Bionic covert anti-reverberation active sonar detection method based on imitating whale whistles

JIANG Jiajia, MIAO Yu, LI Yao, SUN Zhongbo, LI Chunyue,WANG Xianquan, FU Xiao, DUAN Fajie

(1. State Key Lab of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China；2. System Engineering Research Institute, China State Shipbuilding Corporation, Beijing 100036, China)

Abstract： The disguised covert detection method that imitates whale calls has received great attention in recent years because it can solve the traditional problem of the trade-off between long-range detection and covert detection. However, under strong reverberation conditions, traditional echo signal processing methods based on matched filtering will be greatly disturbed. Based on this, a disguised sonar signal waveform design is proposed based on imitating whale calls and computationally efficient anti-reverberation echo signal processing method. Firstly, this article proposed a disguised sonar signal waveform design method based on imitating whale calls. This method uses linear frequency modulation (LFM) signals to replace LFM-like segments in real whale calls, and extracts the envelope of the real whale call’s LFM-like segment to modify the LFM signal. Secondly, this article proposed an echo signal processing method of fractional Fourier transform (FrFT) based on target echo locating of synchronization signals. This method uses the synchronization signal to locate the target echo, and determines the step-size interval of the FrFT based on the information carried by the synchronization signal. Compared with the traditional FrFT, this method effectively reduces the amount of calculation and also improves the anti-reverberation ability. Finally, the excellent performance of the proposed method is verified by simulation results.

Key words： active sonar system； anti-reverberation； disguised sonar waveform design； echo signal processing

0 Introduction

The active sonar system will be inevitably detected and recognized by the enemy detector[1-2]in the process of sending out signals to detect the target. In order to improve the stealth capability of active sonar systems, many methods based on waveform design have been proposed in recent decades[3-5].

Different from traditional methods of low probability of detection (LPD)[6]and low probability of interception (LPI)[7], a bio-inspired covert method has received great attention in recent years[8-11]because it can solve the traditional problem of the trade-off between long-distance detection and covert detection. Because the original marine mammal call pulses have different characteristics from conventional signals in terms of waveform, frequency distribution and time-frequency distribution, the enemy almost always classifies biological signals as ocean noise and filters them out[12-14]. Therefore, imitating biological signals can effectively prevent the enemy from detecting the presence of such detection signals.

At present, there are two main methods for bio-inspired covert method. One is using artificial signals (e.g. continuous wave, LFM) to splice and simulate whale calls. For example, Liu et al.[10]used a large number of LFM signals with different chirp rates to simulate the dolphin whistle. Capus et al.[8]used two LFM signals to simulate the click of a bottlenose dolphin. The advantage of this method is that it can retain the superior performance of the artificial signal, but some characteristics of the constructed signal are different from the real whale sound, leading to unsatisfactory covertness. The other is directly to use real whale sounds or adjust only a little of whale sounds. For example, Jiang et al.[11]adopted two real sperm whale call pulses to form an active sonar signal with good range resolution and Doppler tolerance. The advantage of this method has good covertness, but the detection performance is limited by the characteristics of the whale sound signal.

So far, the bio-inspired covert method usually uses matched filtering as the echo signal processing method. Matched filtering is a common method to analyse and process the detection signal echo, and it is the best receiver under the background of white noise. But the background noise of target echo is not pure Gaussian white noise when the sonar system is located in the strong reverberation environments such as the shallow sea, port, etc. Because of the high cross-correlation between reverberation and target echo, the matched filter output will contain many indistinguishable target echo correlation peaks and reverberation signal correlation peaks, which limits the performance of the matched filter. Therefore, in order to take into account both covert detection and effective detection under strong reverberation conditions, this article focuses on the whale calls imitating disguised sonar signal waveform design method which is suitable for strong reverberation conditions, and anti-reverberation echo signal processing methods.

In order to meet the needs of engineering applications, researchers have proposed a variety of signal detection methods in the reverberant environment[15-17]. Deng et al.[17]used FrFT to identify target echoes in a reverberant environment. This method takes advantage of the good focus of the LFM signal in the fractional Fourier domain by using FrFT to distinguish reverberation signal and target echo. Moreover, since FrFT processes the signal based on the time-frequency plane rotation, it is more sensitive to the Doppler motion of the target and has a higher speed estimation accuracy[18].

Due to the good performance of FrFT under reverberant conditions, this article combines it with the bio-inspired covert detection technology, and proposes a covert detection method suitable for strong reverberant conditions. Because FrFT is mainly applicable to the processing of LFM signals, this article uses LFM signals to replace LFM-like segments in real whale calls, and extracts the envelope of the real whale call’s LFM-like segment to modify the LFM signal. The replacement of the LFM signal is completed without affecting the covertness of the detection signal.

At present, FrFT is widely used in the processing of LFM signals. The main problem of FrFT is that it has a large amount of calculation. First,because of the irreconcilable contradiction exists between the search accuracy and the calculation amount[19-20]. In order to ensure the detection accuracy, only a small step-size can be used to search the step-size interval, which will greatly increase the calculation amount. Second, because of the influence of the strong reverberant environment, the arrival time of the target echo is difficult to be determined by the matched filter. The commonly used method is to perform overlapped windows on the received signal and compare the results of FrFT calculations in each window[21]. Therefore, it is difficult for FrFT to meet the requirements of active sonar systems for real-time signal analysis, so it is generally still at the stage of theoretical research and has not been applied to active sonar systems. In summary, the following work has been done in this paper.

1) A construction method of disguised sonar signal suitable for strong reverberant environment is proposed. LFM signals is used to replace LFM-like segments in real whale calls, and the envelope of the real whale call’s LFM-like segment is extracted to modify the LFM signal. The replacement of the LFM signal is completed without affecting the covertness of the detection signal.

2) Different from the traditional FrFT method of using overlapped windows to locate the target echo, a method of using the synchronization signal to locate the target echo is proposed.The amount of calculation is reduced. And because of the improvement of the positioning accuracy of the target echo, the anti-reverberation performance is also increased.

3) Different from the traditional FrFT method of setting the search step-size and step-size interval, a method of using the synchronization signal to carry the chirp rate information of the LFM signal and setting the search step-size and step-size interval based on the chirp rate information and the target speed estimation interval is proposed. On the basis of reducing the amount of calculation, the detection accuracy of FrFT is improved.

4) A disguised detection method under strong reverberant conditions is proposed, which can guarantee the covertness of the detection process while outputting the sonar signal with high signal-to-noise ratio (SNR), and solve the traditional problem of the trade-off between long-distance detection and covert detection. Simulation verifies that efficient performance of estimating target speed and distance under long-distance and strong reverberant conditions can be achieved by this method.

1 Disguised signal construction

Generally speaking, whale calls can be divided into clicks, whistles and pulse calls[22-24]. Clicks have a short time width, ranging from tens of microseconds to a few milliseconds. And it has a wide frequency band, causing serious attenuation in ocean channels and resulting in a very short operating range, so it is not suitable for the signal construction method in this article. However, whistles and pulse calls have a long duration, ranging from tens of milliseconds to a few seconds. Their operating range is much longer than that of clicks, and the time-frequency contour is changeable, which meets the requirements of the proposed waveform construction method. The difference between whistle and pulse calls is that pulse calls contain multiple harmonic components. For the subsequent echo signal processing stage, the chirp rate of the harmonic components of the LFM segment is different from the fundamental chirp rate, which will interfere with the result of FrFT. Therefore, this article uses whistles to construct the disguised sonar signal.

By studying various classification methods for tonal sounds, it is found that the classification method proposed by Bazúa-Durán and Au[25]has strong versatility, and can be applied to most tonal sounds. By using this classification method as a reference, most tonal sounds can be ascribed to one of the six categories according to their contours, including constant frequency, upsweep, downsweep, concave, convex and sine[26]. In addition to the constant frequency, the others all have LFM-like segments, which can be used to construct the detection signals described in this article.

The waveform design method proposed in this article needs to replace the LFM-like segment in the real whale sound signal with the LFM signal. In order to ensure the covertness and detection performance of the constructed signal, the LFM-like segment of the whale sound signal used for the construction needs to have the following characteristics： (1) The time-frequency contour of the LFM-like segment has a small curvature, which is similar to a LFM signal, ensuring that the time-frequency contour after the replacement is similar to the real whale sound’s time-frequency contour. (2) The time width of the LFM-like segment is relatively large. From the ambiguity function, it can be seen that the speed resolution of the detection signal depends on the time width of the signal. A detection signal with a large time width is conducive to obtaining more accurate speed estimation results. (3) The bandwidth of the LFM-like segment is relatively large. It can also be seen from the ambiguity function that the accuracy of the target distance estimation depends on the signal bandwidth. However, the accuracy of the target distance estimation depends on the estimation accuracy of the target speed in addition to the signal bandwidth. Therefore, when a large time width and bandwidth cannot be achieved at the same time, a large time width should be selected first.

Taking the construction of the downsweep tonal sound of long-finned pilot whale as an example, the specific construction method is shown in Fig.1.

Fig.1 Schematic diagram of construction process

Step 1： Replacing the LFM-like segment with the LFM signal. However, because the rectangular envelope characteristic of LFM signal is quite different from the real whale call, the constructed signal does not have covertness.

Step 2： The whale call envelope of the LFM-like segment in the real whale call is extracted, and the LFM signal is modified by the whale call envelope[27].

Firstly, the STFT with aN-point Hamming window of the whale callx(t) is calculated. And the resultX(τ,ω) is expressed as

(1)

whereω(N) is theN-point Hamming window；t1andt2are the starting time and ending time of the whale callx(t). For thekth STFT blockXk(τk,ωk), its starting time and frequency areτkandωk, respectively.

Secondly, setting a frequency threshold ΔB, and finding the maximum valuePkbetween the frequency [ω-ΔB,ω+ΔB] within the time range of thekth STFT block. The envelope of momentτkis

(2)

Finally, the real whale call envelopeAr(τk) is obtained by using the piecewise cubic Hermit interpolation ofAb(τk). Using the envelopeAr(τk) to multiply the LFM signal, and the LFM signal whose envelope is consistent with the real whale call is obtained.

Step 3： To avoid the abrupt phase change between real whale segment and LFM segment, the phase compensation component Δφ1is added to the LFM segment. The Δφ1is equals to the phase difference between the real whale segment and LFM segment at the connection point, which is calculated by Hilbert Transform.

This method can adopt different types of tonal sound of different kind whales to construct sonar signals. In addition to the downsweep tonal sound of long-finned pilot whale shown in Fig.1, there are also convex tonal sound of short-finned pilot whale is shown in Fig.2(a)-(d),and sine tonal sound of bottle dolphin is shown in Fig.3(a)-(d).

Because of the simplicity of the sonar signal construction method, the sonar signal database can be easily constructed. In practical application, the appropriate sonar signal can be selected in the database according to the actual situation. For example, referring to the real whale calls sequence and using the same type of sonar signals in turn to simulate the real whale calls[27], the sonar signal of local whales was selected in different sea areas, and the sonar signal of current whales was selected in different seasons, so as to achieve better covertness.

Fig.2 Convex tonal sound of short-finned pilot whale

Fig.3 Sine tonal sound of bottle dolphin

Since the contours of tonal sounds have obvious frequency modulation characteristics[28], and present acoustic classifiers usually classify a tonal sound based on its contour, it can be assumed that the covert ability of the artificial detection signal depends on the similarity of contour between the sound and the real whale calls. To assess the covert ability of artificial detection signals, the Pearson correlation coefficient (PCC)[29]is used, which is widely used in the measurement of the similarity between two data sets.

The discrete disguised sonar signal’s time-frequency contour is denoted byfB[n]={fB,1,fB,2,…,fB,n}, and the discrete real whale call’s time-frequency contour is denoted byfR[n]={fR,1,fR,2,…,fR,n}, so the correlation coefficientrbetween them could be calculated by

(3)

From the Eq.(3), it can be found that the closerris to 1, the more similar the time-frequency contour of the disguised sonar signal and the real whale call are, the better the covert ability will be. The correlation coefficients between the disguised sonar signals mentioned above and the real whale calls are shown in Table 1.

Table 1 Correlation coefficients

In order to quickly and accurately locate the LFM segment in the disguised sonar signal at the subsequent echo signal processing, the real whale sound segmentwas intercepted before LFM as the synchronization signal, and the synchronization signal matched filter was used to locate the LFM segment. Compared with directly using the LFM signal matching filter location, the advantage of this method is that the characteristics of the real whale sound segment are diverse, the cross-correlation between different synchronization signals is low, and it is not easy to cause interference among different detection signals. The interception of synchronization signal is shown in Fig.4.

Fig.4 Schematic diagram of synchronization signal and LFM segment

The synchronization signal carries three pieces of information in total. (1) The location information of LFM. It can be directly windowed for FrFT based on the location information. (2) The chirp rate information of LFM. The initial step-size and step-size interval of FrFT can be determined based on the chirp rate information.(3) LFM time length information. The window’s width of FrFT can be determined based on the time length information. The specific method of using the synchronization signal will be described in detail in Section 2.

2 Echo signal processing

Because of the complex formation principle of the reverberation, the reverberation of the LFM signal generally no longer has obvious chirp characteristics. The energy of the reverberation signal is relatively dispersed in the fractional Fourier domain, showing weak focus. However, the echo signal can maintain its chirp characteristics, and the energy is more concentrated in the fractional Fourier domain. In this paper, FrFT is used to separate the reverberation signal and the echo signal in the fractional Fourier transform domain, so as to realize the anti-reverberation detection.

2.1 Fractional Fourier transform

FrFT was introduced initially by Namias[30]in 1980, and since then was being used in various fields. It is a signal processing tool based on the rotation of the time-frequency plane. FrFT is a generalization of the classical Fourier transform and a representation of signals using an orthonormal basis formed by chirps. The transformation kernelK?(t,u) is defined as

(4)

(5)

For any LFM signal, the relationship between its chirp ratekand FrFT is

(6)

wheresis the sampling rate；Nis the total number of time samples, andρ0is the optimal transform order.

2.2 FrFT of target echo

In the detection method described in this article, the estimation of target speed and distance is based on the LFM segment in the disguised sonar signal, and the equation is

f(t)=Acos(2πf0t+πkt2),

(7)

whereAis the whale envelope amplitude parameter used to modify signals；kis the chirp rate；f0is the initial frequency of LFM segment. Considering the Doppler shift of moving target and time delay. The received signal can be expressed as

f(ξt-τ)=ψAcos(2πf0(ξt-τ)+πk(ξt-τ)2),

(8)

whereξis the compression/stretching parameter due to moving target；τis the time delay, andψis the amplitude parameter which is related to target distance and underwater channel influence.

From the Eqs.(7) and (8), the ratio between the chirp rate of the echo signalk′ and the emission signalkis

(9)

It is well known that the relationship between the doppler factorξand the relative radial speed of the target and sonarvis

(10)

wherecis the sound speed in the sea. It can be obtained from the Eqs.(9) and (10) that

(11)

2.3 Echo signal processing method

The specific process of the proposed echo signal processing method is shown in Fig.5.

Firstly, the synchronization signals corresponding to the sonar signals are used as copies for matched filtering. Finding the synchronization signal with the highest correlation peak, its corresponding chirp rate is read aski, and the FrFT order corresponding to this chirp rate is

(12)

wheresis the sampling rate；Nis the total number of time samples.

Fig.5 Schematic diagram of echo signal processing

The submarine’s speed on combat patrols generally does not exceed the so called “maximum low noise” speed which amounts to nearly 8 knots (4 m/s). Often, submarines have to carry out long distance voyages to complete their assigned missions. In order to increase their operational efficiency, submarines in transit move at a maximum speed which guarantees the submarine covertness. Generally this speed does not exceed 15 knots (7.5 m/s)[31]. Therefore, the section of FRFT transform order is

(13)

whereρmis the variation interval of FRFT order caused by the estimated Doppler effect；vm=7.5 m/s is the maximum estimated speed of the target.

Secondly, setting the correlation peak threshold and finding the peak pointtmiof each correlation peak, the point (tmi+Ns) is taken as the starting point of the FrFT transform window, and the point (tmi+Ns+NLFM) is taken as the ending point of the FrFT transform window.NsandNLFMare the number of points of the synchronization signal and the LFM segment, respectively. It depends on their length and the sample rate of the signal. The maximum peak value of the FrFT result of each window is found, and the target speed is calculated according to Eq.(11).

Finally, the LFM segment in the detection signal is used as a copy to perform matched filtering to calculate the distance of the target. According to the target speed, the signal is resampled to compensate for the signal change caused by the Doppler effect. The sampling rates′ used for resampling is

(14)

whereveis the estimated value of the target speed, andsis the sampling rate of the signal. Resampling will compensate for the Doppler effect of the echo signal, so that the cross-correlation between the echo signal and the detection signal will be improved, and resampling will cause the cross-correlation between the reverberation signal and the detection signal to decrease. The result of target echo signal matched filtering before and after compensation is shown in Fig.6.

Fig.6 Schematic diagram of doppler compensation

For the compensated signal, the LFM segment is used in the detection signal as a copy to perform matched filtering. The peak point of the matched filtering is the estimated value of the echo signal’s delayτe, and the distance to the targetris calculated by

(15)

3 Simulation

In the simulation, underwater acoustic channel is generated by Bellhop developed by Mike Porter. The parameters of the generated channel are shown in Table 2, and the sound speed profile and channel impulse response are shown in Fig.7.

Table 2 Parameters of underwater acoustic channel

A strong reverberant environment is simulated by using the element-scattering model[32], and Gaussian white noise is superimposed to simulate random noise in the ocean. The received signalx(t) is

x(t)=s(t)*γ(t)+r(t)+n(t),

(16)

where * is convolution；s(t)is the target echo；γ(t)is the channel impulse response output by Bellhop, which is used to simulate the influence of the underwater acoustic channel on the signal；r(t) is the reverberation, andn(t) is the Gaussian white noise.

Fig.7 (a) Communication simulation system； (b) Sound speed profile

The downsweep, convex and sine detection signal shown in Figs.1-3 are taken as examples. The parameters of whale calls are shown in Table 3, and the parameters of LFM segments are shown in Table 4. SNR=20 dB, SRR=0 dB, the echo signal is simulated as described above, and the time-frequency diagram of the received signal is shown in Fig.8.

Table 3 Parameters of whale calls

Table 4 Parameters of LFM signals

Fig.8 Received signal’s time-frequency image

4 Results and discussion

This article takes the downsweep, convex and sine detection signals as an example for simulation. The target’s speed is 5 m/s and the target’s distance is 10 km. RMSE of speed errors is obtained as shown in Fig.9, and RMSE of distance errors is gotten as shown in Fig.10 by simulating under different SNR and SRR conditions.

Fig.9 RMSE of speed errors of a single target over different SNR and SRR

It can be seen from Fig.9 and Fig.10(a)-(c) that when the SRR is not less than 0 dB, the method can maintain good detection performance, and when the SRR is less than 0 dB, though the reverberation signal has weaker chirp characteristics than the echo signal, its strong energy will affect the estimation of the optimal transformation angle of FrFT, leading to estimation errors of speed and distance.

Fig.10 RMSE of distance errors of a single target over different SNR and SRR

And it can be seen from Fig.9 and Fig.10(d) that the speed estimation accuracy of the downsweep disguised sonar signal with larger time width is higher, and the distance estimation accuracy of convex and sine disguised sonar signals with larger bandwidth is higher. The simulation results are consistent with the previous analysis.

Different from the traditional anti-reverberation FrFT echo signal processing method, the echo signal processing method proposed in this article has the advantages of smaller calculation amount, higher calculation accuracy and stronger anti-reverberation ability. The traditional FrFT method uses overlapped windows to located echo signals. The longer overlapped parts there are, the higher the accuracy of the calculation result will be, but the amount of calculation will also increase. That is to say, the FrFT withNLFMpoints timesnis

(17)

What’s more, it can be seen from Eq.(4) that the principle of FrFT’s focusing effect on the LFM signal is to obtain the decomposition basis of different chirp rate by rotating the transform angleα. If the windowing position is not accurate, the energy of the LFM signal in the FrFT window may be lesser than reverberation. The energy of another rotation angleα1corresponding to the dispersed reverberation signal is higher than the energy of rotation angleα0corresponding to the LFM signal. FrFT will get wrong results, resulting in a decrease in the anti-reverberation performance of this method.

Taking the downsweep, convex and sine detection signal as an example, the proposed method and the traditional FrFT calculation method are used to process the echo signal. The sampling rate is 44.1 kHz, the target distance is 10 km, the target speed is 5 m/s, and SNR=20 dB. The required times of FrFT with the same points using the proposed method and the traditional method is shown in Table 5.

Table 5 Number of calculations by different methods

In addition to the reduction of calculation, to compare the anti-reverberation performance of the proposed method and the traditional FrFT, simulations were performed under different SRR conditions. The RMSE of speed errors are shown in Fig.11 and the RMSE of distance errors are shown in Fig.12. In traditional FrFT simulation, the window overlap width isNoverlap=0.8NLFMandNoverlap=0.2NLFM.

Fig.11 RMSE of speed errors of a single target over different method and SRR

Fig.12 RMSE of distance errors of a single target over different method and SRR

It can be seen from Table 5 that the calculation amount of the proposed method is significantly reduced compared with the traditional FrFT, and it can be seen from Figs.11 and 12 that under reverberation conditions, especially when the SRR is greater than or equal to 0 dB, the proposed method has higher accuracy for target speed and distance estimation.

5 Conclusions

A disguised sonar signal waveform design method is proposed based on imitating whale calls and a computationally efficient anti-reverberation echo signal processing method for strong reverberation environment. LFM segments is used to replace the LFM-like segments in the real whale call, so that the time-frequency contour of the disguised sonar signal is consistent with the real whale call, achieving the covertness detection. Different from the traditional FrFT method, a method by using the synchronization signal to locate the target echo is proposed. Compared with the traditional FrFT signal processing method, the calculation amount of this method is effectively reduced. Moreover, by comparing the RMSE of speed and distance errors, it is proved that this method has better target speed and distance estimation accuracy under reverberation conditions, especially under reverberation conditions greater than or equal to 0 dB. However, under extremely low SRR conditions, the reliability of the synchronization signal matched filter will be interfered by strong reverberation. The threshold of matched filtering needs to be artificially lowered, but this will also increase the amount of calculation. Our future work will be concentrated on more reliable target echo positioning methods under extremely low SRR conditions.