Spectrum sensing method and device based on strong graph product quadratic form

Abstract

The invention discloses a spectrum sensing method and device based on a strong graph product quadratic form, and relates to the technical field of signal processing. The invention discloses a spectrum sensing method based on a strong graph product quadratic form. The method comprises the following steps: calculating a grouping summation power spectrum and an autocorrelation function of an observation signal; according to the grouping summation power spectrum and the self-correlation function, respectively constructing a grouping summation power spectrum sub-quantization graph and a self-correlation function sub-quantization graph; calculating a strong graph product and a graph signal of the strong graph product according to the grouping summation power spectrum sub-quantization graph and the self-correlation function sub-quantization graph; and calculating test statistics according to the graph signal, and comparing the test statistics with a judgment threshold to judge whether the authorized user exists or not. The method provided by the invention has better performance in complex transmission environments such as low signal-to-noise ratio and fading channels, and has a certain engineering application prospect.

Description

Technical Field

[0001] This invention relates to a spectrum sensing method and apparatus based on a strong graph product quadratic form, belonging to the field of signal processing technology. Background Technology

[0002] Cognitive radio (CR) has become a key technology for alleviating the increasingly severe problem of spectrum scarcity, and is also an important supporting technology for realizing intelligent information transmission in 5G and 6G mobile communication systems. Spectrum sensing is a crucial link in cognitive radio signal processing. It supports opportunistic dynamic access for secondary users by detecting the presence or absence of licensed user signals, thereby improving spectrum utilization efficiency.

[0003] Despite significant progress in spectrum sensing research, its performance often degrades in low signal-to-noise ratio (SNR) environments due to multipath effects or channel fading in real-world signal processing scenarios. This not only reduces spectrum utilization efficiency but can also interfere with licensed users. Therefore, achieving effective and reliable detection results in complex environments such as low SNR and fading channels remains a crucial and practically significant challenge. Summary of the Invention

[0004] The purpose of this invention is to provide a spectrum sensing method and apparatus based on a strong graph product quadratic form. By using the grouped summation power spectrum (BSPS) and autocorrelation function (ACF) of the observed signal as independent inputs to the graph transform, a strong graph product is constructed and the test statistic is calculated and compared with the decision threshold to determine whether an authorized user exists, so as to achieve effective and reliable detection in complex transmission environments such as low signal-to-noise ratio and fading channels.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution.

[0006] On one hand, the present invention provides a spectrum sensing method based on a strong graph product quadratic form, comprising:

[0007] Calculate the grouped summation power spectrum and autocorrelation function of the observed signal;

[0008] Based on the grouped summation power spectrum and the autocorrelation function, construct the subquantization plot of the grouped summation power spectrum and the subquantization plot of the autocorrelation function, respectively.

[0009] The strong graph product and the graph signal of the strong graph product are calculated based on the grouped summation power spectrum subquantization map and the autocorrelation function subquantization map;

[0010] The test statistic is calculated based on the graph signal, and the test statistic is compared with the decision threshold to determine whether an authorized user exists.

[0011] Optionally, the calculation process for the grouped summation power spectrum is as follows:

[0012] The power spectrum is uniformly divided into The number of observed signal samples in each block is [number]. , ,and It can be Divisible;

[0013] The samples within each block are summed to obtain the grouped summation power spectrum. :

[0014] ;

[0015] Among them, the observed signal power spectrum The calculation formula is:

[0016] ;

[0017] In the formula, M is the total number of observed signal samples, and j is the imaginary unit in the complex number, i.e. .

[0018] Optionally, the calculation process of the autocorrelation function is as follows:

[0019] First, remove the observed signal. The mean of the values ​​is used to obtain the observation signal with zero mean. :

[0020] ;

[0021] In the formula, The mean of the observed signal, This represents the total number of observed signal samples.

[0022] Then calculate the autocorrelation function. :

[0023] ;

[0024] In the formula, Due to the symmetry of the autocorrelation function, the right half of the autocorrelation function is chosen, i.e. .

[0025] Optionally, the process of constructing the sub-quantization graph is as follows:

[0026] Select the number of vertices Two sub-quantized graphs are constructed by taking the grouped summation power spectrum and autocorrelation function as input signals, respectively.

[0027] The specific construction method is as follows:

[0028] First, the input signal Normalization is performed to obtain the normalized signal. :

[0029] ;

[0030] In the formula, and These are the maximum and minimum values ​​of the input signal, respectively. The number of samples of the input signal;

[0031] Secondly, for a given number of vertices, i.e., the number of quantization levels , Quantization sequence after uniform quantization Represented as:

[0032] ;

[0033] In the formula, ;

[0034] Finally, the quantized sequence is mapped to the vertex set according to the mapping rules. ;

[0035] The mapping rule is:

[0036] ;

[0037] The edges of the graph are determined by the amplitude changes between adjacent samples in the quantized sequence;

[0038] for , ,in Step size;

[0039] At least once and At that time, the vertex and vertex corresponding edges They are connected; otherwise, the vertices are connected. and vertex The spaces are not connected;

[0040] By traversing all input signal samples, the corresponding edge set is obtained as follows: .

[0041] Optionally, the process of calculating the strong graph product is as follows:

[0042] make For the generated having A sub-quantized graph of vertices, where, Let be a vertex of the graph. Let be the edges of the graph. Let be the adjacency matrix of the graph; the strong graph product is represented as:

[0043] ;

[0044] Number of vertices in a strong graph product The adjacency matrix of the strong graph product is represented as:

[0045] ;

[0046] In the formula, The dimension is The identity matrix, This represents the Kronecker product of the matrix.

[0047] Optionally, the graph signal calculation process for the strong graph product is as follows:

[0048] Calculate the grouped summation power spectral quantization plots separately. Vertex probability vectors and autocorrelation function subquantized graph Quantization interval sample sum:

[0049] Grouped summation power spectral quantization plot The vertex probability vector x is represented as:

[0050] ;

[0051] ;

[0052] In the formula, These are the probability vectors for each vertex; This indicates a mapping to a graph. The first in The total number of quantized samples corresponding to each vertex; The number of vertices;

[0053] Autocorrelation function subquantization plot The quantization interval sample and y are represented as:

[0054] ;

[0055] ;

[0056] In the formula, for , will be quantified A subset of normalized signal samples at each quantization level is denoted as , For the first The number of samples in each subset; These represent the samples and sums for each quantization interval;

[0057] Define the vertex probability vector and the Kronecker product of the quantized interval sample sums. Graph signal as a strong graph product:

[0058] ;

[0059] In the formula, These are the Kronecker product of the probability vectors of each vertex and the sum of samples in the quantized interval, respectively.

[0060] Optionally, the process of calculating the test statistic is as follows:

[0061] According to the signal in the figure Laplace matrix of strong graph product Calculate the strong graph product test statistic. :

[0062] ;

[0063] The process of calculating the Laplace matrix of a graph is as follows:

[0064] picture adjacency matrix Represented as:

[0065] ;

[0066] In the formula, , To quantify the number of levels; and ;

[0067] picture degree diagonal matrix Represented as:

[0068] ;

[0069] In the formula, It is a diagonal matrix representation; Respectively with the vertex The number of connected edges;

[0070] The Laplace matrix L of the graph is represented as:

[0071] .

[0072] Optionally, the process of comparing the test statistic with the decision threshold is as follows:

[0073] First, a binary hypothesis test is used to represent the single-node spectrum sensing problem as:

[0074] ;

[0075] In the formula, , For observing signals, For channel gain, It is additive white Gaussian noise. The table represents a pure signal; This indicates the presence of a licensed user signal in the channel. This indicates that there are no licensed user signals in the channel;

[0076] The prerequisite for calculating the judgment threshold is knowledge. Assume the probability distribution of the detection statistic, and use Using training data for the detection statistic under the null hypothesis, data exploration methods were employed to select the distribution with the smallest fitting error to the detection statistic under the null hypothesis from commonly used unimodal distributions, which was then used as the approximate probability distribution of the detection statistic. Simulations showed that the Birnbaum-Saunders distribution could effectively fit the null hypothesis. Assuming the probability distribution of the detection statistic, therefore, for a given false alarm probability... Based on the constant false alarm rate criterion, an approximate decision threshold is obtained through the formula:

[0077] ;

[0078] ;

[0079] In the formula, Let Birnbaum–Saunders distribution (fatigue life distribution) be the probability density function, and let scale parameter be... Shape parameters ;

[0080] Approximate expression for decision threshold for:

[0081] ;

[0082] In the formula, For Birnbaum-Saunders variables, the inverse cumulative distribution function is used.

[0083] Compare the test statistic with the decision threshold to make a test decision:

[0084] .

[0085] Secondly, the present invention provides a spectrum sensing device based on a strong graph product quadratic form, comprising:

[0086] The subquantization graph construction module is used to: calculate the grouped summation power spectrum and autocorrelation function of the observed signal;

[0087] Based on the grouped summation power spectrum and the autocorrelation function, construct the subquantization plot of the grouped summation power spectrum and the subquantization plot of the autocorrelation function, respectively.

[0088] The judgment module is used to: calculate the graph signal of the strong graph product and the graph signal of the strong graph product based on the grouped summation power spectrum subquantization graph and the autocorrelation function subquantization graph;

[0089] The test statistic is calculated based on the graph signal, and the test statistic is compared with the decision threshold to determine whether an authorized user exists.

[0090] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the spectrum sensing method based on strong graph product quadratic form as described in any of the first aspects.

[0091] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0092] 1. The strong graph product quadratic statistic proposed in this invention can effectively fuse the topological and statistical features of two different subgraphs, enhancing the separability and stability of the detection statistic under low signal-to-noise ratio conditions;

[0093] 2. This invention is not sensitive to the choice of the number of graph vertices. Existing graph-based perception algorithms need to ensure that the transformed graph is a complete graph under the null hypothesis or alternative hypothesis, which imposes certain constraints on the setting of the number of graph vertices. It is difficult to obtain the optimal number of vertices when prior information is lacking.

[0094] 3. This invention exhibits good performance in complex transmission environments such as low signal-to-noise ratio and fading channels, and has certain engineering application prospects. Attached Figure Description

[0095] Figure 1 This is a flowchart of the spectrum sensing method based on strong graph product quadratic form of the present invention;

[0096] Figure 2 For the present invention in Assuming the following graph structure diagram is generated. Figure 2 (a) is Assuming the quantization plot is generated by subgrouping and summing the power spectrum, Figure 2 (b) is Assuming the quantization plot generated by the autocorrelation function, Figure 2 (c) is Strong graph product under the assumption;

[0097] Figure 3 For the present invention in Assuming the following graph structure diagram is generated. Figure 3 (a) is Assuming the quantization plot is generated by subgrouping and summing the power spectrum, Figure 3 (b) is Assuming the quantization plot generated by the autocorrelation function, Figure 3 (c) is Strong graph product under the assumption;

[0098] Figure 4 For the present invention in and A schematic diagram of the mean based on the strong graph product quadratic form statistic under the assumption;

[0099] Figure 5 For the present invention in and Histogram and fitted distribution diagram of the test statistic under the hypothesis;

[0100] Figure 6 This is a schematic diagram illustrating the relationship between detection probability and signal-to-noise ratio under different false alarm rates according to the present invention. Detailed Implementation

[0101] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0102] Example 1:

[0103] This embodiment introduces a spectrum sensing method based on strong graph product quadratic forms, such as... Figure 1 As shown, it includes:

[0104] Calculate the grouped summation power spectrum and autocorrelation function of the observed signal;

[0105] Based on the grouped summation power spectrum and the autocorrelation function, construct the subquantization plot of the grouped summation power spectrum and the subquantization plot of the autocorrelation function, respectively.

[0106] The strong graph product and the graph signal of the strong graph product are calculated based on the grouped summation power spectrum subquantization map and the autocorrelation function subquantization map;

[0107] The test statistic is calculated based on the graph signal, and the test statistic is compared with the decision threshold to determine whether an authorized user exists.

[0108] Step 1: Calculate the grouped summation power spectrum and autocorrelation function of the observed signal.

[0109] Step 1.1: Calculate the observed signal Grouped summation power spectrum

[0110] Observation signal The power spectrum can be calculated using the following formula:

[0111] ;

[0112] This embodiment uses the grouped summation power spectrum as input for graph transformation to improve detection performance and reduce computational complexity. First, the power spectrum sequence is uniformly divided into... There are blocks, and the number of samples in each block is . ( ,and It can be (Divisible). Then, the samples within each block are summed to obtain the grouped summation power spectrum:

[0113] ;

[0114] Step 1.2: Calculate the observed signal autocorrelation function

[0115] First, remove the mean of the observed signal to obtain the observed signal with zero mean:

[0116] ;

[0117] In the formula, This represents the average value of the observed signal.

[0118] Then calculate the autocorrelation function:

[0119] ;

[0120] In the formula, Due to the symmetry of the autocorrelation function, the right half of the autocorrelation function is chosen. This is used as the input for the graph transformation.

[0121] Step 2: Constructing a quantization graph

[0122] Choose an appropriate number of vertices Two sub-quantized graphs are constructed by taking the grouped summation power spectrum and autocorrelation function as input signals, respectively. and .

[0123] The specific method for constructing the quantization graph is as follows:

[0124] Step 2.1: Normalization. Assume the input signal is represented as... After normalization, we can obtain

[0125] ;

[0126] In the formula, and These represent the maximum and minimum values ​​of the input signal, respectively. This indicates the number of sample points of the input signal.

[0127] Step 2.2: Quantization and Vertex Mapping. For a given number of quantization levels... (i.e., the number of vertices in the graph) Uniform quantization It is expressed as follows:

[0128] ;

[0129] In the formula, The quantization interval will be mapped to the vertex set according to the following rules. ;

[0130] ;

[0131] Step 2.3: Edge Construction. The edges of the graph are constructed from quantized sequences. The amplitude variation between adjacent samples determines this. , ,in Let the step size be 1. If it exists at least once... and In the case of this, the corresponding edge is considered to be... If the two vertices are connected, then they are considered disconnected. By traversing all samples, the corresponding edge set can be obtained. .

[0132] Step 3: Calculate the strong graph product

[0133] make For the product generated in step 2 A sub-quantized graph of vertices, where Represents the vertices of the graph. Represents the edges of a graph. Let represent the adjacency matrix of the graph. Then the strong graph product can be represented as follows:

[0134] ;

[0135] Among them, the number of vertices in the strong graph product The adjacency matrix of a strong graph product (whose dimension is...) )for

[0136] ;

[0137] In the formula, The dimension is The identity matrix, This represents the Kronecker product operation of matrices.

[0138] Step 4: Define the graph signal

[0139] Step 4.1: Define the subgraph signal VPV: a quantized graph generated by summing the power spectra of groups. Vertex probability vector

[0140] Quantitative chart The vertex probability vector can be represented as:

[0141] ;

[0142] in , This indicates a mapping to a graph. The first in The total number of quantized samples corresponding to each vertex.

[0143] Step 4.2: Define the subgraph signal Quantization plot generated by autocorrelation function Quantization interval samples and

[0144] Assuming the normalized sample in the graph transformation is The number of quantitative levels is The corresponding quantized sample is .for , will be quantified Quantitative levels ( The normalized subset of signal samples is denoted as , For the first The number of samples in each subset.

[0145] Then the quantization interval sample and It can be defined as:

[0146] ;

[0147] Step 4.3: Calculate the graph signal of the strong graph product.

[0148] Define the Kronecker product:

[0149] ;

[0150] It is used as the graph signal of the strong graph product.

[0151] Step 5: Calculate the test statistic

[0152] For the strong graph product constructed in step 3 Using the graph signal calculated in step 4 Laplace matrix of the graph Calculate the test statistic:

[0153] ;

[0154] In this step, the Laplacian matrix of the strong graph product is calculated as follows:

[0155] picture The adjacency matrix is:

[0156] ;

[0157] In the formula, , To quantify the number of levels; and .

[0158] picture The degree diagonal matrix is:

[0159] ;

[0160] In the formula, It is a diagonal matrix representation; Respectively with the vertex The number of connected edges.

[0161] The Laplace matrix of the graph can then be defined as:

[0162] .

[0163] Step 6: Comparison and Decision

[0164] The prerequisite for calculating the judgment threshold is knowledge. We assume a probability distribution for the detection statistic; however, rigorously calculating this distribution is extremely difficult. Therefore, this embodiment utilizes a small number of... Using the training data of the detection statistic under the null hypothesis, data exploration methods are employed to select the distribution that minimizes the fitting error of the detection statistic under the null hypothesis from commonly used unimodal distributions, which is then used as the approximate probability distribution of the detection statistic. Extensive simulations demonstrate that the Birnbaum-Saunders distribution effectively fits the null hypothesis. Assume the probability distribution of the detection statistic. Therefore, for a given false alarm probability... According to the constant false alarm rate criterion, the approximate decision threshold can be obtained by solving the following formula:

[0165] ;

[0166] ;

[0167] In the formula, Let be the probability density function of the Birnbaum–Saunders distribution, and its scale parameter be . Shape parameters Therefore, the decision threshold can be expressed as:

[0168] ;

[0169] In the formula, It is the inverse cumulative distribution function of the Birnbaum-Saunders variable.

[0170] The test statistic is compared with the decision threshold to make a test decision:

[0171] ;

[0172] in, This indicates the presence of a licensed user signal in the channel. This indicates that there are no licensed user signals in the channel.

[0173] like Figure 2 and Figure 3 As shown, in the simulation, the vertices of the subquantized graph are selected as follows: .exist and Under the assumption that the graphs generated by summing the power spectra in groups are all complete graphs. Assuming the quantization plot generated by the autocorrelation function is a complete plot, and Assuming that the autocorrelation function of the observed signal is an impulse function, it is difficult to ensure that all elements in the vertex probability vector of its quantized samples are greater than 0, thus making it difficult to convert it into a complete graph. and Under the assumption that the topological structure of the strong graph product differs between the two assumptions when the number of vertices in both subgraphs is small. Assuming that the strong graph product is a complete graph, and... Assuming it consists of two independent complete graphs, strong graph product amplifies the topological differences between low-order subquantized graphs, allowing for more effective differentiation between the two cases.

[0174] like Figure 4 As shown in the simulation, the signal-to-noise ratio varies from... arrive Step size is The number of vertices in the sub-quantized graph is . Assuming Figure 2 The mean of the subtype statistic is lower than that of the subtype statistic. Assuming Figure 2 The mean of the subtype statistic. And as the signal-to-noise ratio increases, the difference between the two increases. It is precisely because... Figure 2 Subtype statistics can effectively integrate the topological and statistical features of a graph, thereby increasing detection accuracy.

[0175] like Figure 5 As shown, at signal-to-noise ratios of 2 dB and -6 dB, the proposed embodiment... Figure 2 Histograms of the subtype statistic under the null and alternative hypotheses, and the corresponding probability density functions fitted by the Birnbaum-Saunders distribution and the Gaussian mixture model (GMM), respectively. The two show good agreement. Furthermore, the threshold calculated using the approximate formula can effectively distinguish between the two hypotheses.

[0176] like Figure 6 As shown, when the false alarm probability is 0.1, The detection probability can reach 90%. Furthermore, under the same signal-to-noise ratio, the algorithm's detection performance improves with the increase of the false alarm rate. Moreover, the theoretical detection probability calculated using existing distributions is basically consistent with the simulation probability (simulations under both the null and alternative hypotheses were run 5000 times each), which verifies the effectiveness of the approximate formula for the threshold calculation method described in this embodiment.

[0177] Example 2:

[0178] Based on the same inventive concept as Embodiment 1, this embodiment introduces a spectrum sensing device based on a strong graph product quadratic form, comprising:

[0179] The subquantization graph construction module is used to: calculate the grouped summation power spectrum and autocorrelation function of the observed signal;

[0180] Based on the grouped summation power spectrum and the autocorrelation function, construct the subquantization plot of the grouped summation power spectrum and the subquantization plot of the autocorrelation function, respectively.

[0181] The judgment module is used to: calculate the graph signal of the strong graph product and the graph signal of the strong graph product based on the grouped summation power spectrum subquantization graph and the autocorrelation function subquantization graph;

[0182] The test statistic is calculated based on the graph signal, and the test statistic is compared with the decision threshold to determine whether an authorized user exists.

[0183] The specific functions of each module described above are explained in the relevant content of the method in Embodiment 1, and will not be repeated here.

[0184] Example 3:

[0185] Based on the same inventive concept as other embodiments, this embodiment describes a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the spectrum sensing method based on a strong graph product quadratic form as described in any of the embodiments.

[0186] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0187] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0188] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0189] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0190] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A spectrum sensing method based on strong graph product quadratic form, characterized in that, include: Calculate the grouped summation power spectrum and autocorrelation function of the observed signal; Based on the grouped summation power spectrum and the autocorrelation function, construct the subquantization plot of the grouped summation power spectrum and the subquantization plot of the autocorrelation function, respectively. The strong graph product and the graph signal of the strong graph product are calculated based on the grouped summation power spectrum subquantization map and the autocorrelation function subquantization map; The test statistic is calculated based on the graph signal, and the test statistic is compared with the decision threshold to determine whether an authorized user exists.

2. The spectrum sensing method based on strong graph product quadratic form according to claim 1, characterized in that, The calculation process for the grouped summation power spectrum is as follows: The power spectrum is uniformly divided into Block, the number of observed signal samples in each block is , ,and It can be Divisible; The samples within each block are summed to obtain the grouped summation power spectrum. : ； Among them, the observed signal power spectrum The calculation formula is: ； In the formula, M is the total number of observed signal samples, and j is the imaginary unit in the complex number, i.e. .

3. The spectrum sensing method based on strong graph product quadratic form according to claim 1, characterized in that, The calculation process of the autocorrelation function is as follows: First, remove the observed signal. The mean of the values ​​is used to obtain the observation signal with zero mean. : ； In the formula, The mean of the observed signal, This represents the total number of observed signal samples. Then calculate the autocorrelation function. : ； In the formula, Due to the symmetry of the autocorrelation function, the right half of the autocorrelation function is chosen, i.e. .

4. The spectrum sensing method based on strong graph product quadratic form according to claim 1, characterized in that, The process of constructing the sub-quantization graph is as follows: Select the number of vertices Two sub-quantized graphs are constructed by taking the grouped summation power spectrum and autocorrelation function as input signals, respectively. The specific construction method is as follows: First, the input signal Normalization is performed to obtain the normalized signal. : ； In the formula, and These are the maximum and minimum values ​​of the input signal, respectively. The number of samples of the input signal; Secondly, for a given number of vertices, i.e., the number of quantization levels , Quantization sequence after uniform quantization Represented as: ； In the formula, ; Finally, the quantized sequence is mapped to the vertex set according to the mapping rules. ; The mapping rule is: ； The edges of the graph are determined by the amplitude changes between adjacent samples in the quantized sequence; for , ,in Step size; At least once and At that time, the vertex and vertex corresponding edges They are connected; otherwise, the vertices are connected. and vertex The spaces are not connected; By traversing all input signal samples, the corresponding edge set is obtained as follows: .

5. The spectrum sensing method based on strong graph product quadratic form according to claim 1, characterized in that, The process of calculating the strong graph product is as follows: make For the generated having A sub-quantized graph of vertices, where, Let be a vertex of the graph. Let be the edges of the graph. Let be the adjacency matrix of the graph; the strong graph product is represented as: ； Number of vertices in a strong graph product The adjacency matrix of the strong graph product is represented as: ； In the formula, The dimension is The identity matrix, This represents the Kronecker product of the matrix.

6. The spectrum sensing method based on strong graph product quadratic form according to claim 1, characterized in that, The graph signal calculation process for the strong graph product is as follows: Calculate the grouped summation power spectral quantization plots separately. Vertex probability vectors and autocorrelation function subquantized graph Quantization interval sample sum: Grouped summation power spectral quantization plot The vertex probability vector x is represented as: ； ； In the formula, These are the probability vectors for each vertex; This indicates a mapping to a graph. The first in The total number of quantized samples corresponding to each vertex; The number of vertices; Autocorrelation function subquantization plot The quantization interval sample and y are represented as: ； ； In the formula, for , will be quantified A subset of normalized signal samples at each quantization level is denoted as , For the first The number of samples in each subset; These represent the samples and sums for each quantization interval; Define the vertex probability vector and the Kronecker product of the quantized interval sample sums. Graph signal as a strong graph product: ； In the formula, These are the Kronecker product of the probability vectors of each vertex and the sum of samples in the quantized interval, respectively.

7. The spectrum sensing method based on strong graph product quadratic form according to claim 1, characterized in that, The process for calculating the test statistic is as follows: According to the signal in the figure Laplacian matrix of strong graph product Calculate the strong graph product test statistic. : ; The process of calculating the Laplace matrix of a graph is as follows: picture adjacency matrix Represented as: ； In the formula, , To quantify the number of levels; and ; picture degree diagonal matrix Represented as: ； In the formula, It is a diagonal matrix representation; Respectively with the vertex The number of connected edges; The Laplace matrix L of the graph is represented as: 。 8. The spectrum sensing method based on strong graph product quadratic form according to claim 1, characterized in that, The process of comparing the test statistic with the decision threshold is as follows: First, a binary hypothesis test is used to represent the single-node spectrum sensing problem as: ； In the formula, , For observing signals, For channel gain, It is additive white Gaussian noise. The table represents a pure signal; This indicates the presence of a licensed user signal in the channel. This indicates that there are no licensed user signals in the channel; Judgment threshold calculation with The training data for the detection statistic under the null hypothesis is selected from commonly used unimodal distributions, and the distribution that minimizes the fitting error of the detection statistic under the null hypothesis is used as the approximate probability distribution of the detection statistic. The Birnbaum-Saunders distribution can effectively fit the null hypothesis. Assuming the probability distribution of the detection statistic, therefore, for a given false alarm probability... Based on the constant false alarm rate criterion, an approximate decision threshold is obtained through the formula: ； ； In the formula, Let Birnbaum–Saunders distribution be the probability density function and scale parameter. Shape parameters ; Approximate expression for decision threshold for: ； In the formula, For Birnbaum-Saunders variables, the inverse cumulative distribution function is used. Compare the test statistic with the decision threshold to make a test decision: 。 9. A spectrum sensing device based on a strong graph product quadratic form, characterized in that, include: The subquantization graph construction module is used to: calculate the grouped summation power spectrum and autocorrelation function of the observed signal; Based on the grouped summation power spectrum and the autocorrelation function, construct the subquantization plot of the grouped summation power spectrum and the subquantization plot of the autocorrelation function, respectively. The judgment module is used to: calculate the graph signal of the strong graph product and the graph signal of the strong graph product based on the grouped summation power spectrum subquantization graph and the autocorrelation function subquantization graph; The test statistic is calculated based on the graph signal, and the test statistic is compared with the decision threshold to determine whether an authorized user exists.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the spectrum sensing method based on strong graph product quadratic form as described in any one of claims 1 to 8.

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