A signal detection method based on Kendall's harmony coefficient

Abstract

The present invention provides a signal detection method based on Kendall's harmony coefficient, comprising the following steps: obtaining array signals received by multi-channel sensors; calculating the rank statistics of the array signals by row to obtain a rank matrix; calculating the Euclidean square distance of the rank statistics of any two rows of the rank matrix to obtain a distance matrix; calculating the sum of the non-diagonal elements of the distance matrix, and performing linear operations on the summed result to obtain the expression of the test statistic; calculating the corresponding detection threshold according to a given false alarm probability; comparing the size of the test statistic and the detection threshold, so as to determine whether the source signal exists. The method of the present invention not only exhibits robustness against impulse noise, but also has a fast algorithm for the number of channels, and can be applied to fast signal detection in an impulse noise environment.

Description

Technical Field

[0001] The invention belongs to the field of communication technology, and in particular relates to a signal detection method based on Kendall's harmony coefficient. Background Art

[0002] Signal detection is an important signal analysis technology, which is widely used in phased array radar, underwater sonar and mobile communications. Its purpose is to determine whether and when useful signals appear, so that the system can extract more useful high-quality signals through parameter estimation, coding recognition, modulation analysis and other technologies.

[0003] At present, energy detectors are the most popular signal method in Gaussian noise environments. They are widely used because of their simple structure and easy implementation. However, due to factors such as atmospheric radiation and channel interference, in addition to additive Gaussian noise, noise sources in actual scenarios also include some noise that obeys non-Gaussian distributions. These non-Gaussian distribution noises have the characteristics of short duration but large amplitude, and are usually called impulse noise. Due to the presence of impulse noise, the signal-to-noise ratio of the received echo signal will decrease rapidly over a period of time, causing the performance of the energy detector to deteriorate rapidly or even fail. To this end, researchers have proposed a polarity coincidence array that is robust to impulse noise. However, the performance of the polarity coincidence array in an impulse noise environment still needs to be further improved. Summary of the invention

[0004] The purpose of the present invention is to provide a signal detection method based on Kendall's harmonic coefficient to make up for the shortcomings of the prior art in signal detection under impulse noise environment.

[0005] A signal detection method based on Kendall's harmony coefficient comprises the following steps:

[0006] Acquire array signals received by multiple sensors;

[0007] Calculate the rank statistics of the array signal row by row to obtain a rank matrix;

[0008] Calculate the Euclidean square distance of any two rows of the rank statistics of the rank matrix to obtain a distance matrix;

[0009] Calculating the sum of the off-diagonal elements of the distance matrix, and performing a linear operation on the sum result to obtain an expression of the test statistic;

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

[0011] Compare the test statistic and the detection threshold to determine whether the source signal exists.

[0012] Furthermore, the received array signal is specifically:

[0013] z m (i) = h m s(i)+w m (i)

[0014] m=1,2,…,M

[0015] i=1,2,…,N

[0016] Among them, z m (i) is the received signal of the mth sensor at sampling time i, s(i) is the source signal to be detected, h m represents the signal gain of the mth sensor, w m (i) represents the background noise, M is the number of sensors, and N is the signal length.

[0017] Furthermore, the rank statistics of the array signal are calculated row by row to obtain a rank matrix:

[0018]

[0019]

[0020]

[0021] Where Q represents the rank matrix of the corresponding array signal, H represents the heaviside step function, and z m (i) is the received signal of the mth sensor at sampling time i, z m (j) is the received signal of the mth sensor at sampling time j.

[0022] Furthermore, the Euclidean square distance of any two rows of rank statistics of the rank matrix is ​​calculated to obtain a distance matrix:

[0023]

[0024]

[0025] Among them, Qi m To receive the signal z m The rank statistic of (i), Qi n To receive the signal z n The rank statistic of (i).

[0026] Furthermore, the expression of calculating the sum of the off-diagonal elements of the distance matrix and performing a linear operation on the sum result to obtain the test statistic is specifically:

[0027]

[0028] Where M is the number of sensors, N is the signal length, and D ij is the (i, j) element of the distance matrix D.

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

[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, the size of the comparison test statistic and the detection threshold is specifically:

[0033] Compare the test statistic and the detection threshold. If the test statistic is greater than or equal to the detection threshold, the source signal exists; if the test statistic is less than the detection threshold, the source signal does not exist.

[0034] A fast algorithm based on Kendall's harmony coefficient, the technical solution adopted is as follows:

[0035] 1) Obtain the corresponding rank matrix Q according to the received array signal:

[0036]

[0037]

[0038] Where Q represents the rank matrix of the corresponding array signal, H represents the heaviside step function,

[0039]

[0040] 2) Normalizing the rank matrix to obtain a normalized rank matrix

[0041]

[0042]

[0043] 3) Calculate the row mean of the normalized rank matrix to obtain the corresponding mean vector J:

[0044] J=[J1,J2,…,J N ]

[0045]

[0046] 4) Calculate the sum of the squares of the mean vector and perform linear operations on the summed result to obtain a fast implementation expression of the statistic:

[0047]

[0048] Technical effects of the present invention:

[0049] The signal detection method based on Kendall's harmony coefficient provided by the present invention fully suppresses the negative impact of large outliers in impulse noise by using the rank statistics of the signal instead of the original signal value, and shows excellent robustness in the impulse noise environment. Therefore, in the context of impulse noise, Kendall's harmony coefficient is an effective tool for signal detection, which is excellent in both time complexity and performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] 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.

[0051] Figure 1 A schematic flow chart of a signal detection method of the present invention is shown;

[0052] Figure 2 A schematic diagram of realizing the fast algorithm of the present invention is shown;

[0053] Figure 3 A performance comparison chart of existing detection methods and Kendall's harmonic coefficient for signal detection in an impulse noise environment is shown.

[0054] Figure 4 A comparison of the running times of the Kendall harmony coefficient based on the original definition and based on the fast algorithm is shown. DETAILED DESCRIPTION

[0055] 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.

[0056] This embodiment provides a signal detection method based on Kendall's harmony coefficient. Figure 1 As shown, the following steps are included:

[0057] Step S10: Acquire array signals received by multiple sensors;

[0058] Step S20: Calculate the rank statistics of the array signal row by row to obtain a rank matrix;

[0059] Step S30: Calculate the Euclidean square distance between any two rows of the rank statistics of the rank matrix to obtain a distance matrix;

[0060] Step S40: Calculate the sum of the off-diagonal elements of the distance matrix, and perform a linear operation on the sum result to obtain a test statistic T;

[0061] Step S50: According to a given false alarm probability P f Calculate the corresponding detection threshold η;

[0062] Step S60: Compare the test statistic T and the detection threshold η. If the test statistic is greater than or equal to the detection threshold, the source signal exists; if the test statistic is less than the detection threshold, the source signal does not exist.

[0063] As a preferred implementation of this embodiment, the array signal received by the multi-channel sensor at the i-th sampling moment has the following form:

[0064] z m (i) = h m s(i)+w m (i)

[0065] m=1,2,…,M

[0066] i=1,2,…,N

[0067] Among them, z m (i) is the received signal of the mth sensor at sampling time i, s(i) is the source signal to be detected, h m represents the signal gain of the mth sensor, w m (i) represents the background noise, M is the number of sensors (channels), and N is the signal length.

[0068] As a preferred implementation of this embodiment, calculating the rank statistics of the array signal row by row to obtain the rank matrix can be implemented by the following formula:

[0069]

[0070]

[0071] Where Q represents the rank matrix of the corresponding array signal, H represents the heaviside step function,

[0072]

[0073] As a preferred implementation of this embodiment, the Euclidean square distance of any two rows of rank statistics of the rank matrix is ​​calculated to obtain the distance matrix, which can be implemented by the following formula:

[0074]

[0075]

[0076] As a preferred implementation of this embodiment, the calculation of the sum of the off-diagonal elements of the distance matrix and the linear operation of the summation result to obtain the expression of the test statistic can be implemented by the following formula:

[0077]

[0078] As a preferred implementation of this embodiment, the formula for calculating the detection threshold by the false alarm probability is:

[0079]

[0080] 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.

[0081] As a preferred implementation of this embodiment, the signal detection process is implemented by the following judgment:

[0082]

[0083] This embodiment provides a fast algorithm based on Kendall's harmony coefficient, such as Figure 2 As shown, the following steps are included:

[0084] 1) Obtain the corresponding rank matrix Q according to the received array signal:

[0085]

[0086]

[0087] Where Q represents the rank matrix of the corresponding array signal, H represents the heaviside step function,

[0088]

[0089] 2) Normalizing the rank matrix to obtain a normalized rank matrix

[0090]

[0091]

[0092] 3) Calculate the row mean of the normalized rank matrix to obtain the corresponding mean vector J:

[0093] J=[J1,J2,…,J N ]

[0094]

[0095] 4) Calculate the sum of the squares of the mean vector and perform linear operations on the summed result to obtain a fast implementation expression of the statistic:

[0096]

[0097] Example 1

[0098] The present invention will compare and analyze the performance of Kendall's harmony coefficient and existing signal detection algorithms in terms of time complexity and detection probability through Monte Carlo experiments. The experimental parameters are set as follows:

[0099] The signal to be detected is randomly generated from a signal with a length of n=300 and obeying a standard normal distribution.

[0100] The impulse noise of all channels is simulated by the following mixed Gaussian distribution:

[0101]

[0102] Among them, ε=0.04 represents the probability of the pulse component occurring in the entire pulse noise environment, and δ2=50>>δ1 represents the standard deviation of the pulse component. At this time, the system signal-to-noise ratio can be defined as:

[0103]

[0104] exist Figure 3 In the experiment, the number of experiments is 10 4 times, false alarm probability P f =0.1. For the convenience of analysis, assume that the signal gain of all channels is equal: h1 = ... = h M =0.5. Figure 3 The experimental results show that due to the existence of the pulse component, the detection probability curve of the energy detector is close to a P f = 0.1, completely losing detection capability. The polarity coincidence array shows a certain degree of robustness to impulse noise, but its detection performance is inferior to the Kendall harmonic coefficient, indicating that the Kendall harmonic coefficient can be used as a powerful tool for signal detection in an impulse noise environment.

[0105] In order to further analyze the effectiveness of the proposed fast algorithm, the present invention Figure 4 The running time of the Kendall concordance coefficient based on the original definition and the fast algorithm is compared with the number of channels M, where the sample length N = 10. For each value of M, the running time is calculated after 10 3The results of the Monte Carlo simulations are averaged. The simulation platform is MATLAB R2017b software in a PC with AMD Ryzen 55600G and Radeon Graphics 3.90GHz. Figure 4 It can be seen from the simulation results that the fast algorithm proposed in the present invention greatly reduces the time complexity of the Kendall harmony coefficient to the number of channels.

[0106] 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 signal detection method based on Kendall's harmony coefficient, characterized in that: The following steps are involved: Acquire array signals received by multiple sensors; Calculate the rank statistics of the array signal row by row to obtain a rank matrix; Calculate the Euclidean square distance of any two rows of the rank statistics of the rank matrix to obtain a distance matrix; Calculating the sum of the off-diagonal elements of the distance matrix, and performing a linear operation on the sum result to obtain an expression of a test statistic; Calculate the corresponding detection threshold according to the given false alarm probability; Compare the test statistic and the detection threshold to determine whether the source signal exists.

2. The signal detection method based on Kendall's harmony coefficient according to claim 1, characterized in that: The received array signal is specifically: z m (i)=h m s(i)+w m (i) m=1,2,…,M i=1,2,…,N Among them, z m (i) is the received signal of the mth sensor at sampling time i, s(i) is the source signal to be detected, h m represents the signal gain of the mth sensor, w m (i) represents the background noise, M is the number of sensors, and N is the signal length.

3. The signal detection method based on Kendall's harmony coefficient according to claim 1, characterized in that: The rank statistics of the array signal are calculated row by row to obtain a rank matrix: Where Q represents the rank matrix of the corresponding array signal, H represents the heaviside step function, and z m (i) is the received signal of the mth sensor at sampling time i, z m (j) is the received signal of the mth sensor at sampling time j, Q im To receive the signal z m (i) is the rank statistic, M is the number of sensors, and N is the signal length.

4. The signal detection method based on Kendall's harmony coefficient according to claim 1, characterized in that: The Euclidean square distance of any two rows of the rank statistics of the rank matrix is ​​calculated to obtain a distance matrix: Among them, Q im To receive the signal z m The rank statistic of (i), Q in To receive the signal z n (i) is the rank statistic, M is the number of sensors, and N is the signal length.

5. The signal detection method based on Kendall's harmony coefficient according to claim 1, characterized in that: The expression for calculating the sum of the off-diagonal elements of the distance matrix and performing a linear operation on the sum result to obtain the test statistic is specifically: Where M is the number of sensors, N is the signal length, and D ij is the (i,j) element of the distance matrix D.

6. The signal detection method based on Kendall's harmony coefficient according to claim 1, characterized in that: The corresponding detection threshold is calculated according to the given false alarm probability: Among them, Φ -1 (·) represents the inverse function of the standard normal distribution cumulative distribution function Φ, P f is the given false alarm probability, and N is the signal length.

7. The signal detection method based on Kendall's harmony coefficient according to 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 or equal to the detection threshold, the source signal exists; if the test statistic is less than the detection threshold, the source signal does not exist.

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