Method for separating hidden weak signal from single-carrier background signal based on constellation reconstruction

Abstract

The invention discloses a method for separating hidden weak signals from single-carrier background signals based on constellation reconstruction, and belongs to the technical field of wireless communication signal detection. The method solves the problem that a non-partner is difficult to reconnoiter a hidden transmission weak power signal by using a traditional signal detection method. According to the method, a constellation diagram of a single-carrier conventional modulation signal playing a shielding role is reconstructed in a clustering mode, complete reduction of a shielding signal waveform is guaranteed, interference of a conventional communication signal with large power on a hidden weak signal is effectively separated and weakened, and after the preprocessing step, the interference of the conventional communication signal with large power on the hidden weak signal is reduced. And multi-stage signal detection analysis is carried out on the residual signals, so that the recognition capability of hidden weak signals in a complex signal environment is improved, and the detection capability of hidden weak power signals in a shielded scene is improved. The method can be applied to separation of hidden weak signals in single-carrier background signals.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication signal detection, and particularly relates to a method for separating a concealed weak signal from a single-carrier background based on constellation reconstruction. Background Art

[0002] In modern wireless communication systems, in order to improve the concealment and security of communication, information is often hidden and transmitted by embedding a weak-power signal in a conventional communication signal. This method uses a strong-power conventional signal as a cover signal, making it difficult to detect the weak-power signal in the frequency spectrum. The presence of the cover signal significantly increases the difficulty of non-cooperative parties detecting the concealed weak signal, and traditional signal detection methods often fail in such a complex environment.

[0003] To solve the problem that non-cooperative parties have difficulty in detecting concealed weak-power signals, a method of separating the strong-power cover signal can be adopted to eliminate its interference effect, and then detect whether there is a weak-power concealed signal in the residual signal. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that non-cooperative parties have difficulty in detecting concealed weak-power signals transmitted using traditional signal detection methods, and a method for separating concealed weak signals from single-carrier background signals based on constellation reconstruction is proposed.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a method for separating concealed weak signals from single-carrier background signals based on constellation reconstruction, the method specifically includes the following steps:

[0006] Step 1: Perform down-conversion processing on the received signal, and then perform A / D conversion on the signal after down-conversion processing to obtain a digital signal y(n);

[0007] Step 2: Perform IQ modulation on the digital signal y(n), and map the signal waveform after IQ modulation to a constellation diagram;

[0008] Step 3: Estimate the modulation order according to the constellation points in the constellation diagram, and use the estimated modulation order as the estimated number of constellation clusters K;

[0009] Step 4: Cluster the constellation points in the constellation diagram according to the number of constellation clusters estimated in Step 3 to obtain a clustering result;

[0010] Step 5: Calculate the centroid of each constellation cluster in the clustering result of Step 4 Take all the clustering centers As the constellation diagram of the reconstructed cover signal;

[0011] Step 6: Demodulate the constellation diagram obtained in Step 5 through IQ demodulation to obtain the waveform of the reconstructed cover signal;

[0012] Step 7: Subtract the reconstructed cover signal from the digital signal y(n) to obtain the mixed signal waveform of noise, residual signal, and covert signal;

[0013] Step 8: Detect the mixed signal obtained in Step 7.

[0014] Further, the specific process of Step 2 is as follows:

[0015] Divide the digital signal y(n) into two paths, I and Q. Then multiply the I-path signal by the carrier cosω0t and multiply the Q-path signal by the carrier sinω0t. According to the multiplication results, obtain the signal s(t) after IQ modulation:

[0016] s(t) = Icosω0t - Qsinω0t

[0017] where ω0 is the carrier frequency and t is time;

[0018] Obtain all the points corresponding to the signal s(t) on the complex plane, then normalize each point on the complex plane respectively, and use each normalized point as a constellation point;

[0019] Use all the constellation points to form a constellation diagram.

[0020] Further, the specific process of normalizing each point on the complex plane is as follows:

[0021]

[0022] where s i represents the i-th point on the complex plane, s i ' represents the i-th normalized point on the complex plane, s k represents the k-th point on the complex plane, N represents the total number of points on the complex plane, and ||·|| represents calculating the 2-norm.

[0023] Further, the specific process of Step 3 is as follows:

[0024] Step 3-1: Initialize the constellation point set D to include all the constellation points of the constellation diagram, and randomly select a point from the constellation point set D;

[0025] Step 3-2: Use the selected point as the current object, then mark the current object as processed and remove the current object from the constellation point set D. If there are other constellation points in the constellation point set D, continue to execute Step 3-3. If the constellation point set D is empty, directly execute Step 3-4;

[0026] Step 33: Calculate the reachability distance values of each remaining point in the constellation point set D with respect to the current object, and select the constellation point with the smallest reachability distance value with respect to the current object;

[0027] Use the selected constellation point to return and execute Step 32;

[0028] Step 34: Save the processing order of each constellation point and the reachability distance value corresponding to each constellation point;

[0029] Step 35: Draw a curve graph of the constellation point processing order and the reachability distance value according to the saved data. In the curve graph, use the constellation point processing order as the abscissa and the reachability distance value corresponding to the constellation point as the ordinate;

[0030] Detect the number of peaks in the curve graph. The number of peaks plus 1 is the preliminary modulation order estimation result, and then process the preliminary modulation order estimation result to obtain the final modulation order.

[0031] Further, the specific process of Step 33 is as follows:

[0032] Step 331: Obtain the core distance CD of the current object

[0033] Draw a circle with the current object as the center, and obtain the minimum radius when there are M constellation points in the constellation point set D within the circle. Take the obtained minimum radius as the core distance CD of the current object;

[0034] Step 332: Calculate the distance from each constellation point in the constellation point set D to the current object. For the i-th point s i ' in the constellation point set D, record the distance between the point s i ' and the current object as l i , and compare the size of l i with the core distance CD of the current object:

[0035] If l i is greater than or equal to the core distance CD of the current object, then the preliminary reachability distance value i of the point s is l i ;

[0036] If l i is less than the core distance CD of the current object, then the preliminary reachability distance value i of the point s is the core distance CD of the current object;

[0037] Step 333: Compare the preliminary reachability distance values of each constellation point in the constellation point set D, obtain the constellation point with the smallest preliminary reachability distance value, and compare the preliminary reachability distance value of this constellation point with the previous minimum reachability distance value:

[0038] If the preliminary reachable distance value of the constellation point is less than the previous minimum reachable distance value, then the preliminary reachable distance value of the constellation point is the final reachable distance value; otherwise, the final reachable distance value of the constellation point is the previous minimum reachable distance value.

[0039] Furthermore, the process of processing the preliminary modulation order estimation result to obtain the final modulation order is as follows:

[0040] Define the modulation order set A = {2 j}, j = 1, 2,..., 8;

[0041] If the preliminarily estimated modulation order is not within the set A, then select the modulation order closest to the preliminarily estimated modulation order from the set A, and use the selected modulation order as the final modulation order estimation result; if the preliminarily estimated modulation order is within the set A, then the preliminarily estimated modulation order is the final modulation order.

[0042] Furthermore, the specific process of step four is as follows:

[0043] Step four one: Randomly select K constellation points from all the constellation points of the constellation diagram, and use the selected K constellation points as the initial K clustering centers;

[0044] Step four two: For any constellation point that is not a clustering center, calculate the distances from this constellation point to each clustering center respectively, obtain the minimum distance corresponding to this constellation point, and then assign this constellation point to the clustering center corresponding to the minimum distance;

[0045] Similarly, assign each constellation point that is not a clustering center respectively;

[0046] Step four three: Obtain K new clustering centers according to the assignment result of step four two. The specific process is as follows:

[0047] For the k-th cluster, k = 1, 2,..., K, calculate the mean value μ of all points within the k-th cluster k , and use μ1, μ2,..., μ K as the K new clustering centers;

[0048] Step four four: Determine whether the K new clustering centers have changed compared with the K clustering centers obtained in the previous round;

[0049] If the K new clustering centers are exactly the same as the K clustering centers obtained in the previous round, then end the clustering;

[0050] Otherwise, use the K new clustering centers to return and execute step four two.

[0051] Further, the specific process of Step Six is as follows:

[0052] Reconstruct the IQ modulation signal according to the constellation diagram obtained in Step Five

[0053] Multiply the signal by cosω0t, and then integrate the multiplication result, that is, calculate T represents one symbol period of the signal and take the calculation result as the restored I-channel signal;

[0054] Multiply the signal by sinω0t, and then integrate the multiplication result, that is, calculate Take the calculation result as the restored Q-channel signal;

[0055] Merge the restored I-channel signal and the restored Q-channel signal into one path, and take the merged result as the reconstruction result of the cover signal

[0056] Further, the specific process of Step Seven is as follows:

[0057]

[0058] where y res (n) represents the mixed signal of noise, residual signal and covert signal.

[0059] Even further, the specific process of Step Eight is as follows:

[0060] Step Eight One: Input the mixed signal y res (n) into the first-level detection module for detection to detect whether the mixed signal y res (n) follows a normal distribution;

[0061] Step Eight Two: Select the second-level detection module according to the detection result of Step Eight One, specifically:

[0062] If the mixed signal y res (n) follows a normal distribution, then select the cyclic autocorrelation detector;

[0063] If the mixed signal y res (n) does not follow a normal distribution, then select the high-order cumulant detector;

[0064] Step Eight Three: Judge whether there is a weak-power communication signal protected by the cover in the mixed signal y(n) according to the detection result of the second-level detection module.

[0065] The beneficial effects of the present invention are:

[0066] The method of the present invention reconstructs the constellation diagram of the single - carrier conventional modulation signal that serves as a cover through clustering, ensuring the complete restoration of the waveform of the cover signal, effectively separating and weakening the interference of the conventional communication signal with a larger power on the concealed weak signal. After the above - mentioned pre - processing steps, multi - level signal detection and analysis are performed on the remaining signal, improving the recognition ability of the concealed weak signal in a complex signal environment, and helping to improve the detection ability of the concealed weak - power signal in the covered scenario. Description of the Drawings

[0067] Figure 1 is a flowchart of a method for separating concealed weak signals from single - carrier background signals based on constellation reconstruction according to the present invention;

[0068] Figure 2 is a schematic diagram of the constellation diagram change for reconstructing the conventional modulation cover signal and separating the concealed weak signal from the received signal according to the present invention;

[0069] Figure 3 is a flowchart of a method for estimating the modulation order of the cover signal, that is, the number of constellation point clustering clusters;

[0070] Figure 4 is a flowchart for reconstructing the cover signal through constellation point clustering. Detailed Embodiments

[0071] Detailed Embodiment 1: In combination with Figure 1 and Figure 2 this embodiment is described. A method for separating concealed weak signals from single - carrier background signals based on constellation reconstruction according to this embodiment specifically includes the following steps:

[0072] Step 1: The non - cooperative party performs down - conversion processing on the received signal, and then performs A / D conversion on the down - converted signal to obtain the digital signal y(n);

[0073] Step 2: Perform IQ modulation on the digital signal y(n), and map the waveform of the IQ - modulated signal to a constellation diagram;

[0074] Step 3: Estimate the modulation order according to the constellation points in the constellation diagram, and use the estimated modulation order as the estimated number of constellation clusters K;

[0075] Step 4: Cluster the constellation points in the constellation diagram according to the estimated number of constellation clusters in Step 3 to obtain the clustering result;

[0076] Step 5: Calculate the centroid of each constellation cluster in the clustering result of Step 4 Taking all the clustering centers as the constellation diagram of the reconstructed cover signal;

[0077] Step 6: Demodulate the constellation diagram obtained in Step 5 through IQ demodulation to obtain the waveform of the reconstructed cover signal;

[0078] Step 7: Subtract the reconstructed cover signal from the digital signal y(n) to obtain the mixed signal waveform of noise, residual signal, and hidden signal;

[0079] Step 8: Detect the mixed signal obtained in Step 7.

[0080] The present invention is a preprocessing for detecting a hidden weak signal under cover. For the case where the cover signal is a conventional modulated wideband single-carrier signal, first, estimate the modulation order of the unknown wideband single-carrier signal acting as the cover to preliminarily determine the number of constellation clusters, and then reconstruct the constellation of the cover signal according to the number of constellation clusters to restore the waveform of the cover signal. Then, subtract the reconstructed signal from the initial received signal to obtain the residual signal waveform of noise + residual signal + hidden signal. On this basis, import the residual signal into the existing statistical feature analysis module, high-order cumulant analysis module, and cyclic autocorrelation analysis module for detection. It has important application value in enhancing the detection ability of hidden signals under cover.

[0081] Specific Embodiment 2: The difference between this embodiment and Specific Embodiment 1 is that the specific process of Step 2 is as follows:

[0082] Divide the digital signal y(n) into two paths of I and Q, then multiply the I-path signal by the carrier cosw0t, multiply the Q-path signal by the carrier sinw0t, and obtain the signal s(t) after IQ modulation according to the multiplication results:

[0083] s(t) = Icosw0t - Qsinw0t

[0084] where w0 is the carrier frequency and t is the time;

[0085] The signal s(t) can be represented in complex form as I + jQ. Furthermore, obtain all the points corresponding to the signal s(t) on the complex plane, then normalize each point on the complex plane respectively, and use each normalized point as a constellation point;

[0086] Use all the constellation points to form a standard unit variance constellation diagram.

[0087] Other steps and parameters are the same as those in Specific Embodiment 1.

[0088] Specific Embodiment 3: The difference between this embodiment and Specific Embodiment 1 or 2 is that the specific normalization of each point on the complex plane is as follows:

[0089]

[0090] where s i represents the i-th point on the complex plane, and s i ' represents the i-th normalized point on the complex plane, s k represents the k-th point on the complex plane, N represents the total number of points on the complex plane, and ||·|| represents calculating the 2-norm.

[0091] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0092] Specific implementation manner four: Combine Figure 3 to illustrate this implementation manner. The difference between this implementation manner and one of the first to third specific implementation manners is that the specific process of step three is as follows:

[0093] Step 3-1: Initialize the constellation point set D to include all constellation points of the constellation diagram, and randomly select a point from the constellation point set D;

[0094] Step 3-2: Use the selected point as the current object, then mark the current object as processed, and remove the current object from the constellation point set D. If there are other constellation points in the constellation point set D, continue to execute step 3-3. If the constellation point set D is empty, directly execute step 3-4;

[0095] Step 3-3: Calculate the reachable distance value (RD) of each remaining point in the constellation point set D relative to the current object, and select the constellation point with the smallest reachable distance value relative to the current object;

[0096] Use the selected constellation point to return and execute step 3-2;

[0097] Step 3-4: Save the processing order of each constellation point and the reachable distance value corresponding to each constellation point;

[0098] Since in the present invention, a constellation point is first randomly selected from all constellation points, the processing order number of this constellation point is 1. After obtaining the constellation point with the smallest reachable distance value equivalent to this constellation point, the processing order number of the newly obtained constellation point is 2. At the same time, save the processing order of the newly obtained constellation point and the reachable distance value from the newly obtained constellation point to the constellation point with the processing order number 1. And so on, for the newly obtained constellation point with the processing order number n, save the processing order of the newly obtained constellation point and the reachable distance value from the newly obtained constellation point to the constellation point with the processing order number n-1 until the end of the entire processing process;

[0099] Step 3-5: Draw a curve graph of the constellation point processing order and the reachable distance value according to the saved data. In the curve graph, use the constellation point processing order as the abscissa and the reachable distance value corresponding to the constellation point as the ordinate;

[0100] Detect the number of peaks in the detection curve graph. The number of peaks plus 1 is the preliminary modulation order estimation result. Then process the preliminary modulation order estimation result to obtain the final modulation order.

[0101] Other steps and parameters are the same as those in any one of the first to third specific embodiments.

[0102] The present invention preliminarily determines the modulation order by observing the shape of the reachable distance value and the processing sequence curve graph and adjusting the M value. If the curve graph fluctuates violently and the peak distribution is uneven, the M value needs to be increased; if the peak distribution is uneven and there are large troughs, the M value needs to be decreased. Calculate the number of peaks k that appear in the curve graph until the peak distribution is uniform. The number of peaks + 1 is the preliminarily estimated modulation order K.

[0103] Specific embodiment five: The difference between this embodiment and any one of the first to fourth specific embodiments is that the specific process of step three three is as follows:

[0104] Step three three one: Obtain the core distance CD of the current object

[0105] Draw a circle with the current object as the center, and obtain the minimum radius when M constellation points in the constellation point set D are included in the circle. Take the obtained minimum radius as the core distance CD of the current object;

[0106] Step three three two: Calculate the distance from each constellation point in the constellation point set D to the current object. For the i-th point s i ' in the constellation point set D, denote the distance between the point s i ' and the current object as l i , and compare the size of l i with the core distance CD of the current object:

[0107] If l i is greater than or equal to the core distance CD of the current object, then the preliminary reachable distance value i of the point s is l i ;

[0108] If l i is less than the core distance CD of the current object, then the preliminary reachable distance value i of the point s is the core distance CD of the current object;

[0109] Step three three three: Compare the preliminary reachable distance values of each constellation point in the constellation point set D, obtain the constellation point with the smallest preliminary reachable distance value, and compare the preliminary reachable distance value of this constellation point with the previous minimum reachable distance value:

[0110] If the preliminary reachable distance value of the constellation point is less than the previous minimum reachable distance value, then the preliminary reachable distance value of the constellation point is the final reachable distance value; otherwise, the final reachable distance value of the constellation point is the previous minimum reachable distance value.

[0111] Other steps and parameters are the same as those in any one of the first to fourth specific embodiments.

[0112] Specific embodiment six: The difference between this embodiment and any one of the first to fifth specific embodiments is that the preliminary modulation order estimation result is processed to obtain the final modulation order; the specific process is as follows:

[0113] Since common digital modulation methods include binary ASK, FSK, BPSK, 2DPSK, multi - level MASK, MFSK, MPSK, and QAM systems, the modulation order set A is defined as {2 j}, j = 1, 2,..., 8;

[0114] If the preliminarily estimated modulation order is not within the set A, then the modulation order closest to the preliminarily estimated modulation order is selected from the set A, and the selected modulation order is used as the final modulation order estimation result. If the preliminarily estimated modulation order is within the set A, then the preliminarily estimated modulation order is the final modulation order.

[0115] Other steps and parameters are the same as those in any one of the first to fifth specific embodiments.

[0116] It should be noted that when the estimated result of the modulation order is equal to the mean value of two adjacent elements 2 j and 2 j+1 in the set A, then either 2 j or 2 j+1 is randomly selected as the finally estimated modulation order. For example, when the preliminarily estimated modulation order value is 3, either 2 or 4 is randomly selected as the finally estimated modulation order K value.

[0117] Specific embodiment seven: This embodiment is described in combination with Figure 4 as follows. The difference between this embodiment and any one of the first to sixth specific embodiments is that the specific process of step four is as follows:

[0118] Step four one: Randomly select K constellation points from all the constellation points of the constellation diagram, and use the selected K constellation points as the initial K clustering centers;

[0119] Step four two: For any constellation point that is not a clustering center, calculate the distance from this constellation point to each clustering center respectively, obtain the minimum distance corresponding to this constellation point, and then assign this constellation point to the clustering center corresponding to the minimum distance;

[0120] Similarly, each constellation point that is not a clustering center is assigned respectively (each clustering center and the constellation points assigned to it form a cluster);

[0121] Step Four Three: Obtain K new clustering centers according to the assignment results in Step Four Two. The specific process is as follows:

[0122] For the k-th cluster, k = 1, 2, …, K, calculate the mean μ of all points within the k-th cluster k , and take μ1, μ2, …, μ K as the K new clustering centers;

[0123] Step Four Four: Determine whether the K new clustering centers have changed compared with the K clustering centers obtained in the previous round;

[0124] If the K new clustering centers are exactly the same as the K clustering centers obtained in the previous round, end the clustering;

[0125] Otherwise, use the K new clustering centers to return and execute Step Four Two.

[0126] Other steps and parameters are the same as those in any one of the specific implementation manners One to Six.

[0127] When the clustering ends, take the clustering result obtained in the last iteration as the final clustering result. When the clustering ends, the within-cluster sum of squared errors J reaches the minimum:

[0128]

[0129] where C k is the set of points in the k-th cluster, x ki represents the i-th constellation point within C k , μ k is the centroid of the k-th cluster, and ||x ki - μ k || 2 represents the square of the Euclidean distance between the data point x ki and the cluster center μ k .

[0130] Specific implementation manner Eight: The difference between this implementation manner and any one of the specific implementation manners One to Seven is that the specific process of the said Step Six is as follows:

[0131] Reconstruct the IQ modulation signal according to the constellation diagram obtained in Step Five

[0132] Multiply the signal by cosw0t, and then integrate the multiplication result, that is, calculate T represents a symbol period of the signal , and take the calculation result as the restored I-channel signal;

[0133] Multiply the signal by sinw0t, and then integrate the multiplication result, that is, calculate Take the calculation result as the restored Q-channel signal;

[0134] Merge the restored I-channel signal and the restored Q-channel signal into one path, and take the merged result as the reconstruction result of the cover signal

[0135] Other steps and parameters are the same as those in any one of the first to seventh specific embodiments.

[0136] Specific Embodiment Nine: The difference between this embodiment and any one of the first to eighth specific embodiments is that the specific process of step seven is as follows:

[0137]

[0138] where y res (n) represents the mixed signal of noise, residual signal and hidden signal.

[0139] Other steps and parameters are the same as those in any one of the first to eighth specific embodiments.

[0140] Specific Embodiment Ten: The difference between this embodiment and any one of the first to ninth specific embodiments is that the specific process of step eight is as follows:

[0141] Step Eight One: Input the mixed signal y res (n) into a first-level detection module (signal statistical analysis module) for detection to detect whether the mixed signal y res (n) follows a normal distribution;

[0142] Step Eight Two: Select a second-level detection module according to the detection result of Step Eight One, specifically:

[0143] If the mixed signal y res (n) follows a normal distribution, then select a cyclic autocorrelation detector;

[0144] If the mixed signal y res (n) does not follow a normal distribution, then select a high-order cumulant detector;

[0145] Step Eight Three: Judge whether there is a weak-power communication signal protected by the cover in the mixed signal y(n) according to the detection result of the second-level detection module.

[0146] Other steps and parameters are the same as those in any one of the first to ninth specific embodiments.

[0147] This embodiment first uses the signal y res(n) It is input into the signal statistical analysis module for detection, and then the detector for the next step of detection (cyclic autocorrelation detector or high-order cumulant detector) is selected according to the detection result. If there is a weak-power communication signal under cover in the digital signal y(n), the cyclic autocorrelation detector or high-order cumulant detector can be used to further determine whether the signal is a conventional modulation signal or an OFDM signal. If there is no weak-power communication signal under cover in the digital signal y(n), the detection result of the cyclic autocorrelation detector or high-order cumulant detector is that there is no weak-power communication signal under cover.

[0148] The above numerical examples of the present invention are only for illustrating in detail the calculation model and calculation process of the present invention, rather than limiting the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or variations can be made on the basis of the above description. It is impossible to enumerate all the implementation manners here. Any obvious changes or variations derived from the technical solutions of the present invention still fall within the protection scope of the present invention.

Claims

1. A method for separating a concealed weak signal from a single-carrier background signal based on constellation reconstruction, characterized in that: The method specifically comprises the following steps: Step 1: down-convert the received signal, and then perform A / D conversion on the down-converted signal to obtain a digital signal y(n); Step 2: IQ modulate the digital signal y(n), and map the IQ modulated signal waveform into a constellation diagram; Step 3: Estimating the modulation order according to the constellation points in the constellation diagram, and using the estimated modulation order as the estimated number of constellation clusters K; Step 4: clustering the constellation points in the constellation diagram according to the number of constellation clusters estimated in step 3 to obtain a clustering result; Step 5: Calculate the centroid of each constellation cluster in the clustering results of step 4 All cluster centers Constellation diagram as the reconstructed cover signal; Step 6: IQ demodulate the constellation diagram obtained in step 5 to obtain the waveform of the reconstructed cover signal; Step 7: Subtract the reconstructed cover signal from the digital signal y(n) to obtain a mixed signal waveform of noise, residual signal and concealed signal; Step eight: detect the mixed signal obtained in step seven.

2. The method for separating a concealed weak signal from a single-carrier background signal based on constellation reconstruction according to claim 1, characterized in that: The specific process of step 2 is as follows: The digital signal y(n) is divided into two paths, I and Q. The I path signal is multiplied by the carrier cosw0t, and the Q path signal is multiplied by the carrier sinw0t. The IQ modulated signal s(t) is obtained according to the multiplication results: s(t)=Icosw0t-Qsinw0t Where w0 is the carrier frequency and t is the time; Get all the points corresponding to the signal s(t) on the complex plane, then normalize each point on the complex plane, and use each normalized point as a constellation point; All constellation points are used to form a constellation diagram.

3. The method for separating a concealed weak signal from a single-carrier background signal based on constellation reconstruction according to claim 2, characterized in that: The normalization of each point on the complex plane is specifically as follows: Among them, s i represents the i-th point on the complex plane, s i ' represents the i-th normalized point on the complex plane, s k represents the kth point on the complex plane, N represents the total number of points on the complex plane, and ||·|| represents the calculation of the 2-norm.

4. The method for separating a concealed weak signal from a single-carrier background signal based on constellation reconstruction according to claim 3, characterized in that: The specific process of step three is: Step 31: Initialize the constellation point set D including all constellation points of the constellation diagram, and randomly select a point from the constellation point set D; Step 32: take the selected point as the current object, mark the current object as processed, and remove the current object from the constellation point set D. If there are other constellation points in the constellation point set D, continue to execute step 33. If the constellation point set D is empty, directly execute step 34. Step 33: Calculate the reachable distance value of each remaining point in the constellation point set D relative to the current object, and select the constellation point with the smallest reachable distance value relative to the current object; Return to step 32 using the selected constellation point; Step 34: Save the processing order of each constellation point and the reachable distance value corresponding to each constellation point; Step 35: Draw a curve chart of the processing order of the constellation points and the reachable distance values ​​according to the saved data. In the curve chart, the processing order of the constellation points is used as the horizontal axis, and the reachable distance values ​​corresponding to the constellation points are used as the vertical axis; The number of peaks in the detection curve is detected, and the number of peaks plus 1 is the preliminary modulation order estimation result. The preliminary modulation order estimation result is then processed to obtain the final modulation order.

5. The method for separating concealed weak signals from single-carrier background signals based on constellation reconstruction according to claim 4, characterized in that: The specific process of step 33 is as follows: Step 331: Get the core distance CD of the current object Draw a circle with the current object as the center, obtain the minimum radius when the circle contains M constellation points in the constellation point set D, and use the obtained minimum radius as the core distance CD of the current object; Step 332: Calculate the distance from each constellation point in the constellation point set D to the current object. For the i-th point s in the constellation point set D i ', point s i 'The distance to the current object is recorded as l i , compare l i The size of the CD distance from the core of the current object: If l i If the core distance CD of the current object is greater than or equal to the core distance CD of the current object, then point s i 'The initial reachable distance value for l i ; If l i is smaller than the core distance CD of the current object, then point s i 'The initial reachable distance value The core distance CD of the current object; Step 333: Compare the preliminary reachable distance values ​​of each constellation point in the constellation point set D, obtain the constellation point with the minimum preliminary reachable distance value, and compare the preliminary reachable distance value of the constellation point with the previous minimum reachable distance value: If the initial reachable distance value of the constellation point is less than the previous minimum reachable distance value, the initial reachable distance value of the constellation point is the final reachable distance value; otherwise, the final reachable distance value of the constellation point is the previous minimum reachable distance value.

6. The method for separating a concealed weak signal from a single-carrier background signal based on constellation reconstruction according to claim 5, characterized in that: The preliminary modulation order estimation result is processed to obtain the final modulation order; the specific process is: Define the modulation order set A = {2 j }, j = 1, 2, ..., 8; If the initially estimated modulation order is not in set A, the modulation order closest to the initially estimated modulation order is selected from set A, and the selected modulation order is used as the final modulation order estimation result; if the initially estimated modulation order is in set A, the initially estimated modulation order is the final modulation order.

7. The method for separating concealed weak signals from single-carrier background signals based on constellation reconstruction according to claim 6, characterized in that: The specific process of step 4 is as follows: Step 41: randomly select K constellation points from all constellation points in the constellation diagram, and use the selected K constellation points as initial K cluster centers; Step 42: For any constellation point that is not a cluster center, calculate the distance from the constellation point to each cluster center, obtain the minimum distance corresponding to the constellation point, and then assign the constellation point to the cluster center corresponding to the minimum distance; Similarly, each constellation point that is not a cluster center is assigned separately; Step 43: Obtain K new cluster centers according to the allocation results of step 42. The specific process is as follows: For the kth cluster, k = 1, 2, ..., K, calculate the mean μ of all points in the kth cluster k , μ1,μ2,…,μ K As K new cluster centers; Step 44: Determine whether the K new cluster centers have changed compared with the K cluster centers obtained in the previous round; If the K new cluster centers are exactly the same as the K cluster centers obtained in the previous round, clustering is terminated; Otherwise, return to step 42 using K new cluster centers.

8. The method for separating concealed weak signals from single-carrier background signals based on constellation reconstruction according to claim 7, characterized in that: The specific process of step six is ​​as follows: Reconstruct the IQ modulated signal based on the constellation diagram obtained in step 5 The signal Multiply by cosw0t and integrate the result to calculate T indicates signal A symbol period of , and the calculation result is used as the restored I-path signal; The signal Multiply by sinw0t and integrate the result to calculate The calculation result is used as the restored Q-path signal; Combine the restored I-channel signal and the restored Q-channel signal into one channel, and use the combined result as the reconstruction result of the cover signal.

9. The method for separating concealed weak signals from single-carrier background signals based on constellation reconstruction according to claim 8, characterized in that: The specific process of step seven is as follows: Among them, y res (n) represents the mixed signal of noise, residual signal and hidden signal.

10. The method for separating concealed weak signals from single-carrier background signals based on constellation reconstruction according to claim 9, characterized in that: The specific process of step eight is as follows: Step 81: Convert the mixed signal y res (n) Input to the first-level detection module for detection, and detect the mixed signal y res (n) Whether it obeys normal distribution; Step 82: Select a secondary detection module according to the detection result of step 81, specifically: If the mixed signal y res (n) obeys normal distribution, then select the cyclic autocorrelation detector; If the mixed signal y res (n) If it does not obey the normal distribution, a high-order cumulant detector is selected; Step 83: Determine whether there is a protected weak-power communication signal in the mixed signal y(n) according to the detection result of the secondary detection module.

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