Spectrum sensing method based on characteristic value of Kendall rank correlation matrix
Through the spectrum perception method based on the Kendall rank correlation matrix eigenvalue, the problem of performance deterioration of traditional methods in pulse noise environment is solved, and the robustness and accuracy of spectrum perception under pulse interference is improved.
Patent Information
- Application Number
- CN202510410083.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-02
- Publication Date
- 2025-07-04
AI Technical Summary
The performance of traditional spectrum perception methods rapidly deteriorates in impulse noise environments, resulting in a significant reduction in the system signal-to-noise ratio and even failure.
Using a spectrum perception method based on the eigenvalue of the Kendall rank correlation matrix, a Kendall rank correlation matrix is formed by calculating the Kendall rank correlation coefficient of the received signal of the multiple sensor, an eigenvalue is obtained and a test statistic of the mathematical average and the root mean square ratio is constructed, and it is compared with the perceptual threshold to complete spectrum perception.
Effectively suppress large outliers in pulse noise, improve the robustness and accuracy of spectrum perception, and ensure excellent perceptual performance in pulse interference environments.
Smart Images
Figure CN120264445A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of wireless communication, and more specifically, it is a spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix. Background Art
[0002] With the rapid development of wireless communication technology, the demand for spectrum resources is increasing day by day, and the scarcity of spectrum resources has become a bottleneck restricting the further development of wireless communication. To solve this problem, cognitive radio technology has emerged, which improves the spectrum utilization efficiency by dynamically managing spectrum resources. Spectrum sensing, as a basic function of cognitive radio systems, its core task is to find idle frequency bands by continuously monitoring the status of primary users, so as to achieve dynamic access to the spectrum.
[0003] However, in the actual wireless communication environment, the noise sources are complex and variable, and impulsive noise is particularly common. Impulsive noise has characteristics such as short duration and large amplitude, which seriously affects the performance of spectrum sensing. Traditional spectrum sensing methods, such as energy detectors, perform well in Gaussian noise environments, but in impulsive noise environments, due to the large outliers of impulsive noise, the signal-to-noise ratio of the system will be significantly reduced, resulting in a rapid deterioration and even failure of the performance of traditional methods.
[0004] Therefore, those skilled in the art have proposed a spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix to solve the problems raised in the background art. Summary of the Invention
[0005] To solve the above technical problems, the present invention provides a spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix to solve the problems in the prior art that in an impulsive noise environment, due to the large outliers of impulsive noise, the signal-to-noise ratio of the system will be significantly reduced, resulting in a rapid deterioration and even failure of the performance of traditional methods.
[0006] In a first aspect, an embodiment of the present invention provides a spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix, including:
[0007] S1. Obtain the observation signals received by multiple sensors;
[0008] S2. Calculate the Kendall rank correlation coefficient between any two signals to form a Kendall rank correlation matrix;
[0009] S3. Obtain the eigenvalues of the Kendall rank correlation matrix, and calculate the mathematical mean and root mean square of the eigenvalues;
[0010] S4. Construct a test statistic based on the ratio of the mathematical mean of the eigenvalues and the root mean square of the eigenvalues;
[0011] S5. Compare the size of the test statistic and the sensing threshold to complete the sensing process.
[0012] Preferably, the observed signal is specifically:
[0013] x m (n) = h m s(n) + z m (n)
[0014] n = 1, 2…, N
[0015] m = 1, 2…, M
[0016] Wherein, x m (n) is the observed signal received by the m-th sensor at the sampling time n, s(n) is the source signal to be sensed, h m represents the gain coefficient of the m-th sensor, z m (n) represents the background noise, M is the number of sensors, and N is the signal length.
[0017] Preferably, calculating the Kendall rank correlation coefficient between any two signals to form the Kendall rank correlation matrix is specifically:
[0018]
[0019]
[0020] Wherein, r kl represents the Kendall rank correlation coefficient between the k-th signal and the l-th signal, R represents the Kendall rank correlation matrix, sgn(·) is the sign function, and M is the number of sensors.
[0021] Preferably, obtaining the eigenvalues of the Kendall rank correlation matrix and calculating the mathematical mean and root mean square of the eigenvalues is specifically:
[0022]
[0023] Wherein, represents the M eigenvalues of the Kendall rank correlation matrix, E1 represents the mathematical mean of the eigenvalues, E2 represents the root mean square of the eigenvalues, and M is the number of sensors.
[0024] Preferably, constructing a test statistic based on the ratio of the mathematical mean of the eigenvalues and the root mean square of the eigenvalues is specifically:
[0025]
[0026] Wherein, T represents the statistic, and M is the number of sensors.
[0027] Preferably, comparing the size of the test statistic and the sensing threshold to complete the sensing process is specifically:
[0028] Compare the size of the test statistic and the perception threshold. If the test statistic is less than the perception threshold, the spectrum is occupied; otherwise, the spectrum is considered idle.
[0029] In a second aspect, an embodiment of the present invention provides a spectrum sensing system based on the eigenvalues of the Kendall rank correlation matrix, which is applied to the above-mentioned spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix, and includes:
[0030] A signal acquisition module, configured to acquire the observed signals received by multiple sensors;
[0031] A Kendall rank correlation matrix construction module, configured to calculate the Kendall rank correlation coefficient of any two signals and form a Kendall rank correlation matrix;
[0032] An eigenvalue calculation module, configured to obtain the eigenvalues of the Kendall rank correlation matrix and calculate the mathematical average and root mean square of the eigenvalues;
[0033] A test statistic construction module, configured to construct a test statistic based on the ratio of the mathematical average of the eigenvalues and the root mean square of the eigenvalues;
[0034] A spectrum sensing decision module, configured to compare the size of the test statistic and a preset perception threshold, and complete the spectrum sensing process according to the comparison result. If the test statistic is less than the perception threshold, it is determined that the spectrum is occupied; otherwise, it is determined that the spectrum is idle.
[0035] In a third aspect, an embodiment of the present invention further provides a computer storage medium, on which a computer program is stored, and when the program is executed by a processor, the above-mentioned method is implemented.
[0036] In a fourth aspect, an embodiment of the present invention further provides a terminal device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the above-mentioned method is implemented.
[0037] Compared with the prior art, the present invention has the following beneficial effects:
[0038] The present invention effectively suppresses large outliers in impulse noise through Kendall rank correlation transformation, and constructs a statistic based on the mathematical average and root mean square of the eigenvalues of the Kendall rank correlation matrix, and has strong robustness under impulse interference; therefore, in an environmental noise containing impulse components, the spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix has excellent sensing performance. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 It is a schematic flowchart of the spectrum sensing method of the present invention;
[0040] Figure 2 It is a comparison graph of the detection probability of the energy detector and the Kendall rank correlation matrix eigenvalue detector of the present invention for spectrum sensing in a pulsed noise environment;
[0041] Figure 3 It is a framework diagram of the spectrum sensing system based on the eigenvalues of the Kendall rank correlation matrix of the present invention. Specific implementation mode
[0042] The following further describes the implementation mode of the present invention in detail in conjunction with the drawings and embodiments. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.
[0043] Embodiment 1: The present invention provides a spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix, as Figure 1 shown, including:
[0044] S1. Obtain the observation signals received by multiple sensors;
[0045] S2. Calculate the Kendall rank correlation coefficients of any two signals to form a Kendall rank correlation matrix;
[0046] S3. Obtain the eigenvalues of the Kendall rank correlation matrix, and calculate the mathematical average and root mean square of the eigenvalues;
[0047] S4. Construct a test statistic based on the ratio of the mathematical average of the eigenvalues and the root mean square of the eigenvalues;
[0048] S5. Compare the size of the test statistic and the sensing threshold to complete the sensing process.
[0049] As can be seen from the above, this method effectively suppresses the large outliers in the pulsed noise through the Kendall rank correlation transformation, and constructs a statistic based on the mathematical average and root mean square of the eigenvalues of the Kendall rank correlation matrix, thus showing strong robustness in a pulsed interference environment; in an environmental noise containing pulsed components, this method can ensure excellent spectrum sensing performance.
[0050] As a preferred implementation mode of this embodiment, the observation signal received by the m-th sensor at time n has the following form:
[0051] x m (n) = h m s(n) + z m (n)
[0052] n = 1, 2…, N
[0053] m = 1, 2…, M
[0054] where, x m$(n)$ is the observation signal received by the $m$-th sensor at sampling time $n$, $s(n)$ is the source signal to be sensed, and $h$ m represents the gain coefficient of the $m$-th sensor, and $z$ m $(n)$ represents the background noise, $M$ is the number of sensors, and $N$ is the signal length.
[0055] As can be seen from the above, the specific composition of the observation signal is clarified, including factors such as the source signal to be sensed, the gain coefficient of the sensor, and the background noise. This provides an accurate data basis for the subsequent calculation of the Kendall rank correlation coefficient and the spectrum sensing process; by considering the gain coefficient of the sensor and the background noise, this method can more accurately describe the signal situation in the actual wireless communication environment, thereby improving the accuracy and reliability of spectrum sensing.
[0056] As a preferred implementation manner of this embodiment, the calculation of the Kendall rank correlation coefficient between any two signals to form a Kendall rank correlation matrix is specifically as follows:
[0057]
[0058] where $r$ kl represents the Kendall rank correlation coefficient between the $k$-th signal and the $l$-th signal, $R$ represents the Kendall rank correlation matrix, $sgn(·)$ is the sign function, and $M$ is the number of sensors.
[0059] As can be seen from the above, this method can quantify the correlation between any two signals and comprehensively reflect the overall correlation structure between multiple signals by constructing a Kendall rank correlation matrix; the Kendall rank correlation coefficient is robust to large outliers in impulse noise and can effectively suppress the influence of these outliers on the correlation analysis; therefore, in an impulse interference environment, this method can provide more accurate and reliable correlation information, laying a solid foundation for subsequent eigenvalue calculation and spectrum sensing decision-making.
[0060] As a preferred implementation manner of this embodiment, the obtaining of the eigenvalues of the Kendall rank correlation matrix and the calculation of the mathematical mean and root mean square of the eigenvalues are specifically as follows:
[0061]
[0062] where represents the $M$ eigenvalues of the Kendall rank correlation matrix, $E1$ represents the mathematical mean of the eigenvalues, $E2$ represents the root mean square of the eigenvalues, and $M$ is the number of sensors.
[0063] As can be seen from the above, this method can extract the main information in the Kendall rank correlation matrix, i.e., the eigenvalues, and further summarize the statistical characteristics of these eigenvalues by calculating the mathematical mean and root mean square; the mathematical mean of the eigenvalues reflects the overall level of the matrix eigenvalues, while the root mean square reflects the degree of dispersion of the eigenvalues; the above statistics provide key data for constructing the test statistic subsequently, which helps to more accurately judge the occupancy status of the spectrum during the spectrum sensing process, thereby improving the utilization efficiency of spectrum resources and the performance of wireless communication systems.
[0064] As a preferred implementation manner of this embodiment, constructing the test statistic based on the ratio of the mathematical mean of the eigenvalues and the root mean square of the eigenvalues is specifically as follows:
[0065]
[0066] Where T represents the statistic and M is the number of sensors.
[0067] As can be seen from the above, this method can use the statistical characteristics of the eigenvalues to construct an effective test statistic for the decision-making process of spectrum sensing; by comparing the test statistic with a preset sensing threshold, it can accurately judge whether the spectrum is occupied; this method not only considers the overall level (mathematical mean) of the eigenvalues, but also considers the degree of dispersion (root mean square) of the eigenvalues, so as to be able to more comprehensively reflect the eigenvalue distribution characteristics of the Kendall rank correlation matrix; therefore, during the spectrum sensing process, this method can provide a more reliable and accurate decision-making basis, which helps to improve the utilization efficiency of spectrum resources and the performance of wireless communication systems.
[0068] As a preferred implementation manner of this embodiment, comparing the magnitudes of the test statistic and the sensing threshold to complete the sensing process is specifically as follows:
[0069] Compare the magnitudes of the test statistic and the sensing threshold. If the test statistic is less than the sensing threshold, the spectrum is occupied; otherwise, it is considered that the spectrum is idle.
[0070] Specifically, the spectrum sensing process is realized through the following decision:
[0071]
[0072] As can be seen from the above, by setting a reasonable sensing threshold and comparing the test statistic with it, the conclusion of whether the spectrum is occupied can be quickly obtained; this method not only simplifies the decision-making process of spectrum sensing, but also improves the accuracy and reliability of the decision-making; in a wireless communication system, this helps to achieve the effective utilization and dynamic management of spectrum resources, thereby meeting the growing spectrum demand and promoting the further development of wireless communication technologies.
[0073] To analyze the performance of the Kendall rank correlation matrix eigenvalue detector and the energy detector in spectrum sensing under impulse noise, the present invention will be verified through Monte Carlo experiments.
[0074] The experimental parameters are set as follows:
[0075] The source signal is randomly generated by a signal of length N = 100 that follows a standard normal distribution.
[0076] The impulse noise is simulated by a mixture of Gaussian distributions:
[0077]
[0078] Among them, ε = 0.05 represents the probability of the impulse component occurring in the entire impulse noise environment, and δ2 = 10 >> δ1 represents the standard deviation of the impulse component; at this time, the signal-to-noise ratio of the received signal can be defined as:
[0079]
[0080] Through Monte Carlo experiments, by comparing and analyzing the performance of the Kendall rank correlation matrix eigenvalue detector and the energy detector at different signal-to-noise ratios, it can be verified that the Kendall rank correlation matrix eigenvalue detector is robust in an impulse noise environment; the number of experiments is 10 4 times, the false alarm probability P f = 0.1, the number of sensors M = 4, and the gain coefficients h1 = h2 =... = h4 = 1; the experimental results are as Figure 2 shown.
[0081] From Figure 2 the experimental results, it can be seen that due to the presence of the impulse component, the detection probability curve of the energy detector is close to a horizontal line of P f = 0.1 and completely loses the detection effect, while the Kendall rank correlation matrix eigenvalue detector has a high detection probability, demonstrating robustness to impulse interference, indicating that the Kendall rank correlation matrix eigenvalue detector can be used as a powerful tool for spectrum sensing in an impulse interference environment.
[0082] Example 2: Different from Example 1, before calculating eigenvalues such as the Kendall rank correlation coefficient, multi-scale feature extraction is introduced. For example, using the wavelet transform algorithm, features of different scales are extracted from the original signal. The formula of the wavelet transform algorithm includes:
[0083]
[0084] Among them, x[n] is the original signal; ψ j,k [n] is the wavelet function, where j is the scale parameter and k is the translation parameter; C j, where k is the wavelet coefficient, representing the characteristics of the signal at different scales.
[0085] As can be seen from the above, this method can capture the characteristics of the signal more comprehensively; by adjusting the scale parameter and translation parameter, the wavelet transform algorithm can analyze the signal in detail at different scales and extract the characteristic information contained in different frequency ranges. The above multi-scale features provide a richer data basis for the subsequent calculation of Kendall rank correlation coefficient and spectrum sensing, which helps to enhance the adaptability and sensing accuracy of the spectrum sensing method to complex signal environments.
[0086] Embodiment 3: Different from Embodiment 1, in step S3, after extracting the multi-scale features, they can be combined with the features of the Kendall rank correlation matrix to construct a more comprehensive test statistic; for example, the energy or entropy of each IMF can be used as an additional feature to construct a new test statistic together with the eigenvalues of the Kendall rank correlation matrix. The construction of the test statistic combined with multi-scale features is as follows:
[0087] Let E i be the energy of the i-th IMF, H i be its entropy, and λ j be the j-th eigenvalue of the Kendall rank correlation matrix. The following test statistic can be constructed:
[0088]
[0089] where mean(λ) is the mathematical average of the eigenvalues of the Kendall rank correlation matrix; sum(E) is the sum of the energies of all IMFs; and max(H) is the maximum value among the entropies of all IMFs.
[0090] As can be seen from the above, this step can comprehensively reflect the characteristics of the signal by integrating various feature information; by using the energy and entropy of the IMF as additional features and combining them with the eigenvalues of the Kendall rank correlation matrix, a more comprehensive statistic can be constructed. This statistic not only contains the energy distribution information of the signal at different scales but also considers the correlation structure of the signal; this comprehensive feature fusion method helps to enhance the adaptability and robustness of the spectrum sensing method to complex signal environments, improve the accuracy and reliability of spectrum sensing, and thus better meet the requirements of wireless communication systems for efficient utilization of spectrum resources.
[0091] Embodiment 4:
[0092] As Figure 3 shown, Figure 3 A spectrum sensing system based on the eigenvalues of the Kendall rank correlation matrix provided by an embodiment of the present invention is applied to the above spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix, including:
[0093] A signal acquisition module, configured to acquire observation signals received by multiple sensors;
[0094] A Kendall rank correlation matrix construction module, configured to calculate the Kendall rank correlation coefficient between any two signals and form a Kendall rank correlation matrix;
[0095] An eigenvalue calculation module, configured to obtain the eigenvalues of the Kendall rank correlation matrix and calculate the mathematical average and root mean square of the eigenvalues;
[0096] A test statistic construction module, configured to construct a test statistic based on the ratio of the mathematical average of the eigenvalues to the root mean square of the eigenvalues;
[0097] A spectrum sensing decision module, configured to compare the test statistic with a preset sensing threshold, and complete the spectrum sensing process according to the comparison result. If the test statistic is less than the sensing threshold, it is determined that the spectrum is occupied; otherwise, it is determined that the spectrum is idle.
[0098] Embodiment 5:
[0099] The embodiment of the present invention further provides a computer storage medium, on which a computer program is stored, and when the program is executed by a processor, the above-mentioned spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix is implemented.
[0100] Embodiment 6:
[0101] The embodiment of the present invention further provides a terminal device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the computer program, the above-mentioned spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix is implemented.
[0102] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above-mentioned exemplary embodiments, and can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, in any aspect, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention.
Claims
1. A spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix, characterized in that, Including: S1. Obtain the observation signals received by multiple sensors; S2. Calculate the Kendall rank correlation coefficient between any two signals to form a Kendall rank correlation matrix; S3. Obtain the eigenvalues of the Kendall rank correlation matrix, and calculate the mathematical mean and root mean square of the eigenvalues; S4. Construct a test statistic based on the ratio of the mathematical mean of the eigenvalues and the root mean square of the eigenvalues; S5. Compare the size of the test statistic and the sensing threshold to complete the sensing process.
2. The spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix according to claim 1, wherein: The observation signals are specifically: x m y(n) = h m s(n) + z m (n) It should be noted that in the original text, the variable name in seems incorrect. It should probably be "y(n)" instead of "(n)". This translation is based on the corrected assumption. If the original is indeed "(n)", it might be a very unusual or incorrect notation in this context. n = 1, 2…, N m = 1, 2…, M where x m (n) is the observation signal received by the m-th sensor at sampling time n, s(n) is the source signal to be sensed, h m represents the gain coefficient of the m-th sensor, z m (n) represents the background noise, M is the number of sensors, and N is the signal length.
3. The spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix according to claim 1, characterized in that: The calculation of the Kendall rank correlation coefficient between any two signals to form a Kendall rank correlation matrix is specifically: where r kl represents the Kendall rank correlation coefficient between the k-th signal and the l-th signal, R represents the Kendall rank correlation matrix, sgn(·) is the sign function, and M is the number of sensors.
4. The spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix according to claim 1, wherein: The obtaining of the eigenvalues of the Kendall rank correlation matrix and the calculation of the mathematical mean and root mean square of the eigenvalues are specifically: Among them, represents M eigenvalues of the Kendall rank correlation matrix, E1 represents the mathematical average of the eigenvalues, E2 represents the root mean square of the eigenvalues, and M is the number of sensors.
5. The spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix according to claim 1, wherein: The construction of the test statistic based on the ratio of the mathematical mean of the eigenvalues and the root mean square of the eigenvalues is specifically: where T represents the statistic and M is the number of sensors.
6. The spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix according to claim 1, characterized in that: The comparison of the size of the test statistic and the sensing threshold to complete the sensing process is specifically: Compare the size of the test statistic and the sensing threshold. If the test statistic is less than the sensing threshold, the spectrum is occupied; otherwise, it is considered that the spectrum is idle.
7. A spectrum sensing system based on the eigenvalues of the Kendall rank correlation matrix, characterized in that: Applied to a spectrum sensing method based on the eigenvalues of the Kendall rank correlation matrix as described in any one of claims 1 - 6, including: A signal acquisition module for obtaining the observation signals received by multiple sensors; A Kendall rank correlation matrix construction module for calculating the Kendall rank correlation coefficient between any two signals and forming a Kendall rank correlation matrix; An eigenvalue calculation module for obtaining the eigenvalues of the Kendall rank correlation matrix and calculating the mathematical mean and root mean square of the eigenvalues; A test statistic construction module for constructing a test statistic based on the ratio of the mathematical mean of the eigenvalues and the root mean square of the eigenvalues; A spectrum sensing decision module for comparing the size of the test statistic and a preset sensing threshold, and completing the spectrum sensing process according to the comparison result. If the test statistic is less than the sensing threshold, it is determined that the spectrum is occupied; otherwise, it is determined that the spectrum is idle.
8. A computer storage medium, on which a computer program is stored, characterized in that, When the program is executed by a processor, the method described in claims 1 - 6 is implemented.
9. A terminal device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, the method described in claims 1 - 6 is implemented.