPSK modulated signal, and the Taylor series model is used to simulate the nonlinear distortion of the power amplifier for five radiation source signals.

[0082] The relationship diagram shows that the uniform amplitude range of the signal after preprocessing with different radiation sources corresponds to the non-uniform amplitude range of the signal before distortion. Therefore, the probability distribution of the uniform amplitude range of the signal after preprocessing with different radiation sources is actually the probability distribution of the non-uniform amplitude range of the signal before distortion.

[0083] Taking the first interval as an example, L1 is 2 and k is 8. Figure 2 The enlarged image shows the amplitude of the power amplifier output signal of the five radiation sources after preprocessing The first interval of [0,0.25] corresponds to the amplitude intervals of the five radiation source signals before distortion: [0,0.239], [0,0.214], [0,0.193], [0,0.180], and [0,0.165]. Because the amplitude intervals of the signals from different radiation sources before distortion are different, but the signal types are the same, the probability distribution of the number of sample points in the interval will be different. This difference can be used to identify individual radiation sources.

[0084] Preferably, A2 specifically includes the following:

[0085] After preprocessing, the amplitude range of the real signal is mainly in [0,2], so the value of L1 is 2. Calculate the ratio of the number of samples in each interval to the total number of samples, that is, the probability that the sample falls in each interval, and obtain the eigenvector A=[A1,A2,…,A k ]. i is the amplitude of the signal normalized to the mean The probability of falling in the i-th amplitude interval, the interval range is as follows:

[0086]

[0087] when When x is the signal of different radiation sources before distortion abs Interval and Therefore, we can use the signal distortion The probability distribution falling in each interval extracts the nonlinear distortion characteristics of the power amplifier of the radiation source.

[0088] Reference Figure 3 At a signal-to-noise ratio of 15dB, the QPSK signals from five radiating sources were each sampled for 100k samples, yielding a probability distribution of these samples across eight amplitude intervals. The signal amplitude intervals range from small to large, and the degree of distortion ranges from mild to severe. Therefore, the characteristic vector A derived from the probability distribution of the sample points across k intervals reflects the degree of distortion of the radiating source signal in each amplitude interval, preserving local characteristics.

[0089] This algorithm focuses on extracting the instantaneous amplitude characteristics of real signals, but loses the envelope characteristics of real signals. Figure 5 It can be seen that the proposed real signal amplitude interval probability distribution algorithm achieves a high recognition rate, but it can still be further improved.

[0090] Nonlinear distortion is particularly severe at high signal amplitudes, necessitating focused feature extraction. Real signal envelope distortion is the result of the superposition of the real signal amplitude and the real signal amplitude distortion shifted by π / 2. At any instant, the real signal envelope exceeds max(real signal amplitude, real signal amplitude shifted by π / 2). The envelope, a line connecting the peak-to-peak values of the signal amplitude, further highlights nonlinear distortion at large signal amplitudes. The real signal envelope is the analytic signal amplitude. To compensate for features lost in the algorithm and further improve the recognition rate of the new algorithm, nonlinear distortion is also reflected in the analytic signal amplitude. Therefore, a probability distribution of the circular intervals of the constellation diagram is proposed.

[0091] Preferably, the S2 specifically includes the following steps:

[0092] B1: The real signal received after the power amplifier distortion is converted into an analytical signal by Hilbert transform, the instantaneous amplitude mean of the analytical signal is normalized, and a constellation diagram is drawn from the signal;

[0093] B2: Take the constellation radius range of the preprocessed analytical signal as [0, L2], and divide it into k concentric ring intervals. Calculate the probability of the number of sample points in each ring interval to obtain the feature vector.

[0094] Preferably, B1 specifically includes the following:

[0095] The Hilbert transform of y(t) is,

[0096]

[0097] For a discrete analytic signal, its amplitude is,

[0098]

[0099] The amplitude mean normalized analytical signal is,

[0100]

[0101] The amplitude of the analytical signal after preprocessing is,

[0102]

[0103] Where, is the analytical signal normalized by the mean amplitude, and j represents the jth radiation source individual.

[0104] Preferably, B2 specifically includes the following:

[0105] After preprocessing, the amplitude range of the analytical signal is mainly in [0,1.5], so the radius L2 is set to 1.5. Calculate the ratio of the number of sample points in each circular interval to the total number of sample points, that is, the probability that the sample point falls within each circular interval, and obtain the feature vector B = [B1, B2, ..., B k ]. B i is the amplitude mean normalized analytical signal The probability of falling within the i-th concentric ring interval, the ring range is shown as follows:

[0106]

[0107] Preferably, the S3 specifically includes the following steps:

[0108] C1: In actual communication, the received signal is a real signal. The nonlinear distortion of the power amplifier is directly reflected in the amplitude compression of the real signal. The amplitude interval probability distribution algorithm is used to extract a feature vector A from the real signal. However, the signal has rich nonlinear distortion information at large amplitudes, and analyzing the signal amplitude can better highlight the nonlinear distortion of the signal at large amplitudes. Therefore, the constellation diagram ring interval probability distribution algorithm is used to extract a feature vector B. The two feature vectors are combined into a feature vector [A1, A2, ..., A k ,B1,B2,…,B k ] as the final extracted features;

[0109] C2: Send the sample feature vector and label into the support vector machine (SVM) classifier for training and recognition.

[0110] Preferably, C2 specifically includes the following:

[0111] Set the input data samples and learning labels as follows:

[0112] X={x1,x2,…,x N}

[0113] y={y1,y2,…,y N}

[0114] Where x n =[A1,A2,…,A k ,B1,B2,…,B k ]∈X, where n represents the nth sample.

[0115] It is sent to the support vector machine (SVM) classifier for training. The radial basis Gaussian kernel function is selected in the SVM, and a 5-fold cross validation is set to find the optimal parameters. The kernel function is used to map the features to a high-dimensional space, and the optimal segmentation plane is found in the high-dimensional space to obtain the learning model. The joint feature vector x in the test sample is n It is sent to the learned model classifier for test identification to achieve the purpose of individual radiation source identification.

[0116] Simulation results schematic diagram reference Figure 4-11 , simulation parameter settings:

[0117] The behavioral modeling of the power amplifier of the present invention uses a memoryless nonlinear Taylor series model, and simulates different radiation source signals by setting different Taylor series coefficients.

[0118] The Taylor series model of the nonlinear distortion characteristics of the power amplifier is as follows:

[0119]

[0120] Where x(n) is the power amplifier input signal, y(n) is the power amplifier output signal, is the coefficient of the Taylor series, j represents the jth radiation source, and i represents the Taylor order. The amplitude / amplitude (AM / AM) compression characteristics of the power amplifier are mainly related to odd harmonics, and even harmonics can be filtered out by the filter. Therefore, the Taylor order i only takes odd numbers 1, 3, and 5.

[0121] The coefficients of the Taylor series are set to

[0122]

[0123] Among them, Re is the real part, s(n) is the shaping filter signal, f c is the carrier frequency of the signal, fs is the signal sampling frequency.

[0124] The simulation signal adopts QPSK modulation mode, the raised cosine shaping filter roll-off coefficient α=0.35, and the carrier frequency f c is 3KHz, sampling rate f s The simulation is performed under an AWGN channel environment with a 10 kHz frequency and a symbol rate of 1 KBaud. In the SNR range [0 dB, 20 dB], each radiator signal has 200 total samples at each SNR, 50% of which are used for training and 50% for testing. The number of training samples, M, is 100. Therefore, across the entire SNR range, there are 5500 samples for training and 5500 samples for testing. The sampling point length, N, of each signal sample is 2000.

[0125] In order to compare the recognition effects of the features proposed by different algorithms, the classifiers of the algorithm of the present invention and the comparison algorithm all use Gaussian kernel support vector machine (SVM), and the simulation results of the experiment are the average values obtained after performing 100 Monte Carlo experiments.

[0126] Reference Figure 4 The number of real signal amplitude intervals and circular intervals in the analytic signal constellation is crucial for recognition performance. Choosing an interval that is too large will ignore features within the interval, resulting in performance loss. Choosing an interval that is too small will increase the number of intervals k and the dimension of the feature vector, which can easily lead to overfitting of the classifier. Therefore, it is necessary to find a k value that balances performance and feature dimension. Experiments with different k values revealed that when k was 8, performance was relatively high. However, increasing k further resulted in almost constant performance, which is inefficient. Therefore, k was set to 8, resulting in a 16-dimensional feature vector.

[0127] The proposed feature vector A is used to identify the radiation source, which is referred to as AIPD. The proposed feature vector B is used to identify the radiation source, which is referred to as CIPD. The joint feature vector is used to identify the radiation source, which is referred to as APD. When the sample length is the same, the recognition performance of the three algorithms is compared. Figure 5 As shown in Figure 2, the features proposed by APD are more comprehensive and significant, so the recognition rate is significantly improved compared with the individual algorithms. APD is the final algorithm of the present invention.

[0128] Reference Figure 6 , select three common methods to compare with the algorithm proposed in this patent, the comparison methods are SIB method, PAPR method, EM 2 The recognition rate of the algorithm of the present invention is higher than that of the comparison algorithm starting from 0dB, and the recognition rate increases fastest as the signal-to-noise ratio increases. At 10dB, the recognition rate of the algorithm of the present invention is improved by about 30% compared with the SIB method.

[0129] In order to study the influence of small training sample set or short sample length on the recognition performance of the algorithm of the present invention and common algorithms, simulation experiments were carried out. Figure 7-10 The simulation results of different algorithms for reducing the number of training samples are shown in Figure 7 The dotted line shows that the solid line is when M=100 and the dotted line is when M=10. The effect of the number of training samples M on the recognition performance of the algorithm of the present invention is shown in the figure. Figure 8 The simulation results of different algorithms for shortening sample length are shown in Figure 9 The dotted line shows that the solid line is when N=2000 and the dotted line is when N=1000. The effect of sample length N on the recognition performance of the algorithm of the present invention is shown in the figure. Figure 10 As shown in the figure, it can be seen that when the number of training samples decreases or the sample length shortens, the recognition rate of common algorithms drops significantly at high signal-to-noise ratios, especially the SIB and PAPR methods. However, the recognition performance of the algorithm of the present invention decreases slightly at low signal-to-noise ratios and is insensitive to the number of training samples M and sample length N at high signal-to-noise ratios. When the signal-to-noise ratio is 20dB, the recognition rate of the algorithm of the present invention still reaches over 99% after M and N are reduced, which is higher than that of common algorithms.

[0130] The algorithm is robust to the number and length of training samples, achieving good recognition results even with small sample sizes and maintaining stable performance. Furthermore, a small training sample set significantly reduces the complexity of SVM classifier training and learning, improving the efficiency of radiation source identification and making it suitable for practical applications.

[0131] In order to study the effect of the signal-to-noise ratio prior information as one dimension in the feature vector on the performance of radiation source recognition, comparative experiments were carried out. Figure 11 As shown, the simulation results of the known signal-to-noise ratio are as follows Figure 11 As shown by the dotted line, the simulation results of unknown signal-to-noise ratio are as follows Figure 11 The solid line shows this. It can be seen that the PAPR method is extremely sensitive to prior information about the signal-to-noise ratio. While the other two common algorithms are still affected by this prior information at high signal-to-noise ratios, the algorithm of the present invention is insensitive to this prior information when the SNR is ≥ 8dB. Therefore, the algorithm of the present invention achieves good recognition performance without requiring a signal-to-noise ratio estimation, effectively avoiding the SNR estimation step and simplifying the emitter identification process.

[0132] The specific calculation process of the radiation source identification system based on amplitude probability distribution difference can be found in the above embodiment, and the embodiment of the present invention will not be described in detail here.

[0133] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A radiation source identification algorithm based on amplitude probability distribution difference, characterized in that: The steps include: S1: Perform amplitude mean normalization preprocessing on the real signal, evenly divide the real signal amplitude interval, and obtain the probability distribution of the sample points in each amplitude interval; S2: Perform Hilbert transform on the real signal to obtain the analytical signal, perform amplitude mean normalization preprocessing on the analytical signal, evenly divide the circular intervals of the constellation diagram of the analytical signal, and calculate the probability distribution of the sample points in each circular interval; S3: Combine the feature vectors proposed by S1 and S2 into one feature vector and use the support vector machine classifier to identify the radiation source; The S1 specifically includes the following steps: A1: In non-cooperative communication, the power amplification factor of the received signal is unknown. Therefore, it is necessary to perform instantaneous amplitude mean normalization preprocessing on the received real signal after the power amplifier nonlinear distortion. A2: Get the amplitude of the pre-processed signal The range is , which is divided equally into amplitude intervals, calculate the probability of the number of sample points in each amplitude interval, and obtain the feature vector; A2 specifically includes the following: The amplitude range of the real signal after preprocessing is mainly ,therefore Take the value as 2, calculate the ratio of the number of sample points in each interval to the total number of sample points, that is, the probability that the sample point falls in each interval, and get the eigenvector , is the amplitude of the preprocessed signal Falling in The probability of falling within a range of magnitudes is as follows: ， when When the signal of different radiation sources is distorted Interval and At this time, the signal distortion is used The probability distribution falling in each interval is used to extract the nonlinear distortion characteristics of the power amplifier of the radiation source; The S2 specifically includes the following steps: B1: The real signal received after the power amplifier distortion is converted into an analytical signal by Hilbert transform, the instantaneous amplitude mean of the analytical signal is normalized, and a constellation diagram is drawn from the signal; B2: Take the radius range of the constellation diagram of the pre-processed analytical signal as and divide it into concentric ring intervals, calculate the probability of the number of sample points in each ring interval, and obtain the feature vector; B1 specifically includes the following: The Hilbert transform is: ， For a discrete analytic signal, its amplitude is: ， The amplitude mean normalized analytical signal is: ， The amplitude of the analytical signal after preprocessing is: ， Where, is the amplitude mean normalized analytical signal, Indicates the Individual radiation source; B2 specifically includes the following: The amplitude range of the analytical signal after preprocessing is mainly , at this time the radius Take the value as 1.5, calculate the ratio of the number of sample points in each circular interval to the total number of sample points, that is, the probability that the sample point falls within each circular interval, and obtain the characteristic vector , is the amplitude mean normalized analytical signal Falling in The probability of being in the interval of concentric rings, the range of the rings is shown as follows: 。 2. The radiation source identification algorithm based on amplitude probability distribution difference according to claim 1 is characterized in that: A1 specifically includes the following: The real signal received after the nonlinear distortion of the power amplifier The instantaneous amplitude mean normalization preprocessing is: ， In the Taylor model Substitute into the above formula: , make ,but ， In the above formula, is the amplitude of the amplitude mean normalized signal, Indicates the Individual radiation sources, To get the real part, is the shaping filter signal, is the carrier frequency of the signal, is the signal sampling frequency, are the coefficients of the Taylor series, Represents the Taylor order, from the formula When the value is fixed, the signal of different radiation sources and related.

3. The radiation source identification algorithm based on amplitude probability distribution difference according to claim 2, characterized in that: The S3 specifically includes the following steps: C1: In actual communication, the received signal is a real signal. The nonlinear distortion of the power amplifier is directly reflected in the amplitude compression of the real signal. The amplitude interval probability distribution algorithm is used to extract a feature vector for the real signal. , the signal is rich in nonlinear distortion information at large amplitudes, and analyzing the signal amplitude can better highlight the nonlinear distortion of the signal at large amplitudes. Using the constellation diagram ring interval probability distribution algorithm, a feature vector can be extracted , combine the two eigenvectors into one eigenvector As the final extracted features; C2: Send the sample feature vector and label into the support vector machine classifier for training and recognition.

4. The radiation source identification algorithm based on amplitude probability distribution difference according to claim 3 is characterized in that: C2 specifically includes the following: Set the input data samples and learning labels as follows: ， Where, ,in, Indicates the samples; It is sent to the support vector machine classifier for training. The radial basis Gaussian kernel function is selected in the support vector machine, and a 5-fold cross validation is set to find the optimal parameters. The features are mapped to the high-dimensional space through the kernel function, and the optimal segmentation plane is found in the high-dimensional space to obtain the learning model. The joint feature vector in the test sample is It is sent to the learned model classifier for test identification to achieve the purpose of individual radiation source identification.

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