A Recognition Method for Measurement and Control Composite Modulation Signals Based on the Characteristics of Cyclic Claw Print Diagrams

Abstract

The present invention discloses a method for identifying measurement and control composite modulation signals based on cyclic claw print map features, belonging to the field of information and signal processing. First, according to the standards of the Consultative Committee for Space Data Systems, an ideal composite modulation signal set under a unified carrier system is generated, and the normalized cyclic spectrum is calculated. Secondly, the top view of the three-dimensional normalized cyclic spectrum is transformed into a 16-bit quantized grayscale matrix. Then, two-dimensional discrete cosine transform is used to further extract features from the cyclic claw print matrix. Next, linear discriminant analysis is used to reduce the dimension of the extracted feature matrix, obtaining feature vectors and constructing a training set. The actual identification process is as follows: The receiving end stores the feature training set of the composite modulation signal and the random forest classifier pre-trained with the training set, without other prior knowledge. When a test signal is received, the above method is used to solve the feature vector of the current test signal, and the feature vector is input into the random forest classifier to complete the composite debugging identification process.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing, and particularly relates to the design of signal modulation mode recognition for composite modulation signals. Background Art

[0002] Composite Modulation (CM) refers to a multi-layer modulation scheme in which multi-user baseband data is modulated onto a unified carrier using different modulation methods. It has excellent transmission efficiency, anti-interception ability, and security, and is widely used in Telemetry, Tracking and Command (TT&C) systems and broadband space communications. CM is considered an important modulation method for future sixth-generation wireless communication networks, cognitive space communication networks, and the Internet of Things. In order to perform cognitive communication in a crowded spectrum, intelligent receivers in next-generation communication systems need to blindly identify the modulation type of received signals without any prior knowledge. Therefore, Automatic Composite Modulation Classification (ACMC) is the key mechanism to achieve this goal.

[0003] Traditional automatic modulation classification (AMC) methods can generally be divided into two categories: likelihood-based (LB) decision theory methods and feature-based (FB) decision theory methods. These methods all assume that the target (transmitted) signal is single-layer modulated. The LB decision theory method performs a likelihood ratio test on a statistical model fitted to a given (training) observation data set. However, existing LB methods usually cannot obtain satisfactory AMC results due to reasons such as the lack of a closed-form solution, high computational complexity, and probabilistic mismatch between the underlying model and the actual statistics of the received signal data. Since CM signals are much more complex than single-layer modulated signals, applying LB methods to ACMC is much more difficult than to AMC. On the other hand, FB methods distinguish various modulation types through feature extraction and pattern recognition. Existing FB methods combine continuous demodulation, that is, "layer-by-layer identification and demodulation (LI&D)". The receiver needs to first identify the outer-layer modulation type of the received CM signal using existing FB methods, and then demodulate the received signal for further inner-layer modulation identification. However, this LI&D FB method requires perfect carrier and time synchronization of the received CM signal, so the usage scenario is somewhat limited. In addition, a feature extraction method based on a phase-locked loop and goodness of fit has also been proposed for the recognition of composite modulation signals, but this method loses effectiveness when the phase-locked loop loses lock. High-order cumulants (HOC) can be extracted as signal statistical features for signal blind recognition, but its huge computational amount consumes a large amount of memory resources and has poor timeliness. Currently, only a small number of literatures have proposed ACMC methods. Therefore, it is urgent to explore and implement efficient ACMC technologies.

[0004] In addition, various deep learning models are also adopted in AMC, including convolutional neural networks, self-attention models, generative adversarial networks, etc. This popular deep learning model usually has the advantages of high training recognition accuracy and light weight. However, the ACMC performance of deep learning models highly depends on extracting appropriate features to effectively distinguish different CM schemes, and it is difficult to extract features of composite modulation signals. Currently, there is no deep learning network directly designed for composite modulation signals. How to design a brand-new and efficient composite modulation recognition architecture without increasing the computational complexity and feature extraction difficulty will be a key issue concerned and solved by the present invention.

[0005] The present invention has not been publicly published in domestic or foreign publications, has not been publicly used at home and abroad, or made known to the public in other ways. Summary of the Invention

[0006] The object of the present invention is to overcome the deficiencies of existing composite modulation recognition methods and construct a complete recognition process for composite modulation signals of the unified carrier system in space TT&C. The advantages of this estimation process are high accuracy, good anti-interference performance, effective resistance to phase noise, frequency offset and timing error introduced by the space link, less prior knowledge required, and lower computational complexity and calculation amount.

[0007] Based on the normalized second-order cyclic spectrum analysis of composite modulation signals, the present invention constructs a new image representation of composite modulation signals: cyclic-paw-print (CPP), which can uniquely characterize different types of composite modulation signals; then uses discrete cosine transform (DCT) to further extract features from the CPP grayscale matrix, and uses linear discriminant analysis (LDA) to reduce the dimension of the DCT coefficient matrix; finally, a random forest classifier is introduced for classification and recognition, and the overall recognition scheme is as Figure 1 shown;

[0008] The technical solution of the present invention is a method for recognizing TT&C composite modulation signals based on cyclic-paw-print features, and the method includes:

[0009] Step 1: Construct an ideal composite modulation signal feature training set at different signal-to-noise ratios stored at the receiving end

[0010] Step 1.1: Generate an ideal composite modulation signal set;

[0011] Without loss of generality, this paper considers a unified frequency band two-layer composite modulation scheme. The signal set contains ten composite modulation signals under the unified carrier system, namely PCM / BPSK / PM, PCM / QPSK / PM, PCM / BPSK1 + BPSK2 / PM, PCM / QPSK1 + QPSK2 / PM, PCM / BPSK + QPSK / PM, PCM / BPSK / FM, PCM / QPSK / FM, PCM / BPSK1 + BPSK2 / FM, PCM / QPSK1 + QPSK2 / FM, PCM / BPSK + QPSK / FM, and their modulation indices are all 1.2; the ideal composite modulation signal has no noise interference, does not consider phase noise and Doppler frequency shift, and the model of its transmitted signal s(t) is as follows:

[0012]

[0013] where, f c is the main carrier frequency, Φ 0is the initial phase of the main carrier, represents taking the real part, is the equivalent low - pass signal:

[0014]

[0015] where A represents the modulation signal amplitude, K PM , K FM are the modulation indices of two composite modulation methods respectively. PCM / M - PSK / P represents Pulse - Code Modulation / M - ary Phase - Shift Keying / Phase Modulation, PCM / M - PSK / FM represents Pulse - Code Modulation / M - ary Phase - Shift Keying / Frequency Modulation. Among them, M - ary Phase - Shift Keying is used for inner - layer sub - carrier modulation, and Phase Modulation or Frequency Modulation is used for outer - layer modulation. s i (t) is the inner - layer modulation signal, which is specifically divided into Binary Phase - Shift Keying (BPSK), Quadrature Phase - Shift Keying (QPSK) and multi - user combination methods in the present invention. represents the number of inner - layer modulation signals, that is, the number of users under the unified carrier system;

[0016] The signal model of inner - layer modulation is as follows:

[0017]

[0018] m i = 1, 2,..., M i , 0 ≤ t ≤ T i

[0019] where,

[0020]

[0021] where, f i is the carrier frequency of inner - layer residual - carrier modulation, M i represents the number of symbols of phase - shift keying modulation (the number of phase states), m i represents the index of the phase state, φ i,0 is the initial phase of inner - layer residual - carrier modulation, i is the number of inner - layer modulation signals, i = 1, 2... I, g i (t) represents a rectangular pulse, T i represents the duration of the i - th shaping pulse;

[0022] Step 1.2: Calculate the three - dimensional normalized cyclic spectrum of the ideal composite modulation signal under different signal - to - noise ratios

[0023] Now consider the above - mentioned composite modulation signal transmitted through an additive white Gaussian noise channel. Therefore, the received signal r(t) can be expressed as

[0024] r(t) = s(t) + n(t) (2)

[0025] where n(t) represents AWGN with a mean of 0 and a variance of σ 2 ;

[0026] For the ideal discrete composite modulation signals at different signal-to-noise ratios, the fast Fourier transform accumulation method in the second-order cyclic theory is used to obtain the second-order cyclic autocorrelation function; given the spectral frequency f and the cyclic frequency ε, based on the cyclic periodogram smoothed in the time domain is expressed as:

[0027]

[0028] where g′(·) is a normalized weight function with a time-domain width of Δt = NT s , N is the number of sampling points in each Fourier transform window, T s is the time-domain sampling period, f 1 and f 2 are the filter center frequencies used in the FAM method, where f 1 = f + ε / 2, f 2 = f + ε / 2, denotes the conjugate of R T (·), λ represents a variable, is the complex demodulation of the discrete composite modulation signal r(n), which can be obtained by the following formula:

[0029]

[0030] where ω(λ) represents a rectangular window function with a time-domain sampling length of T = N′T s , the bandwidth of this function is consistent with the frequency resolution Δf of the second-order cyclic spectrum in formula (5), N′ represents the number of samples in the window, r(·) represents the discrete composite modulation signal; the cyclic autocorrelation function is unbiasedly calculated by the time-domain smoothed cyclic period quantity , and the formula is:

[0031]

[0032] The cyclic spectrum obtained thereby is a three-dimensional spectrum with non-negative amplitudes, and this spectrum contains 2N + 1 cyclic frequencies, ε = ε p , p = -N, -N + 1,..., N and N + 1 spectral frequencies f = f q , q = -N′ / 2, -N′ / 2 + 1,..., N′ / 2; furthermore, normalization processing is performed to obtain the normalized second-order cyclic spectrum which is expressed as:

[0033]

[0034] Step 1.3: Perform a cyclic claw print grayscale matrix mapping on the obtained three-dimensional normalized cyclic spectrum;

[0035] The three-dimensional normalized cyclic spectrum obtained from Step 1.2 is converted into its top view; the top view of the three-dimensional cyclic spectrum is represented by a two-dimensional P×Q matrix, i.e.:

[0036] C r =[C r (p,q)] 0≤p≤P-1,0≤q≤Q-1 , P = 2N + 1, Q = N' + 1 (9)

[0037] C r The elements in are the normalized non-negative amplitude values when the given cyclic frequency ε and spectral frequency f ;

[0038] Furthermore, the elements in C r are quantized using 16 bits, thereby converting the picture into a 16-bit grayscale matrix, denoted as:

[0039]

[0040] where represents rounding down;

[0041] The normalized second-order cyclic spectrum of the composite modulation signal is converted into a P×Q grayscale matrix, i.e., the cyclic claw print diagram feature matrix:

[0042] C = [C(p,q)] 0≤p≤P-1,0≤q≤Q-1 ;

[0043] Step 1.4: Further perform feature extraction on the cyclic claw print diagram feature matrix using the discrete cosine transform;

[0044] Perform a two-dimensional discrete cosine transform on the cyclic claw print diagram matrix C(p,q) to obtain the discrete cosine transform coefficient matrix

[0045]

[0046] where u = 0, 1,..., P - 1, v = 0, 1,..., Q - 1, and where β u and β v represent two corresponding multiplication factors, which can be expressed as:

[0047]

[0048]

[0049] Step 1.5: Project the discrete cosine transform coefficient matrix from the high-dimensional data space to the low-dimensional data space using the linear discriminant analysis method;

[0050] In the training phase, for the k-th composite modulation method P in the composite modulation candidate set, k for the signal sequence, k = 1, 2,..., K, calculate the corresponding discrete cosine transform coefficient matrix by Steps 1.2 and 1.3

[0051] After each modulation signal has undergone ρ trials, the l-th discrete cosine transform coefficient matrix generated by the k-th composite modulation scheme can be expressed as where l = 1, 2,..., ρ; first perform row-by-row dimensionality reduction, and the within-class scatter matrix is calculated by the following formula:

[0052]

[0053] where represents the mean matrix of the column vectors;

[0054] Next, the between-class scatter matrix can be calculated by the following formula:

[0055]

[0056] where

[0057] Then solve and calculate the following formula:

[0058]

[0059] where λ d is the d-th largest eigenvalue of, and the corresponding eigenvector is Thus, a D×P left projection matrix is established to reduce the rows of the matrix from P to D, where in the formula is the corresponding d-th column vector, d = 1, 2,..., D;

[0060] Perform the linear discriminant analysis method on the D×Q matrix to obtain the Q×D right projection matrix for column dimensionality reduction, and the new feature matrix is calculated by the following formula:

[0061]

[0062] Since in formula (16) has a rank of at most K - 1, so D ≤ K - 1; each new feature matrix given by formula (17) is further expanded into a vector i.e., the vector has a dimension of 1 × D 2 , and the vector is the final composite modulation feature vector, from which the training feature set is constructed

[0063] Step 2: For one or more types of composite modulation signals actually received at the receiving end, obtain the normalized second-order cyclic spectrum according to the above method to obtain the cyclic fingerprint map matrix;

[0064] Step 3: Perform discrete cosine transform processing on the obtained cyclic fingerprint map matrix, and then use the discrete cosine transform projection matrices and calculated in the training stage to reduce the dimension of the discrete cosine transform coefficient matrix and expand it into a vector to obtain the test set of the actually received signal

[0065] Step 4: Use a random forest classifier for classification and recognition output.

[0066] Furthermore, the specific method of Step 4 is as follows:

[0067] Step 4.1: The receiving end first uses the training set of ideal composite modulation signals at different signal-to-noise ratios to train the random forest classifier;

[0068] Step 4.2: After the receiving end receives the transmitted composite modulation signal, obtain the test set of the actually received signal according to Steps 2 and 3 above and use it as the input of the pre-trained random forest classifier at the receiving end; at this time, each decision tree in the random forest will output a predicted modulation type index corresponding to the composite modulation scheme candidate set where represents the k-th composite modulation type, k = 1, 2,..., K; according to the predictions of all the trees in the random forest, a set of quantity sets of predicted indices can be obtained: where represents the number of occurrences of the composite modulation type index in all the predictions of the trees; therefore, the composite modulation scheme of the test signal is identified as:

[0069]

[0070] where

[0071]

[0072] The present invention first obtains a grayscale feature image from the NSCS top view of a composite modulation signal, then further extracts features through DCT, uses LDA to reduce the dimension of the features, and finally completes classification and recognition by a random forest. Since there is good distinguishability between the NSCS top views of different composite modulation signals and the dimension of the final features is small, the present invention has the advantages of less required prior knowledge, high accuracy, good anti-interference performance, etc. compared with other existing composite modulation recognition methods. In addition, it can effectively combat the phase noise, frequency offset, and timing error introduced by the space link, and effectively reduces the computational complexity, demonstrating excellent performance. Brief Description of the Drawings

[0073] Figure 1 It is a schematic diagram of the overall flow scheme for automatic composite modulation recognition of the present invention;

[0074] Figure 2 It is a comparison diagram of Pcc between the automatic composite modulation recognition technology proposed by the present invention and the method based on high-order cumulants (HOC) under the channel background of additive white Gaussian noise. The length of the received signal sample points of both methods is 2048;

[0075] Figure 3 It is a comparison diagram of Pcc between the automatic composite modulation recognition technology proposed by the present invention and the method based on high-order cumulants (HOC) under the channel background of additive white Gaussian noise. The length of the received signal sample points of the new method is 2048, and the lengths of the received signal sample points of the HOC method are 2048, 10 4 10 5 10 6 ;

[0076] Figure 4 It is a comparison diagram of Pcc between the automatic composite modulation recognition technology proposed by the present invention and the modulation recognition method based on deep learning under the channel background of additive white Gaussian noise;

[0077] Figure 5 It is a comparison diagram of Pcc of the automatic composite modulation recognition technology proposed by the present invention at different signal-to-noise ratios under the channel background of additive white Gaussian noise with timing error;

[0078] Figure 6 It is a comparison diagram of Pcc of the automatic composite modulation recognition technology proposed by the present invention at different signal-to-noise ratios under the channel background of additive white Gaussian noise with phase offset;

[0079] Figure 7 It is a comparison diagram of Pcc of the automatic composite modulation recognition technology proposed by the present invention at different signal-to-noise ratios under the channel background of additive white Gaussian noise with frequency offset. Detailed Embodiment

[0080] According to the composite modulation signal modulation index estimation process pointed out by the present invention, the specific implementation of the present invention is divided into three parts: the recognition accuracy analysis of the ACMC technology proposed by the present invention, the anti-interference and robustness performance research, and the algorithm complexity analysis.

[0081] According to the standards of the Consultative Committee for Space Data Systems (CCSDS), the composite modulation candidate set adopted by the present invention contains 10 signals, which are divided into two subcarrier combination methods, namely PCM / BPSK / PM, PCM / QPSK / PM, PCM / (BPSK1+BPSK2) / PM, PCM / (QPSK1+QPSK2) / PM, PCM / (BPSK1+QPSK2) / PM, PCM / (BPSK1+BPSK2) / FM, PCM / (QPSK1+QPSK2) / FM, PCM / (BPSK1+QPSK2) / FM, PCM / BPSK / FM, and PCM / QPSK / FM. The modulation parameters are given in Table 1. In these composite modulation systems, the subcarrier modulation methods adopt binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK). In a single-user scenario, the subcarrier modulation method is one of them; in a dual-user scenario, the subcarrier modulation method is a linear combination of two-way BPSK, two-way QPSK, or BPSK and QPSK; the subcarrier will be further modulated onto the main carrier, and the main carrier modulation method is phase modulation (PM) or frequency modulation (FM). When the internal and external carrier modulations are combined, the modulation index is taken as 1.2, that is, K PM ,K FM =1.2. The present invention considers the influence of additive white Gaussian noise. The FFT window size for generating the second-order cyclic spectrum in the FAM is set to N = 64, and the size of the CPP matrix is 65×4097. For each composite modulation method, ρ = 350 interference-free CM training signals are generated, so 350 training feature vectors are obtained. The AWGN channel and the signal-to-noise ratio (SNR) range from -15 to 15 dB are considered. In each experiment, 2048 signal samples (symbols) are randomly generated by the computer for each CM method, and 500 Monte Carlo experiments are carried out at each signal-to-noise ratio.

[0082] The present invention measures the recognition accuracy of composite modulation according to the probability of correct classification (Pcc), that is, the mean value of the recognition correct rates of all composite modulation signals in the composite modulation candidate set, and introduces timing error, phase offset, and frequency offset to the signals respectively to conduct anti-interference and robustness performance analysis. In addition, the computational complexity of the proposed new ACMC scheme is analyzed.

[0083] 1. Analysis of Composite Modulation Recognition Accuracy

[0084] First, using the same training and test signal data, on the premise that the number of received signal samples (the length of the received time-domain signal) N = 2048, the Pcc obtained by the proposed new ACMC method (denoted by "Proposed" in the figure) is evaluated and compared with the statistical feature method based on high-order cumulants (HOC), as Figure 2 shown. Since the existing HOC-based method uses four cumulant features, it is fair to compare the performance of the HOC-based method with the performance of the proposed new ACMC technology under the condition of D = 2 (the final feature vector dimension is 1×4). According to Figure 2 , the proposed new ACMC scheme is significantly superior to the existing HOC-based method at all signal-to-noise ratios. In addition, the higher the dimension D 2 of the final feature vector, the higher the Pcc obtained by the proposed new ACMC scheme. When the dimension of the final feature vector is the largest, that is, D 2 = 81, the Pcc of the proposed new ACMC scheme reaches 100% when SNR≥5dB.

[0085] Secondly, since the high-order cumulant features are very sensitive to the number of signal samples, the reduction of the number of signal samples often leads to a significant reduction in recognition accuracy. Therefore, the number of received signal samples N of the HOC method is increased, which are N = 2048, 10 4 , 10 5 , 10 6 respectively. Under the condition that other parameter settings remain unchanged, the HOC-based method is tested again on CM signals of different lengths, while the number of received signal samples N of the new ACMC method of the present invention is still 2048. The results are as Figure 3 shown. When D 2 = 4 (that is, the two ACMC schemes use the same number of features), the HOC-based method can only be superior to the new ACMC scheme proposed by the present invention when N≥10 4 and SNR≥10dB. However, when D = 9 (or D 2When (SNR = 81), the proposed new ACMC scheme is superior to the HOC-based method when SNR < 10 dB, and has the same Pcc as the HOC-based method when SNR ≥ 10 dB and a large number of sample points (N ≥ 10 6 ) are used.

[0086] Finally, the ACMC method proposed in the present invention is also compared with the modulation recognition method based on a deep learning network (DL). The CPP images obtained from the normalized three-dimensional cyclic spectrum will be directly input into three networks commonly used for image recognition: ResNet, MobileNet V2, and ShuffleNet. According to Figure 4 the results, the recognition results Pcc of these three deep learning networks cannot reach 100% under all SNR conditions, and perform poorly under low SNR conditions, with Pcc remaining at about 20%. However, the ACMC method proposed in the present invention has a Pcc exceeding 90% at 0 dB and can reach 100% when SNR is greater than 5 dB.

[0087] 2. Anti-interference and robustness performance analysis

[0088] (1) Timing error analysis

[0089] Assume that the receiver does not achieve complete synchronization of the timing error of the received composite modulation signal, and there will be a residual time error at this time. In the present invention, the residual time error τ is set to 2.5%, 5%, 7.5%, and 10% of the symbol period T s respectively, and other simulation parameter settings are the same as those in Table 1. The Pcc of the 10 signals in the candidate set described in the present invention under the condition of timing synchronization (indicated by "τ = 0" in the figure) and the four set time errors are compared as Figure 5 shown. The Pcc of the method described in the present invention remains basically the same under different timing errors, and the performance degradation is not obvious. Therefore, the ACMC method described in the present invention is not sensitive to time errors.

[0090] (2) Phase offset analysis

[0091] Assume that the receiver does not achieve complete synchronization of the phase of the received composite modulation signal, and the residual phase errors Δθ are set to π / 16, π / 8, 3π / 16, and π / 4 respectively. Other simulation parameter settings are the same as the previous settings. The Pcc of the 10 signals in the candidate set described in the present invention under the condition of phase synchronization (indicated by "Δθ = 0" in the figure) and the four set phase errors are compared as Figure 6As shown, the Pcc of the method of the present invention does not decrease significantly under different phase errors, and the performance degradation with the increase of phase error is not obvious. The recognition rate can still reach more than 80% at 0 dB, maintaining relatively good recognition performance.

[0092] (3) Frequency offset analysis

[0093] Assume that the receiver does not achieve complete synchronization of the main carrier frequency offset of the received composite modulation signal, and the residual frequency offsets Δf are set to 0.025f c , 0.05f c , 0.075f c and 0.1f c respectively, and other simulation parameter settings remain unchanged. The comparison of Pcc obtained from the 10 signals in the candidate set of the present invention under frequency synchronization conditions (indicated by "Δf = 0" in the figure) and the four set frequency offsets is as Figure 7 shown. Under the worst condition (Δf = 0.1f c ), the corresponding Pcc can still reach 85% at 0 dB. Therefore, the ACMC method of the present invention is not sensitive to frequency errors.

[0094] 3. Computational complexity analysis

[0095] The computational complexity of the ACMC method of the present invention has four parts: the construction of the CPP gray matrix based on second-order cyclic spectrum analysis, the calculation of the DCT coefficient matrix, the dimensionality reduction processing using LDA, and the classification output of the random forest classifier. Assume that the number of signal samples of the composite modulation signal received at the receiving end is N. Under the worst calculation condition, the computational complexity of the ACMC method proposed by the present invention in a single experiment is: where and represent the number and average depth of the decision trees of the random forest respectively; and the computational complexity of the ACMC method based on HOC in a single experiment is: The computational complexity of the present invention is significantly lower than that of the statistical feature method.

[0096] Table 1 below shows the simulation parameter settings in the specific implementation process. The parameter settings in this table are given according to the unified standard formulated by the Consultative Committee for Space Data Systems (CCSDS) to generate 10 composite modulation signals in the modulation candidate set under the unified carrier system.

[0097] Table 1: Simulation parameter settings

[0098] Parameter Value Radio frequency 2.15 GHz Intermediate frequency 70 MHz Subcarrier 1 frequency 8 KHz Subcarrier 2 frequency 16 KHz Symbol rate 4 KSps Sampling rate 200 MHz Initial phase of main carrier 0 rad Initial phase of subcarrier 0 rad Transmission channel setting AWGN Signal-to-noise ratio (SNR) [-15 dB, 15 dB]

Claims

1. A method for identifying measurement and control composite modulation signals based on the characteristics of cyclic claw-print diagrams, the method includes: Step 1: Construct an ideal composite modulation signal feature training set at different signal-to-noise ratios stored at the receiving end Step 1.1: Generate an ideal composite modulation signal set; Without loss of generality, a two-layer composite modulation scheme with a unified frequency band is considered. The signal set contains ten composite modulation signals under ten unified carrier systems, namely PCM / BPSK / PM, PCM / QPSK / PM, PCM / BPSK1+BPSK2 / PM, PCM / QPSK1+QPSK2 / PM, PCM / BPSK+QPSK / PM, PCM / BPSK / FM, PCM / QPSK / FM, PCM / BPSK1+BPSK2 / FM, PCM / QPSK1+QPSK2 / FM, PCM / BPSK+QPSK / FM, and their modulation indices are all 1.2; the ideal composite modulation signal has no noise interference, and phase noise and Doppler frequency shift are not considered. The model of its transmitted signal s(t) is as follows: where f c is the main carrier frequency, Φ 0 is the initial phase of the main carrier, represents taking the real part, is the equivalent low-pass signal: Among them, A represents the modulation signal amplitude, K PM , K FM are the modulation indices of two composite modulation methods respectively. PCM / M-PSK / PM represents pulse code modulation / multi-level phase shift keying / phase modulation, and PCM / M-PSK / FM represents pulse code modulation / multi-level phase shift keying / frequency modulation. Among them, multi-level phase shift keying is used for inner sub-carrier modulation, and phase modulation or frequency modulation is used for outer modulation. s i (t) is the inner modulation signal, which is specifically divided into binary phase shift keying BPSK, quadrature phase shift keying QPSK and multi-user combination methods, represents the number of inner modulation signals, that is, the number of users under the unified carrier system; The signal model of the inner-layer modulation is as follows: Where where f i is the carrier frequency of the inner-layer residual carrier modulation, M i represents the number of symbols of the phase shift keying modulation (the number of phase states), m i represents the index of the phase state, φ i,0 is the initial phase of the inner-layer residual carrier modulation, i is the number of inner-layer modulation signals, i = 1, 2... I, g i (t) represents a rectangular pulse, T i represents the duration of the i-th shaping pulse; Step 1.2: Calculate the three-dimensional normalized cyclic spectrum of the ideal composite modulation signal under different signal-to-noise ratios Now consider the above composite modulation signal transmitted through an additive white Gaussian noise channel. Therefore, the received signal r(t) can be expressed as r(t) = s(t) + n(t) (2) where n(t) represents an AWGN with a mean of 0 and a variance of σ 2 ; The fast Fourier transform accumulation method in the second-order cyclic theory is used to obtain the second-order cyclic autocorrelation function of the ideal discrete composite modulation signal at different signal-to-noise ratios; given the spectral frequency f and the cyclic frequency ε, the cyclic periodogram based on time-domain smoothing is expressed as: where g′(·) is a normalized weight function with a time-domain width of Δt = NT s , N is the number of sampling points for each Fourier transform window, and T s is the time-domain sampling period, f 1 and f 2 are the center frequencies of the filters used in the FAM method, where f 1 = f + ε / 2, f 2 = f + ε / 2, denotes the conjugate of R T (·), λ represents a variable, and R T (λ, f 1 ), R T (λ, f 2 ) is the complex demodulation of the discrete composite modulation signal r(n) and can be obtained by the following formula: where ω(λ) represents a rectangular window function with a time-domain sampling length of T = N′T s The bandwidth of this function is consistent with the frequency resolution Δf of the second-order cyclic spectrum in formula (5). N′ represents the number of samples within the window, and r(·) represents the discrete composite modulation signal; the cyclic autocorrelation function is realized by the time-domain smoothed cyclic period quantity to achieve unbiased calculation. The formula is as follows: The resulting cyclic spectrum is a three-dimensional spectrum with non-negative amplitudes, and the spectrum contains 2N + 1 cyclic frequencies, ε = ε p , p = -N, -N + 1,..., N and N + 1 spectral frequencies f = f q , q = -N' / 2, -N' / 2 + 1,..., N' / 2; furthermore, normalization processing is performed to obtain the normalized second-order cyclic spectrum Expressed as: Step 1.3: Perform a cyclic claw-print grayscale matrix mapping on the obtained three-dimensional normalized cyclic spectrum; The three-dimensional normalized cyclic spectrum obtained in Step 1.2 is converted into its top view; the top view of the three-dimensional cyclic spectrum is represented by a two-dimensional P×Q matrix, i.e.: C r The elements in are the normalized non - negative magnitude values when the given cyclic frequency is ε and the spectral frequency is f; ; Further quantize the elements in C r using 16-bit quantization, thereby converting the picture into a 16-bit grayscale matrix, expressed as: wherein represents rounding down; Convert the normalized second-order cyclic spectrum of the composite modulation signal into a grayscale matrix of P×Q, that is, the cyclic footprint map feature matrix: Step 1.4: Further extract features from the cyclic claw-print diagram feature matrix using the discrete cosine transform; Perform a two-dimensional discrete cosine transform on the cyclic claw-print diagram matrix C(p,q) to obtain the discrete cosine transform coefficient matrix where \(u = 0,1,\cdots,P - 1\), \(v = 0,1,\cdots,Q - 1\), and where \(\beta\) u and \(\beta\) v represent two corresponding multiplication factors and can be expressed as: Step 1.5: Use the linear discriminant analysis method to project the discrete cosine transform coefficient matrix from the high-dimensional data space to the low-dimensional data space; In the training phase, for the k-th composite modulation method P in the composite modulation candidate set k of the signal sequence, where k = 1, 2, …, K, the corresponding discrete cosine transform coefficient matrix is calculated by steps 1.2 and 1.3 After each modulation signal has undergone ρ trials, the l-th discrete cosine transform coefficient matrix generated by the k-th composite modulation scheme can be expressed as where l = 1, 2, …, ρ; first, perform dimensionality reduction row by row, and the within-class scatter matrix is calculated by the following formula: Among them represents the mean matrix of column vectors; Next, the between-class scatter matrix can be calculated by the following formula: Among them Then solve and calculate the following formula: where λ d is the d-th largest eigenvalue of and the corresponding eigenvector is Thus, a D×P left projection matrix is established to reduce the rows of matrix from P to D, where is the corresponding d-th column vector, and d = 1, 2, …, D; For the D×Q matrix perform linear discriminant analysis to obtain the right projection matrix of Q×D for column dimensionality reduction. The new feature matrix is calculated by the following formula: Since the rank of in formula (16) is at most K - 1, D ≤ K - 1; each new feature matrix given by formula (17) is further expanded into a vector i.e., the vector has a dimension of 1 × D 2 , and the vector is the final composite modulation feature vector, from which the training feature set Step 2: Obtain the cyclic claw-print diagram matrix by calculating the normalized second-order cyclic spectrum of a certain or multiple composite modulation signals actually received at the receiving end according to the above method; Step 3: Perform discrete cosine transform processing on the obtained cyclic claw print matrix, and then use the discrete cosine transform projection matrix calculated in the training phase and Reduce the dimension of the discrete cosine transform coefficient matrix and expand it into a vector to obtain the test set of the actual received signal Step 4: Use a random forest classifier for classification and recognition output.

2. A method for identifying measurement and control composite modulation signals based on the characteristics of cyclic claw-print diagrams as described in claim 1, characterized in that The specific method of step 4 is: Step 4.1: The receiver first uses the training set of ideal composite modulation signals at different signal-to-noise ratios to train a random forest classifier; Step 4.2: After the receiving end receives the transmitted composite modulation signal, obtain the test set of the actual received signal according to the above Steps 2 and 3 Use it as the input to the pre-trained random forest classifier at the receiving end; at this time, each decision tree in the random forest will output a predicted modulation type index corresponding to the composite modulation scheme candidate set where represents the k-th composite modulation type, k = 1, 2, …, K; according to the predictions of all trees in the random forest, a set of quantity sets of predicted indices can be obtained: where represents the number of occurrences of the composite modulation type index in all the predictions of the trees; therefore, the composite modulation scheme of the test signal is identified as: Where

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