A Kernel Correlation Coefficient Signal Detection Method Resistant to Impulse Noise

Abstract

The present invention provides a method for detecting a signal of a kernel correlation coefficient that is resistant to impulse noise, comprising the following steps: obtaining received signals of two receivers; calculating the lower quartile, median and upper quartile of the received signals, and constructing a corresponding Gaussian kernel function; performing Gaussian kernel transformation on the received signals based on the Gaussian kernel function, and performing correlation operations on the transformed two-way signals to construct a statistic; calculating a corresponding threshold value according to a given false alarm probability; and performing comparative analysis on the size of the statistic and the threshold value, thereby completing the detection process. The method of the present invention does not require the foreknowledge of channel prior information, has low implementation complexity, has strong robustness against impulse noise, and can achieve high-precision signal detection under background noise containing impulse components.

Description

Technical Field

[0001] The invention belongs to the field of communication technology, and in particular relates to a pulse noise-resistant kernel correlation coefficient signal detection method. Background Art

[0002] Signal detection is an important signal analysis technology that is widely used in radar, sonar, communications and other fields. The task of signal detection is to determine whether the signal of interest exists through signal processing technology, so that the system can subsequently extract useful high-quality signals through parameter estimation, code recognition, modulation analysis and other technologies.

[0003] At present, the energy detector is a classic signal detection algorithm in the literature. It is widely popular because of its simple form, complete theory and easy implementation. When the background noise satisfies the Gaussian distribution, the energy detector is the most widely used detection scheme. However, due to natural factors such as atmospheric electromagnetic pulse radiation and human factors such as industrial interference generated by electromagnetic equipment, the actual noise source not only contains additive Gaussian noise components, but also some irregular burst interference noise. These interference noises have the characteristics of short duration but large amplitude, which are usually called impulse noise. Due to the existence of impulse noise, the signal-to-noise ratio of the received signal will decrease rapidly within a period of time, causing the performance of the energy detector to deteriorate rapidly or even fail. Summary of the invention

[0004] To address the above problems, the present invention uses Gaussian kernel transform of the signal to suppress large outliers in pulse noise, and then designs statistics by calculating the correlation function of the two transformed signals, thereby achieving high-precision signal detection in an impulse noise environment.

[0005] The technical solution of the present invention is as follows:

[0006] A method for detecting a nuclear correlation coefficient signal resistant to impulse noise comprises the following steps:

[0007] Obtaining receiving signals of two receivers;

[0008] Calculate the lower quartile, median and upper quartile of the two received signals respectively, and construct the corresponding Gaussian kernel function;

[0009] Based on the Gaussian kernel function, Gaussian kernel transformation is performed on the two received signals, and correlation operation is performed on the transformed two signals to construct statistics;

[0010] Calculate the corresponding threshold value according to the given false alarm probability;

[0011] Compare and analyze the size of the statistics and threshold value to determine the detection result of the source signal.

[0012] Furthermore, the two receiving signals are specifically:

[0013] x1(i)=θ1s(i)+z1(i)

[0014] x2(i)=θ2s(i)+z2(i)

[0015] i=1,2…,n

[0016] in, is the received signal of the two receivers, s(i) is the source signal, θ m ≤1, m=1,2 represents the signal attenuation factor, z m (i), m=1,2 represents background noise, and n is the signal length.

[0017] Furthermore, the formula for calculating the lower quartile, median and upper quartile of the received signal is:

[0018]

[0019] in, is the lower quartile of the mth signal, v m is the median of the mth signal, is the upper quartile of the mth signal, Represents the new samples generated by arranging the received signals of the mth receiver in ascending order of signal amplitude, that is, Satisfy the conditions Represents the largest integer not greater than x.

[0020] Furthermore, the Gaussian kernel function for transforming the received signal is:

[0021]

[0022] in, represents the width of the Gaussian kernel function, v m is the median of the mth signal, κ m (·,·,·) represents the function of Gaussian kernel transformation on the m-th signal, x m (i) is the received signal of the mth receiver at time i.

[0023] Furthermore, the calculation formula for performing Gaussian kernel transformation on the two received signals based on the Gaussian kernel function is:

[0024]

[0025] in, represents the width of the Gaussian kernel function, v m is the median of the mth signal, κ m(·,·,·) represents the function of Gaussian kernel transformation on the m-th signal, x m (i) is the received signal of the mth receiver at time i, x' m (i) is the signal after Gaussian kernel transformation.

[0026] Furthermore, the statistics are constructed by performing correlation operation on the two transformed signals:

[0027]

[0028] in, are the two signals after Gaussian kernel transformation, and n is the signal length.

[0029] Furthermore, the corresponding threshold value is calculated according to the given false alarm probability as follows:

[0030]

[0031] Among them, Φ -1 (·) represents the inverse function of the standard normal distribution cumulative distribution function Φ, P f is a given false alarm probability.

[0032] Furthermore, a comparative analysis of the statistics and threshold values ​​is performed as follows:

[0033] Compare and analyze the size of the statistic and the threshold value. If the statistic is less than the threshold value, the source signal does not exist; if the statistic is greater than or equal to the threshold value, the source signal is considered to exist.

[0034] Technical effects of the present invention:

[0035] The present invention fully suppresses the harmful effects of large outliers in impulse noise by performing Gaussian kernel transformation on the signal, and exhibits excellent robustness in an impulse noise environment. Therefore, in an environment with impulse components, the Gaussian kernel correlation coefficient signal detection method is an effective tool for signal detection, and its performance is very good. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings generally illustrate various embodiments by way of example and not limitation, and together with the description and claims, serve to illustrate the embodiments of the invention. Where appropriate, the same reference numerals are used throughout the drawings to refer to the same or similar parts. Such embodiments are illustrative and are not intended to be exhaustive or exclusive embodiments of the present apparatus or method.

[0037] Figure 1 A schematic flow chart of a signal detection method of the present invention is shown;

[0038] Figure 2A schematic structural diagram of a signal detection method of the present invention is shown;

[0039] Figure 3 A comparison chart of detection probabilities of energy detector and Gaussian kernel correlation coefficient signal detection method in a Gaussian noise environment is shown.

[0040] Figure 4 A comparison chart of detection probabilities of energy detector and Gaussian kernel correlation coefficient signal detection method in a pulse noise environment is shown. DETAILED DESCRIPTION

[0041] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0042] This embodiment provides a method for detecting a kernel correlation coefficient signal that is resistant to impulse noise. Figure 1 As shown, the following steps are included:

[0043] Step S10: obtaining reception signals of two receivers;

[0044] Step S20: Calculate the lower quartile, median and upper quartile of the two received signals according to the received signals of the two receivers, and construct a corresponding Gaussian kernel function;

[0045] Step S30: performing Gaussian kernel transformation on the two received signals, and calculating the correlation function of the two transformed signals to construct a test statistic T;

[0046] Step S40: According to the given false alarm probability P f Calculate the corresponding threshold value λ;

[0047] Step S50: Compare and analyze the size of the statistic and the threshold value. If the statistic T is less than the threshold value λ, the source signal does not exist. Otherwise, it is considered that the source signal exists, thus completing the detection process.

[0048] As a preferred implementation of this embodiment, the received signals of the two receivers at the i-th sampling moment have the following form:

[0049] x1(i)=θ1s(i)+z1(i)

[0050] x2(i)=θ2s(i)+z2(i)

[0051] i=1,2…,n

[0052] in, is the received signal of the two receivers, s(i) is the source signal, θ m≤1, m=1,2 represents the signal attenuation factor, z m (i), m=1,2 represents background noise, and n is the signal length.

[0053] The object of the present invention is to determine whether the source signal s exists by measuring the correlation between the received signals of two receivers.

[0054] As a preferred implementation of this embodiment, the lower quartile of the m-th received signal is calculated. medianv m and upper quartile They can be achieved by the following formulas:

[0055]

[0056] in Represents the new samples generated by arranging the received signals of the mth receiver in ascending order of signal amplitude, that is, Satisfy the conditions Represents the largest integer not greater than x.

[0057] As a preferred implementation of this embodiment, the Gaussian kernel function for transforming the m-th received signal is:

[0058]

[0059] in, represents the width of the Gaussian kernel function, v m is the median of the mth signal, κ m (·,·,·) is the function of Gaussian kernel transformation on the m-th received signal, x m (i) is the received signal of the mth receiver at sampling time i.

[0060] As a preferred implementation of this embodiment, Gaussian kernel transformation of the m-th received signal based on the Gaussian kernel function is implemented by the following formula:

[0061]

[0062] in, are the two signals after Gaussian kernel transformation, and n is the signal length.

[0063] As a preferred implementation of this embodiment, the test statistic is constructed by the following formula:

[0064]

[0065] in, are the two signals after Gaussian kernel transformation, and n is the signal length.

[0066] As a preferred implementation of this embodiment, the formula for calculating the threshold value by the false alarm probability is:

[0067]

[0068] where Φ -1 (·) represents the inverse function of the standard normal distribution cumulative distribution function Φ, P f is a given false alarm probability.

[0069] As a preferred implementation of this embodiment, the signal detection process is implemented by the following judgment:

[0070]

[0071] Theoretical basis for calculating threshold values.

[0072] According to the independence of the two received signals and combined with the large sample asymptotic theory, the mean of the statistic under the null hypothesis can be written as:

[0073]

[0074] It is not difficult to prove that when the sample length is large enough, the median of the signal sample is approximately equal to the mean of the signal. At this time, combined with the symmetry of the definite integral, we can get:

[0075]

[0076] The mean of the statistic

[0077] According to the relationship between variance and mean, the calculation formula of statistical variance is:

[0078]

[0079] Then the variance of the statistic can be approximated as:

[0080]

[0081] It is not difficult to find that but

[0082]

[0083] When the sample length n is large enough, the false alarm probability P f It is expressed by the following formula:

[0084]

[0085] At this time, the calculation formula of the threshold value can be obtained by inverting it.

[0086] Example 1

[0087] In order to analyze the performance of the Gaussian kernel correlation coefficient signal detection method and the energy detector in signal detection under Gaussian noise and impulse noise, the present invention will be verified through Monte Carlo experiments. Figure 2 : is a schematic diagram of the detection structure of the Gaussian kernel correlation coefficient signal detection method, where x1(1), x1(2)…, x1(n) and x2(1), x2(2)…, x2(n) are the received signals of the two receivers respectively. v1, and v2, are the lower quartile, median and upper quartile of the two received signals respectively. x'1(1), x'1(2), …, x'1(n) and x'2(1), x'2(2), …, x'2(n) are the signals of the two received signals after Gaussian kernel transformation respectively. T is the statistic constructed by correlation operation of the two transformed signals. Finally, the statistic T is compared with the threshold value λ to obtain the result of the binary hypothesis test (H0: source signal does not exist or H1: source signal exists).

[0088] The experimental parameters are set as follows:

[0089] The source signal is randomly generated from a signal with a length of n=100 that obeys a standard normal distribution.

[0090] Impulse noise is simulated by a mixture of Gaussian distributions:

[0091]

[0092] Where ε represents the probability of the pulse component occurring in the entire pulse noise environment, and σ2=10>>σ1 represents the standard deviation of the pulse component. At this time, the signal-to-noise ratio of the received signal can be defined as:

[0093]

[0094] Through Monte Carlo experiments, the performance of Gaussian kernel correlation coefficient signal detection method and energy detector under different signal-to-noise ratios is compared and analyzed. It can be verified that Gaussian kernel correlation coefficient signal detection method has comparable performance to energy detector under Gaussian noise and has good robustness under impulse noise environment. The number of experiments is 10 5 times, false alarm probability P f =0.05, signal attenuation factor θ1=θ2=0.5. The experimental results are as follows Figure 3 and Figure 4 shown.

[0095] Depend on Figure 3The experimental results show that in a Gaussian noise (ε=0) environment, the detection probability of the Gaussian kernel correlation coefficient signal detection method is almost consistent with the energy detector, indicating its excellent performance in signal detection under Gaussian noise.

[0096] Depend on Figure 4 The experimental results show that due to the existence of the pulse component (ε = 0.05), the detection probability curve of the energy detector is close to P f = 0.05, completely losing the detection effect, while the Gaussian kernel correlation coefficient signal detection method has a higher detection probability and shows robustness to impulse noise, indicating that the Gaussian kernel correlation coefficient signal detection method can be used as a powerful tool for signal detection in an impulse noise environment.

[0097] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for detecting a nuclear correlation coefficient signal resistant to impulse noise, characterized in that: The following steps are involved: Get the received signals of the two receivers, specifically: x1(i)=θ1s(i)+z1(i) x2(i)=θ2s(i)+z2(i) i=1,2…,n in, is the received signal of the two receivers, s(i) is the source signal, θ m ≤1, m=1,2 represents the signal attenuation factor, z m (i), m = 1, 2 represents background noise, n is the signal length; Calculate the lower quartile, median and upper quartile of the two received signals respectively, and construct the corresponding Gaussian kernel function; The formula for calculating the lower quartile, median, and upper quartile of the received signal is: in, is the lower quartile of the mth signal, v m is the median of the mth signal, is the upper quartile of the mth signal, Represents the new samples generated by arranging the received signals of the mth receiver in ascending order of signal amplitude, that is, Satisfy the conditions Represents the largest integer not greater than x; Based on the Gaussian kernel function, Gaussian kernel transformation is performed on the two received signals, and correlation operation is performed on the transformed two signals to construct statistics; The Gaussian kernel function for transforming the two received signals is: in, represents the width of the Gaussian kernel function, v m is the median of the mth signal, κ m (·,·,·) represents the function of Gaussian kernel transformation on the m-th signal, x m (i) is the received signal of the mth receiver at time i; Calculate the corresponding threshold value according to the given false alarm probability; Compare and analyze the size of the statistics and threshold value to determine the detection result of the source signal.

2. The method for detecting a nuclear correlation coefficient signal resistant to impulse noise according to claim 1, characterized in that: The calculation formula for Gaussian kernel transformation of two received signals based on Gaussian kernel function is: in, represents the width of the Gaussian kernel function, v m is the median of the mth signal, κ m (·,·,·) represents the function of Gaussian kernel transformation on the m-th signal, x m (i) is the received signal of the mth receiver at time i, x' m (i) is the signal after Gaussian kernel transformation.

3. The method for detecting a kernel correlation coefficient signal resistant to impulse noise according to claim 1, characterized in that: The statistics constructed by performing correlation operations on the two transformed signals are as follows: in, are the two signals after Gaussian kernel transformation, and n is the signal length.

4. The method for detecting a kernel correlation coefficient signal resistant to impulse noise according to claim 1, characterized in that: The corresponding threshold value calculated according to the given false alarm probability is specifically: Among them, Φ -1 (·) represents the inverse function of the standard normal distribution cumulative distribution function Φ, P f is a given false alarm probability.

5. The method for detecting a kernel correlation coefficient signal resistant to impulse noise according to claim 1, characterized in that: The comparison and analysis of the statistics and threshold values ​​are as follows: The size of the statistic and the threshold value are compared and analyzed. If the statistic is less than the threshold value, the source signal does not exist; if the statistic is greater than or equal to the threshold value, it is considered that the source signal exists.

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