A modulation recognition method based on primary and secondary asynchronous undersampling and dynamic decision

Abstract

A modulation identification method based on asynchronous undersampling and dynamic decision-making in satellite communication is disclosed. The method involves: the main channel acquiring the baseband signal at an undersampling rate lower than the signal bandwidth; the auxiliary channel acquiring zero-crossing features of the signal through asynchronous clock intervals, generating complementary sampling sequences to suppress aliasing distortion and reduce dependence on high-speed ADCs; dynamically calculating the channel reliability coefficient based on the weighted variance of the main and auxiliary channel signals; employing multi-level joint feature classification and dynamic confidence decision-making during modulation identification; the first level uses coarse classification features for rapid screening, and the second level activates fine classification features for accurate identification; dynamically adjusting the dual-channel weighted fusion classification results according to the real-time confidence difference threshold; triggering the auxiliary channel's zero-crossing feature re-extraction and decision iteration when the difference exceeds the limit, until a consistent modulation type is output. This invention improves identification accuracy under dynamic channels while reducing hardware costs through complementary sampling and dynamic weighting mechanisms.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication modulation identification technology, and relates to a modulation identification method based on master-slave asynchronous undersampling and dynamic decision-making. Background Technology

[0002] With the rapid development of satellite communication technology towards higher frequencies and wider bandwidths, the identification of non-cooperative signal modulation faces severe challenges. To reliably acquire satellite signals in unknown frequency bands and bandwidths, the receiver needs to configure a high-speed analog-to-digital converter (ADC) according to the Nyquist sampling theorem. However, in high-frequency scenarios such as the Ka band (26.5-40GHz), ADC modules that meet the sampling rate requirements are expensive and consume a lot of power, which seriously restricts the technological development of high-frequency broadband satellite communication monitoring.

[0003] To reduce hardware costs, the industry has attempted to adopt undersampling schemes, also known as equivalent time sampling, which sacrifices sampling rate for cost optimization. However, undersampling can cause signal spectral aliasing, leading to severe distortion of time and frequency domain characteristics. For example, when the sampling rate is less than twice the bandwidth, the time-frequency joint features relied upon by traditional modulation recognition (such as instantaneous amplitude variance and spectral symmetry) will be biased due to aliasing interference, directly affecting recognition accuracy. In addition, existing single-channel fixed sampling strategies may lead to sampled data failure in certain scenarios (such as synchronous sampling at zero crossings of periodic signals), further limiting their engineering practicality.

[0004] Under the dual constraints of dynamic channel environments and limited hardware resources, the limitations of traditional modulation recognition methods become more pronounced. In low-Earth orbit satellite communications, the high-speed movement of terminals exacerbates Doppler frequency offset and channel time-varying characteristics, causing the signal-to-noise ratio (SNR) to fluctuate drastically within the range of 0-20 dB. Existing methods typically employ fixed feature sets and static calculation strategies, failing to dynamically adjust feature weights based on SNR or optimize resource allocation mechanisms. At low SNR, insufficient feature noise immunity leads to a sharp drop in recognition rate, while at high SNR, redundant computation results in wasted resources. More seriously, the aliasing effect caused by undersampling couples with dynamic channel interference, resulting in extremely low overall recognition rates for traditional methods in real satellite scenarios, making it difficult to meet the needs of non-cooperative signal monitoring. Summary of the Invention

[0005] To address the technical challenges of low modulation identification accuracy in satellite communication, particularly due to high hardware costs for high-frequency signal reception, severe undersampling aliasing distortion, and poor dynamic channel adaptability, this invention provides a modulation identification method based on asynchronous undersampling and dynamic decision-making. This method employs a dual-channel asymmetric sampling architecture: the main channel acquires the baseband signal at an undersampling rate lower than the signal bandwidth, while the auxiliary channel acquires zero-crossing features at asynchronous clock intervals, generating complementary sampling sequences to suppress aliasing distortion and reduce reliance on high-speed ADCs. The method dynamically calculates channel reliability coefficients based on the weighted variance of the main and auxiliary channel signals. During modulation identification, multi-level joint feature classification and dynamic confidence decision-making are used. The first level employs coarse classification features (anti-aliasing time-domain statistics) for rapid screening, while the second level activates fine classification features (cross-channel fusion features) for accurate identification. Based on a real-time confidence difference threshold, the dual-channel weighted fusion classification results are dynamically adjusted. When the difference exceeds the limit, the auxiliary channel's zero-crossing features are re-extracted and decision-making iterates until a consistent modulation type is output. This method improves recognition accuracy in dynamic channels while reducing hardware costs through complementary sampling and dynamic weighting mechanisms.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention discloses a modulation recognition method based on master-slave asynchronous undersampling and dynamic decision-making, comprising the following steps:

[0008] Step 1: Asynchronously acquire the analog signal x(t) using the main and auxiliary channels to obtain the digital signal;

[0009] The sampling periods for the main and auxiliary channels are T respectively. s1 and T s2 And satisfy T s1 / T s2 = m / s, where m and s are coprime positive integers. The asynchronous sampling time difference between the main and auxiliary channels is Δt. After sampling, the main digital signal x1[n] and the auxiliary digital signal x2[n] are obtained respectively:

[0010]

[0011] Where t is a continuous time variable and n is the index of the sampling sequence.

[0012] Step 2: Spectrum monitoring and signal-to-noise ratio estimation;

[0013] Windowed FFT processing is performed on signals x1[n] and x2[n] respectively to obtain spectral data X1[k] and X2[k]:

[0014]

[0015] Where k is the index of the spectrum sequence, w[n] is the Hanning window function, and N is the number of FFT points.

[0016] Main channel signal-to-noise ratio (SNR1):

[0017]

[0018] In the formula, k peak The main lobe index of the signal spectrum is used, and the calculation method for the auxiliary channel SNR2 is the same as that for the main channel.

[0019] Step 3: Perform digital down-conversion and low-pass filtering on signals x1[n] and x2[n] respectively based on the center frequency and bandwidth of the main and auxiliary channels to obtain zero intermediate frequency signals y1[n] and y2[n]:

[0020]

[0021] Among them, f LO1 The center frequency of the main channel, f LO2 The center frequency of the auxiliary channel is B1, and the signal bandwidths of the two channels are B2 and B1, respectively. The LPF is a low-pass filter with a cutoff frequency F. c =B i / 2+Δf,i=1,2,Δf is the protection interval;

[0022] Step 4: Extracting cumulative features across orders;

[0023] y1[n] and y2[n] are combined according to their temporal relationship to obtain y3[n]. Cumulative features are extracted from y1[n], y2[n] and y3[n] respectively using equation (3):

[0024]

[0025] In the formula, i = 1, 2, 3, which represent the indices of different sequences, and C pq denoted as cum(·), where p is the order of the cumulant, i.e., the number of random variables in cum(·); * denotes the conjugate operation on the sequence values, where q is the number of conjugates of the random variables in cum(·), 0 ≤ q ≤ p / 2. The calculation definition of cum(·) is as follows:

[0026]

[0027] In the formula, Φ iterates over all values ​​from 1 to p. Traverse the values ​​in Φ, where η is The number of elements in the sequence, E represents the mean operation on the sequence, and j represents the number of elements in the sequence. The index of an element in the middle.

[0028] The cumulative characteristic C is calculated according to the above formula (3).40 C 41 C 42 C 63 C 80 ;This leads to the characteristic of cross-order cumulative quantities:

[0029]

[0030] Further, the cross-order cumulant eigenvector F is obtained. i =[F1,F2,F3,F4], i=1,2,3.

[0031] Step 5: Calculate the cross-channel cumulative fusion feature vector T, which represents the new feature formed by combining the features of data from different channels:

[0032] T=λ1F1+λ2F2+F3 (7)

[0033] Where λ1 and λ2 represent the reliability weights of the main and auxiliary channels, respectively.

[0034] Step 6: Input the generated cross-order cumulative feature vector F1 and cross-channel cumulative fusion feature vector T into the pre-trained multi-level decision tree model to perform multi-level joint feature classification and dynamic confidence decision to obtain the modulation recognition result, that is, modulation recognition is realized based on master-slave asynchronous undersampling and dynamic decision.

[0035] The first level of the decision tree model performs coarse classification based on the main channel feature vector F1, and uses the main channel features to initially divide the signal and generate a candidate modulation type set; the second level uses T obtained in step 5 to perform fine-grained discrimination on the candidate set obtained from the coarse classification.

[0036] Calculate the Euclidean distance between T and the preset template, i.e.:

[0037]

[0038] in, For offline training features, ||·||2 is the Euclidean norm.

[0039] The modulation type corresponding to the minimum distance is selected as the candidate result output, and the confidence index Conf = 1 / (1+D) is calculated. c ).

[0040] If the confidence level Conf≥0.7, the candidate result is directly output as the final modulation recognition result;

[0041] If the confidence level Conf < 0.7, then calculate feature F. i mean The pre-trained multi-level decision tree model is re-inputted for classification to obtain the modulation recognition type. If the new classification result is consistent with the candidate result, the result is output as the final modulation recognition result. If they are inconsistent, the recognition and classification are performed independently based on F2 and F3 respectively. Then, all modulation recognition results are selected by majority voting mechanism to select the highest frequency modulation type as the final modulation recognition result and output it. That is, modulation recognition is realized based on master-slave asynchronous undersampling and dynamic decision.

[0042] Furthermore, to address noise and multipath interference in the actual system, the modulation identification results obtained in step 6 are subjected to stability testing.

[0043] The system processes data in units of time slots, with each time slot containing N sampling points. SNR avg The average signal-to-noise ratio of the primary and secondary channels. The differential characteristics of adjacent time slots are:

[0044] ΔF=||F i,t -F i,t-1 ||2 (9)

[0045] Where F i,t Let be the cross-order cumulative feature vector of the t-th time slot of the i-th data set.

[0046] The sliding window is L, storing the ΔF values ​​of the most recent L time slots, i.e.: [ΔF t-L+1 ,ΔF t-L+2 ,…,ΔF t If the mean and difference standard thresholds within this window are:

[0047]

[0048] If ΔF > σ, the current time slot is determined to have abnormal fluctuations in characteristics. The classification result of the previous time slot is then maintained, but the confidence level is reduced.

[0049] Conf = Conf·e -αΔF ,α=0.1 (11)

[0050] If ΔF≤σ, then the characteristic is stable and the confidence level remains unchanged.

[0051] When ΔF exceeds σ for 5 consecutive time slots, it is determined that a signal switching may occur. The feature buffer is immediately reset and the classification parameters are reinitialized to avoid interference from historical data to the new signal.

[0052] Beneficial effects:

[0053] 1. This invention discloses a modulation recognition method based on asynchronous undersampling and dynamic decision-making. Through a dual-channel asynchronous undersampling mechanism, utilizing the non-integer multiple sampling period relationship and the complementarity of the two channels, it achieves complete extraction of key signal features at a sampling frequency significantly lower than the Nyquist rate. Combined with the statistical stability of higher-order cumulant parameters, it achieves high recognition accuracy for common modulation signals such as QPSK and 16QAM while reducing hardware costs, making it particularly suitable for blind signal recognition needs in non-cooperative communication scenarios.

[0054] 2. This invention discloses a modulation recognition method based on asynchronous undersampling of primary and secondary channels and dynamic decision-making. By combining cross-channel joint cumulative feature extraction with a dynamic weighted decision tree classification architecture, it effectively integrates the complementary statistical characteristics of primary and secondary channels. Utilizing the inherent Gaussian noise resistance of cumulative features, it maintains high recognition accuracy even in low signal-to-noise ratio and multipath interference environments. Its dynamic weighting mechanism (adaptively adjusting channel contribution weights based on real-time signal-to-noise ratio) solves the performance degradation problem caused by single-channel failure in traditional methods, reducing the misclassification rate in complex environments.

[0055] 3. This invention discloses a modulation recognition method based on asynchronous undersampling and dynamic decision-making. It introduces time-domain differential feature variable analysis and confidence feedback control, detects abrupt feature events through sliding window statistics, and combines a dynamic data window length adjustment mechanism and a majority voting strategy to ensure the system remains robust under signal switching or sudden strong interference conditions. This design effectively improves the continuity of recognition in dynamic channel environments and ensures the reliability of signal recognition in complex scenarios. Attached Figure Description

[0056] Figure 1 This is a flowchart of a modulation recognition method with asynchronous primary and secondary sampling and dynamic decision-making disclosed in this invention;

[0057] Figure 2 This is a schematic diagram of the equivalent time sampling principle;

[0058] Figure 3 This is a partial result graph of the F1 parameters in the example;

[0059] Figure 4 This is a partial result graph of the F2 parameter in the example;

[0060] Figure 5 This is a partial result graph of the F3 parameter in the example;

[0061] Figure 6 This is a schematic diagram of the decision tree for classifying the signal set in the example. Detailed Implementation

[0062] To enable those skilled in the art to more deeply understand the implementation ideas of the present invention, the technical solutions of the present invention will be described carefully and clearly below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other implementation cases obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0063] Example 1

[0064] This method is applicable to dynamic channel modulation identification scenarios using non-cooperative satellite signals, significantly reducing hardware costs and power consumption while improving identification robustness. Addressing the challenge of large frequency band spans for unknown signals, a dual-channel asynchronous undersampling architecture replaces the traditional single-channel high-speed sampling scheme: the main channel captures baseband features at a sampling rate lower than the signal bandwidth using equivalent time sampling technology, while the auxiliary channel acquires zero-crossing features through asynchronous clock intervals, leveraging the complementarity of the dual-channel signals to suppress complete aliasing distortion. During feature extraction, the feature set is dynamically selected based on real-time channel quality (signal-to-noise ratio, SNR): coarse-grained time-domain statistics for anti-aliasing classification are extracted, while fine-grained cross-channel fusion cumulative features are used for classification. A multi-level decision tree is used for initial modulation type screening and fine-grained identification, and a confidence difference threshold is introduced to trigger feature re-extraction and iterative optimization of classification results in the auxiliary channel, replacing the traditional fixed differential correction mechanism. This method achieves high-reliability modulation identification under low sampling rate conditions through dual-channel dynamic collaboration and a closed-loop decision mechanism, while reducing dependence on high-speed ADCs.

[0065] The specific steps of the embodiments of the present invention will be described below with reference to specific scenarios:

[0066] A schematic diagram of the equivalent time sampling principle is shown below. Figure 1 In practical implementation, it is applicable to the identification and analysis of common modulation methods of non-cooperative satellite signals, and can be combined with equipment such as drones to improve the system's dynamism.

[0067] This embodiment discloses a low-cost modulation recognition method based on equivalent time sampling, and the specific implementation steps are as follows:

[0068] When the input signal type is {BPSK, QPSK, 8PSK, 16QAM, 64QAM, OFDM}, and the transmitted signal uses a simulated dataset with a symbol rate R... s =150Msps, carrier frequency f c =1GHz, shaped using a root-raised cosine filter, with a roll-off factor α = 0.35.

[0069] Step 1: Asynchronously acquire the analog signal x(t) using the main and auxiliary channels to obtain the digital signal;

[0070] The main channel sampling frequency is 200MHz, the auxiliary channel sampling frequency is 195MHz, and the asynchronous sampling time difference between the main and auxiliary channels is Δt = 1ms. The digital signals x1[n] and x2[n] are obtained respectively, and their expressions are as follows:

[0071]

[0072] Step 2: Spectrum monitoring and signal-to-noise ratio estimation;

[0073] Windowed FFT processing is performed on signals x1[n] and x2[n] respectively to obtain spectral data X1[k] and X2[k]:

[0074]

[0075] Where w[n] is the Hanning window function, and N is the number of FFT points, taken as N=2. 10 =1024.

[0076] Main channel signal-to-noise ratio (SNR1):

[0077]

[0078] In the formula, k peak The main lobe index is used for the signal spectrum. The calculation method for the auxiliary channel SNR2 is the same as that for the main channel. Based on the spectrum and sampling rate, it can be seen that SNR1 is slightly smaller than SNR2 here.

[0079] Step 3: Perform digital down-conversion and low-pass filtering on signals x1[n] and x2[n] respectively based on the center frequency and bandwidth of the main and auxiliary channels to obtain zero intermediate frequency signals y1[n] and y2[n]:

[0080]

[0081] Among them, f LO1 The center frequency of the main channel, f LO2 The center frequency of the auxiliary channel is B1, and the signal bandwidths of the two channels are B2 and B1, respectively. The LPF is a low-pass filter with a cutoff frequency F. c =B i / 2+Δf, i=1,2, Δf is the protection interval; here B i Take 80MHz, and Δf is taken as 50MHz.

[0082] Step 4: Extracting cumulative features across orders;

[0083] y1[n] and y2[n] are combined according to their temporal relationship to obtain y3[n]. Cumulative features are extracted from y1[n], y2[n] and y3[n] respectively using equation (15):

[0084]

[0085] In the formula, i = 1, 2, 3, which represent the indices of different sequences, and C pq denoted as cum(·), where p is the order of the cumulant, i.e., the number of random variables in cum(·); * denotes the conjugate operation on the sequence values, where q is the number of conjugates of the random variables in cum(·), 0 ≤ q ≤ p / 2. The calculation definition of cum(·) is as follows:

[0086]

[0087] In the formula, Φ iterates over all values ​​from 1 to p. Traverse the values ​​in Φ, where η is The number of elements in the sequence, E represents the mean operation on the sequence, and j represents the number of elements in the sequence. The index of an element in the middle.

[0088] Based on the above formula (16), the following cumulative characteristic C can be calculated. 20 C 21 C 20 C 40 C 41 C 42 C 60 C 63 C 80 ;

[0089] The following are theoretical values ​​of the cumulative values ​​for some common modulation schemes, where E is the value of the acquired signal y. i The average power of (n).

[0090] Table 1 Theoretical values ​​of common modulated signal accumulation

[0091]

[0092] As calculated from the table above, |C| for single-carrier signals and OFDM signals 42 The values ​​differ significantly, and this value can be used to distinguish between single-carrier signals and OFDM signals. For single-carrier signals, based on the calculation of higher-order cumulants, further characteristic parameters are extracted:

[0093]

[0094] As shown in equation (17) above, the absolute values ​​of the cumulative quantities of each order of the signal are used when extracting the feature parameters, thus eliminating phase jitter. Furthermore, the feature parameters are all in the form of ratios, eliminating the influence of channel jitter on the parameters. The theoretical values ​​of the feature parameters of the single-carrier digital modulation signal are shown in Table 2 below:

[0095] Table 2 Theoretical values ​​of characteristic parameters of single-carrier signals

[0096]

[0097] Further, the cross-order cumulant eigenvector F is obtained. i =[F1,F2,F3,F4], i=1,2,3.

[0098] Step 5: Calculate the cross-channel cumulative fusion feature vector T, which represents the new feature formed by combining the features of data from different channels:

[0099] T=λ1F1+λ2F2+F3 (19)

[0100] Where λ represents the channel reliability weight,

[0101] By using SNR (channel reliability) weighting, interference from low-quality channels and redundant features is suppressed. Under this condition, λ1≈λ2≈1 / 2, so modulation identification can be directly performed through F1, F2 and F3.

[0102] Step 6: Perform decision tree classification based on the aforementioned feature parameters F1, F2, and F3. For coarse classification, the main channel data F1 can be used directly to identify the modulation scheme of the single-carrier signal. Combined with Step 4, modulation identification can be completed for the signal set {OFDM, 2ASK, BPSK, MFSK, QPSK, 8PSK, 16QAM, 64QAM}. The specific steps are as follows:

[0103] Step 6.1: Utilize the eigenvalue |C 42 The signal set can be divided into two modulation methods: single-carrier and OFDM.

[0104] Step 6.2: Further identify and analyze the single-carrier modulation. Using the eigenvalue F1, the single-carrier signal set can be divided into two major categories: {BPSK} and {MFSK, QPSK, 8PSK, 16QAM, 64QAM}.

[0105] Step 6.3: For the signal set {BPSK} that has been classified, the two modulation methods can be identified based on the feature parameter F3.

[0106] Step 6.4: For the signal set {QPSK, 8PSK, 16QAM, 64QAM}, it can be further classified according to the characteristic parameter F2, and can be divided into {8PSK} and {QPSK, 16QAM, 64QAM}.

[0107] Step 6.5: The characteristic parameter F3 can further divide the signal set {QPSK, 16QAM, 64QAM} into {QPSK} and {16QAM, 64QAM}.

[0108] Step 6.6: For the signal set {16QAM, 64QAM}, it can be distinguished and identified based on the characteristic parameter F4. This completes the identification of the modulation scheme of the entire signal set.

[0109] Step 6.7: If the output confidence level is less than 0.7, enable the auxiliary channel data for identification processing, start the parallel-voting decision process, and output the final result through majority voting to avoid the failure of a single model.

Claims

1. A modulation identification method based on primary-secondary asynchronous undersampling and dynamic decision, characterized in that: Includes the following steps, Step 1: The analog signal x(t) is asynchronously acquired using the main and auxiliary channels to obtain digital signals x1[n] and x2[n], respectively; Step 2: Based on x1[n] and x2[n] from Step 1, perform spectral analysis to obtain signal-to-noise ratio estimates SNR1 and SNR2; Step 3: Perform digital down-conversion and low-pass filtering on signals x1[n] and x2[n] respectively based on the center frequency and bandwidth of the main and auxiliary channels to obtain zero intermediate frequency signals y1[n] and y2[n]: Step 4: Concatenate y1[n] and y2[n] from Step 3 in the time domain to obtain y3[n], and extract the cumulative features across the three sets of data to obtain F. i i = 1, 2, 3; Step 5: {SNR1, SNR2} and F obtained from step 2 i Compute the cross-channel accumulation fusion feature vector T: Step 6: Input the F1 obtained in Step 4 and the T obtained in Step 5 into the pre-trained multi-level decision tree model to perform multi-level joint feature classification and dynamic confidence decision to obtain the modulation recognition result, that is, modulation recognition is realized based on master-slave asynchronous undersampling and dynamic decision.

2. The modulation identification method based on primary and secondary asynchronous undersampling and dynamic decision of claim 1, wherein: The specific implementation method of step 1 is as follows: The sampling periods for the main and auxiliary channels are T respectively. s1 and T s2 And satisfy T s1 / T s2 = m / s, where m and s are coprime positive integers. The asynchronous sampling time difference between the main and auxiliary channels is Δt. After sampling, the main digital signal x1[n] and the auxiliary digital signal x2[n] are obtained respectively: Where t is a continuous time variable and n is the index of the sampling sequence.

3. The modulation identification method based on primary-secondary asynchronous undersampling and dynamic decision of claim 1, wherein: The specific implementation method of step 2 is as follows: Windowed FFT processing is performed on signals x1[n] and x2[n] respectively to obtain spectral data X1[k] and X2[k]: Where k is the index of the spectrum sequence, w[n] is the Hanning window function, and N is the number of FFT points; Main channel signal-to-noise ratio (SNR1): In the formula, k peak The main lobe index of the signal spectrum, the secondary channel SNR2 calculation method is consistent with the main channel.

4. The modulation identification method based on primary and secondary asynchronous undersampling and dynamic decision of claim 1, wherein: The specific implementation method of step 3 is as follows: Based on the center frequency and bandwidth of the main and auxiliary channels, digital down-conversion and low-pass filtering are performed on signals x1[n] and x2[n] respectively to obtain zero-IF signals y1[n] and y2[n]: Among them, f LO1 The center frequency of the main channel, f LO2 The center frequency of the auxiliary channel is B1, and the signal bandwidths of the two channels are B2 and B1, respectively. The LPF is a low-pass filter with a cutoff frequency F. c =B i / 2+Δf, i=1,2, Δf is the protection interval.

5. The modulation identification method based on primary-secondary asynchronous undersampling and dynamic decision of claim 1, wherein: The specific implementation method of step 4 is as follows: y1[n] and y2[n] are combined according to their temporal relationship to obtain y3[n]. Cumulative features are extracted from y1[n], y2[n] and y3[n] respectively using equation (3): In the formula, i = 1, 2, 3, which represent the indices of different sequences, and C pq This represents the higher-order cumulant of the signal, where p is the order of the cumulant, i.e., the number of random variables in cum(·). * indicates the conjugate operation on the sequence values, where q is the number of conjugates of the random variables in cum(·), 0 ≤ q ≤ p / 2; the calculation definition of cum(·) is as follows: In the formula, Φ iterates over all values ​​from 1 to p. Traverse the values ​​in Φ, where η is The number of elements in the sequence, E represents the mean operation on the sequence, and j represents the number of elements in the sequence. The index of the element; The cumulative amount feature C is calculated according to the above formula (3) 40 ,C 41 ,C 42 ,C 63 ,C 80 ; and further obtains the cross-order cumulative amount feature: Further, the cross-order cumulant feature vector F is obtained i = [F1, F2, F3, F4], i = 1, 2, 3.

6. The modulation identification method based on primary-secondary asynchronous undersampling and dynamic decision of claim 1, wherein: The specific implementation method of step 5 is as follows: Calculate the cross-channel cumulative fusion feature vector T, which represents the new feature formed by the combination of data features from different channels: T=λ1F1+λ2F2+F3 (6) Wherein, λ1, λ2 respectively represent the reliability weight of the primary and secondary channels, λ2 = 1 - λ1.

7. The modulation identification method based on primary-secondary asynchronous undersampling and dynamic decision of claim 1, wherein: In step 6, The first level of the decision tree model performs coarse classification based on the main channel feature vector F1, and uses the main channel features to initially classify the signal and generate a set of candidate modulation types. The second level uses the T obtained in step 5 to perform fine-grained discrimination on the candidate set obtained from the coarse classification. Calculate the Euclidean distance between T and the preset template, i.e.: wherein, ||·||2is the Euclidean norm; The modulation type corresponding to the minimum distance is selected as the candidate result output, and a confidence index Conf = 1 / (1+D) is calculated c ); If the confidence level Conf≥0.7, the candidate result is directly output as the final modulation recognition result; If the confidence level Conf < 0.7, then calculate feature F. i mean The pre-trained multi-level decision tree model is re-inputted for classification to obtain the modulation recognition type. If the new classification result is consistent with the candidate result, the result is output as the final modulation recognition result. If they are inconsistent, the recognition and classification are performed independently based on F2 and F3 respectively. Then, all modulation recognition results are selected by majority voting mechanism to select the highest frequency modulation type as the final modulation recognition result and output it. That is, modulation recognition is realized based on master-slave asynchronous undersampling and dynamic decision.

8. The modulation identification method based on primary-secondary asynchronous undersampling and dynamic decision of claim 7, wherein: To address noise and multipath interference in the actual system, the modulation identification results obtained in step 6 are subjected to stability testing. Data is processed in time slots, each time slot containing N sample points, SNR avg The average signal-to-noise ratio of the primary and secondary channels; the differential characteristic of adjacent time slots is ΔF = ||F i,t - F i,t-1 ||2 (8) where F i,t is the cross-order cumulant feature vector for the tth time slot of the ith set of data; The sliding window is L, storing the ΔF values ​​of the most recent L time slots, i.e.: [ΔF t-L+1 ,ΔF t-L+2 ,…,ΔF t If the mean and difference standard thresholds within this window are: If ΔF > σ, the current time slot is determined to have abnormal fluctuations in characteristics. The classification result of the previous time slot is then maintained, but the confidence level is reduced. Conf = Conf e -αΔF , a = 0.1 (10) If ΔF≤σ, then the characteristic is stable and the confidence level remains unchanged.

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