Method for identifying individual radiation sources under digital predistortion of power amplifier

Abstract

Method for identifying individual radiation sources under digital predistortion of power amplifiers. The present invention relates to a method for identifying individual radiation sources. The purpose of the present invention is to solve the problem that existing power amplifier linearization technologies weaken the nonlinear effect of power amplifiers while improving signal quality, resulting in a decline in the performance of individual radiation source identification. The process is as follows: First, obtain a trained digital predistortion trainer; Second, extract multi-domain features from the radiation source signals output by the labeled digital predistortion trainer. The process is as follows: 2.1 Extract contour integral bispectrum features; 2.2 Extract horizontal visibility graph features; 2.3 Extract individual features based on intrinsic time-scale decomposition; Third, obtain a trained SincNet network; Fourth, extract multi-domain features from the radiation source signals to be measured output by the digital predistortion trainer; Fifth, identify the category of the individual signal of the radiation source to be measured after predistortion. The present invention is used in the field of individual radiation source identification.

Description

Technical Field

[0001] The present invention relates to a method for identifying individual radiation sources. Background Art

[0002] The technology of identifying individual radiation sources plays an important role in fields such as communication, intelligence, and modern warfare. With the increasing development of modern communication technology, a series of optimization means such as power amplifier linearization technology have emerged. While these technical means improve the signal quality, they weaken the non-linear effect of the power amplifier, making the individual characteristics of the power amplifier converge and the individual differences of the radiation source weaken. As one of the main sources of the "fingerprint" of the radiation source, the linearization technology of the power amplifier may cause a decline in the individual recognition performance, showing an antagonistic relationship with the radiation source individual recognition technology. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem that the existing power amplifier linearization technology weakens the non-linear effect of the power amplifier while improving the signal quality, resulting in a decline in the radiation source individual recognition performance, and to propose a method for identifying individual radiation sources under digital predistortion of the power amplifier.

[0004] The specific process of the method for identifying individual radiation sources under digital predistortion of the power amplifier is as follows:

[0005] Step 1: Obtain a trained digital predistortion trainer;

[0006] Step 2: Input the undistorted different radiation source signals with labels into the predistorter, and the predistorter outputs the predistorted different radiation source signals with labels;

[0007] The predistorted different radiation source signals with labels output by the predistorter are input into the power amplifier, and the power amplifier outputs the different radiation source signals with labels;

[0008] The different radiation source signals with labels output by the power amplifier are input into The output signals are input into the trained digital predistortion trainer, and the digital predistortion trainer outputs the radiation source signals;

[0009] Extract multi-domain features from the radiation source signals output by the digital predistortion trainer with labels;

[0010] The specific process is as follows:

[0011] Step 2-1: Extract the contour integral bispectrum features from the radiation source signals output by the digital predistortion trainer;

[0012] Step 2-2: Extract the horizontal visibility graph features from the radiation source signals output by the digital predistortion trainer, and calculate the waveform entropy and Fisher information measure of the horizontal visibility graph features,

[0013] Step 2-3: Extract the individual features based on the intrinsic time-scale decomposition from the radiated source signal output by the digital predistortion trainer. The individual features based on the intrinsic time-scale decomposition include sample entropy, energy entropy, first moment, and second moment;

[0014] Step 3: Input the extracted multi-domain features with labels into the SincNet network for training to obtain a trained SincNet network;

[0015] Step 4: Input the radiated source signal to be measured into the predistorter, and the predistorter outputs the predistorted radiated source signal to be measured;

[0016] Input the predistorted radiated source signal to be measured into the power amplifier, and the power amplifier outputs the radiated source signal;

[0017] The radiated source signal output by the power amplifier is input into The output signal is input into the trained digital predistortion trainer, and the digital predistortion trainer outputs the radiated source signal to be measured;

[0018] Extract the multi-domain features from the radiated source signal to be measured output by the digital predistortion trainer;

[0019] Step 5: Input the multi-domain features extracted in Step 4 into the trained SincNet network to complete the identification of the radiated source individual signal after predistortion and identify the category of the radiated source individual signal after predistortion.

[0020] The beneficial effects of the present invention are as follows:

[0021] The present invention solves the problem of the negative impact of the predistortion technology on the radiated source individual identification. In order to improve the radiated source individual identification performance, a radiated source individual identification method for signal local features is further proposed.

[0022] The linearization means based on the predistortion technology and the classification and identification method based on the SincNet network involved in the present invention. By using the QRD-RLS predistortion technology to predistort the radiated source signal, and then extracting the multi-domain features of the processed signal for classification and identification, the negative impact of the predistortion technology on the radiated source identification is verified; then, aiming at the local features of the signal, a classification and identification method of the SincNet network is proposed, and the identification rate is improved by 3% - 5% under low signal-to-noise ratio. Description of the Drawings

[0023] Figure 1 is the flow chart of the present invention;

[0024] Figure 2 is the schematic diagram of the identification rate of the LFM signal without predistortion;

[0025] Figure 3Schematic diagram of the recognition rate of the LFM signal after QRD-RLS predistortion. Specific implementation mode

[0026] Specific implementation mode 1: The specific process of the radiation source individual recognition method under the power amplifier digital predistortion in this implementation mode is as follows:

[0027] Step 1: Obtain a trained digital predistortion trainer;

[0028] Step 2: Input the undistorted different radiation source signals with labels into the predistorter, and the predistorter outputs the predistorted different radiation source signals with labels;

[0029] The predistorted different radiation source signals with labels output by the predistorter are input into the power amplifier, and the power amplifier outputs the different radiation source signals with labels;

[0030] The different radiation source signals with labels output by the power amplifier are input into The output signal is input into the trained digital predistortion trainer, and the digital predistortion trainer outputs the radiation source signal;

[0031] Extract multi-domain features from the radiation source signal output by the digital predistortion trainer with labels;

[0032] The specific process is as follows:

[0033] Step 2-1: Extract the contour integral bispectrum features from the radiation source signal output by the digital predistortion trainer;

[0034] Step 2-2: Extract the horizontal visibility graph (HVG) features from the radiation source signal output by the digital predistortion trainer, calculate the waveform entropy and Fisher information measure of the horizontal visibility graph (HVG) features,

[0035] Step 2-3: Extract the individual features based on the intrinsic time-scale decomposition (ITD) from the radiation source signal output by the digital predistortion trainer, and the individual features based on the intrinsic time-scale decomposition include sample entropy, energy entropy, first moment and second moment;

[0036] Step 3: Input the extracted multi-domain features with labels into the SincNet network for training to obtain a trained SincNet network;

[0037] Step 4: Input the radiation source signal to be measured into the predistorter, and the predistorter outputs the predistorted radiation source signal to be measured;

[0038] Input the predistorted radiation source signal to be measured into the power amplifier, and the power amplifier outputs the radiation source signal;

[0039] The radiation source signal output by the power amplifier is input into The output signal is input into the trained digital predistortion trainer, and the digital predistortion trainer outputs the radiation source signal to be measured;

[0040] Extract multi-domain features from the radiation source signal to be measured output by the digital predistortion trainer;

[0041] Step Five: Input the multi-domain features extracted in Step Four into the trained SincNet network to complete the identification of the post-predistortion radiation source individual signal, and identify the category of the post-predistortion radiation source individual signal (that is, identify the category. Each category has many signals. When classifying and identifying, identify whether this signal is the first category, the second category, or the third category).

[0042] Specific Embodiment Two: The difference between this embodiment and Specific Embodiment One is that in Step One, the trained digital predistortion trainer is obtained; the specific process is as follows:

[0043] The undistorted different radiation source signals with labels are input into the predistorter, and the predistorter outputs the predistorted different radiation source signals v pd (n);

[0044] The predistorted different radiation source signals with labels output by the predistorter are input into the power amplifier, and the power amplifier outputs the signal v pa ;

[0045] The signal v pd (n) output by the predistorter is input into the delay device (the delay device is for the purpose of being simultaneous with the output of the digital predistortion trainer);

[0046] The signal v pa output by the power amplifier is input The output signal is input into the digital predistortion trainer, and the digital predistortion trainer outputs the signal G is the power amplifier gain;

[0047] The signal output by the digital predistortion trainer and the signal v pd (n) output by the delay device are subtracted to output the error e(n). The error e(n) trains the model parameters of the digital predistortion trainer through an adaptive algorithm. When the digital predistortion trainer model is exactly the inverse model of the power amplifier, there is Then the training ends to obtain the corresponding trained digital predistortion trainer; otherwise, the error e(n) continues to train the model parameters of the digital predistortion trainer through the adaptive algorithm until

[0048] The expression is:

[0049]

[0050] Among them, k and q are the order and depth of the digital predistortion trainer of the MP model, respectively, and w kq is the digital predistortion coefficient, is the output signal of the digital predistortion trainer, v pa is the power amplifier output signal with tags, n is the time series, k = odd means k is odd; G is the gain of the power amplifier.

[0051] Other steps and parameters are the same as those in the first specific implementation manner.

[0052] Specific implementation manner three: The difference between this implementation manner and the first or second specific implementation manner is that in step 21, contour integral bispectrum features are extracted from the output radiation source signal of the digital predistortion trainer; the specific process is as follows:

[0053] The expression of the bispectrum definition is

[0054]

[0055] where ω1, ω2 are angular frequencies, and B x (ω1, ω2) is the bispectrum value, τ1, τ2 are time delays, and c 3x is the third-order cumulant, j is the imaginary unit, and j 2 = -1.

[0056] where c 3x (τ1, τ2) = E[x(t)x(t + τ1)x(t + τ2)], and the two-dimensional Fourier transform of c 3x (τ1, τ2) gives the bispectrum value B x (w1, w2); x(t) is the sequence value at time t, and E[ ] is the mean operation.

[0057] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0058] Specific implementation manner four: The difference between this implementation manner and any one of the first to third specific implementation manners is that in step 22, horizontal visibility graph (HVG) features are extracted from the output radiation source signal of the digital predistortion trainer, and the waveform entropy and Fisher information measure of the horizontal visibility graph (HVG) features are calculated. The calculation process is as follows:

[0059] Step 221: First, perform Hilbert transform on the output radiation source signal of the digital predistortion trainer to obtain the instantaneous amplitude, instantaneous phase, and instantaneous frequency of each signal of the predistorted signal;

[0060] Step Two Two Two: Then calculate the waveform entropy of the horizontal visibility graph (HVG) features, where the waveform entropy includes the instantaneous amplitude waveform entropy, the instantaneous phase waveform entropy, and the instantaneous frequency waveform entropy;

[0061] The formula is as follows:

[0062]

[0063]

[0064]

[0065] Among them, E represents the instantaneous amplitude waveform entropy, E′ represents the instantaneous phase waveform entropy, E″ represents the instantaneous frequency waveform entropy, and P i represents the ratio of the instantaneous amplitude of the i-th signal to the instantaneous amplitude of the total signal; P i′ represents the ratio of the instantaneous phase of the i′-th signal to the instantaneous phase of the total signal; P i″ represents the ratio of the instantaneous frequency of the i″-th signal to the instantaneous frequency of the total signal; L represents the number of signals;

[0066] Step Two Two Three: Calculate the Fisher information measure of the horizontal visibility graph (HVG) features, where the Fisher information measure includes the instantaneous amplitude Fisher information measure, the instantaneous phase Fisher information measure, and the instantaneous frequency Fisher information measure;

[0067] The formula is as follows:

[0068]

[0069]

[0070]

[0071] Among them, P a represents the ratio of the instantaneous amplitude of the a-th signal to the instantaneous amplitude of the total signal, P a′ represents the ratio of the instantaneous phase of the a′-th signal to the instantaneous phase of the total signal, P a″ represents the ratio of the instantaneous frequency of the a″-th signal to the instantaneous frequency of the total signal, Ef represents the instantaneous amplitude Fisher information measure, Ef′ represents the instantaneous phase Fisher information measure, Ef″ represents the instantaneous frequency Fisher information measure; F c is the normalization constant, and M represents the number of signals.

[0072] Other steps and parameters are the same as those in any one of the specific embodiments one to three.

[0073] Embodiment 5: The difference between this embodiment and any one of Embodiments 1 to 4 is that in Step 23, individual features based on Intrinsic Time-scale Decomposition (ITD) are extracted from the radiation source signal output by the digital predistortion trainer. The individual features based on intrinsic time-scale decomposition include sample entropy, energy entropy, first moment, and second moment. The specific process is as follows:

[0074] Step 231: The predistorted signal is decomposed by ITD into a baseline signal component with a monotonic trend and a series of intrinsic rotation signal components.

[0075] The radiation source signal output by the digital predistortion trainer is subjected to intrinsic time-scale decomposition and decomposed into a baseline signal L t and a rotation component H t ;

[0076] The implementation process is as follows

[0077] X t = LX t + HX t = L t + H t

[0078] where X t is the radiation source signal output by the digital predistortion trainer, L and H are the extraction operators for the baseline signal and the rotation component respectively, and L t and H t are the baseline signal and the rotation component respectively;

[0079] Step 232: Extract the sample entropy (Sample Entropy, SampEn) of L t and H t ;

[0080] Step 233: Extract the energy entropy, first moment, and second moment (Entropy and First and Second Order Moments, EM t and H t 2 ) of L ).

[0081] Other steps and parameters are the same as any one of Embodiments 1 to 4.

[0082] Embodiment 6: The difference between this embodiment and any one of Embodiments 1 to 5 is that in Step 232, the sample entropy (Sample Entropy, SampEn) of L t and H t is extracted, and the calculation process is as follows:

[0083] The baseline signal L t and the rotation component Ht Construct a time series {x(i)}, where N is the length of the series, x(i) is the i-th data vector, and construct {x(i)} into an m-dimensional vector X(i):

[0084] X(i) = [x(i), x(i + 1),..., x(i + m - 1)]

[0085] where i = 1, 2,..., N - m + 1;

[0086] 1) First, solve for the vector distance d(i, j):

[0087]

[0088] where k is the k-th dimension, k = 1,..., m - 1, and x(j) is the j-th data vector;

[0089] 2) For each i, count the number of distances d(i, j) < r between the vector x(i) corresponding to each i and other vectors. The ratio of this number to the total number of distances N - m + 1 is denoted as

[0090] 3) Define B (m) (r) as

[0091]

[0092] where r is the similarity tolerance. In this paper, it is taken as 0.25 times the standard deviation; B (m) (r) is the mean of N - m ;

[0093] 4) Increase the dimension m by 1, and then repeat the above steps 1) - 2) to obtain and further obtain B (m+1) (r);

[0094] 5) Calculate the sample entropy of the sequence

[0095]

[0096] where SampEn(m, r, N) is the sample entropy, m is the embedding dimension of the sample entropy, generally taken as 1 or 2, in this invention it is taken as 2, r is the similarity tolerance, generally taken as 0.1 - 0.25 times the standard deviation of the input sequence, and in this invention it is taken as 0.25 times the standard deviation.

[0097] Other steps and parameters are the same as those in any one of the first to fifth specific embodiments.

[0098] Specific Embodiment Seven: The difference between this embodiment and any one of the first to sixth specific embodiments is that in step 233, L t and H tEnergy entropy, first moment, and second moment (Entropy and First and Second Order Moments, EM 2 ); The specific process is as follows:

[0099] Step 2331: Extract the t energy entropy of L t and H

[0100] The baseline signal L t and the rotational component H t constitute the time unit G t and the frequency unit G w (The baseline signal L t contains frequency and time, and the rotational component H t contains frequency and time. With time as the horizontal axis and frequency as the vertical axis, p qc is the proportion of the energy of each time-frequency unit in the total time and frequency units.);

[0101] The energy entropy is

[0102]

[0103] where I is the energy entropy, p qc is the proportion of each time-frequency unit in the total time-frequency units, G t is the time unit with a resolution of Δt, G w is the frequency unit with a resolution of Δω, q is the qth time unit in the time unit with a resolution of Δt, c is the cth frequency unit in the frequency unit with a resolution of Δω, q = 1,..., G t , c = 1,..., G w ;

[0104] Step 2332: Extract the t first moment of L t and H

[0105] The baseline signal L t and the rotational component H t constitute an image matrix. Take the grayscale of the image to form a grayscale image matrix (The baseline signal L t contains frequency and time, and the rotational component H t contains frequency and time. With time as the horizontal axis and frequency as the vertical axis, the corresponding area is composed of pixel points.);

[0106] The expression is

[0107]

[0108] where μ is the first moment, B d,fis the pixel size of the grayscale image matrix (d, f), M ～ is the number of rows of the grayscale image matrix, N ～ is the number of columns of the grayscale image matrix;

[0109] Step 2333: Extract L t and H t The second-order moments of, and the expression is

[0110]

[0111] where is the second-order moment.

[0112] Other steps and parameters are the same as those in any one of the specific embodiments 1 to 6.

[0113] Specific embodiment 8: The difference between this embodiment and any one of the specific embodiments 1 to 7 is that the SincNet network sequentially includes: an input layer, a filter structure, a first pooling layer, a first convolutional layer, a second pooling layer, a second convolutional layer, a third pooling layer, a first fully-connected layer, a second fully-connected layer, a third fully-connected layer, a fourth fully-connected layer, a BN layer, a LeakyReLU activation function, a Dropout layer, a softmax layer, and an output layer.

[0114] Other steps and parameters are the same as those in any one of the specific embodiments 1 to 7.

[0115] Specific embodiment 9: The difference between this embodiment and any one of the specific embodiments 1 to 8 is that the filter structure is an 80-dimensional filter structure, the starting bandwidth of each filter is about 0.37 MHz, and the starting frequency and cut-off frequency of the filter structure are continuously distributed from 0 to 30 MHz.

[0116] Other steps and parameters are the same as those in any one of the specific embodiments 1 to 8.

[0117] Specific embodiment 10: The difference between this embodiment and any one of the specific embodiments 1 to 9 is that the first pooling layer is a pooling layer with a window size of 3;

[0118] The convolutional kernel sizes of the first convolutional layer and the second convolutional layer are both 5×5;

[0119] The second pooling layer and the third pooling layer are pooling layers with a window size of 3;

[0120] The ratio of the Dropout layer is 0.5.

[0121] Other steps and parameters are the same as those in any one of the specific embodiments 1 to 9.

[0122] The pre-distortion processed signal is input into the SincNet network. At a sampling rate of 60 MHz, the first layer of the SincNet in the network is set with a total of 80-dimensional filters. The starting bandwidth of each filter is approximately 0.37 MHz. The starting frequency and cut-off frequency of the structure are continuously distributed from 0 to 30 MHz, and the one-dimensional signal sequence input is intercepted in the frequency domain. On this basis, a pooling layer with a window size of 3 is used for dimensionality reduction. The output passes through two pairs of convolutional layers with a convolutional kernel size of 5*5 and a pooling layer with a window size of 3 to embed the underlying features of the samples. Then, through four fully connected layers, a BN layer is also set after the fully connected layers. The LeakyReLU activation function is adopted, and the Dropout ratio is set to 0.5. Finally, after normalization by the softmax layer, the extraction and recognition of the individual signal features of the radiation source after pre-distortion are completed.

[0123] The following embodiments are used to verify the beneficial effects of the present invention:

[0124] Embodiment 1:

[0125] In the case of no pre-distortion, for three different individual radiation sources, the selected features of the present invention all show a relatively high recognition rate. Especially at a relatively low signal-to-noise ratio of -5 to 5 dB, the individual recognition rate of most features reaches more than 80%. However, in the power amplifier system after pre-distortion, only some features can maintain a relatively high recognition rate. Under the condition of a signal-to-noise ratio of -5 to 5 dB, the individual recognition rate of most features can only reach 60%. The recognition accuracy of all features has deteriorated to varying degrees after pre-distortion.

[0126] Through the classification accuracy of each feature, in this paper, the reduction in the recognition rate under the conditions of with and without pre-distortion is used to measure its applicability and effectiveness, as shown in Table 1.

[0127] Table 1 Comparison of the deterioration of the recognition performance of each feature with and without pre-distortion

[0128]

[0129] Basically, the recognition performance of all features has deteriorated to varying degrees within the selected signal-to-noise ratio range, indicating that the spurious degree in the non-main signal region of the time-frequency image of the output signal after pre-distortion processing is significantly lower. Analyzing the time-frequency diagrams of the output signals of different radiation sources after pre-distortion, they are all closer to the input signal, that is, the energy is concentrated in the main signal region. The existing features are strongly dependent on the waveform amplitude, and the digital pre-distortion technology corrects the nonlinear effect of the power amplifier, making the individual differences weaken.

[0130] Embodiment 2:

[0131] The one-dimensional time series of the signal after pre-distorting the input number is recognized using the SincNet structure. Training is carried out using 1000 sampling points of single pulses for a total of 1500 samples from three radiation source signals, with 500 samples for each. Testing is carried out using 1000 sampling points of pulses from the same 1500 samples but at different time periods.

[0132] An adaptive learning rate function is set. The batch is set to input 128 samples, with 1000 sampling points for each sample. Training is carried out using the RMSprop optimizer. Finally, the filter frequency band learned by the first layer of SincNet is the signal sensitive region.

[0133] The performance of the interpretable network constructed in this paper is verified. The final recognition accuracies at different signal-to-noise ratios are shown in Table 2. Among them, ITD-EM2-SVM is obtained by extracting ITD-Hilbert-EM2 features and using SVM for classification under the condition of no pre-distortion. The present invention takes it as an ideal recognition model of the traditional method without pre-distortion. The closer the performance of the recognition method for the pre-distorted radiation source signal is, the better the recognition effect is, and the stronger the antagonism to the pre-distortion technology is.

[0134] Table 2 Recognition Accuracies of SincNet at Different Signal-to-Noise Ratios

[0135]

[0136]

[0137] The present invention can also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention. However, these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. Method for identifying individual radiation sources under digital predistortion of power amplifiers, characterized in that: The specific process of the method is as follows: Step 1: Obtain a trained digital predistortion trainer; Step 2: Input the undistorted different radiation source signals with labels into the predistorter, and the predistorter outputs the predistorted different radiation source signals with labels; The predistorted different radiation source signals with labels output by the predistorter are input into a power amplifier, and the power amplifier outputs different radiation source signals with labels; Input of different tagged radiation source signals output by the power amplifier The output signal is input into the trained digital predistortion trainer, and the digital predistortion trainer outputs the radiation source signal; Extract multi-domain features from the radiation source signals output by the digital predistortion trainer with labels; The specific process is as follows: Step 2-1: Extract the contour integral bispectrum features from the radiation source signals output by the digital predistortion trainer; Step 2-2: Extract the horizontal visibility graph features from the radiation source signals output by the digital predistortion trainer, and calculate the waveform entropy and Fisher information measure of the horizontal visibility graph features; Step 2-3: Extract the individual features based on intrinsic time-scale decomposition from the radiation source signals output by the digital predistortion trainer, and the individual features based on intrinsic time-scale decomposition include sample entropy, energy entropy, first moment, and second moment; Step 3: Input the extracted multi-domain features with labels into the SincNet network for training to obtain a trained SincNet network; Step 4: Input the radiation source signal to be measured into the predistorter, and the predistorter outputs the predistorted radiation source signal to be measured; Input the predistorted radiation source signal to be measured into the power amplifier, and the power amplifier outputs the radiation source signal; Input of the radiation source signal output by the power amplifier The output signal is input into the trained digital predistortion trainer, and the digital predistortion trainer outputs the radiation source signal to be measured; Extract multi-domain features from the radiation source signals to be measured output by the digital predistortion trainer; Step 5: Input the multi-domain features extracted in Step 4 into the trained SincNet network to complete the identification of the individual radiation source signals after predistortion, and identify the category of the individual radiation source signals after predistortion.

2. The method for identifying individual radiation sources under digital pre-distortion of power amplifiers according to claim 1, wherein: In Step 1, obtain a trained digital predistortion trainer; the specific process is as follows: The tagged non-pre-distorted different radiation source signals are input into the pre-distorter, and the pre-distorter outputs the tagged pre-distorted different radiation source signals v pd (n); The pre-distorter outputs tagged pre-distorted signals of different radiation sources to the power amplifier, and the power amplifier outputs the tagged signal v pa ; The tagged signal v output by the predistorter pd (n) input delay element; Tagged signal v output by the power amplifier pa Input The output signal is input to the digital predistortion trainer, and the digital predistortion trainer outputs a signal G is the power amplifier gain; The output signal of the digital predistortion trainer and the output signal v pd (n) are subtracted to output the error e(n). The error e(n) trains the model parameters of the digital predistortion trainer through an adaptive algorithm. When the digital predistortion trainer model is exactly the inverse model of the power amplifier, there is Then the training ends to obtain the corresponding trained digital predistortion trainer; otherwise, the error e(n) continues to train the model parameters of the digital predistortion trainer through the adaptive algorithm until The expression is: where k and q are the order and depth of the digital predistortion trainer of the MP model, respectively, and w kq is the digital predistortion coefficient, is the output signal of the digital predistortion trainer, v pa is the power amplifier output signal with labels, n is the time series, k = odd means k is odd; G is the gain of the power amplifier.

3. The method for identifying individual radiation sources under digital pre-distortion of power amplifiers according to claim 2, wherein: In Step 2-1, extract the contour integral bispectrum features from the radiation source signals output by the digital predistortion trainer; The specific process is as follows: The expression of the bispectrum definition is where ω1 and ω2 are angular frequencies, B x (ω1, ω2) is the bispectrum value, τ1 and τ2 are time delays, c 3x is the third-order cumulant, j is the imaginary unit, j 2 = -1.

4. The method for identifying individual radiation sources under digital pre-distortion of a power amplifier according to claim 3, wherein: In Step 2-2, extract the horizontal visibility graph features from the radiation source signals output by the digital predistortion trainer, calculate the waveform entropy and Fisher information measure of the horizontal visibility graph features, and the calculation process is as follows: Step 2-2-1: First, perform Hilbert transform on the radiation source signals output by the digital predistortion trainer to obtain the instantaneous amplitude, instantaneous phase, and instantaneous frequency of each signal of the predistorted signal; Step 2-2-2: Then calculate the waveform entropy of the horizontal visibility graph features, and the waveform entropy includes instantaneous amplitude waveform entropy, instantaneous phase waveform entropy, and instantaneous frequency waveform entropy; The formula is as follows: Among them, E represents the instantaneous amplitude waveform entropy, E′ represents the instantaneous phase waveform entropy, E″ represents the instantaneous frequency waveform entropy, and P i represents the ratio of the instantaneous amplitude of the i-th signal to the instantaneous amplitude of the total signal; P i′ represents the ratio of the instantaneous phase of the i′-th signal to the instantaneous phase of the total signal; P i″ represents the ratio of the instantaneous frequency of the i″-th signal to the instantaneous frequency of the total signal; L represents the number of signals; Step 2-2-3: Calculate the Fisher information measure of the horizontal visibility graph features, and the Fisher information measure includes instantaneous amplitude Fisher information measure, instantaneous phase Fisher information measure, and instantaneous frequency Fisher information measure; The formula is as follows: where P a represents the ratio of the instantaneous amplitude of the ath signal to the instantaneous amplitude of the total signal, and P a′ represents the ratio of the instantaneous phase of the a'th signal to the instantaneous phase of the total signal, and P a″ represents the ratio of the instantaneous frequency of the a''th signal to the instantaneous frequency of the total signal, Ef represents the instantaneous amplitude Fisher information measure, Ef' represents the instantaneous phase Fisher information measure, and Ef'' represents the instantaneous frequency Fisher information measure; F c is a normalization constant, and M represents the number of signals.

5. The method for identifying individual radiation sources under digital pre-distortion of a power amplifier according to claim 4, characterized in that: In Step 2-3, extract the individual features based on intrinsic time-scale decomposition from the radiation source signals output by the digital predistortion trainer, and the individual features based on intrinsic time-scale decomposition include sample entropy, energy entropy, first moment, and second moment; the specific process is as follows: Step 231: Perform intrinsic time-scale decomposition on the radiation source signal output by the digital predistortion trainer, and decompose it into a baseline signal L t and a rotational component H t ; The implementation process is as follows X t = LX t + HX t = L t + H t Among them, X t is the radiation source signal output by the digital pre-distortion trainer. L and H are the extraction operators for the baseline signal and the rotation component respectively. L t and H t are the baseline signal and the rotation component respectively; Step 232: Extract the sample entropy of L t and H t ; Step 233: Extract L t and H t 's energy entropy, first-order moment, and second-order moment.

6. The method for identifying individual radiation sources under digital predistortion of a power amplifier according to claim 5, wherein: Extract L in step 232 t and H t The sample entropy is calculated as follows: Baseline signal L t and rotational component H t constitute a time series {x(i)}, where N is the length of the series, x(i) is the i-th data vector, and {x(i)} is constructed into an m-dimensional vector X(i): X(i) = [x(i), x(i + 1), ···, x(i + m - 1)] where i = 1, 2, ···, N - m + 1; 1) First, solve the vector distance d(i, j): where k is the k-th dimension, k = 1, ···, m - 1, and x(j) is the j-th data vector; 2) For each i, count the number of distances d(i,j) < r between the vector x(i) corresponding to each i and other vectors. The ratio of this number to the total number of distances N - m + 1 is denoted as 3) Definition B (m) (r) is where r is the similarity tolerance; 4) Increase the dimension m by 1 again, and then repeat the above steps 1) - 2) to obtain further obtain B (m+1) (r); 5) Calculate the sequence sample entropy where SampEn(m, r, N) is the sample entropy, m is the embedding dimension of the sample entropy, and r is the similarity tolerance.

7. The method for identifying individual radiation sources under digital pre-distortion of a power amplifier according to claim 6, characterized in that: Extract L in step 233 t and H t for their energy entropy, first-order moment, and second-order moment. The specific process is as follows: Step 2331: Extract the energy entropy of L t and H t ; the process is as follows: Baseline signal L t and rotational component H t constitute time unit G t and frequency unit G w ; The energy entropy is where I is the energy entropy, and p qc is the proportion of each time-frequency unit in the total time-frequency units, G t is the time unit with a resolution of Δt, G w is the frequency unit with a resolution of Δω, q is the q-th time unit in the time unit with a resolution of Δt, c is the c-th frequency unit in the frequency unit with a resolution of Δω, q = 1, ..., G t , c = 1, ···, G w ; Step 2332: Extract L t and H t 's first moment, the process is as follows: Baseline signal L t and rotational component H t constitute an image matrix, take the grayscale of the image, and constitute a grayscale image matrix; The expression is where μ is the first moment, B d,f is the pixel size of the grayscale image matrix (d,f), M ～ is the number of rows of the grayscale image matrix, N ～ is the number of columns of the grayscale image matrix; Step 2333: Extract the second moment of L t and H t The expression is Among them, is the second moment.

8. The method for identifying individual radiation sources under digital pre-distortion of power amplifiers according to claim 7, characterized in that: The SincNet network sequentially includes: an input layer, a filter structure, a first pooling layer, a first convolutional layer, a second pooling layer, a second convolutional layer, a third pooling layer, a first fully connected layer, a second fully connected layer, a third fully connected layer, a fourth fully connected layer, a BN layer, a LeakyReLU activation function, a Dropout layer, a softmax layer, and an output layer.

9. The method for identifying an individual radiation source under digital pre-distortion of a power amplifier according to claim 8, characterized in that: The filter structure is an 80-dimensional filter structure, and the starting frequency and cut-off frequency of the filter structure are continuously distributed from 0 to 30 MHz.

10. The method for identifying individual radiation sources under digital pre-distortion of a power amplifier according to claim 9, characterized in that: The first pooling layer is a pooling layer with a window size of 3; The convolutional kernel sizes of the first convolutional layer and the second convolutional layer are both 5×5; The second pooling layer and the third pooling layer are pooling layers with a window size of 3; The ratio of the Dropout layer is 0.5.

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