Non-cooperative underwater acoustic pulse signal detection method and system based on power-w and fractional order spectral entropy

Abstract

The invention discloses a non-cooperative underwater sound pulse signal detection method based on power-w and fractional order spectral entropy. The method comprises the following steps: performing fractional order Fourier transform on a received non-cooperative underwater sound pulse signal; the optimal order p of fractional Fourier transform is found through a traversal method; performing v-th power processing on the energy of the frequency domain signal after the p-order fractional order Fourier transform to obtain an improved fractional order power spectrum; performing normalization processing on the improved fractional order power spectrum E, and calculating an entropy value T corresponding to the data; calculating an entropy value of the background noise, taking the entropy value as a fixed threshold value, comparing the fixed threshold value with the entropy value obtained by calculation, and if the fixed threshold value is greater than the entropy value obtained by calculation, judging that there is a signal; otherwise, no signal exists. According to the method, the detection effect can still keep excellent under the condition of low signal-to-noise ratio, and the robustness is higher.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic signal recognition, and in particular is a non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional-order spectral entropy. Background Art

[0002] The detection of non-cooperative underwater acoustic pulse signals is generally achieved by whether they have certain characteristics. At present, the detection methods for unknown signals can be divided into time domain detection, frequency domain detection and time-frequency domain detection. The most common detection method in time domain detection is energy detection, which determines the presence or absence of a signal by comparing the energy on the time axis with the size of the preset threshold value. It has extremely low requirements for prior information of the signal and small amount of calculation, but it will fail under low signal-to-noise ratio conditions. The common detection method in frequency domain detection is information entropy detection, which determines the presence or absence of a signal by the complexity of the system. This method has excellent detection effect when detecting single-frequency signals, but for linear frequency modulation signals, its detection effect is limited compared to the gain of time domain detection. In recent years, with the gradual improvement of detection methods, more detection methods have been extended to the time-frequency domain. Common time-frequency domain detection methods include short-time Fourier transform, wavelet transform, fractional-order Fourier transform, etc. The detection effect of fractional Fourier transform on LFM signal is better than that of conventional time domain and frequency domain detection. After the received signal is subjected to fractional Fourier transform, the energy of the signal is obviously concentrated in the frequency domain, which is more convenient for detection. However, as the signal-to-noise ratio is further reduced, the detection effect will be significantly reduced. Summary of the invention

[0003] Purpose of the invention: In order to obtain better underwater acoustic pulse signal detection effect under low signal-to-noise ratio conditions, the present invention proposes a non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional-order spectral entropy.

[0004] Technical solution: A non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy, comprising the following steps:

[0005] Step 1: Perform a fractional Fourier transform on the received non-cooperative underwater acoustic pulse signal; find the optimal order p of the fractional Fourier transform by traversal method;

[0006] Step 2: Perform v-th power processing on the energy of the frequency domain signal after the p-order fractional Fourier transform to obtain an improved fractional power spectrum;

[0007] Step 3: Normalize the improved fractional power spectrum E and calculate the entropy value T corresponding to the data;

[0008] Step 4: Calculate the entropy value of the background noise as a fixed threshold, and compare it with the entropy value calculated in step 3. If the fixed threshold is greater than the entropy value calculated in step 3, it is determined that there is a signal; otherwise, there is no signal.

[0009] Furthermore, in step 1, the fractional Fourier transform of the received non-cooperative underwater acoustic pulse signal is specifically performed as follows:

[0010] The p-order fractional Fourier transform of the signal x(t):

[0011]

[0012] F p [x(t)] represents the p-order fractional Fourier transform of the signal x(t), t represents time, and u represents frequency; where,

[0013]

[0014] Where: K p (t,u) is the kernel function of the fractional Fourier transform, α is the rotation angle of the signal, α=pπ / 2, and the amplitude factor j is an imaginary number and n is an arbitrary integer.

[0015] Furthermore, in step 1, the optimal order p of the fractional Fourier transform is found by traversal method: set p∈[0,2], set the step size to 0.01, substitute the traversal order into equation (2), and obtain the maximum |X p (u)| 2 When , it is the optimal order p.

[0016] Furthermore, the improved fractional-order power spectrum E in step 2 is:

[0017]

[0018] X p (u) is the p-order fractional Fourier transform of the signal, and N represents the total number of spectral lines in the fractional domain.

[0019] Furthermore, the improved fractional-order power spectrum E is normalized, and the normalized probability density distribution is:

[0020]

[0021] Where N represents the total number of spectral lines in the fractional domain, k represents each spectral line after discrete Fourier transform, that is, the sampling sample of each point after discrete Fourier transform; p (k) Satisfy:

[0022]

[0023] Calculate the entropy value T corresponding to the improved fractional power spectrum E:

[0024]

[0025] Furthermore, the fixed threshold is the mean entropy value of the background noise obtained through multiple experiments, which is set as the threshold γ

[0026]

[0027] H0 indicates that there is no signal, and H1 indicates that there is a signal.

[0028] A non-cooperative underwater acoustic pulse signal detection system based on power-law and fractional spectral entropy, including a fractional Fourier transform module, a power-law module, a fractional spectral entropy module and a determination module;

[0029] The fractional Fourier transform module performs a fractional Fourier transform on the received non-cooperative underwater acoustic pulse signal; finds the optimal order p of the fractional Fourier transform by a traversal method;

[0030] The power-law module performs v-th power processing on the energy of the frequency domain signal after the p-th order fractional Fourier transform to obtain an improved fractional power spectrum;

[0031] The fractional-order spectrum entropy module normalizes the improved fractional-order power spectrum E and calculates the entropy value T corresponding to the data;

[0032] The determination module calculates the entropy value of the background noise as a fixed threshold, and compares it with the entropy value calculated by the fractional spectral entropy module. If the fixed threshold is greater than the entropy value calculated by the fractional spectral entropy module, it is determined that there is a signal; otherwise, there is no signal.

[0033] Beneficial effect: Power-law is combined with fractional power spectrum entropy. The traditional power spectrum is raised to the power of v (a large number of experiments show that v is 2.5), the difference between noise and signal is increased, and the entropy detection is performed on the processed power spectrum. The detection effect can still be excellent under low signal-to-noise ratio conditions. Compared with traditional energy detection with a detection efficiency of 50%, the signal-to-noise ratio required by the present invention is only -14dB, which is nearly 8dB of gain and has higher robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a detection flow chart of the present invention;

[0035] Figure 2 A three-dimensional graph for searching for the best order

[0036] Figure 3 The performance advantage of the improved detection algorithm for CW pulse signals over the traditional detection method;

[0037] Figure 4The performance advantage of the improved detection algorithm for LFM pulse signals over the traditional detection method; DETAILED DESCRIPTION

[0038] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0039] Embodiment 1:

[0040] like Figure 1 As shown, the non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy includes the following steps:

[0041] Step 1: Perform a fractional Fourier transform on the received non-cooperative underwater acoustic pulse signal; find the optimal order p of the fractional Fourier transform by traversal method;

[0042] Step 2: Perform v-th power processing on the energy of the frequency domain signal after the p-order fractional Fourier transform to obtain an improved fractional power spectrum;

[0043] Step 3: Normalize the improved fractional power spectrum E and calculate the entropy value T corresponding to the data;

[0044] Step 4: Calculate the entropy value of the background noise as a fixed threshold, and compare it with the entropy value calculated in step 3. If the fixed threshold is greater than the entropy value calculated in step 3, it is determined that there is a signal; otherwise, there is no signal.

[0045] Preferably, the fractional-order Fourier transform of the received non-cooperative underwater acoustic pulse signal in step 1 is specifically performed as follows:

[0046] The p-order fractional Fourier transform of the signal x(t):

[0047]

[0048] F p [x(t)] represents the p-order fractional Fourier transform of the signal x(t), t represents time, and u represents frequency; where,

[0049]

[0050] Where: K p (t,u) is the kernel function of the fractional Fourier transform, α is the rotation angle of the signal, α=pπ / 2, and the amplitude factor j is an imaginary number and n is an arbitrary integer.

[0051] Preferably, the optimal order p of the fractional Fourier transform is found by traversal in step 1 as follows: set p∈[0,2], set the step size to 0.01, substitute the traversal order into formula (2), and obtain the maximum |Xp (u)| 2 When , it is the optimal order p.

[0052] Preferably, the improved fractional-order power spectrum E in step 2 is:

[0053]

[0054] X p (u) is the p-order fractional Fourier transform of the signal, and N represents the total number of spectral lines in the fractional domain.

[0055] Preferably, the improved fractional-order power spectrum E is normalized, and the normalized probability density distribution is:

[0056]

[0057] Where N represents the total number of spectral lines in the fractional-order domain, k represents the spectral lines after discrete Fourier transform, that is, the sampling samples of each point after discrete Fourier transform; u above represents the concept of frequency domain.

[0058] where g p (k) Satisfy:

[0059]

[0060] The improved power spectrum entropy expression in the fractional-order domain is:

[0061]

[0062] Furthermore, the fixed threshold is the mean entropy value of the background noise obtained through multiple experiments, which is set as the threshold γ, that is, the principle of the improved fractional power spectrum entropy detection is:

[0063]

[0064] H0 indicates that there is no signal, and H1 indicates that there is a signal.

[0065] Embodiment 2:

[0066] A non-cooperative underwater acoustic pulse signal detection system based on power-law and fractional spectral entropy, including a fractional Fourier transform module, a power-law module, a fractional spectral entropy module and a determination module;

[0067] The fractional Fourier transform module performs a fractional Fourier transform on the received non-cooperative underwater acoustic pulse signal; finds the optimal order p of the fractional Fourier transform by a traversal method;

[0068] The power-law module performs v-th power processing on the energy of the frequency domain signal after the p-th order fractional Fourier transform to obtain an improved fractional power spectrum;

[0069] The fractional-order spectrum entropy module normalizes the improved fractional-order power spectrum E and calculates the entropy value T corresponding to the data;

[0070] The determination module calculates the entropy value of the background noise as a fixed threshold, and compares it with the entropy value calculated by the fractional spectral entropy module. If the fixed threshold is greater than the entropy value calculated by the fractional spectral entropy module, it is determined that there is a signal; otherwise, there is no signal.

[0071] The characteristics of the invention are verified by the following experiments:

[0072] The advancement and robustness of the invention were verified using real data from Qiandao Lake.

[0073] First, the basic parameters used in this method are explained as follows: The example signal form and its parameters in this method are as follows: the sampling frequency is 10000Hz; the center frequency of the LFM signal is 2000Hz, the linear modulation frequency is 8000Hz / s, and the pulse width is 50ms; the center frequency of the CW signal is 1500Hz, and the pulse width is 100ms; after confirming the parameters, follow the steps below:

[0074] (1) Process the received signal using short-time fractional Fourier transform

[0075] The p-order fractional Fourier transform of the signal x(t):

[0076]

[0077] in,

[0078]

[0079] Where: K p (t,u) is the kernel function of the fractional Fourier transform, α=pπ / 2, the amplitude factor n is an arbitrary integer. When p = 1, α = p / 2, the fractional Fourier transform is the Fourier transform itself. The kernel function is symmetric, so we only need to consider p∈[0,2]. To obtain the optimal order p, the amplitude of the signal after the fractional Fourier transform is required to be the largest, that is, |X p (u) 2 The value is the largest. According to the calculation formula, the amplitude is a three-dimensional function of the time variable t, the order p and the frequency variable u. The order p corresponding to the highest point in the three-dimensional image is the optimal order. Figure 2 shown.

[0080] The present invention is compared with common detection methods in terms of detection efficiency. Figure 2 , 3 Compared with conventional energy detection, the performance is greatly improved, about 8dB (the detection effect can be determined by observing the signal-to-noise ratio required when the detection efficiency reaches 50%). Figure 2 It is a comparison of the detection efficiency of single-frequency signals (CW signals). The signal-to-noise ratio required by the present invention is about -13dB, which is better than -12dB of fractional-order power spectrum entropy detection, -11dB of v-power energy detection, and -6dB of energy detection. Figure 3 The detection efficiency of the linear frequency modulation signal (LFM signal) is compared. The signal-to-noise ratio required by the present invention is about -15dB, which is better than the -13dB of fractional power spectrum entropy detection, better than the -11dB of v-power energy detection, and better than the -6dB of energy detection. By comparing the single-frequency signal and the linear frequency modulation signal, it can be seen that the detection method of the present invention has a certain degree of performance improvement, but in the process of detecting the linear frequency modulation signal, the gain is more obvious.

[0081] The selection of threshold value has a great influence on the detection efficiency, so when setting the threshold value, the present invention adopts 1000 Monk Carlo experiments, conducts random experiments on real environmental noise, obtains a set of environmental entropy values, averages the values, and uses the calculated average value as the threshold to determine whether the signal exists. This can effectively avoid the threshold being too large, which makes the false alarm rate of signal detection too large; it can also avoid the threshold being too small, which makes the detection efficiency of signal detection low. In summary, the present invention can be applied to non-cooperative underwater acoustic pulse signal detection, and still has good detection efficiency under low signal-to-noise ratio conditions.

Claims

1. A non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy, characterized in that: The following steps are involved: Step 1: Perform a fractional Fourier transform on the received non-cooperative underwater acoustic pulse signal; find the optimal order p of the fractional Fourier transform by traversal method; Step 2: Perform v-th power processing on the energy of the frequency domain signal after the p-order fractional Fourier transform to obtain an improved fractional power spectrum; Step 3: Normalize the improved fractional power spectrum E and calculate the entropy value T corresponding to the data; Step 4: Calculate the entropy value of the background noise as a fixed threshold, and compare it with the entropy value calculated in step 3. If the fixed threshold is greater than the entropy value calculated in step 3, it is determined that there is a signal; otherwise, there is no signal.

2. The non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy according to claim 1 is characterized in that: In step 1, the fractional Fourier transform of the received non-cooperative underwater acoustic pulse signal is specifically performed as follows: The p-order fractional Fourier transform of the signal x(t): F p [x(t)] represents the p-order fractional Fourier transform of the signal x(t), t represents time, and u represents frequency; where, Where: K p (t,u) is the kernel function of the fractional Fourier transform, α is the rotation angle of the signal, α=pπ / 2, and the amplitude factor j is an imaginary number and n is an arbitrary integer.

3. The non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy according to claim 2 is characterized in that: In step 1, the optimal order p of the fractional Fourier transform is found by traversal method: set p∈[0,2], set the step size to 0.01, substitute the traversal order into equation (2), and obtain the maximum |X p (u)| 2 When , it is the optimal order p.

4. The non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy according to claim 1, characterized in that: The improved fractional power spectrum E in step 2 is: X p (u) is the p-order fractional Fourier transform of the signal, and N represents the total number of spectral lines in the fractional domain.

5. The non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy according to claim 1 is characterized in that: The improved fractional-order power spectrum E is normalized, and the normalized probability density distribution is: Where N represents the total number of spectral lines in the fractional domain, k represents each spectral line after discrete Fourier transform; p (k) Satisfy: Calculate the entropy value T corresponding to the improved fractional power spectrum E:

6. The non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy according to claim 5 is characterized in that: The fixed threshold is the mean entropy value of the background noise obtained through multiple experiments, which is set as the threshold γ. H0 indicates that there is no signal, and H1 indicates that there is a signal.

7. A non-cooperative underwater acoustic pulse signal detection system based on power-law and fractional spectral entropy, characterized in that: It includes fractional Fourier transform module, power-law module, fractional spectral entropy module and judgment module; The fractional Fourier transform module performs a fractional Fourier transform on the received non-cooperative underwater acoustic pulse signal; finds the optimal order p of the fractional Fourier transform by a traversal method; The power-law module performs v-th power processing on the energy of the frequency domain signal after the p-th order fractional Fourier transform to obtain an improved fractional power spectrum; The fractional-order spectrum entropy module normalizes the improved fractional-order power spectrum E and calculates the entropy value T corresponding to the data; The determination module calculates the entropy value of the background noise as a fixed threshold, and compares it with the entropy value calculated by the fractional spectral entropy module. If the fixed threshold is greater than the entropy value calculated by the fractional spectral entropy module, it is determined that there is a signal; otherwise, there is no signal.

8. The non-cooperative underwater acoustic pulse signal detection system based on power-law and fractional spectral entropy according to claim 7, characterized in that: The power-law module performs the following processing to obtain an improved fractional-order power spectrum E: X p (u) is the p-order fractional Fourier transform of the signal, N is the total number of spectral lines in the fractional domain, and u is the frequency.

9. The non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy according to claim 7 is characterized in that: The improved fractional-order power spectrum E is normalized, and the normalized probability density distribution is: Where N represents the total number of spectral lines in the fractional domain, k represents each spectral line after discrete Fourier transform; p (k) Satisfy: Calculate the entropy value T corresponding to the improved fractional power spectrum E:

10. The non-cooperative underwater acoustic pulse signal detection method based on power-law and fractional spectral entropy according to claim 9 is characterized in that: The fixed threshold is the mean entropy value of the background noise obtained through multiple experiments, which is set as the threshold γ H0 indicates that there is no signal, and H1 indicates that there is a signal.

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