A kurtosis-based broadband spectrum sensing method, system, device, and storage medium

Abstract

This invention discloses a kurtosis-based broadband spectrum sensing method, system, device, and storage medium. The method includes the following steps: S1: Sampling the broadband spectrum using a filter to obtain the acquired received signal; S2: Constructing a Hankel matrix based on the received signal and predefined reference information; S3: Performing singular value decomposition on the Hankel matrix and using a kurtosis-based judgment method to separate the signal space and noise space to determine the number of primary users occupying the frequency band; S4: Estimating the specific frequency location occupied by each primary user using the Prony-Kung method. This invention improves the accuracy of spectrum detection over a broadband range and reduces the complexity of broadband spectrum sensing.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology for target detection, and more specifically, to a broadband spectrum sensing method, system, device, and storage medium based on kurtosis. Background Technology

[0002] Unmanned aerial vehicles (UAVs) are characterized by high mobility, low equipment cost, and low risk. As UAV performance gradually improves, they will increasingly be used for communication, jamming, reconnaissance, and support missions. On the other hand, the electromagnetic spectrum environment during UAV flight is complex and variable, subject to interference from various factors. Therefore, accurately locating the communication frequency points within a short timeframe and a wide bandwidth during communication—that is, spectrum sensing—is one of the foundations for ensuring the success of communication missions.

[0003] Drones have their own unique characteristics. First, their payload capacity is limited; second, they maintain high-speed movement for most of the time. Considering these characteristics, existing broadband spectrum sensing methods have significant drawbacks when applied to drone applications. Current broadband spectrum sensing can be broadly categorized into multi-channel broadband sensing and general broadband sensing. For multi-channel broadband sensing, the entire frequency band is pre-divided into multiple channels. A primary user uses one or more channels at a given time, and the presence or absence of the primary user signal on each channel can be determined sequentially using relatively mature narrowband detection technology. When the primary user signal can appear at any location within the broadband range with any bandwidth, it falls under general broadband sensing. For this type of broadband spectrum sensing, it is necessary not only to determine the presence of the primary user signal but also to determine the specific location of the frequency band occupied by the primary user signal. The aforementioned multi-channel broadband sensing is further divided into serial sensing and parallel sensing. Serial sensing detects one channel at a time, scanning the entire frequency band sequentially. This takes a considerable amount of time to sense a broadband frequency band, which is clearly unsuitable for rapidly changing wireless communication scenarios. Parallel scanning sensing is more time-efficient than serial scanning detection, but requires significantly more equipment, resulting in substantial cost. In conventional broadband spectrum sensing methods, compressed sensing relies on the sparsity of the frequency bands occupied by the signal, while simultaneously requiring complete or partial signal recovery, significantly limiting the applicability of such methods. Therefore, when channel information is unknown or limited, a better broadband spectrum blind detection method is needed. Summary of the Invention

[0004] In order to address the shortcomings and defects of the existing technology, this invention proposes a broadband spectrum sensing method, system, device, and storage medium based on kurtosis, which improves the accuracy of spectrum detection in the broadband range and reduces the complexity of broadband spectrum sensing.

[0005] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows:

[0006] A broadband spectrum sensing method based on kurtosis, comprising the following steps:

[0007] S1: Use a filter to sample the broadband spectrum to obtain the acquired received signal;

[0008] S2: Construct the Hankel matrix based on the received signal and the set reference information;

[0009] S3: Perform singular value decomposition on the Hankel matrix, use a kurtosis-based judgment method to separate the signal space and noise space, and determine the number of main users occupying the frequency band;

[0010] S4: Use the Prony-Kung method to estimate the specific frequency location occupied by each master user.

[0011] Preferably, in S1, specifically, let the bandwidth to be detected be B, and let P users be transmitting signals within this bandwidth, with the center frequency of the Pth user being f. P The signal bandwidth is B P A filter is used to sample the signal;

[0012] The mathematical expression for the received signal after acquisition is:

[0013]

[0014] Where ρ represents the received signal-to-noise ratio; y N It is the received signal after acquisition, including the main user signal and noise; h p s represents the channel through which the p-th user arrives at the detector; p f represents the p-th randomly transmitted signal; p Let represent the frequency position of the p-th primary user in the broadband, Δt be the sampling interval for acquiring signal data, N be the number of samples, and w be the frequency position of the p-th primary user in the broadband. N It is complex Gaussian white noise, obeying CN(0,δ) 2 ).

[0015] Furthermore, S2, the specific steps are as follows:

[0016] The dataset of received signals acquired within the time interval N·Δt is {y1,y2,…,y}. N} can be written in the form of a vector as follows:

[0017]

[0018] Equation (2) can be written in matrix form as follows:

[0019]

[0020] Among them, c P =h P ·s P , This represents the set of all complex numbers with a size of N rows and 1 column, where j represents the imaginary unit;

[0021] From equation (3), it can be seen that if noise is temporarily ignored, the sample vector Y is located at the support vector. The generated space is completely composed of the occupied frequency points f1, f2, ..., f P Therefore, the spectrum sensing problem is actually the problem of determining the subspace;

[0022] make

[0023]

[0024] The final model expression of equation (3) is obtained as follows:

[0025]

[0026] The one-dimensional time series, i.e., Y N×1 Converting it to a matrix with a multidimensional space, it can be written in Hankel matrix form as follows:

[0027]

[0028] Where Q and L are two positive integers satisfying the conditions Q + L - 1 = N, Q ≥ P, L ≥ P, and Q ≥ L + 1; when N is even, then the value is fixed. An integer; when N is odd, then a fixed value is chosen. An integer that satisfies L = N - Q + 1.

[0029] Furthermore, in S3, the singular value decomposition of the Hankel matrix in S2 yields the following form:

[0030] H Q×L =UDV H (7)

[0031] Where U represents a unitary matrix of size Q×L, V represents a unitary matrix of size L×L, and D is an L×L diagonal matrix, D=diag(d1,d2,…,d L ), diag represents taking the diagonal elements, d1, d2, ..., d L All are diagonal elements, and d1≥d2≥…≥d P >>d P+1 ≥

[0032] dP+2 ≥…≥d L ≥0.

[0033] Furthermore, S3 uses a kurtosis-based determination method to separate the signal space and noise space to determine the number of primary user signals occupying the frequency band, as follows:

[0034] S301: Perform ZF preprocessing on the noisy received signal, and denote the processed signal as... Take the first row to the (Q-1)th row and the first column to the (W)th column of matrix U, and denote it as U. a Take the 2nd row to the Qth column and the 1st column to the Wth column of matrix U and denote them as U. b W≤L;

[0035] S302: Let λ = e jθ Where θ∈[-π,π]; divide [-π,π] into R equal parts, resulting in R λ values, and substitute these R λ values ​​into (U... b -λU a ) H (U b -λU a In the given information, we find the eigenvalues ​​of the given information and select the smallest eigenvalue, thus obtaining R smallest eigenvalues, as shown in the following formula:

[0036] f(λ)=min(eig||U b -λU a ||) (8)

[0037] Where λ represents the generalized eigenvalue of the matrix bundle, and θ represents the incident angle of the signal;

[0038] S303: The calculation equation is as follows:

[0039]

[0040] Find the peak value of g(λ), arrange the peak values ​​in descending order, and denote the angle corresponding to each peak value as . Here, i represents the number of peaks;

[0041] S304: The obtained i angles are used to construct i guide vectors, denoted as b. i :

[0042]

[0043] Let all the guide vectors form a matrix B = [b1, b2, ..., b i Then, take the first column, the second column, ..., the i-th column of B in sequence, and... Perform residual calculations to obtain the residuals of column vector i.

[0044] S305: Preprocess the residuals obtained in S304 as follows: Separate the real and imaginary parts of each residual array element and merge them to obtain a first array. Calculate the mean of the elements in the first array. Then, subtract the mean from each element in the first array to obtain a second array with a mean of 0, denoted as t. i ;

[0045] S306: Use kurtosis to determine the Gaussianity of the data distribution in the second array:

[0046]

[0047] When kurt(t) i When ) > 0, it follows a super-Gaussian distribution; when kurt(t) > 0, it follows a super-Gaussian distribution. i When ) < 0, it follows a sub-Gaussian distribution;

[0048] When kurt(t) i When ) = 0, it follows a Gaussian distribution; when the kurtosis formula calculates kurt(t)... i The column number that approaches 0 is the estimated number of primary users, denoted as .

[0049] Furthermore, for S304, the residual calculation is as follows:

[0050]

[0051] in, B(,1:i) represents the first i columns of matrix B.

[0052] Furthermore, in S4, the Prony-Kung method is used to estimate the specific frequency location occupied by each primary user, as follows:

[0053] S401: Take the first row to the (Q-1)th row and the first column to the (Q-1)th column of matrix U. Let U1 be a column; take the 2nd row to the Qth row and the 1st column to the Qth column of matrix U. Let it be denoted as U2:

[0054]

[0055]

[0056] S402: Calculate matrix (U1) H U1) -1 U1 H The eigenvalues ​​of U2 are:

[0057] eig{(U1 H U1) -1 U1 H U2}(15)

[0058] The eigenvalues ​​can be obtained, denoted as . Where eig represents taking the eigenvalue;

[0059] S403: The phase angle is obtained according to equation (16):

[0060]

[0061] We obtain λ j The phase angle, denoted as Where angle represents the angle at which the eigenvalue is taken, θ j To represent the true perspective, It is θ j The estimated value;

[0062] S404: Order Get f j The estimated value is denoted as f j These are the frequencies that are actually being used.

[0063] A kurtosis-based broadband spectrum sensing system includes:

[0064] The sampling module is used to sample the broadband spectrum using a filter to obtain the acquired received signal.

[0065] The matrix construction module is used to construct a Hankel matrix based on the received signal and the set parameter information.

[0066] The module for determining the number of primary users is used to perform singular value decomposition on the Hankel matrix and use a kurtosis-based judgment method to separate the signal space and noise space to determine the number of primary users occupying the frequency band.

[0067] The frequency point determination module is used to estimate the frequency point location occupied by each master user using the Prony-Kung method.

[0068] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the kurtosis-based broadband spectrum sensing method.

[0069] A computer-readable storage medium storing a computer program thereon, characterized in that: when the computer program is executed by a processor, it implements the steps of the kurtosis-based broadband spectrum sensing method.

[0070] The beneficial effects of this invention are as follows:

[0071] This invention uses a method to transform a single-dimensional time series into a matrix with multi-dimensional spatial features, namely the Hankel matrix, and uses a kurtosis-based judgment method to determine the number of primary user signals. Then, the Prony-Kung method is used to estimate the specific frequency point location occupied by the primary user.

[0072] This invention uses only one filter to sense the entire broadband spectrum in parallel. It uses a kurtosis-based judgment method to achieve the performance requirements of general broadband spectrum sensing, namely, to detect the number of signals and their specific frequency band positions in the broadband spectrum.

[0073] This invention can accurately detect the number of main users in a short time and determine the location of the occupied frequency points, thereby improving the accuracy of spectrum detection in the broadband range and reducing the complexity of broadband spectrum sensing. Attached Figure Description

[0074] Figure 1 This is a flowchart of the broadband spectrum sensing method based on kurtosis described in this invention.

[0075] Figure 2 This is a simulation diagram showing the accuracy of estimating the number of primary users using the kurtosis-based broadband spectrum sensing method described in this invention.

[0076] Figure 3 This is a simulation diagram of the average error probability of the actually occupied frequency points and the estimated frequency points under different signal-to-noise ratios in the broadband spectrum sensing method based on kurtosis described in this invention.

[0077] Figure 4 This is a framework diagram of the broadband spectrum sensing system based on kurtosis in Example 2. Detailed Implementation

[0078] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0079] Example 1

[0080] This embodiment further improves the broadband spectrum sensing technology for multiple main users and one sensing user (one UAV), enhancing the spectrum sensing capability and thus further improving the ability to find spectrum holes.

[0081] Assume there are P (randomly selected) main users transmitting signals, and N sensing users. r (A drone) is sensing the main user signal. Table 1 below shows the general parameter settings, which can be used to sense the broadband spectrum.

[0082] Table 1 Parameter Settings

[0083] parameter set up <![CDATA[Perceived User N r > 1 number of Vandermonde experiments 1000 Number of samples N 300 <![CDATA[Matrix H Q×L Number of rows]]> 150 <![CDATA[Matrix H Q×L Number of columns]]> 151 Number of main users P 4:1:10 Signal-to-noise ratio ρ 8:2:16 Spectrum bandwidth B 20MHz Sampling interval Δt <![CDATA[5×10 -8 s]]> <![CDATA[Center frequency f1]]> 0 Spectrum bandwidth allocation d <![CDATA[(f1-B / 2):(f1+B / 2)]]> <![CDATA[Sampling frequency f s > 20MHz W 16 R 3000

[0084] like Figure 1 As shown, a broadband spectrum sensing method based on kurtosis is described, and the method includes the following steps:

[0085] S1: Use a filter to sample the broadband spectrum to obtain the acquired received signal;

[0086] S2: Construct the Hankel matrix based on the received signal and the set reference information;

[0087] S3: Perform singular value decomposition on the Hankel matrix, use a kurtosis-based judgment method to separate the signal space and noise space, and determine the number of main users occupying the frequency band;

[0088] S4: Use the Prony-Kung method to estimate the specific frequency location occupied by each master user.

[0089] In a specific embodiment, in the broadband spectrum sensing, there are P main users transmitting signals and one sensing user (UAV). S1, specifically, let the bandwidth to be detected be B, within which P users are transmitting signals, and the center frequency of the Pth user is f. P The signal bandwidth is B P A filter is used to sample the signal.

[0090] The mathematical expression for the received signal after acquisition is:

[0091]

[0092] Where ρ represents the received signal-to-noise ratio; y N It is the received signal after acquisition, including the main user signal and noise; h p s represents the channel through which the p-th user arrives at the detector; p f represents the p-th randomly transmitted signal; p Let represent the frequency position of the p-th primary user in the broadband, Δt be the sampling interval for acquiring signal data, N be the number of samples, and w be the frequency position of the p-th primary user in the broadband. N It is complex Gaussian white noise, obeying CN(0,δ) 2 ).

[0093] In this embodiment, a filter is used to sample the frequency band B = 20MHz at equal intervals, and the sampling time interval Δt is (5 × 10) -8The broadband spectrum is divided into (0-20MHz / 2):(0+20MHz / 2), i.e., d = (-10MHz:10MHz). P primary users are transmitting signals within this bandwidth. The center frequency of each primary user's signal is within the spectral range of d. The bandwidth of the transmitted signal is unknown. Within a time range of 300×Δt, the transmitted sample data {y1,y2,…,y} can be obtained. 300 These data originate from a user's symbol and can be represented as follows:

[0094]

[0095] Where h1, h2, ..., h P This represents the channels through which P users arrive at the detector.

[0096] {h1,h2,…,h P The values ​​follow a complex Gaussian distribution with mean 0 and variance 1, and are randomly generated.

[0097] s1, s2, ..., sP represent randomly transmitted signals, from Randomly select f1, f2, ..., f P This represents the frequency position occupied by P primary users in the broadband, w N It is complex Gaussian noise, obeying CN(0,δ) 2 ), here δ 2 =1, j represents the imaginary unit, in this embodiment

[0098]

[0099] In a specific embodiment, S2, the specific steps are as follows:

[0100] The dataset of received signals acquired within the time interval N·Δt is Y. 300×1 =[y1,y2,…,y 300 ] T Where T denotes transpose, it can be written in the form of the following vector:

[0101]

[0102] Equation (2) can be written in matrix form as follows:

[0103]

[0104] Among them, c P =h P ·s P , This represents the set of all complex numbers with a size of N rows and 1 column, where j represents the imaginary unit.

[0105] From equation (3), it can be seen that if noise is temporarily ignored, the sample vector Y is located at the support vector. The generated space is completely composed of the occupied frequency points f1, f2, ..., f P Therefore, the problem of spectrum sensing is actually the problem of determining subspaces.

[0106] make

[0107]

[0108] The final model expression of equation (3) is obtained as follows:

[0109]

[0110] The one-dimensional time series, i.e., Y 300×1 The vector is converted into a matrix with a multidimensional space, which can be written in Hankel matrix form as follows:

[0111]

[0112] Where Q and L are two positive integers satisfying the conditions Q + L - 1 = 300, Q ≥ P, L ≥ P, and Q ≥ L + 1; when N is even, then the value is fixed. An integer; when N is odd, then a fixed value is chosen. Let L be an integer such that L = N - Q + 1. Here, Q is 151 and L is 150.

[0113] Furthermore, in S3, the singular value decomposition of the Hankel matrix in S2 yields the following form:

[0114] H 151×150 =UDV H (7)

[0115] Where U represents a unitary matrix of size Q×L (i.e., 151×150), V represents a unitary matrix of size L×L (i.e., 150×150), and D is an L×L (i.e., 150×150) diagonal matrix, D = diag(d1, d2, ..., d...). 150 ), diag represents taking the diagonal elements, d1, d2, ..., d L All are diagonal elements, and d1≥d2≥…≥d P >>d P+1 ≥…≥d 150 ≥0. The first P singular values ​​are much larger than the later singular values, while the last 150-P singular values ​​are very small.

[0116] Furthermore, S3 uses a kurtosis-based determination method to separate the signal space and noise space to determine the number of primary user signals occupying the frequency band, as follows:

[0117] S301: Provide the noisy received signal {y1,y2,…,y} 300 Perform ZF preprocessing, and denote the processed signal as... Take the first row to the Q-1 (i.e., 150th row) row and the first column to the W=16th column of matrix U, and denote it as U. a Take the 2nd row to the Q=151st column and the 1st column to the W=16th column of matrix U and denote them as U. b ;W≤L.

[0118] S302: Let λ = e jθ Where θ∈[-π,π]; divide [-π,π] into R = 3000 parts, resulting in 3000 λ values. Substitute these 3000 λ values ​​into (U... b -λU a ) H (U b -λU a In the equation, we find their eigenvalues ​​and select the smallest eigenvalue, thus obtaining R = 3000 smallest eigenvalues, as shown in the following formula:

[0119] f(λ)=min(eig||U b -λU a ||) (8)

[0120] Where λ represents the generalized eigenvalue of the matrix bundle, and θ represents the incident angle of the signal.

[0121] S303: The calculation equation is as follows:

[0122]

[0123] Find the peak value of g(λ), arrange the peak values ​​in descending order, and denote the angle corresponding to each peak value as . Here, i represents the number of peaks; and P ≤ i ≤ 16.

[0124] S304: The obtained i angles are used to construct i guide vectors, denoted as b. i :

[0125]

[0126] Let all the guide vectors form a matrix B = [b1, b2, ..., b i Then, take the first column, the second column, ..., the i-th column of B in sequence, and... Perform residual calculations to obtain the residuals of column vector i.

[0127] S305: Preprocess the residuals obtained in S304 as follows: Separate the real and imaginary parts of each residual array element and merge them to obtain a first array. Calculate the mean of the elements in the first array. Then, subtract the mean from each element in the first array to obtain a second array with a mean of 0, denoted as t. i ;

[0128] S306: Use kurtosis to determine the Gaussianity of the data distribution in the second array:

[0129]

[0130] When kurt(t) i When ) > 0, it follows a super-Gaussian distribution; when kurt(t) > 0, it follows a super-Gaussian distribution. i When ) < 0, it follows a sub-Gaussian distribution.

[0131] When kurt(t) i When ) = 0, it follows a Gaussian distribution; when the kurtosis formula calculates kurt(t)... i The column number that approaches 0 is the estimated number of primary users, denoted as .

[0132] According to equation (11), i kurtosis values ​​will be obtained and displayed in descending order. When kurt(t i The column number that approaches 0 is the estimated number of primary users, denoted as .

[0133] In a specific embodiment, S304, the residual is calculated as follows:

[0134]

[0135] in, B(,1:i) represents the first i columns of matrix B.

[0136] In one specific embodiment, when the estimated number of primary users is the same as the actual number of primary users occupying broadband spectrum, that is... If so, the next step can be to estimate the specific frequency points in the broadband spectrum occupied by the main user.

[0137] In this embodiment, S4, the Prony-Kung method is used to estimate the specific frequency point location occupied by each primary user, as follows:

[0138] S401: Take rows 1 to Q-1 (i.e., row 150) of matrix U, and columns 1 to Q-1 (i.e., column 150). Let U1 be a column; take the 2nd row to the Q=151st row and the 1st column to the Q=151st column of matrix U. Let it be denoted as U2:

[0139]

[0140]

[0141] S402: Calculate matrix (U1) H U1) -1 U1 H The eigenvalues ​​of U2 are:

[0142] eig{(U1 H U1) -1 U1 H U2}(15)

[0143] The eigenvalues ​​can be obtained, denoted as . Where eig represents taking the eigenvalue;

[0144] S403: The phase angle is obtained according to equation (16):

[0145]

[0146] We obtain λ j The phase angle, denoted as Where angle represents the angle at which the eigenvalue is taken, θ j To represent the true perspective, It is θ j The estimated value;

[0147] S404: Order Get f j The estimated value is denoted as f j These are the frequencies that are actually being used.

[0148] Next, the average estimation accuracy is used to estimate the error probability of the estimated frequencies:

[0149]

[0150] Reference Figure 2 As shown, the accuracy of the number of primary users is detected. The accuracy of estimating the number of primary users by the method of this invention continuously increases with the improvement of the signal-to-noise ratio. (Refer to...) Figure 3 As shown, the test detects the average estimation error probability of a frequency point when the number of primary users is unknown. It can be seen that the error probability decreases as the signal-to-noise ratio gradually increases. At 8dB, the average error probability is 1.78%, and at 16dB it can be reduced to 0.03%. Moreover, the average error probability continues to decrease as the signal-to-noise ratio increases. The conclusions drawn from the above two cases verify the effectiveness of the method of the present invention.

[0151] This embodiment transforms a one-dimensional time series into a matrix with multi-dimensional spatial characteristics, namely the Hankel matrix. A kurtosis-based method is used to determine the number of primary user signals, and the Prony-Kung method is then used to estimate the specific frequency locations occupied by the primary users. Simulation results show that the method for estimating the number of primary signals is effective, and the accuracy of frequency estimation is also high.

[0152] Example 2

[0153] Based on the kurtosis-based broadband spectrum sensing method described in Embodiment 1, this embodiment also provides a kurtosis-based broadband spectrum sensing system, including:

[0154] The sampling module is used to sample the broadband spectrum using a filter to obtain the acquired received signal.

[0155] The matrix construction module is used to construct a Hankel matrix based on the received signal and the set parameter information.

[0156] The module for determining the number of primary users is used to perform singular value decomposition on the Hankel matrix and use a kurtosis-based judgment method to separate the signal space and noise space to determine the number of primary users occupying the frequency band.

[0157] The frequency point determination module is used to estimate the frequency point location occupied by each master user using the Prony-Kung method.

[0158] Example 3

[0159] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the kurtosis-based broadband spectrum sensing method as described in Embodiment 1.

[0160] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0161] Example 4

[0162] A computer-readable storage medium having a computer program stored thereon, wherein when executed by a processor, the computer program implements the steps of the kurtosis-based broadband spectrum sensing method as described in Embodiment 1.

[0163] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0164] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A broadband spectrum sensing method based on kurtosis, characterized in that: The method includes the following steps: S1: Use a filter to sample the broadband spectrum to obtain the acquired received signal; S2: Construct the Hankel matrix based on the received signal and the set reference information; S3: Perform singular value decomposition on the Hankel matrix, use a kurtosis-based judgment method to separate the signal space and noise space, and determine the number of main users occupying the frequency band; S4: Use the Prony-Kung method to estimate the specific frequency location occupied by each primary user; S3 uses a kurtosis-based determination method to separate the signal space and noise space to determine the number of primary user signals occupying the frequency band, as detailed below: S301: Perform ZF preprocessing on the noisy received signal, and denote the processed signal as... Take the first row of matrix U to... Row, first column to the W Column, denoted as Take the 2nd row to the Qth row and the 1st column to the Qth column of matrix U. W List as ; ; S302: Order ,in ;Will Divide into R equal parts, and you will get R items. Value, R Substitute in sequence In the above, we find their eigenvalues ​​and select the smallest eigenvalue, thus obtaining R smallest eigenvalues, as shown in the following formula: （8） in, Represents the generalized eigenvalues ​​of a matrix bundle. Indicates the angle of incidence of the signal; S303: The calculation equation is as follows: （9） Seeking The peak values ​​are arranged from largest to smallest, and the angles corresponding to the peak values ​​are denoted as . , here The number of peak values; S304: The obtained i Each angle constitutes i A guide vector, denoted as : （10） Let all the guide vectors form a matrix. Then take them in sequence. The first column, the first two columns, ,forward i Columns, and Make a residual, and then obtain i Column vector residuals; S305: Preprocess the residuals obtained in S304 as follows: Separate the real and imaginary parts of each residual array element and merge them to obtain a first array. Calculate the mean of the elements in the first array. Then, subtract the mean from each element in the first array to obtain a second array with a mean of 0, denoted as . ; S306: Use kurtosis to determine the Gaussianity of the data distribution in the second array: （11） when When, it follows a super-Gaussian distribution; when At that time, it follows a sub-Gaussian distribution; when When the distribution is Gaussian, the kurtosis formula calculates... The column number that approaches 0 is the estimated number of primary users, denoted as . .

2. The broadband spectrum sensing method based on kurtosis according to claim 1, characterized in that: S1, specifically, let the bandwidth to be detected be... B Within this bandwidth P The user is sending a signal, the [number]th user. P The center frequency of each user is The signal bandwidth is A filter is used to sample the signal; The mathematical expression for the received signal after acquisition is: (1) in, Indicates the received signal-to-noise ratio; It is the received signal after acquisition, including the main user signal and noise; Indicates the first p The channel through which each user arrives at the detector; Indicates the first p A random transmitted signal; Indicates the first p Each primary user occupies a frequency point in the broadband. This is the sampling interval for acquiring signal data, where N represents the number of samples. It is complex Gaussian white noise, which obeys... .

3. The broadband spectrum sensing method based on kurtosis according to claim 2, characterized in that: S2, the specific steps are as follows: exist The dataset of received signals acquired within a given time period is It can be written in the form of a vector as follows: （2） Equation (2) can be expressed in matrix form as follows: （3） in, , , This represents the set of all complex numbers with a size of N rows and 1 column. Represents the imaginary unit; From equation (3), it can be seen that if noise is temporarily ignored, then the sample vector It is in the support vector In the generated space, and the space is entirely composed of occupied frequency points Therefore, the spectrum sensing problem is actually the problem of determining the subspace; make （4） The final model expression of equation (3) is obtained as follows: （5） One-dimensional time series, i.e. Converting it to a matrix with a multidimensional space, it can be written in Hankel matrix form as follows: （6） in, Q , L Given two positive integers, satisfying the condition , , ,and ;when N If the number is even, then it is fixed. An integer; when N If the number is odd, then it is fixed. An integer that satisfies .

4. The broadband spectrum sensing method based on kurtosis according to claim 3, characterized in that: S3, Singular value decomposition of the Hankel matrix in S2, has the following form: （7） where, U represents a unitary matrix of size , V represents a unitary matrix of size , D is a diagonal matrix, , denotes taking diagonal elements, are all diagonal elements, and .

5. The broadband spectrum sensing method based on kurtosis according to claim 4, characterized in that: S304, the residual calculation is as follows: （12） in, = / , Representation matrix B The former i List.

6. The broadband spectrum sensing method based on kurtosis according to claim 4, characterized in that: S4. The Prony-Kung method is used to estimate the specific frequency location occupied by each primary user, as follows: S401: Take the first row of matrix U... Row, column 1 to row 2 Column, denoted as Take the 2nd row to the Qth row and the 1st column to the Qth column of matrix U. List as : （13） （14） S402: Calculate the matrix The eigenvalues, namely: （15） The eigenvalues ​​can be obtained, denoted as . ,in This indicates taking the eigenvalue; S403: The phase angle is obtained according to equation (16): （16） get The phase angle, denoted as , ,in Indicates the angle at which the eigenvalue is taken. Representing the true perspective, yes The estimated value; S404: Order ,get The estimated value is denoted as , These are the frequencies that are actually being used. .

7. A broadband spectrum sensing system based on kurtosis, characterized in that: include: The sampling module is used to sample the broadband spectrum using a filter to obtain the acquired received signal. The matrix construction module is used to construct a Hankel matrix based on the received signal and the set parameter information. The module for determining the number of primary users is used to perform singular value decomposition on the Hankel matrix and use a kurtosis-based judgment method to separate the signal space and noise space to determine the number of primary users occupying the frequency band. The frequency point determination module is used to estimate the frequency point location occupied by each master user using the Prony-Kung method; Primary user number determination module: Using a kurtosis-based method, the signal space and noise space are separated to determine the number of primary user signals occupying the frequency band, as detailed below: S301: Perform ZF preprocessing on the noisy received signal, and denote the processed signal as... Take the first row of matrix U to... Row, first column to the W Column, denoted as Take the 2nd row to the Qth row and the 1st column to the Qth column of matrix U. W List as ; ; S302: Order ,in ;Will Divide into R equal parts, and you will get R items. Value, R Substitute in sequence In the above, we find their eigenvalues ​​and select the smallest eigenvalue, thus obtaining R smallest eigenvalues, as shown in the following formula: （8） in, Represents the generalized eigenvalues ​​of a matrix bundle. Indicates the angle of incidence of the signal; S303: The calculation equation is as follows: （9） Seeking The peak values ​​are arranged from largest to smallest, and the angles corresponding to the peak values ​​are denoted as . , here The number of peak values; S304: The obtained i Each angle constitutes i A guide vector, denoted as : （10） Let all the guide vectors form a matrix. Then take them in sequence. The first column, the first two columns, ,forward i Columns, and Make a residual, and then obtain i Column vector residuals; S305: Preprocess the residuals obtained in S304 as follows: Separate the real and imaginary parts of each residual array element and merge them to obtain a first array. Calculate the mean of the elements in the first array. Then, subtract the mean from each element in the first array to obtain a second array with a mean of 0, denoted as . ; S306: Use kurtosis to determine the Gaussianity of the data distribution in the second array: （11） when When, it follows a super-Gaussian distribution; when At that time, it follows a sub-Gaussian distribution; when When the distribution is Gaussian, the kurtosis formula calculates... The column number that approaches 0 is the estimated number of primary users, denoted as . .

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the kurtosis-based broadband spectrum sensing method as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the kurtosis-based broadband spectrum sensing method as described in any one of claims 1 to 6.

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