Energy detection method and device based on Gaussian kernel under non-Gaussian noise and medium

Abstract

The invention discloses an energy detection method and device based on a Gaussian kernel under non-Gaussian noise and a medium, and relates to the technical field of communication. The method comprises the following steps: acquiring an array signal received by a multi-antenna system; constructing a Gaussian kernel function based on a set Gaussian kernel width, and performing Gaussian kernel transformation on the array signal by using the Gaussian kernel function; calculating the energy of the array signal after Gaussian kernel transformation, and constructing test statistics based on the energy; calculating a detection threshold according to a given false alarm probability; and performing comparative analysis on the test statistics and the detection threshold to obtain a signal detection result. According to the method, the negative influence of a large abnormal value in the non-Gaussian noise can be suppressed based on Gaussian kernel transformation of the signal, and then the test statistic is constructed by calculating the energy of the transformed array signal, so that excellent detection performance is obtained in a non-Gaussian noise environment.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a Gaussian kernel-based energy detection method, device and medium under non-Gaussian noise. Background Art

[0002] In the field of signal processing such as radar, sonar and communication, signal detection in noise is an important research topic. Traditional signal detection methods, such as energy detectors, usually assume that the background noise follows a Gaussian distribution. However, the noise sources in actual systems all have typical non-Gaussian characteristics, that is, compared with Gaussian noise, their probability density functions have thicker tails, which are usually called non-Gaussian noise. Since the large outliers of non-Gaussian noise can cause the performance of energy detectors to deteriorate seriously, researchers have proposed some signal detectors that are resistant to non-Gaussian noise, including polarity coincidence arrays and logarithmic moment detectors. The design principle of this type of method is to use nonlinear functions to suppress the negative impact of outliers in non-Gaussian noise, but the nonlinear functions (sign functions and logarithmic functions) used in these two methods will bring a certain degree of information loss, resulting in poor performance. Summary of the invention

[0003] The purpose of the present invention is to provide a Gaussian kernel-based energy detection method, device and medium under non-Gaussian noise, which can improve the energy detection performance under non-Gaussian noise interference.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] An energy detection method based on Gaussian kernel under non-Gaussian noise, comprising:

[0006] Acquire array signals received by a multi-antenna system;

[0007] Constructing a Gaussian kernel function based on a set Gaussian kernel width, and performing a Gaussian kernel transformation on the array signal using the Gaussian kernel function;

[0008] Calculating the energy of the array signal after Gaussian kernel transformation, and constructing a test statistic based on the energy;

[0009] Calculate the detection threshold according to the given false alarm probability;

[0010] The test statistic and the detection threshold are compared and analyzed to obtain a signal detection result.

[0011] Optionally, the array signal is specifically expressed as:

[0012]

[0013] Among them, H 0 Indicates that the source signal does not exist, H1 Indicates the coexistence of source signal and noise, z m (n) is the array signal received by the mth receiving antenna at time n, s(n) is the source signal to be detected, h m ≤1, indicating the signal gain of the mth receiving antenna, M is the number of receiving antennas, N is the signal length, w m (n) represents the background noise of the mth receiving antenna at time n.

[0014] Optionally, the Gaussian kernel function is constructed based on the set Gaussian kernel width, and the Gaussian kernel function is used to perform Gaussian kernel transformation on the array signal. Specifically, the calculation includes:

[0015]

[0016] Among them, κ(z,η) represents the Gaussian kernel function, z represents the input data, η represents the Gaussian kernel width, z m (n) is the array signal received by the mth receiving antenna at time n, is the array signal after Gaussian kernel transformation, M is the number of receiving antennas, and N is the signal length.

[0017] Optionally, the energy of the array signal after Gaussian kernel transformation is calculated, and a test statistic is constructed based on the energy, and the specific calculation includes:

[0018]

[0019] in, is the array signal after Gaussian kernel transformation, G n represents the energy of the transformed array signal at time n, T represents the test statistic, M is the number of receiving antennas, and N is the signal length.

[0020] Optionally, the detection threshold is calculated according to a given false alarm probability, and the specific calculation includes:

[0021]

[0022] Among them, λ represents the detection threshold, Φ -1 (·) represents the inverse function of the standard normal distribution cumulative distribution function Φ, P f For a given false alarm probability, μ = Mω 2 , Indicates that the array signal after transformation is in H 0 Assume that the k-th order absolute moment, H 0 Indicates that the source signal does not exist, M is the number of receiving antennas, and N is the signal length.

[0023] Optionally, the comparative analysis of the test statistic and the detection threshold to obtain a signal detection result is specifically performed as follows:

[0024] The test statistic is compared with the detection threshold. If the test statistic is greater than the detection threshold, the signal detection result is determined to be the presence of the source signal; if the test statistic is less than or equal to the detection threshold, the signal detection result is determined to be the absence of the source signal.

[0025] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the energy detection method based on Gaussian kernel under non-Gaussian noise.

[0026] The present invention also provides a computer-readable storage medium, characterized in that it stores a computer program, and when the computer program is executed by a processor, it implements the energy detection method based on Gaussian kernel under non-Gaussian noise as described above.

[0027] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0028] The present invention discloses a Gaussian kernel-based energy detection method, device and medium under non-Gaussian noise, the method comprising obtaining an array signal received by a multi-antenna system; constructing a Gaussian kernel function based on a set Gaussian kernel width, and using the Gaussian kernel function to perform a Gaussian kernel transformation on the array signal; calculating the energy of the array signal after the Gaussian kernel transformation, and constructing a test statistic based on the energy; calculating a detection threshold according to a given false alarm probability; and comparing and analyzing the test statistic and the detection threshold to obtain a signal detection result. The present invention can suppress the negative impact of large outliers in non-Gaussian noise based on the Gaussian kernel transformation of the signal, and then construct a test statistic by calculating the energy of the transformed array signal, thereby obtaining excellent detection performance in a non-Gaussian noise environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0030] Figure 1 Schematic diagram of the process of the energy detection method based on Gaussian kernel under non-Gaussian noise of the present invention;

[0031] Figure 2Schematic diagram of the detection structure in this embodiment;

[0032] Figure 3 This is a comparison diagram of detection probabilities of signal detection in a non-Gaussian noise environment between the Gaussian kernel energy detector in this embodiment and the existing detection algorithm;

[0033] Figure 4 Schematic diagram of the effect of Gaussian kernel width on the detection performance of the detection method in this embodiment. DETAILED DESCRIPTION

[0034] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] The purpose of the present invention is to provide a Gaussian kernel-based energy detection method, device and medium under non-Gaussian noise, which can improve the energy detection performance under non-Gaussian noise interference.

[0036] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] As a first aspect, the present invention provides Figure 1 An energy detection method based on Gaussian kernel under non-Gaussian noise is shown, comprising:

[0038] Acquire array signals received by a multi-antenna system;

[0039] Constructing a Gaussian kernel function based on a set Gaussian kernel width, and performing a Gaussian kernel transformation on the array signal using the Gaussian kernel function;

[0040] Calculating the energy of the array signal after Gaussian kernel transformation, and constructing a test statistic based on the energy;

[0041] Calculate the detection threshold according to the given false alarm probability;

[0042] The test statistic and the detection threshold are compared and analyzed to obtain a signal detection result.

[0043] As a specific implementation, the array signal received by the multi-antenna system at time n has the following form:

[0044]

[0045] Among them, H 0 Indicates that the source signal does not exist, H1 Indicates the coexistence of source signal and noise, z m (n) is the array signal received by the mth receiving antenna at time n, s(n) is the source signal to be detected, h m ≤1, indicating the signal gain of the mth receiving antenna, M is the number of receiving antennas, N is the signal length, and non-Gaussian noise w m (n) is described by the following Gaussian mixture model:

[0046]

[0047] Where f(w) represents the probability density function of non-Gaussian noise, represents the variance of the Gaussian component in non-Gaussian noise, represents the variance of the non-Gaussian component in the non-Gaussian noise, and ε represents the occurrence probability of the non-Gaussian component in the non-Gaussian noise.

[0048] As a specific implementation, a Gaussian kernel function is constructed based on a set Gaussian kernel width, and Gaussian kernel transformation is performed on the array signal through the following formula:

[0049]

[0050] Among them, κ(z,η) represents the Gaussian kernel function, z represents the input data, η represents the Gaussian kernel width, z m (n) is the array signal received by the mth receiving antenna at time n, is the corresponding array signal after Gaussian kernel transformation, M is the number of receiving antennas, and n is the signal length.

[0051] As a specific implementation, the energy of the array signal after Gaussian kernel transformation is calculated, and the formula for constructing the test statistic based on the energy is:

[0052]

[0053] in is the array signal after Gaussian kernel transformation, G n represents the energy of the transformed array signal at time n, and T represents the test statistic.

[0054] As a specific implementation method, the test statistic and the detection threshold are compared and analyzed to obtain the signal detection result as follows:

[0055] The test statistic is compared with the detection threshold. If the test statistic is greater than the detection threshold, the signal detection result is determined to be the presence of the source signal; if the test statistic is less than or equal to the detection threshold, the signal detection result is determined to be the absence of the source signal.

[0056] Regarding the transformed array signal in H 0 The k-th order absolute moment under the assumption The calculation formula is as follows:

[0057]

[0058] in, represents the variance of the Gaussian component in non-Gaussian noise, represents the variance of the non-Gaussian component in the non-Gaussian noise, ε represents the occurrence probability of the non-Gaussian component in the non-Gaussian noise, η is the Gaussian kernel width, represents the gamma function.

[0059] The theoretical basis is as follows. According to the definition, we can get:

[0060]

[0061] in,

[0062]

[0063]

[0064] make You can get:

[0065]

[0066] in, It has zero mean and variance Gaussian distribution.

[0067] Similarly, You can get:

[0068]

[0069] in, It has zero mean and variance Gaussian distribution.

[0070] For a zero mean and variance σ 2 The calculation formula for the k-th order absolute moment of a Gaussian distributed random variable x is:

[0071]

[0072] Based on this result, we can get:

[0073]

[0074] Combining the above two equations, we can get the transformed array signal in H0 The k-th order absolute moment ω under the assumption k expression.

[0075] Based on the above technical solution, the following embodiments are provided.

[0076] In order to analyze the performance of the Gaussian kernel energy detector in signal detection under non-Gaussian noise, the present invention will be verified through Monte Carlo experiments. Figure 2 is a schematic diagram of the detection structure of the Gaussian nuclear energy detector, where is the array signal received by the multi-antenna system, is the array signal after Gaussian kernel transformation, G 1 ,G 2 ,…,G N is the nuclear energy of the signal, T is the constructed test statistic, and finally the comparison and analysis of the test statistic T and the detection threshold λ yields the result of the binary hypothesis test (H 0 : Source signal does not exist or H 1 : source signal exists).

[0077] Through Monte Carlo experiments, the performance of Gaussian kernel energy detector and existing detection algorithms under different signal-to-noise ratios is compared and analyzed, which verifies that Gaussian kernel energy detector has good robustness in non-Gaussian noise environment. The number of experiments is 10 4 The signal gains of all antennas are assumed to be equal to a constant h, that is, h 1 =…=h M =h, the number of antennas is M = 4, the source signal s is randomly generated by a signal of length N = 100 that obeys the standard normal distribution, and the variance of the background noise is set to δ 1 =1 and The experimental results are as follows Figure 3 and Figure 4 shown.

[0078] exist Figure 3 The false alarm probability is P f =0.05, and the probability of non-Gaussian noise is ε=0.1. The simulation considers two cases: η=2 and η=8. It can be seen from the results in the figure that in a non-Gaussian noise environment, the detection probability curve of the energy detector is a horizontal line close to the false alarm probability, and the detection ability is completely lost. The polarity coincidence array, logarithmic moment detector and Gaussian core energy detector show good robustness to non-Gaussian noise, and the detection probability curve is relatively high. In addition, the Gaussian core energy detector has a higher detection probability curve than the polarity coincidence array and logarithmic moment detector, and the detection performance is better, which shows that the Gaussian core energy detector can be used as a powerful tool for signal detection in a non-Gaussian noise environment.

[0079] Figure 4 The detection probability curve of the Gaussian kernel energy detector with the change of Gaussian kernel width is analyzed under five different ε (ε∈{0,0.05,0.10,0.15,0.20}) values, where the false alarm probability P f = 0.01 and signal gain h = 0.5. Figure 4 The experimental results show that with the increase of Gaussian kernel width η, the detection probability of Gaussian kernel energy detector increases first and then decreases, and the maximum detection probability appears at about η = 3. In addition, the Gaussian kernel energy detector has a higher detection probability in the kernel width range of η∈[2,4], that is, the kernel width value of η∈[2,4] can ensure that the Gaussian kernel energy detector obtains excellent detection performance.

[0080] As a second aspect, the present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the energy detection method based on Gaussian kernel under non-Gaussian noise as described above.

[0081] As a third aspect, the present invention further provides a computer-readable storage medium, characterized in that it stores a computer program, and when the computer program is executed by a processor, it implements the energy detection method based on Gaussian kernel under non-Gaussian noise as described above.

[0082] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0083] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A Gaussian kernel-based energy detection method under non-Gaussian noise, characterized in that: include: Acquire array signals received by a multi-antenna system; Constructing a Gaussian kernel function based on a set Gaussian kernel width, and performing a Gaussian kernel transformation on the array signal using the Gaussian kernel function; Calculating the energy of the array signal after Gaussian kernel transformation, and constructing a test statistic based on the energy; Calculate the detection threshold according to the given false alarm probability; The test statistic and the detection threshold are compared and analyzed to obtain a signal detection result.

2. The energy detection method based on Gaussian kernel under non-Gaussian noise according to claim 1, characterized in that: The array signal is specifically expressed as: Among them, H0 means that the source signal does not exist, H1 means that the source signal and noise coexist, and z m (n) is the array signal received by the mth receiving antenna at time n, s(n) is the source signal to be detected, h m ≤1, indicating the signal gain of the mth receiving antenna, M is the number of receiving antennas, N is the signal length, w m (n) represents the background noise of the mth receiving antenna at time n.

3. The energy detection method based on Gaussian kernel under non-Gaussian noise according to claim 1, characterized in that: The Gaussian kernel function is constructed based on the set Gaussian kernel width, and the Gaussian kernel function is used to perform Gaussian kernel transformation on the array signal. The specific calculation includes: Among them, κ(z,η) represents the Gaussian kernel function, z represents the input data, η represents the Gaussian kernel width, z m (n) is the array signal received by the mth receiving antenna at time n, is the array signal after Gaussian kernel transformation, M is the number of receiving antennas, and B is the signal length.

4. The energy detection method based on Gaussian kernel under non-Gaussian noise according to claim 1, characterized in that: The energy of the array signal after Gaussian kernel transformation is calculated, and a test statistic is constructed based on the energy. Specifically, the calculation includes: in, is the array signal after Gaussian kernel transformation, G n represents the energy of the transformed array signal at time n, T represents the test statistic, M is the number of receiving antennas, and N is the signal length.

5. The energy detection method based on Gaussian kernel under non-Gaussian noise according to claim 1, characterized in that: The detection threshold is calculated according to the given false alarm probability, and the specific calculation includes: Among them, λ represents the detection threshold, Φ -1 (·) represents the inverse function of the standard normal distribution cumulative distribution function Φ, P f For a given false alarm probability, μ = Mω2, It represents the k-order absolute moment of the transformed array signal under the H0 assumption, where H0 means that the source signal does not exist, M is the number of receiving antennas, and N is the signal length.

6. The energy detection method based on Gaussian kernel under non-Gaussian noise according to claim 1, characterized in that: The test statistic and the detection threshold are compared and analyzed to obtain a signal detection result, and the specific process is as follows: The test statistic is compared with the detection threshold. If the test statistic is greater than the detection threshold, the signal detection result is determined to be the presence of the source signal; if the test statistic is less than or equal to the detection threshold, the signal detection result is determined to be the absence of the source signal.

7. An electronic device, characterized in that: The electronic device comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the energy detection method based on Gaussian kernel under non-Gaussian noise according to any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: The device stores a computer program, which, when executed by a processor, implements the energy detection method based on Gaussian kernel under non-Gaussian noise as described in any one of claims 1 to 6.

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