Signal detection method based on logarithmic rank transformation under non-Gaussian noise

Abstract

The invention belongs to the technical field of signal detection, and provides a signal detection method based on logarithmic rank transformation under non-Gaussian noise, which comprises the following steps: S10, acquiring sampling signals received by two paths of sensors; s20, calculating ranks and anti-ranks of the two paths of sampling signals, and performing logarithmic rank transformation on the two paths of sampling signals; s30, a test statistic is constructed based on the inner product of the two paths of converted signals; s40, calculating the variance of the test statistics and setting a detection threshold; s50, comparing the test statistic with the detection threshold, and determining a detection result of the target signal; according to the method, the problem of large abnormal values in non-Gaussian noise can be effectively solved, and the robustness of signal detection is remarkably improved by calculating the rank and the anti-rank of the sampling signal and performing logarithmic rank transformation; the test statistic is constructed based on the inner product of the converted signal, and the detection threshold is set in combination with the preset false alarm probability, so that accurate signal detection in the non-Gaussian noise environment is realized, and the method has wide application prospect and important practical value.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal detection, and specifically relates to a signal detection method based on logarithmic rank transformation under non-Gaussian noise. Background Art

[0002] Signal detection is an important task in the field of communication technology, and has wide applications especially in phased array radars, underwater sonars, mobile communications and other fields. Traditional signal detection methods, such as energy detectors, have good detection performance under Gaussian noise background.

[0003] However, in the actual environment, the noise often exhibits non-Gaussian characteristics, including a large number of outliers with short duration but large amplitude. These outliers will significantly reduce the system signal-to-noise ratio, resulting in the failure of traditional signal detection methods.

[0004] Therefore, there is an urgent need to develop a method that can effectively detect signals in a non-Gaussian noise environment. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a signal detection method based on logarithmic rank transformation under non-Gaussian noise, so as to solve the problems in the prior art that the noise often exhibits non-Gaussian characteristics, including a large number of outliers with short duration but large amplitude, and these outliers will significantly reduce the system signal-to-noise ratio, resulting in the failure of traditional signal detection methods, etc.

[0006] The object of the present invention is achieved by the following scheme:

[0007] A signal detection method based on logarithmic rank transformation under non-Gaussian noise, comprising:

[0008] S10. Obtain the sampled signals received by two sensors;

[0009] S20. Calculate the ranks and inverse ranks of the two sampled signals, and perform logarithmic rank transformation on the two sampled signals;

[0010] S30. Construct a test statistic based on the inner product of the two transformed signals;

[0011] S40. Calculate the variance of the test statistic and set a detection threshold;

[0012] S50. Compare the magnitudes of the test statistic and the detection threshold to determine the detection result of the target signal.

[0013] In one embodiment, the two sampled signals are specifically:

[0014] x i = θ1s i + z i

[0015] y i = θ2s i + w i

[0016] i = 1, 2…, n

[0017] where {x i , y i} are the sampling signals received by the two sensors at time i, s i is the target signal to be detected, θ1 and θ2 represent the channel gain coefficients, z i and w i represent non-Gaussian noise, and n is the signal length.

[0018] In one embodiment, calculating the rank and anti-rank of the two sampling signals specifically is

[0019]

[0020] where R i and are respectively the rank and anti-rank of the sample point x i , Q i and are respectively the rank and anti-rank of the sample point y i , H{·} represents the step function, and n is the signal length.

[0021] In one embodiment, the logarithmic rank transformation of the two sampling signals specifically is:

[0022]

[0023] where x' i represents the signal after the logarithmic rank transformation of the sample point x i , y' i represents the signal after the logarithmic rank transformation of the sample point y i , sgn{·} represents the sign function, ln{·} represents the logarithmic function, and n is the sample length.

[0024] In one embodiment, constructing the test statistic based on the inner product of the two transformed signals specifically is:

[0025]

[0026] where T represents the test statistic, and n is the sample length.

[0027] In one embodiment, calculating the variance of the test statistic and setting the detection threshold specifically is:

[0028]

[0029] β i = sgn(2i - n - 1)ln(n + 1 - |2i - n - 1|)

[0030] λ = σΦ -1 (1 - P f )

[0031] where σ 2 represents the variance of the test statistic, λ represents the detection threshold, P f represents the false alarm probability, Φ -1 represents the quantile function of the standard normal distribution, and n is the sample length.

[0032] In one embodiment, comparing the magnitudes of the test statistic and the detection threshold specifically includes:

[0033] Compare the magnitudes of the test statistic and the detection threshold. If the test statistic is greater than the detection threshold, the target signal exists; otherwise, it is considered that the target signal does not exist.

[0034] In a second aspect, the present application provides a signal detection system based on logarithmic rank transformation under non - Gaussian noise, which is configured with the following modules:

[0035] A signal acquisition module, configured to acquire sampling signals received by two sensors, where the sampling signals include the target signal to be detected and non - Gaussian noise;

[0036] A rank and inverse rank calculation module, configured to calculate the rank and inverse rank of the two sampling signals;

[0037] A logarithmic rank transformation module, configured to perform logarithmic rank transformation on the two sampling signals to obtain the transformed signals;

[0038] A test statistic construction module, configured to construct a test statistic based on the inner product of the two transformed signals;

[0039] A detection threshold setting module, configured to calculate the variance of the test statistic and set the detection threshold according to a preset false alarm probability;

[0040] A signal detection module, configured to compare the magnitudes of the test statistic and the detection threshold. If the test statistic is greater than the detection threshold, it is determined that the target signal exists; otherwise, it is determined that the target signal does not exist.

[0041] In a third aspect, the present application further provides a computer device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, it implements the above - mentioned signal detection method based on logarithmic rank transformation under non - Gaussian noise.

[0042] Fourthly, the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned signal detection method based on logarithmic rank transformation under non-Gaussian noise is realized.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1. By introducing logarithmic rank transformation, the present invention effectively solves the problem that traditional signal detection methods fail in non-Gaussian noise environments and improves the robustness of signal detection.

[0045] 2. By accurately calculating the rank and anti-rank of the sampled signals and constructing a test statistic using the characteristics of the transformed signals, the present invention realizes more accurate signal detection.

[0046] 3. By reasonably setting the detection threshold according to the preset false alarm probability, the present invention ensures the objectivity and reliability of the detection results and provides a new and effective signal detection method for the field of communication technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a schematic flowchart of the signal detection method of the present invention;

[0048] Figure 2 is a comparison graph of the detection probabilities of the energy detector and the logarithmic rank transformation detector of the present invention for signal detection in a non-Gaussian noise environment;

[0049] Figure 3 is a framework diagram of the signal detection system based on logarithmic rank transformation under non-Gaussian noise of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] The following further describes in detail the embodiments of the present invention with reference to the drawings. The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of the present invention.

[0051] Embodiment: The present invention provides a signal detection method based on logarithmic rank transformation under non-Gaussian noise, as Figure 1 shown, including the following steps:

[0052] Step S10: Obtain the sampled signals received by two sensors;

[0053] Step S20: Calculate the rank and anti-rank of the two sampled signals, and perform logarithmic rank transformation on the two sampled signals;

[0054] Step S30: Construct a test statistic T based on the inner product of the two transformed signals;

[0055] Step S40: Calculate the variance of the test statistic and set the detection threshold;

[0056] Step S50: Compare the magnitudes of the test statistic T and the detection threshold λ. If the test statistic T is greater than the detection threshold λ, the target signal exists; otherwise, it is considered that the target signal does not exist.

[0057] As can be seen from the above, this method can effectively address the problem of large outliers in non-Gaussian noise. By calculating the rank and anti-rank of the sampled signal and performing a logarithmic rank transformation, the robustness of signal detection is significantly improved. A test statistic is constructed based on the inner product of the transformed signal, and the detection threshold is set in combination with the preset false alarm probability, achieving accurate signal detection in a non-Gaussian noise environment, with broad application prospects and important practical value.

[0058] As a preferred implementation manner of this embodiment, the sampled signals received by the two sensors at time i have the following form:

[0059] x i = θ1s i + z i

[0060] y i = θ2s i + w i

[0061] i = 1, 2…, n

[0062] Where, {x i , y i} are the sampled signals received by the two sensors at time i, s i is the target signal to be detected, θ1 and θ2 represent the channel gain coefficients, z i and w i represent non-Gaussian noise, and n is the signal length.

[0063] As can be seen from the above, the definition of the form of the sampled signals received by the two sensors at a certain time clarifies the key elements in the signal, including the target signal to be detected, the channel gain coefficients, and non-Gaussian noise, etc., providing a solid foundation for subsequent rank and anti-rank calculations, logarithmic rank transformation, and construction of the test statistic, and thus helping to accurately model the signal detection process, improve the accuracy and reliability of signal detection, and ensure effective detection of the target signal in a non-Gaussian noise environment.

[0064] As a preferred implementation manner of this embodiment, the rank and anti-rank of the two sampled signals can be calculated by the following formula:

[0065]

[0066] Where, R i and are the sample points xi The rank and inverse rank, Q i and are the rank and inverse rank of the sample point y i respectively, H{·} represents the step function, and n is the signal length.

[0067] As can be seen from the above, by calculating the rank and inverse rank of the signal, this method can more effectively capture the dynamic changes in the signal, especially the large outliers in non-Gaussian noise; furthermore, it provides key information for the subsequent logarithmic rank transformation, which helps to enhance the robustness of signal detection and improve the signal detection performance in complex noise environments.

[0068] As a preferred implementation manner of this embodiment, the logarithmic rank transformation of the two-channel sampling signals can be implemented by the following formula:

[0069]

[0070] where x' i represents the signal after the logarithmic rank transformation of the sample point x i and y' i represents the signal after the logarithmic rank transformation of the sample point y i respectively, sgn{·} represents the sign function, ln{·} represents the logarithmic function, and n is the sample length.

[0071] As can be seen from the above, the formula for calculating the logarithmic rank transformation of the two-channel sampling signals further enhances the robustness of the signal detection method against non-Gaussian noise by applying the logarithmic function and the sign function to transform the rank and inverse rank; the logarithmic rank transformation can reduce the influence of large outliers on signal detection, making the signal features more prominent, thereby improving the accuracy of signal detection; furthermore, it provides strong support for constructing the test statistic based on the inner product of the transformed signals subsequently, and is one of the key technologies for realizing effective signal detection under non-Gaussian noise.

[0072] As a preferred implementation manner of this embodiment, the test statistic is constructed by the following formula:

[0073]

[0074] where T represents the test statistic and n is the sample length.

[0075] As can be seen from the above, the test statistic constructed in this way can more accurately reflect the similarity and difference between signals, especially in non-Gaussian noise environments; furthermore, it provides a reliable basis for setting the detection threshold according to the preset false alarm probability subsequently, which is an important link for realizing accurate signal detection and helps to improve the performance and reliability of signal detection.

[0076] As a preferred implementation of this embodiment, calculate the variance of the test statistic and set the detection threshold as:

[0077]

[0078] β i = sgn(2i - n - 1)ln(n + 1 - |2i - n - 1|)

[0079] λ = σΦ -1 (1 - P f )

[0080] where σ 2 represents the variance of the test statistic, λ represents the detection threshold, P f represents the false alarm probability, Φ -1 represents the quantile function of the standard normal distribution, and n is the sample length.

[0081] As can be seen from the above, the formula for calculating the variance of the test statistic and setting the detection threshold can accurately calculate the detection threshold according to the preset false alarm probability and sample length; furthermore, it ensures that the signal detection process has a clear judgment basis, making the detection result more objective and reliable; by reasonably setting the detection threshold, this method can effectively distinguish the target signal from the noise, reduce the situations of misjudgment and missed judgment, and improve the performance and stability of signal detection, especially suitable for signal detection tasks in non-Gaussian noise environments.

[0082] As a preferred implementation of this embodiment, the signal detection process is realized through the following decision:

[0083]

[0084] In summary: By accurately calculating the rank and anti-rank of the sampled signal and performing logarithmic rank transformation, a test statistic that can accurately reflect the signal characteristics is constructed, and the detection threshold is set according to the preset false alarm probability, realizing robust signal detection in a non-Gaussian noise environment; this method has broad application prospects and important practical value, can significantly improve the accuracy and reliability of signal detection, and makes positive contributions to the development of the communication technology field.

[0085] Working principle: First, obtain the sampled signals containing non-Gaussian noise received by two sensors. By calculating the rank and anti-rank of these signals and subsequent logarithmic rank transformation, the large outliers in the non-Gaussian noise are effectively suppressed; then, use the inner product of the transformed signals to construct a test statistic to measure the similarity between signals; by calculating the variance of the test statistic and setting the corresponding detection threshold, finally compare the size of the test statistic with the detection threshold to accurately determine the presence or absence of the target signal; this method realizes robust signal detection in a non-Gaussian noise environment and has broad application prospects.

[0086] Experimental Example: To analyze the performance of the logarithmic rank transform detector and the energy detector in signal detection under non-Gaussian noise, the present invention will be verified through Monte Carlo experiments.

[0087] The experimental parameters are set as follows:

[0088] The target signal is randomly generated by a signal of length n = 200 that follows a standard normal distribution.

[0089] The background noise is modeled by a Cauchy distribution with a location parameter of 0 and a scale parameter of γ. At this time, the system signal-to-noise ratio can be defined as:

[0090]

[0091] Through Monte Carlo experiments, by comparing and analyzing the performance of the logarithmic rank transform detector and the energy detector at different signal-to-noise ratios, it can be verified that the logarithmic rank transform detector has strong robustness in a Cauchy noise environment; the number of experiments is 10 4 times, the false alarm probability P f = 0.1, and the channel gain coefficients θ1 = θ2 = 1; the experimental results are as Figure 2 shown.

[0092] From Figure 2 the experimental results, it can be seen that due to the existence of large outliers in the Cauchy noise, the detection probability curve of the energy detector is close to a horizontal line with P f = 0.1, completely losing the detection effect, while the logarithmic rank transform detector has a higher detection probability and better detection performance.

[0093] A signal detection system based on logarithmic rank transform under non-Gaussian noise, as Figure 3 shown, this system is configured with the following modules:

[0094] A signal acquisition module, used to acquire the sampled signals received by two sensors, where the sampled signals include the target signal to be detected and non-Gaussian noise;

[0095] A rank and inverse rank calculation module, used to calculate the rank and inverse rank of the two sampled signals;

[0096] A logarithmic rank transform module, used to perform logarithmic rank transform on the two sampled signals to obtain the transformed signals;

[0097] A test statistic construction module, used to construct a test statistic based on the inner product of the two transformed signals;

[0098] A detection threshold setting module, used to calculate the variance of the test statistic and set the detection threshold according to a preset false alarm probability;

[0099] A signal detection module, configured to compare the magnitude of the test statistic with the detection threshold. If the test statistic is greater than the detection threshold, it is determined that the target signal exists; otherwise, it is determined that the target signal does not exist.

[0100] In one embodiment, the present application further provides a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the above-mentioned signal detection method based on logarithmic rank transformation under non-Gaussian noise is implemented.

[0101] In one embodiment, the present application further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned signal detection method based on logarithmic rank transformation under non-Gaussian noise is implemented.

[0102] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. Moreover, the specific features, structures, materials, or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0103] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can refer to the partial descriptions of the method embodiments. The device embodiments described above are only illustrative. The components described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the present disclosure solution. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0104] The above-mentioned embodiments only represent several implementation manners of the embodiments of the present application. The descriptions are relatively specific and detailed, but should not be construed as a limitation on the patent scope of the application embodiments. It should be noted that for those of ordinary skill in the art, without departing from the concept of the embodiments of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the embodiments of the present application.

Claims

1. A signal detection method based on log-rank transform under non-Gaussian noise, characterized in that: include: S10, obtaining sampling signals received by two sensors; S20, calculating the rank and inverse rank of the two-channel sampling signals, and performing logarithmic rank transformation on the two-channel sampling signals; S30, constructing a test statistic based on the inner product of the two transformed signals; S40, calculating the variance of the test statistic and setting the detection threshold; S50: Compare the test statistic and the detection threshold to determine the detection result of the target signal.

2. The signal detection method based on log-rank transformation under non-Gaussian noise as claimed in claim 1, characterized in that: The two sampling signals are specifically: x i =θ1s i +z i y i =θ2s i +w i i=1,2…,n Among them, {x i ,y i } is the sampling signal received by the two sensors at time i, s i is the target signal to be detected, θ1 and θ2 represent the channel gain coefficients, z i and w i represents non-Gaussian noise, and n is the signal length.

3. The signal detection method based on log-rank transformation under non-Gaussian noise as claimed in claim 1, characterized in that: The calculation of the rank and inverse rank of the two sampling signals is specifically as follows: Among them, R i and They are the sample points x i The rank and anti-rank of Q i and They are sample points y i , H{·} represents the step function, and n is the signal length.

4. The signal detection method based on log-rank transformation under non-Gaussian noise as claimed in claim 1, characterized in that: The logarithmic rank transformation of the two sampling signals is specifically calculated as follows: Among them, x' i Represents the sample point x i The signal after log-rank transformation, y' i Represents the sample point y i After the log-rank transformed signal, sgn{·} represents the sign function, ln{·} represents the logarithmic function, and n is the sample length.

5. The signal detection method based on log-rank transformation under non-Gaussian noise as claimed in claim 1, characterized in that: The test statistic constructed based on the inner product of the two transformed signals is as follows: Where T is the test statistic and n is the sample length.

6. The signal detection method based on log-rank transformation under non-Gaussian noise as claimed in claim 1, characterized in that: The calculation of the variance of the test statistic and setting the detection threshold are specifically as follows: β i =sgn(2i-n-1)ln(n+1-|2i-n-1|) λ=σΦ -1 (1-P f ) Among them, σ 2 represents the variance of the test statistic, λ represents the detection threshold, P f represents the false alarm probability, Φ -1 Represents the quantile function of the standard normal distribution, where n is the sample length.

7. The signal detection method based on log-rank transformation under non-Gaussian noise as claimed in claim 1, characterized in that: The size of the comparison test statistic and the detection threshold is specifically: Compare the test statistic and the detection threshold. If the test statistic is greater than the detection threshold, the target signal exists; otherwise, it is considered that the target signal does not exist.

8. A signal detection system based on log-rank transform under non-Gaussian noise, characterized in that: A signal detection method based on log-rank transformation under non-Gaussian noise according to any one of claims 1 to 7, comprising: A signal acquisition module, used to acquire sampling signals received by two sensors, wherein the sampling signals include a target signal to be detected and non-Gaussian noise; A rank and inverse rank calculation module, used to calculate the rank and inverse rank of the two sampling signals; A log-rank transformation module, used for performing log-rank transformation on the two sampling signals to obtain transformed signals; A test statistic construction module, used to construct a test statistic based on the inner product of the two transformed signals; A detection threshold setting module, used to calculate the variance of the test statistic and set the detection threshold according to a preset false alarm probability; The signal detection module is used to compare the test statistic with the detection threshold. If the test statistic is greater than the detection threshold, it is determined that the target signal exists; otherwise, it is determined that the target signal does not exist.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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