Improved method for detecting peak value line spectrum amplitude correction periodogram

Abstract

The invention discloses an improved method for peak value line spectrum amplitude correction periodogram detection, which comprises the following steps of: firstly, carrying out discrete sampling on a received signal r (t) to obtain r (n), calculating FFT (Fast Fourier Transform) of each segment of data as Ri (k) according to the segment length of M and the stepping of S, i = 0, 1,... I, and I is the segment number of segments; performing square operation on the amplitude and multiplying by a coefficient 1 / M to obtain a periodogram of each section of signal; and setting the lower boundary frequency fl = f0-fd, the upper boundary frequency fh = f0 + fd and the corresponding discrete frequencies kl and kh of the search frequency band, taking the maximum value of the peak value in the multi-segment periodic diagram search frequency band, correcting the amplitude of the peak value, and comparing the corrected amplitude with a threshold. The sensitivity of the algorithm to Doppler frequency shift is reduced, and the beacon signal detection performance is improved.

Description

Technical Field

[0001] The invention relates to an improved method for peak line spectrum amplitude correction periodogram detection, in particular to an improved method for multi-copy correlation integral matching detection and peak line spectrum amplitude correction periodogram detection, belonging to the technical field of signal processing. Background Art

[0002] Traditional matched filters and periodogram detectors are suitable for detecting underwater acoustic beacon signals. However, when transmitted in actual ocean channels, the matching results and periodograms will be affected by various factors, which will reduce the performance of the detector.

[0003] First, the relative motion between the target and the receiver will cause the Doppler effect, resulting in the frequency shift of the signal and the stretching and contraction of the time domain signal. Then, when the matching signal is generated using known signal parameters and matched with the received signal for filtering, the correlation will be reduced and the matching result will be distorted. The ideal matching result is a triangular peak, while the triangular peak characteristics of the matching result affected by Doppler deteriorate, presenting a hump-shaped or more distorted waveform. For a periodogram with Doppler frequency shift, the peak frequency of the periodogram is offset relative to the original beacon signal frequency, and the amplitude at the beacon signal frequency may become very low. At this time, if the threshold detection is based only on the amplitude of a single frequency point, the detection performance will be seriously degraded.

[0004] The distortion caused by channel transmission to the signal mainly considers the FFD effect and TSD effect. The FFD effect can be regarded as the modulation of the signal by the time-varying function. It will not increase the frequency components that do not belong to the original signal, but it will distort the time-frequency characteristics of the original signal, making it difficult to observe. The matching result is also equivalent to being modulated by the time-varying function. It is difficult to intuitively observe the existence of the triangular peak, and the peak amplitude of the periodogram near the beacon frequency is reduced or even submerged. The TSD effect is mainly a multipath effect. Due to the superposition of signals with different phases, the time domain signal is expanded, resulting in distortion of the matching results and the periodogram, and violent fluctuations, thereby reducing the detection performance of the detector. Summary of the invention

[0005] Purpose of the invention: In view of the problems and shortcomings existing in the prior art, the present invention analyzes the characteristics of underwater acoustic beacon signals and the various factors affecting signal detection, and proposes improved methods of multi-copy correlation integral matching detection and peak line spectrum amplitude corrected periodogram detection to reduce the algorithm's sensitivity to Doppler frequency shift and improve the beacon signal detection performance.

[0006] Technical solution: An improved method for peak line spectrum amplitude correction periodogram detection. First, discrete sampling of the received signal r(t) is performed to obtain r(n). The FFT of each segment of data is calculated with a segment length of M and a step of S to obtain R. i(k), i = 0, 1, ... I, I is the number of segments. Then square its amplitude and multiply it by the coefficient 1 / M to get the periodogram of each signal segment. Set the lower boundary frequency f of the search band l =f 0 -f d , the upper boundary frequency is f h =f 0 +f d , the corresponding discrete frequency is k l and k h , take the maximum value of the peak value in the search frequency band of the multi-segment periodogram, correct the peak amplitude, and compare the corrected amplitude with the threshold.

[0007] When the search sonar's speed is v, the Doppler frequency shift is

[0008]

[0009] Therefore, the search frequency band range is set to the lower boundary frequency f l =f 0 -f d , the upper boundary frequency is f h =f 0 +f d , in the frequency band f l to f h The requirement can be met by searching for the peak value of the periodic diagram for detection and judgment.

[0010] When actually calculating the periodogram, the partially overlapping segmented FFT is used to calculate the spectrum. At the same time, the segment length and step of the segmented FFT can also be theoretically designed according to the beacon signal parameters to achieve better detection performance with less computation. At this time, GLRT is rewritten as

[0011]

[0012] or

[0013]

[0014] Among them, R i (k) is the sampling signal r of the i-th segment i DFT of (n), k l and k h is the discrete index of the frequency band boundary when searching for the peak of the spectrum. For a given false alarm probability P FA ,have

[0015]

[0016] Where L = I(M / 2-1), then the constant false alarm detection threshold is

[0017]

[0018] Since the underwater acoustic beacon signal is a single frequency signal, the Rife algorithm is used to correct the peak frequency amplitude to reduce the impact of spectrum leakage. The M-point FFT of the underwater acoustic beacon signal is:

[0019]

[0020] Where k = 0, 1, 2, ... M / 2-1, Δf = f s / M is the frequency resolution. Then the amplitude spectrum is

[0021]

[0022] When k is close to f 0 / Δf, the amplitude spectrum is approximately

[0023]

[0024] Assume that the peak line spectrum frequency found is f 1 , the corresponding amplitude is A 1 , the second highest line spectrum frequency is f 2 , the corresponding amplitude is A 2 , the real frequency of the signal is f 0 , the corresponding amplitude is A 0 , then

[0025]

[0026] The amplitude correction factor is

[0027]

[0028] in,

[0029] BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a principle diagram of periodogram detection based on peak amplitude correction according to an embodiment of the present invention;

[0031] Figure 2 1 is a comparison diagram of the detection results of the traditional matched filter and the multi-copy correlation integrator under various channel conditions of the embodiment of the present invention (a) Gaussian white noise channel; (b) Doppler-affected channel (v=2.2m / s); (c) FFD channel; (d) TSD channel;

[0032] Figure 3The comparison diagram of the original periodogram and the modified periodogram under various channel conditions; (a) Gaussian white noise channel; (b) Doppler-affected channel (v = 2.2 m / s); (c) FFD channel; (d) TSD channel;

[0033] Figure 4 : This is a comparison chart of the detection performance of each detector under different channel environments; (a) Gaussian white noise channel; (b) Doppler-affected channel (v=2.2m / s); (c) FFD channel; (d) TSD channel. DETAILED DESCRIPTION

[0034] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0035] An improved method for peak line spectrum amplitude correction periodogram detection uses multiple copy signals to resist the Doppler effect with low computational complexity. For the detection of underwater acoustic beacon signals, conventional matched filters and periodogram detectors are improved by combining the time-frequency characteristics of the signal to improve their resistance to Doppler and channel distortion.

[0036] Since the Doppler effect is caused by the relative motion between the black box acoustic beacon and the search sonar, and the black box is stationary, the search sonar's speed is slow and known, so when the search sonar's speed is v, the telescopic deviation of the pulse signal corresponding to each Doppler speed is theoretically calculated, and then combined with the signal sampling frequency, the Doppler speed scanning interval is set, thereby reducing the amount of blind scanning calculations. Assume that the search Doppler speed is v n ,1≤n≤N, then the copy signal corresponding to each Doppler velocity is s n (t), 1≤n≤N, and then matched filter processing is performed with the received signal. Considering the multi-peak structure of the matched filter output, a copy correlation integrator is used to improve the detection performance, and the square amplitude of the matched filter output is used for detection, that is,

[0037]

[0038] Finally, the maximum value among the N matching result peaks is taken as the test statistic, that is,

[0039] T(r)=max(max(y 1 (t)),max(y 2 (t)),...,max(y N (t))) (2)

[0040] If the test statistic T(r) ≥ γ, then the hypothesis H1 If the signal is less than the threshold, then the hypothesis H is determined. 0 The signal does not exist. Assume that the noise has zero mean and variance is σ 2 Gaussian distribution, given the false alarm probability P FA ,have

[0041]

[0042] Then the expression of constant false alarm threshold is

[0043] γ=-2σ 2 ln(P FA ) (4)

[0044] Set the searched Doppler velocity to v n ,1≤n≤N, the received signal r(t) is matched with multiple copy signals for filtering, the amplitude of each filter output is squared, the peak value of each matching result is taken, and finally the maximum value of the N peak values ​​is compared with the threshold γ of formula (4).

[0045] Due to the influence of Doppler frequency shift, using the amplitude of a single frequency point for judgment will affect the detection performance. In addition, the frequency of the underwater acoustic beacon signal is relatively high, and the high sampling frequency set at this time will lead to lower frequency resolution and spectrum leakage, which will cause the spectrum features to be unclear or even disappear. Since the arrival time is unknown, if the frequency of each n 0 The calculation will be very large. Aiming at the above problems of periodogram detector, a periodogram detector based on peak amplitude correction is proposed, which improves the original periodogram detector by setting search band, segmented FFT and peak amplitude correction.

[0046] Given that the frequency of the underwater acoustic beacon signal is known, the theoretical value of the Doppler frequency shift is calculated and an appropriate search frequency band is designed to ensure that the actual frequency of the signal is covered and the false alarm is reduced. When the speed of the search sonar is v, the Doppler frequency shift is

[0047]

[0048] Therefore, the search frequency band range is set to the lower boundary frequency f l =f 0 -f d , the upper boundary frequency is f h =f 0 +f d , in the frequency band f l to f h The requirement can be met by searching for the peak value of the periodic diagram for detection and judgment.

[0049] When actually calculating the periodogram, the partially overlapping segmented FFT is used to calculate the spectrum. At the same time, the segment length and step of the segmented FFT can also be theoretically designed according to the beacon signal parameters to achieve better detection performance with less computation. At this time, GLRT is rewritten as

[0050]

[0051] or

[0052]

[0053] Among them, R i (k) is the sampling signal r of the i-th segment i DFT of (n), k l and k h is the discrete index of the frequency band boundary when searching for the peak of the spectrum. For a given false alarm probability P FA ,have

[0054]

[0055] Where L = I(M / 2-1), then the constant false alarm detection threshold is

[0056]

[0057] Since the underwater acoustic beacon signal is a single frequency signal, the Rife algorithm is used to correct the peak frequency amplitude to reduce the impact of spectrum leakage. The M-point FFT of the underwater acoustic beacon signal is:

[0058]

[0059] Where k = 0, 1, 2, ... M / 2-1, Δf = f s / M is the frequency resolution. Then the amplitude spectrum is

[0060]

[0061] When k is close to f 0 / Δf, the amplitude spectrum is approximately

[0062]

[0063] Assume that the peak line spectrum frequency found is f 1 , the corresponding amplitude is A 1 , the second highest line spectrum frequency is f 2 , the corresponding amplitude is A 2 , the real frequency of the signal is f 0 , the corresponding amplitude is A 0 , then

[0064]

[0065] The amplitude correction factor is

[0066]

[0067] in,

[0068]

[0069] The detection principle of underwater acoustic beacon signal based on peak amplitude modified periodogram detector is as follows Figure 1 First, the received signal r(t) is discretely sampled to obtain r(n), and the FFT of each segment of data is calculated with a segment length of M and a step size of S to obtain R i (k), i = 0, 1, ... I, I is the number of segments. Then square its amplitude and multiply it by the coefficient 1 / M to get the periodogram of each signal segment. Set the lower boundary frequency f of the search band l =f 0 -f d , the upper boundary frequency is f h =f 0 +f d , the corresponding discrete frequency is k l and k h , take the maximum value of the peak value in the search frequency band of the multi-segment periodogram, correct the peak amplitude, and compare the corrected amplitude with the threshold.

[0070] Performance simulation analysis

[0071] The performance of the underwater acoustic beacon signal detector with improved multi-copy correlation integrator and modified periodogram under different channel conditions is analyzed. The signal sampling frequency f in the simulation s =98304Hz, the beacon signal frequency is f 0 =37.5kHz, pulse width τ =9ms, period T =1s. Firstly, the changes of matching results and periodogram results under different channel conditions are analyzed, and then the detection performance under different channel conditions is analyzed.

[0072] Comparative analysis of matching results and periodogram results

[0073] The results of traditional matched filter detector and multi-copy correlation integrator under Gaussian white noise channel, Doppler affected channel, FFT and TSD channel are as follows Figure 2 (a)-(d) show the original periodogram and the amplitude-corrected periodogram results. Figure 3 As shown in (a)-(d).

[0074] from Figure 2It can be seen that under the Gaussian white noise channel, the multi-copy correlation integrator is similar to the traditional matched filter detector. It can be intuitively observed that the matching result is in the shape of a triangular peak with a high signal-to-noise ratio. Under the influence of Doppler, the original matched filter result is seriously distorted, the characteristics of the triangular peak are lost, the amplitude fluctuates violently, and the signal-to-noise ratio is low. The multi-copy correlation integrator compensates for the distortion of the matching result, can restore the shape of the triangular peak, and improve the signal-to-noise ratio. Under the FFD distortion channel, the original matching result is more seriously distorted, and the obvious triangular peak can no longer be seen at the original signal pulse position. In the TSD channel, the matching amplitude at the noise even exceeds the matching amplitude at the signal pulse, and the characteristics of the signal have been submerged by the noise, which will lead to more false alarms in the detection results. The matching result of the multi-copy correlation integrator also compensates for the distortion of the matching result to a certain extent, restores the characteristics of the triangular peak, improves the signal-to-noise ratio, and facilitates subsequent detection and judgment.

[0075] from Figure 3 It can be seen that in the Gaussian white noise channel, due to spectrum leakage, the amplitude at the original beacon signal frequency cannot be accurately obtained. After amplitude correction, the peak frequency used for judgment is closer to the actual signal frequency, and the amplitude is also improved. In channels affected by Doppler and channels with FFD and TSD distortion, the actual frequency of the signal deviates from the theoretical frequency value, and the amplitude at the beacon signal frequency in the original periodogram is lower. In the improved periodogram, due to the setting of the search band, the actual signal frequency after frequency shift can still be searched, and the corrected peak amplitude is closer to the amplitude corresponding to the actual frequency, and the peak line spectrum amplitude is also higher.

[0076] Detection performance analysis

[0077] The detection probability curve P is drawn below d The relationship between different signal-to-noise ratios (SNRs) is used to measure the detection performance by the relative SNR required to achieve a 90% detection probability. FA =0.001, the signal-to-noise ratio SNR range is -25dB to 10dB, with an interval of 1dB. Figure 4 (a) shows the detection probability curves of the matched filter detector, the improved multi-copy correlation integrator and the amplitude-corrected periodogram detector under Gaussian white noise channel. Figure 4 (b) shows the detection probability curve of each detector under the Doppler-affected channel. Figure 4 (c) and Figure 4 (d) shows the detection probability curves of each detector under FFD channel and TSD channel respectively.

[0078] First, the detection performance of the improved detector is compared with that of the traditional matched filter detector: in the Gaussian white noise channel, the performance of the improved multi-copy correlation integrator and the traditional matched filter detector is similar, while the amplitude-corrected periodogram detector loses about 3.5dB of performance compared with the two; in the channel with Doppler influence, the performance of the traditional matched filter detector drops significantly, while the improved detector has good robustness, the multi-copy correlation integrator improves the performance of the traditional matched filter detector by nearly 8dB, and the amplitude-corrected periodogram detector improves the performance of the traditional matched filter detector by about 5.5dB; in the FFD channel, the performance of all detectors is reduced, the multi-copy correlation integrator improves the performance of the traditional matched filter detector by nearly 3dB, and the amplitude-corrected periodogram detector improves the performance of the traditional matched filter detector by about 1.5dB. In the TSD channel, the multi-copy correlation integrator improves the performance of the traditional matched filter detector by nearly 4dB, and the amplitude-corrected periodogram detector improves the performance of the traditional matched filter detector by about 5dB. In summary, when the channel has Doppler effects and distortion, the improved detector has improved performance compared to the traditional matched filter.

[0079] Secondly, the detection performance of the two improved detectors is compared and analyzed: in each channel, the improved multi-copy correlation integrator improves the performance of the amplitude-corrected periodogram detector by about 1.5-4dB.

[0080] From the above analysis, it can be seen that in various channel environments, the multi-copy correlation integrator has the best detection performance, which is better than the amplitude-corrected periodogram detector and the traditional matched filter detector; under the influence of Doppler and channel distortion channels, the amplitude-corrected periodogram detector performs better than the traditional matched filter detector. It can be seen that the improved detector can resist the influence of Doppler and channel distortion and obtain higher detection performance.

Claims

1. An improved method for peak line spectrum amplitude correction periodogram detection, characterized in that: First, the received signal r(t) is discretely sampled to obtain r(n), and the FFT of each segment of data is calculated with a segment length of M and a step size of S to obtain R i (k), i = 0, 1, ... I, I is the number of segments; then square its amplitude and multiply it by the coefficient 1 / M to obtain the periodogram of each signal segment; set the lower boundary frequency f of the search band l =f0-f d , the upper boundary frequency is f h =f0+f d , the corresponding discrete frequency is k l and k h , take the maximum value of the peak value in the search frequency band of the multi-segment periodogram, correct the peak amplitude, and compare the corrected amplitude with the threshold.

2. The improved method for peak line spectrum amplitude correction periodogram detection according to claim 1, characterized in that: When the search sonar's speed is v, the Doppler frequency shift is Therefore, the search frequency band range is set to the lower boundary frequency f l =f0-f d , the upper boundary frequency is f h =f0+f d , in the frequency band f l to f h The requirement is met by searching for the peak of the periodic graph for detection and judgment.

3. The improved method for peak line spectrum amplitude correction periodogram detection according to claim 1, characterized in that: When actually calculating the periodogram, the partially overlapping segmented FFT is used to calculate the spectrum. At the same time, the segment length and step of the segmented FFT can also be theoretically designed according to the beacon signal parameters; GL RT is rewritten as or Among them, R i (k) is the sampling signal r of the i-th segment i DFT of (n), k l and k h is the discrete index of the frequency band boundary when searching for the peak of the spectrum. For a given false alarm probability P FA ,have Where L = I(M / 2-1), then the constant false alarm detection threshold is 4. The improved method for peak line spectrum amplitude correction periodogram detection according to claim 1, characterized in that: Since the underwater acoustic beacon signal is a single frequency signal, the Rife algorithm is used to correct the peak frequency amplitude. The M-point FFT of the underwater acoustic beacon signal is: Where k = 0, 1, 2, ... M / 2-1, Δf = f s / M is the frequency resolution. Then the amplitude spectrum is When k is close to f0 / Δf, the amplitude spectrum is approximately Assume that the searched peak line spectrum frequency is f1, the corresponding amplitude is A1, the second highest line spectrum frequency is f2, the corresponding amplitude is A2, the real frequency of the signal is f0, the corresponding amplitude is A0, then we have The amplitude correction factor is in,

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