CN-122002299-A - Spectrum sensing method and device based on strong graph product quadratic form

CN122002299ACN 122002299 ACN122002299 ACN 122002299ACN-122002299-A

Abstract

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

Inventors

WU SHANSHAN
HU GUOBING
GU BIN

Assignees

南京信息职业技术学院

Dates

Publication Date: 20260508
Application Date: 20260127

Claims (10)

1. The spectrum sensing method based on the strong graph product quadratic form is characterized by comprising the following steps of: Calculating a grouping sum power spectrum and an autocorrelation function of the observed signal; Respectively constructing a sub-quantization map of the grouping sum power spectrum and a sub-quantization map of the autocorrelation function according to the grouping sum power spectrum and the autocorrelation function; Calculating a strong graph product and a graph signal of the strong graph product according to the grouping sum power spectrum sub-quantization graph and the autocorrelation function sub-quantization graph; And calculating test statistics according to the image signals, and comparing the test statistics with a decision threshold to judge whether an authorized user exists or not.
2. The spectrum sensing method based on strong graph product quadratic form according to claim 1, wherein the calculation process of the grouping summation power spectrum is: Evenly dividing the power spectrum into Blocks, the number of observation signal samples in each block is , And (2) and Can be used as Removing; summing the samples within each block to obtain a group summed power spectrum : ; Wherein the signal is observed Power spectrum of (2) The calculation formula is as follows: ; Wherein M is the total sample number of the observed signal, 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, wherein the calculation process of the autocorrelation function is: first remove the observed signal To obtain the zero-mean observed signal : ; In the formula, In order to observe the mean value of the signal, The total sample number of the observation signal; Thereby calculating an autocorrelation function : ; In the formula, And, due to the symmetry of the autocorrelation function, the right half of the autocorrelation function is selected, i.e 。
4. The spectrum sensing method based on strong graph product quadratic form according to claim 1, wherein the process of constructing the sub-quantization graph is: Selecting the number of vertices Respectively taking the grouping summation power spectrum and the autocorrelation function as input signals to construct two sub-quantized graphs; the specific construction method comprises the following steps: First, to the input signal Normalizing to obtain normalized signal : ; In the formula, And Respectively the maximum and minimum of the input signal, Is the number of samples of the input signal; second, for a given number of vertices, i.e. quantization levels , Uniformly quantized quantization sequence Expressed as: ; in the formula, ; Finally, mapping the quantized sequence to the vertex set according to the mapping rule ; The mapping rule is: ; the edges of the graph are determined by the amplitude variation between adjacent samples of the quantized sequence; For the following , Wherein Is the step length; At least once present And is also provided with When the vertex is And a vertex Corresponding edge Is connected, otherwise the vertex And a vertex The two are not communicated; by traversing all input signal samples, the corresponding edge set is obtained as 。
5. The spectrum sensing method based on strong graph product quadratic form according to claim 1, wherein the process of calculating strong graph product is: Order the To generate with A sub-quantized map of the vertices, wherein, As the vertex of the figure, As an edge of the figure, Is an adjacency matrix of the graph, and the strong graph product is expressed as: ; Number of vertices in strong graph product The adjacency matrix of the strong graph product is expressed as: ; in the formula, Representing dimensions as Is used for the matrix of units of (a), Representing the kronecker product of the matrix.
6. The spectrum sensing method based on strong graph product quadratic form according to claim 1, wherein the graph signal calculation process of the strong graph product is: Separately computing a sub-quantized map of a packet-sum power spectrum Vertex probability vector and autocorrelation function sub-quantized graph of (2) Quantization interval samples of (a) and: Grouping sum power spectrum sub-quantization map Is expressed as the vertex probability vector x: ; ; in the formula, Respectively representing each vertex probability vector; mapping of representation representations to graphs The first of (3) The total number of quantized samples corresponding to the vertexes; The number of the top points is counted; Auto-correlation function sub-quantization map The quantization interval samples and y of (2) are expressed as: ; ; wherein for the formula (VI) Will be quantized to Normalized signal sample subsets of the quantization levels are noted as , Is the first The number of samples in the subset; respectively summing samples of each quantization interval; cronecker product defining vertex probability vector and quantization interval sample sum Graph signal as strong graph product: ; in the formula, The kronecker product of each vertex probability vector and quantization interval sample sum is respectively.
7. The spectrum sensing method based on strong graph product quadratic form according to claim 1, wherein the process of calculating test statistics is: From picture signals Laplacian matrix integrated with strong graph Calculation of strong graph product test statistic : ; The Laplace matrix calculation process of the graph is as follows: Drawing of the figure Adjacent matrix of (a) Expressed as: ; in the formula, , Number of quantization steps; And is also provided with ; Drawing of the figure Degree diagonal matrix of (a) Expressed as: ; in the formula, A diagonal matrix representation; Respectively are respectively with the vertexes 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, wherein the comparing and judging process of the test statistic and the decision threshold is: Firstly, adopting binary hypothesis test to represent the single-node spectrum sensing problem as: ; in the formula, , In order to observe the signal, For the channel gain to be a function of the channel gain, In the case of additive white gaussian noise, The table is a pure signal; indicating the presence of an authorized user signal in the channel, Indicating that no authorized user signal is present in the channel; By means of decision threshold calculation The assumed test statistic training data is used to screen out the distribution with minimum fitting error to the test statistic under the null hypothesis from the common unimodal distribution as the approximate probability distribution of the test statistic, and the Birnbaum-Saunders distribution can be effectively fitted Assuming a probability distribution of detection statistics, therefore, for a given false alarm probability According to the constant false alarm criterion, obtaining an approximate judgment threshold through a formula: ; ; in the formula, Probability density function, scale parameter, for Birnbaum-Saunders distribution Shape parameter ; Decision threshold approximation expression The method comprises the following steps: ; in the formula, An inverse cumulative distribution function of Birnbaum-Saunders variables; comparing the test statistic with a judgment threshold, and performing test judgment: 。
9. a spectrum sensing device based on strong graph product quadratic form, comprising: the sub-quantization diagram construction module is used for calculating a grouping summation power spectrum and an autocorrelation function of an observation signal; Respectively constructing a sub-quantization map of the grouping sum power spectrum and a sub-quantization map of the autocorrelation function according to the grouping sum power spectrum and the autocorrelation function; The judging module is used for calculating a strong graph product and a graph signal of the strong graph product according to the grouping sum power spectrum sub-quantized graph and the autocorrelation function sub-quantized graph; And calculating test statistics according to the image signals, and comparing the test statistics with a decision threshold to judge whether an authorized user exists or not.
10. A computer readable storage medium having stored thereon a computer program/instruction which, when executed by a processor, implements the steps of the strong-product quadratic based spectrum sensing method of any one of claims 1 to 8.

Description

Spectrum sensing method and device based on strong graph product quadratic form Technical Field The invention relates to a spectrum sensing method and device based on strong graph product quadratic form, and belongs to the technical field of signal processing. Background Cognitive Radio (CR) has become a key technology for alleviating the problem of scarce spectrum resources that are increasingly serious in the current generation, and is also an important supporting technology for implementing intelligent information transmission in 5G and 6G mobile communication systems. The spectrum sensing is a key link in the processing of cognitive radio signals, and provides support for secondary users to realize opportunistic dynamic access by detecting whether signals of authorized users exist or not, so that the spectrum utilization efficiency is improved. In spite of some progress in the extensive research on spectrum sensing, in an actual signal processing scene, spectrum sensing performance in a low signal-to-noise environment tends to be degraded due to multipath effects or channel fading. This may not only lead to reduced spectrum efficiency but may also cause interference to authorized users. Therefore, how to achieve an effective and reliable detection result under complex environments such as low signal-to-noise ratio and fading channel is still an important and realistic challenge. Disclosure of Invention The invention aims to provide a frequency spectrum sensing method and device based on a strong graph product quadratic form, which are used for realizing effective and reliable detection under complex transmission environments such as low signal-to-noise ratio, fading channels and the like by taking a grouping summation power spectrum (BSPS) of an observation signal and an autocorrelation function (ACF) as independent inputs of graph transformation, constructing a strong graph product, calculating test statistics and comparing with a decision threshold to judge whether an authorized user exists. In order to achieve the above purpose, the invention is realized by adopting the following technical scheme. In one aspect, the present invention provides a spectrum sensing method based on strong graph product quadratic form, including: Calculating a grouping sum power spectrum and an autocorrelation function of the observed signal; Respectively constructing a sub-quantization map of the grouping sum power spectrum and a sub-quantization map of the autocorrelation function according to the grouping sum power spectrum and the autocorrelation function; Calculating a strong graph product and a graph signal of the strong graph product according to the grouping sum power spectrum sub-quantization graph and the autocorrelation function sub-quantization graph; And calculating test statistics according to the image signals, and comparing the test statistics with a decision threshold to judge whether an authorized user exists or not. Optionally, the calculation process of the grouping sum power spectrum is as follows: Evenly dividing the power spectrum into Blocks, the number of observation signal samples in each block is,And (2) andCan be used asRemoving; summing the samples within each block to obtain a group summed power spectrum : ; Wherein the signal is observedPower spectrum of (2)The calculation formula is as follows: ; Wherein M is the total sample number of the observed signal, j is the imaginary unit in the complex number, i.e 。 Optionally, the calculating process of the autocorrelation function is as follows: first remove the observed signal To obtain the zero-mean observed signal: ; In the formula,In order to observe the mean value of the signal,The total sample number of the observation signal; Thereby calculating an autocorrelation function : ; In the formula,And, due to the symmetry of the autocorrelation function, the right half of the autocorrelation function is selected, i.e。 Optionally, the process of constructing the sub-quantization map is as follows: Selecting the number of vertices Respectively taking the grouping summation power spectrum and the autocorrelation function as input signals to construct two sub-quantized graphs; the specific construction method comprises the following steps: First, to the input signal Normalizing to obtain normalized signal: ; In the formula,AndRespectively the maximum and minimum of the input signal,Is the number of samples of the input signal; second, for a given number of vertices, i.e. quantization levels ,Uniformly quantized quantization sequenceExpressed as: ; in the formula, ; Finally, mapping the quantized sequence to the vertex set according to the mapping rule; The mapping rule is: ; the edges of the graph are determined by the amplitude variation between adjacent samples of the quantized sequence; For the following ,WhereinIs the step length; At least once present And is also provided withWhen the vertex isAnd a vertexCorresponding edgeIs connected, otherwis