Signal Detection Method and System Based on Anti-Eigenvalues of Spearman Rank Correlation Matrix

Abstract

The present invention provides a signal detection method and system based on the anti-eigenvalue of the Spearman rank correlation matrix. The method of the present invention includes: obtaining observation signals received by multiple sensors; calculating the Spearman rank correlation coefficients of any two signals to form a Spearman rank correlation matrix; obtaining the eigenvalues of the Spearman rank correlation matrix and calculating the corresponding anti-eigenvalues; calculating a statistic based on the sum of the anti-eigenvalues; setting a detection threshold and comparing the magnitudes of the statistic and the detection threshold to complete the detection process. The present invention uses the Spearman rank correlation transformation of the signal to suppress the negative impact of impulse noise, designs a corresponding statistic by calculating the sum of the anti-eigenvalues of the Spearman rank correlation matrix, and thus realizes high-performance signal detection under impulse interference. The present invention has strong robustness against impulse noise and can perform signal detection in background noise containing impulse components.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and more particularly, to a signal detection method and system based on the anti-eigenvalues of the Spearman rank correlation matrix. Background Art

[0002] In the field of communication technologies, signal detection is one of the core tasks of signal processing, and its purpose is to identify the presence or absence of useful signals from complex background noise. The accuracy and reliability of signal detection are crucial for subsequent operations such as parameter estimation and coding identification. Signal detection methods usually need to consider the statistical characteristics of noise to optimize the detection performance. In an ideal situation, background noise is usually assumed to follow a Gaussian distribution, and in this case, traditional energy detectors can achieve good performance. However, the noise in the actual communication environment is often more complex, especially the presence of impulse noise, which poses new challenges to signal detection.

[0003] Currently, energy detectors are widely used in the field of signal detection due to their excellent characteristics such as easy implementation, simple structure, and complete theory. Energy detectors determine the presence or absence of signals by measuring the energy of the signals. When the background noise follows a Gaussian distribution, energy detectors can effectively detect useful signals, with high detection accuracy and low false alarm rate. In addition, the implementation of energy detectors does not require assumptions about the prior knowledge of signals, so they have wide applicability in practical applications.

[0004] However, in the real environment, noise sources often exhibit impulse characteristics, that is, they contain some outliers with short durations but large amplitudes. These outliers will submerge the useful signal components, resulting in a rapid decrease in the signal-to-noise ratio of the system. In this case, due to the sensitivity of traditional energy detectors to impulse noise, their detection performance will significantly decline or even completely fail. The presence of impulse noise makes traditional signal detection methods unable to effectively distinguish signals from noise, and thus unable to accurately identify the presence or absence of useful signals. Therefore, existing signal detection technologies have obvious deficiencies in the face of impulse interference and cannot meet the high requirements for signal detection in the actual communication environment. Summary of the Invention

[0005] According to the above-mentioned technical problems, a signal detection method based on the anti-eigenvalues of the Spearman rank correlation matrix under impulse interference is provided. The present invention uses the Spearman rank correlation transformation of signals to suppress the negative impact of impulse noise, and then designs a corresponding statistic by calculating the sum of the anti-eigenvalues of the Spearman rank correlation matrix, thereby achieving high-performance signal detection under impulse interference.

[0006] The technical means adopted by the present invention are as follows:

[0007] A signal detection method based on the anti-eigenvalue of the Spearman rank correlation matrix, comprising:

[0008] S1. Obtain the observation signals received by multiple sensors;

[0009] S2. Calculate the Spearman rank correlation coefficients between any two signals to form a Spearman rank correlation matrix;

[0010] S3. Obtain the eigenvalues of the Spearman rank correlation matrix and calculate the corresponding anti-eigenvalues;

[0011] S4. Calculate a statistic based on the sum of the anti-eigenvalues;

[0012] S5. Set a detection threshold and compare the size of the statistic and the detection threshold to complete the detection process.

[0013] Further, in step S1, the obtained observation signal is specifically:

[0014]

[0015] where, represents the th observation signal received by the th sensor at the sampling time represents the source signal to be detected, represents the th gain coefficient of the th sensor, represents the background noise, represents the signal length, represents, represents the number of sensors.

[0016] Further, step S2 specifically includes:

[0017] S21. Calculate the Spearman rank correlation coefficients between any two signals, and the calculation formula is as follows:

[0018]

[0019] where, represents the th signal and the th signal represents in the th signal represents in the th signal; represents, represents, Indicates the number of sensors; Indicates the signal length;

[0020] S22. Based on the Spearman rank correlation coefficient calculated in step S21, form a Spearman rank correlation matrix, the formula is as follows:

[0021]

[0022] Wherein, Indicates the Spearman rank correlation matrix, Indicates the Spearman rank correlation coefficient between the first signal and the second signal, Indicates the first signal and the Spearman rank correlation coefficient between the signal of the th road, Indicates the Spearman rank correlation coefficient between the second signal and the first signal, Indicates the second signal and the Spearman rank correlation coefficient between the signal of the th road, Indicates the Spearman rank correlation coefficient between the signal of the th road and the first signal, Indicates the Spearman rank correlation coefficient between the signal of the th road and the second signal.

[0023] Furthermore, step S3 specifically includes:

[0024] S31. Obtain the eigenvalues of the Spearman rank correlation matrix , wherein, ;

[0025] S32. Based on the obtained eigenvalues , calculate the corresponding inverse eigenvalues, the calculation formula is as follows:

[0026]

[0027] Wherein, Indicates the th inverse eigenvalue, , Indicates the floor function symbol, Indicates the number of sensors; Indicates the th eigenvalue of the Spearman rank correlation matrix, Indicates the th eigenvalue of the Spearman rank correlation matrix.

[0028] Furthermore, in step S4, based on the sum of the inverse eigenvalues, calculate the statistic, the calculation formula is as follows:

[0029]

[0030] Among them, represents a statistic.

[0031] Furthermore, step S5 specifically includes:

[0032] S51. Set a detection threshold, denoted as ,

[0033] S52. Compare the statistic with the detection threshold . If , it means the source signal exists; if , it means the source signal does not exist.

[0034] The present invention also provides a signal detection system based on the inverse eigenvalue of the Spearman rank correlation matrix implemented by the above-mentioned signal detection method based on the inverse eigenvalue of the Spearman rank correlation matrix, including:

[0035] A signal acquisition module, configured to acquire the observed signals received by multiple sensors;

[0036] A Spearman rank correlation matrix calculation module, configured to calculate the Spearman rank correlation coefficients of any two signals to form a Spearman rank correlation matrix;

[0037] An eigenvalue acquisition and inverse eigenvalue calculation module, configured to acquire the eigenvalues of the Spearman rank correlation matrix and calculate the corresponding inverse eigenvalues;

[0038] A statistic calculation module, configured to calculate a statistic based on the sum of the inverse eigenvalues;

[0039] A detection module, configured to set a detection threshold and compare the sizes of the statistic and the detection threshold to complete the detection process.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] The present invention effectively suppresses large outliers in impulse noise through the Spearman rank correlation transformation, and calculates a statistic based on the sum of the inverse eigenvalues of the Spearman rank correlation matrix, showing excellent robustness under impulse interference. Therefore, in an environmental noise containing impulse components, the signal detection method based on the inverse eigenvalue of the Spearman rank correlation matrix has excellent detection performance.

[0042] For the above reasons, the present invention can be widely promoted in fields such as communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0044] Figure 1 This is the flowchart of the method of the present invention.

[0045] Figure 2 This is a comparison chart of the detection probabilities of the energy detector and the anti-eigenvalue detector of the Spearman rank correlation matrix for signal detection in a pulse noise environment provided by an embodiment of the present invention. Detailed implementation manners

[0046] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0047] It should be noted that the terms "including" and "having" in the specification and claims of the present invention and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units does not necessarily have to be limited to those clearly listed steps or units, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products, or devices.

[0048] As Figure 1 shown, the present invention provides a signal detection method based on the anti-eigenvalue of the Spearman rank correlation matrix under pulse interference, including:

[0049] S1. Obtain the observed signals received by multiple sensors;

[0050] S2. Calculate the Spearman rank correlation coefficients of any two signals to form a Spearman rank correlation matrix;

[0051] S3. Obtain the eigenvalues of the Spearman rank correlation matrix and calculate the corresponding anti-eigenvalues;

[0052] S4. Calculate a statistic based on the sum of the anti-eigenvalues;

[0053] S5. Set a detection threshold and compare the size of the statistic and the detection threshold to complete the detection process.

[0054] In specific implementation, as a preferred implementation manner of the present invention, in step S1, the obtained observation signal is specifically:

[0055]

[0056] wherein, represents the observation signal received by the th path sensor at the sampling moment represents the source signal to be detected, represents the gain coefficient of the th path sensor, represents the background noise, represents the signal length, represents the number of sensors.

[0057] In specific implementation, as a preferred implementation manner of the present invention, step S2 specifically includes:

[0058] S21. Calculate the Spearman rank correlation coefficient between any two paths of signals, and the calculation formula is as follows:

[0059]

[0060] wherein, represents the Spearman rank correlation coefficient between the th path signal and the th path signal, represents the rank statistic in the th path signal, represents the rank statistic in the th path signal; represents the number of sensors; represents the signal length;

[0061] S22. Based on the Spearman rank correlation coefficient calculated in step S21, form a Spearman rank correlation matrix, and the formula is as follows:

[0062]

[0063] wherein, represents the Spearman rank correlation matrix, represents the Spearman rank correlation coefficient between the first path signal and the second path signal, represents the Spearman rank correlation coefficient between the first path signal and the th path signal, represents the Spearman rank correlation coefficient between the second signal and the first signal, represents the Spearman rank correlation coefficient between the second signal and the signal, represents the Spearman rank correlation coefficient between the signal and the first signal, represents the Spearman rank correlation coefficient between the signal and the second signal.

[0064] In specific implementation, as a preferred implementation manner of the present invention, step S3 specifically includes:

[0065] S31. Obtain the eigenvalues of the Spearman rank correlation matrix , where ;

[0066] S32. Based on the obtained eigenvalues , calculate the corresponding inverse eigenvalues. The calculation formula is as follows:

[0067]

[0068] where represents the th inverse eigenvalue, , represents the floor function symbol, represents the number of sensors; represents the th eigenvalue of the Spearman rank correlation matrix, represents the th eigenvalue of the Spearman rank correlation matrix.

[0069] In specific implementation, as a preferred implementation manner of the present invention, in step S4, based on the sum of the inverse eigenvalues, calculate a statistic. The calculation formula is as follows:

[0070]

[0071] where represents the statistic.

[0072] In specific implementation, as a preferred implementation manner of the present invention, step S5 specifically includes:

[0073] S51. Set a detection threshold, denoted as ,

[0074] S52. Compare the statistic with the detection threshold The magnitude, if , it indicates the existence of the source signal; if , it indicates the non - existence of the source signal.

[0075] Corresponding to the signal detection method based on the anti - eigenvalue of the Spearman rank - correlation matrix in this application, this application also provides a signal detection system based on the anti - eigenvalue of the Spearman rank - correlation matrix, including:

[0076] A signal acquisition module, configured to acquire the observed signals received by multiple sensors;

[0077] A Spearman rank - correlation matrix calculation module, configured to calculate the Spearman rank - correlation coefficients of any two signals to form a Spearman rank - correlation matrix;

[0078] An eigenvalue acquisition and anti - eigenvalue calculation module, configured to acquire the eigenvalues of the Spearman rank - correlation matrix and calculate the corresponding anti - eigenvalues;

[0079] A statistic calculation module, configured to calculate a statistic based on the sum of the anti - eigenvalues;

[0080] A detection module, configured to set a detection threshold and compare the magnitudes of the statistic and the detection threshold to complete the detection process.

[0081] For the embodiments of the present invention, since they correspond to the above - mentioned embodiments, the description is relatively simple. For relevant similarities, please refer to the description in the above - mentioned embodiments, and details will not be elaborated here.

[0082] Embodiment

[0083] In order to analyze the performance of the anti - eigenvalue detector of the Spearman rank - correlation matrix and the energy detector in signal detection under impulse noise, the present invention will be verified through Monte Carlo experiments. The experimental parameter settings are as follows:

[0084] The source signal is randomly generated by a signal of length subject to a standard normal distribution.

[0085] The impulse noise is simulated by a mixture of Gaussian distributions:

[0086]

[0087] Among them, represents the probability of the impulse component occurring in the entire impulse - noise environment, represents the standard deviation of the impulse component. At this time, the signal - to - noise ratio of the received signal can be defined as:

[0088]

[0089] Through Monte Carlo experiments, the performance of the Spearman rank correlation matrix anti-eigenvalue detector and the energy detector at different signal-to-noise ratios is compared and analyzed, which can verify that the Spearman rank correlation matrix anti-eigenvalue detector is robust in an impulsive noise environment.

[0090] The number of experiments is times, the false alarm probability is , the number of sensors is , and the gain coefficient is . The experimental results are as shown in Figure 2 . As can be seen from the experimental results of Figure 2 , due to the existence of the impulse component, the detection probability curve of the energy detector is close to a horizontal line and completely loses its detection effect. However, the Spearman rank correlation matrix anti-eigenvalue detector has a relatively high detection probability, demonstrating its robustness to impulse interference, indicating that the Spearman rank correlation matrix anti-eigenvalue detector can be used as a powerful tool for signal detection in an impulse interference environment.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A signal detection method based on the inverse eigenvalue of the Spearman rank correlation matrix, characterized in that: include: S1, obtaining observation signals received by multiple sensors; S2. Calculate the Spearman rank correlation coefficient of any two signals to form a Spearman rank correlation matrix, which specifically includes: S21. Calculate the Spearman rank correlation coefficient of any two signals. The calculation formula is as follows: in, Indicates Road signal and The Spearman rank correlation coefficient between the road signals, express In the Rank statistics in the path signal, express In the Rank statistics in path signals; , , Indicates the number of sensors; Indicates the signal length; S22, based on the Spearman rank correlation coefficient calculated in step S21, a Spearman rank correlation matrix is ​​formed, and the formula is as follows: in, represents the Spearman rank correlation matrix, represents the Spearman rank correlation coefficient between the first signal and the second signal, Indicates the first signal and the The Spearman rank correlation coefficient between the road signals, represents the Spearman rank correlation coefficient between the second signal and the first signal, Indicates the second signal and the The Spearman rank correlation coefficient between the road signals, Indicates The Spearman rank correlation coefficient between the first signal and the second signal, Indicates The Spearman rank correlation coefficient between the first signal and the second signal; S3. Obtain the eigenvalues ​​of the Spearman rank correlation matrix and calculate the corresponding inverse eigenvalues, including: S31. Get the Spearman rank correlation matrix Eigenvalues ,in, ; S32, based on acquisition Eigenvalues , calculate the corresponding inverse eigenvalue, the calculation formula is as follows: in, Indicates The inverse eigenvalues, , Represents the lower rounding symbol, Indicates the number of sensors; represents the Spearman rank correlation matrix eigenvalues, represents the Spearman rank correlation matrix eigenvalues; S4. Calculate the statistic based on the sum of the inverse eigenvalues. The calculation formula is as follows: in, represents a statistic; S5. Set the detection threshold and compare the statistics with the detection threshold to complete the detection process.

2. The signal detection method based on the inverse eigenvalue of the Spearman rank correlation matrix according to claim 1, characterized in that: In step S1, the observed signal obtained is specifically: in, Indicates The road sensor at the sampling time The received observation signal, represents the source signal to be detected, Indicates The gain factor of the sensor, represents the background noise, , Indicates the signal length, , Indicates the number of sensors.

3. The signal detection method based on the inverse eigenvalue of the Spearman rank correlation matrix according to claim 1, characterized in that: Step S5 specifically includes: S51, set the detection threshold, denoted as , S52. Comparative Statistics and detection threshold The size of , it means the source signal exists; if , it means the source signal does not exist.

4. A signal detection system based on the inverse eigenvalue of the Spearman rank correlation matrix implemented by the signal detection method based on the inverse eigenvalue of the Spearman rank correlation matrix according to any one of claims 1 to 3, characterized in that: include: A signal acquisition module is used to acquire observation signals received by multiple sensors; A Spearman rank correlation matrix calculation module is used to calculate the Spearman rank correlation coefficient of any two signals to form a Spearman rank correlation matrix; The eigenvalue acquisition and inverse eigenvalue calculation module is used to obtain the eigenvalues ​​of the Spearman rank correlation matrix and calculate the corresponding inverse eigenvalues; A statistics calculation module, used for calculating statistics based on the sum of inverse eigenvalues; The detection module is used to set the detection threshold and compare the size of the statistic with the detection threshold to complete the detection process.

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