Sonar can accurately detect fixed targets and determine target distance, it has poor concealment and limited range and is susceptible to reverberation interference. The detection signal emitted by active sonar encounters obstacles or targets in the propagation path of water, and is then affected by reflection, refraction, and scattering, resulting in signal delay and overlap. The signals are subsequently received at the receivers, forming echo signals with reverberation (Huang and Wang, 2019). The influence of reverberation on active sonar like synthetic aperture sonar (Zhang et al., 2023a; Zhang et al., 2023b), communication sonar (Yu et al., 2018), multibeam sonar (Neasham et al., 2007) and other active sonars should be completely reviewed. Underwater interface reverberation is an important factor limiting the detection performance of active sonar in shallow water environments. Unlike noise interference, reverberation has non-smooth statistical characteristics and is usually mixed with the target echo, which is challenging to distinguish (Faure, 1964).

Previous works on reverberation in signal processing mainly focus on the study of detectors under specific reverberation conditions (Bharathi and Mohanty, 2019) and the spatiotemporal distribution characteristics of reverberation; researchers have studied robust detection performance under various reverberation distribution conditions. Some researchers have attempted to reduce the effect of reverberation on target echo by designing a transmission waveform, such as frequency-hopping signals encoded with particular frequencies (Costas, 1984), Q-function sonar signals (Cox and Lai, 1994), and SFM signals (Ward, 2001). However, enough high frequency is needed to achieve a reverberation suppression effect, which leads to a low utilization rate of the low-frequency band and affects the range accuracy.

Some researchers study anti-reverberation processing on signals received by sonar. Marine reverberation has a strong temporal correlation with target echo signals.Target echo signals cannot be effectively found by regularly matched filtering methods as the two spectra overlap in the frequency domain. In order to improve the performance of coherent processing in reverberation, Kay et al. used the AR pre-whitening processing method to filter out reverberation as white noise under certain conditions (Kay and Salisbury, 1990). Higher gain and more effectively detected target echoes can be obtained through matched filter by Wu et al. (Wu et al., 2018), but local stationarity of the reverberation is required as a premise (Widrow et al., 1967), which is widely used in ALE (Adaptive Line Enhancement) algorithm (Ma et al., 2021). However, it has strict requirements for the channel environment. H.M. Ozaktas and L.B. Almeida filtered the signal based on the time-frequency focus difference between the echo and reverberation in the Fourier transform domain to achieve reverberation suppression (Ozaktas et al., 1996; Zhang et al., 2019; Mejjaoli and Omri, 2020). However, The LMS algorithm performs adaptive filtering based on the error between input and output of the channel, which has strict requirements on the channel environment. Freburger et al. used the principal component inversion algorithm to project the received signal into two subspaces based on the power difference between different backgrounds, thereby achieving reverberation separation (Freburger and Tufts, 1997). When the power of the target echo signal is similar to that of the reverberation signal, distinguishing between the two becomes difficult.

With the development of artificial intelligence (AI) technology, deep neural networks have brought new research ideas to solve the shallow sea sonar reverberation problem. As a hot research direction in the field of machine learning, GAN (Ashraf et al., 2021) has become a popular model in the field of deep learning due to its advantages of generating high-quality samples, learning unlabeled data, supporting multi-modal data and innovation (Zhan et al., 2019) (Dong and Yang, 2018). Recently, Gans have evolved from image generation to reverberation data generation Hu et al. (2023). Gans are also used to generate spatial impulse responses, with the aim of enhancing high-quality RIRs with existing real RIRs (Ratnarajah et al., 2023). In the field of underwater acoustic engineering, it is theoretically feasible to use GAN for active sonar reverberation suppression to solve the problem of reverberation suppression under high reverberation environment.

This paper proposes a Wasserstein generative adversarial network model with a gradient penalty (RSWGAN-GP) to solve reverberation suppression of sonar signals. Sonar signals are different from the picture, and a one-dimensional convolutional approach is built in this paper to process the signal data. The generation side of the adversarial network is made according to the U-net network (Ronneberger et al., 2015) to encode the original reverberation signal data, and the decoder generates the anti-reverberant signal data. The discriminator uses the design idea of SkipNet (Abrahamyan et al., 2021) that the discriminator to achieve a balance of speed and accuracy. In order to realize the fast and accurate training of the countermeasure network, the structure design referred to WGAN-GP comprehensively. In the experiment, simulation is used to supplement the data set to solve the difficulty of Marine experiment data sampling and insufficient data set. Our main contributions are concluded as follows:

The rest of the article is organized as follows. Section 2 starts with a brief review of some related works. In Section 3, some data preliminary work is presented, which includes RSWGAN-GP reverberation data generation, signal time gain control, and automatic gain control. In Section 4, the reverberation suppression method based on RSWGAN-GP is proposed, and the generation network, discrimination network, and error loss are explained respectively. In Section 5, experiments are given to verify the effectiveness of the method, and in Section 6, conclusions are given. In active sonar, the commonly used detection signals include single continuous wave (CW), LFM, NLFM, BPSK and other signals. In this paper, the research object of active sonar signal feature enhancement is selected as the typical CW signal for research.

After the signal is received, the received signal will be processed by the active sonar system. In this part, the hardware implementation of the processing will be reproduced by the following algorithm. At the same time, the signals that generate the training set data will be processed in the same way.

The active sonar device processes the received signal in the following way. After the hardware receives the sonar signal, the sonar signal will go through time-varying gain and automatic signal gain control processing so that the long-distance echo signal power is stronger and more convenient for subsequent processing. After processing, the generated training set is closer to the actual data. Figure 1 shows the signal state of each process.

The processing of the signal in the hardware device after receiving is shown in Figures 1B–D, and the signal processing process will be explained below.

The echo received by the active sonar system, and the generated echo signal with target information in Section 4.1 are shown in Figure 1A, and the circled position is the target echo.Time-Variable Gain (TVG) Innami and Kasai (2012). According to the sonar equation, it can be obtained that the echo margin of the sonar is determined by the difference between the echo signal level and the background interference level.

In Eq. (1), DT represents the detection threshold and is the strength of the echo signal received by the sonar, TL represents the propagation loss because the active sonar is bidirectional, so 2TL defines its complete propagation loss; SL represents the sound source level; NL represents the noise level; DI represents the directivity index; TS represents the target strength. For most sonar systems, including multibeam sonar, the propagation loss (TL) is compensated by the TVG device inside the receiver. The ideal TVG curve should follow the expectation of sonar propagation loss, i.e.

In Eq. (2), r represents the action distance, and a is the loss factor, a function of frequency. Figure 1B shows that the signal passes through the TVG and that the distant signal is no longer attenuated as the distance increases.

Signal Automatic Gain Control (AGC) (Zhang et al., 2017). In practice, automatic gain control is typically implemented through circuit design. However, AGC needs to be implemented for the experimental simulation of the sonar data set. The signal adjustment must be automatically adjusted based on the input and output data size, which initially requires numerous logarithmic operations. In order to implement these operations are avoided, a simple comparison operation is used with a gain lookup table instead. The algorithm can be described as follows.

The left side is transformed into the adjusted value between two adjacent gain coefficients G(n + 1) and G(n) in dB format for better clarity. Following the estimation of the average power of the output signal, a comparison is made with the reference power to determine the appropriate method for adjusting the gain coefficient based on the outcome of this comparison. In Figure 1C, the AGC equalizes the signal strength and partially suppresses reverberation through processing. There are hardware limitations to consider in practical usage. The hardware restricts the received signal and simulates how the part of the signal that exceeds the limit would appear. Figure 1D illustrates this simulation. Figure 1E displays the desired output result of the network, which will be utilized to calculate the Jensen-Shannon Divergence (JSD), aiming to bring the output result closer to it.

In both experimental and simulation data, some signals exhibit peak clipping phenomena and cannot be restored to complete sine waves, making traditional methods ineffective. After undergoing the above (B), (C), and (D) processing and normalization, the simulated signal has inputs with the same dynamic range.

In order to solve the problem of limited suppression effect in a high reverberation environment, a reverberation suppression framework based on the Generative adversarial network is proposed. A nonlinear mapping from the sonar detection signal with reverberation to the sonar signal with reverberation suppression is established, where the input data is the signal propagation time series. The output is the corresponding time series after reverberation suppression. Due to the scarcity of actual data with reverberation signals, the training of RSWGAN-GP will face the problem of overfitting, reducing its generalization performance. To this end, the generation of virtual reverberation data is implemented in this section by combining statistical modeling and a multi-highlight model. The training data set is expanded by mixing real and virtual reverberation data while ensuring the consistency of its distribution pattern. Then, the theoretical signal gain control was calculated by signal propagation theory to form a time series signal for artificial intelligence model learning. The implementation of this part is shown in Figure 2.

The data generated in Part 4.1 is mixed with real data for Part 4.3, 4.4, and the gradient penalty part is invoked for training.

This section validates the advancedness of the proposed model and method. For this purpose, we conducted marine experiments to verify that RSWGAN-GP can effectively suppress the reverberation of sonar signals and collect actual data in the field for verification. RSWGAN-GP, with other excellent reverberation suppression methods, compared to prove the effectiveness of the reverberation suppression method proposed. The following sections explain the detailed description and summary of the experiments.

In the experiment, the active sonar with 30-element with a self-receiving function is used to transmit a continuous wave (CW) signal with a f s = 250 k H z sampling rate and a f = 30 k H z frequency. The size of the training data set is 6000 data samples in total, among which 2520 actual sonar data samples are obtained through experiments, and 3480 data samples are generated by the underwater active sonar reverberation simulation method. The simulation data and actual data are randomly arranged, and the training set and the verification set are in a 5:1 ratio. The actual data are used to verify the reverberation suppression effect of the model obtained at the end of training. The experiments were conducted in one of the bays in Qingdao. Figure 8 shows the experimental scenario.

Figure 8A is a schematic diagram of the relative position of the active sonar and the target during the test. In the figure, x h 1 = 200 m is the shortest distance from the relative position, and x h 2 = 300 m is the longest distance from the relative position, active sonar is at the same position as the target at sea level d s = d t ∈ [ 5 , 10 ] . In Figure 8B, the experiment in the harbor can minimize the error caused by the ship’s swing caused by wind and waves. The narrowest point of the harbor exit is 200m, and the target ship tows the target at a distance of 200-300m from the active sonar. Figures 8A, B show the experimental active sonar equipment and the detected target, respectively. The detected target is a cylindrical object with an internal cavity with a diameter of 533mm and a length of 3m. The essential experimental data of the validation method are obtained in sea trials.

The data are collected and used as the validation set to validate each epoch in the training process. The active sonar of the signal is subjected to reverberation suppression, and the signal change during training is shown in Figure 9.

In Figure 9, the time domain diagram shows that the model is trained by mixing simulation data with actual acquisition data, and the trained model is used to process the experimental results of the active sonar signal data of the ocean experiment. The figure shows the results of sonar signal processing of model pairs produced by different iterations. In the Epoch 1-50 iteration training process, the processed sonar signal still has the phenomenon of signal chipping. Still, it shows the state of strong reverberation, and the target position cannot be visually observed from the time domain. Starting from Epoch 60-100, the chipping phenomenon of the echo signal disappears, the correct sinusoidal signal can be restored, and the neural network can already find the desired target feature state. From Epoch 110 onwards, the target can be precisely located, and in subsequent training iterations, the target echo feature can be highlighted while suppressing the strong reverberation state during sonar propagation. When the model training iteration is above Epoch 210, the target echo signal can be observed macroscopically from the time domain diagram. Reverberation changes in the middle state of the network as shown below:

The above-processed feature map, which results from the processing of the network X E n N = X D e N , results in a 288×25 feature array. Feature array is where the network will generate features, which will then be upsampled to recover the signal. In Figure 10, some features of the signal increase and decrease as the epoch increases, representing anti-reverberation operations. From Figure 10A, it can be seen that the convolution features of the signal at the beginning are dispersed to each corner of the array. After iteration, some features weaken, as shown in Figure 10B, which is reflected in the signal that the reverberation part begins to weaken, and then the features disappear, as shown in Figure 10C. Finally, the target echo features are enhanced, as shown in Figure 10D, and the corresponding display in the echo signal explored by sonar is the enhancement of the echo signal.

During the training process, convergence is achieved by continuously correcting errors. The loss curve changes during the training process of RSWGAN-GP, including the generator loss curve and the discriminator loss curve, as shown in Figure 11.

Figure 10 shows the training loss curves of RSWGAN-GP under various weight decay and learning rate(lr) settings. Figure 10A is the line chart of the generator loss variation, and Figure 10B is the curve chart of the discriminator loss variation. By setting different parameter values, rapid convergence of the network can be achieved when weight decay and learning rate are set to 0.00001 and 0.0001, respectively. As shown in the figure, in the WGAN-GP network, the generator loss continuously approaches 0, and the discriminator loss continuously approaches 0. The loss of the generator shows a rising trend, and the loss of the discriminator shows a decreasing trend. During training, the generator and discriminator are in a state of mutual competition, and their loss values should fluctuate up and down. The trend shown in the figure represents the main direction.

For applications where target detection will be performed after signal processing, the difference between before and after signal processing is shown in Figure 12.

Figure 12 shows the target position detection map after nonlinear processors in matching fields on CW signal processing Sun and Li (2019), where the target indicates the target’0s location, which is about 204 m—the comparison between the original data and the data after RSWGAN-GP processing is shown. In the original data, before the target position, there is the influence of reverberation on its judgment. When making a prediction, the highest correlation position changes and the highest point in front is judged as the target position. When comparing the red line with the blue line, it is evident that the signal processed by RSWGAN-GP can reduce the influence of reverberation when making target judgments, increasing the success rate of target judgments. Here, four contrasting points are selected, as shown in Table 3.

Among the data points, the first three are reverberation points, and the comparison shows that the reverberation is well suppressed, and the fourth is the target point. The SRR is improved after echo suppression. The data comparison can prove that the well-trained model can suppress the reverberation well, making the correlation increase by 0.022 and the reverberation part decrease by 0.3 on average.

There are many excellent algorithms in water acoustics reverberation suppression, here will use collected data for various methods to compare with the method proposed in this paper. The comparison results after processing the sonar signal are shown in Figure 13.

In Figure 13A, the Original signal is unprocessed, the reverberation power is 0.398, the signal echo power is 0.432, and its SRR is 0.361dB, the highlighted red part indicates the position of the target echo, which cannot be effectively identified from the figure. 2D-AR PreWhitener is used to eliminate correlation and frequency correlation in the signal Li et al. (2008) so that the signal is flatter in the frequency domain, and the processed echo sonar signal shows the position of the target echo. The least mean square filter (LMS) processes the echo signal Kim et al. (2000), and the reverberation component is suppressed, decreasing amplitude. Adaptive fractional Fourier transforms (FrFt) for suppressing reverberation Yu et al. (2022), Although the reverberation is partially suppressed, the actual impact is not apparent. The PCI-SVM reverberation suppression method combines Principal Component Inversion (PCI) and Support Vector Machine (SVM) techniques Wang et al. (2021). This method selects suitable and effective feature values through SVM to extract the main features for reverberation suppression. The figure shows that this method performs better than the previous ones. We present the impact of the RSWGAN-GP method proposed in this paper. Compared to the excellent methods, the reverberation component is effectively suppressed, and the echo component is more visible and prominent. The detailed data comparison is presented in Table 4.

Figure 13B compares SRR results processed by different methods under different SINR environments. In actual use, the reverberation signal processing SINR is between 0 dB and 10 dB. In order to reflect the processing ability of a high reverberation environment, the signal is mainly concentrated between -10 dB and 10 dB (data comparison in the middle of the two blue colors in the figure). As can be seen from the figure, RSWGAN-GP and PCI-SVM methods are significantly superior to other methods. At the same time, RSWGAN-GP is 3 dB higher than the PCI-SVM method at SINR -10 dB, and the advantages become more evident as SINR increases. The advantage of RSWGAN-GP is that it can learn many high reverberation data to improve the processing ability of high-reverberation data. In Figures 13A, B, we compare different reverberation suppression methods to demonstrate the effectiveness of RSWGAN-GP in suppressing reverberation.

Figure 14 shows the processing results and time-frequency distribution of raw signal, AR pre-whitening, LMS, FrFt, PCI-SVM and RSWGAN-GP, respectively. Experimental results show that the algorithm can effectively suppress reverberation and extract target echo components under high SRR conditions. At the same time, the time-frequency structure of the target highlight echo remains unchanged. The processing results of the original signal distribution are shown in Figure 14A. It can be seen that there is some substantial reverberation interference near the target echo, but its energy is weaker than the target echo. The signal processed by 2D-AR PreWhitener, LMS, FrFt and PCI-SVM is shown in Figures 14B–E, and the target echo energy is still not obvious. As shown in Figure 14F, the RSWAGN-GP processing results show that the overall reverberation background has been effectively removed, and only a tiny part of weak background interference remains near the target echo.

The superiority of the proposed method can be seen in Figures 12, 13, and the detailed parameters are listed here for comparison, including reverberation amplitude, echo amplitude, reverberation power, echo power and SRR. The specific parameters are shown in Table 4.

The findings in Table 4 demonstrate that the RSWGAN-GP method proposed in this study is the most efficient technique for attenuating reverberation compared to the other methods evaluated. With a remarkable improvement in the reverberation ratio by 15dB, RSWGAN-GP significantly enhances speech quality from 0.83dB to 16.79 dB. The PCI-SVM algorithm comes in a close second, mainly when the optimal rank is 42, as determined by the SVM classification experiment, resulting in a significant improvement in the SRR by around 13dB. The 2D-AR PreWhitener, LMS, and FrFt techniques also improve the reverberant environment by -0.024dB, -2.68dB, and 0.12dB, respectively. Nevertheless, their ultimate effects are less substantial than those of RSWGAN-GP and PCI-SVM.

The effectiveness of the RSWGAN-GP method proposed in this paper for suppressing reverberation in sonar signals is demonstrated through experiments. Using experimental data from the ocean during training shows that features are extracted and amplified during the training iterations. By comparing the results of the algorithms, it is evident that this method can significantly improve signal quality. The improved SRR is 15.169 dB, demonstrating the method’s effectiveness and superiority for reverberation suppression.

Reverberation suppression of echo signals is a crucial issue in active sonar systems. This paper presents a novel RSWGAN-GP method for suppressing reverberation in sonar signals using the generative adversarial network. This reverberation suppression network employs a one-dimensional convolutional network to process the signal content. RSWGAN-GP refers to U-net and DenseNet, using skip network structure and dense connection network to suppress sonar signal reverberation efficiently. Comparison using actual collected data demonstrates the effectiveness of the proposed method, which can effectively suppress the active sonar reverberation signal, improving SRR by approximately 10 dB, better than other methods.

Through several experiments, it was discovered that the processing model trained by RSWGAN-GP has specific requirements for the transmission pulse width. The transmission pulse width of the signal needs to be adjusted for different detection distances, but the model’s pulse width for echo signal processing is not sensitive to the width. However, this relationship may be specific to the dataset used. In future research, efforts will be made to improve the model’s generalization capabilities to process signals with different pulse widths efficiently.

The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding authors.

ZW: Writing – original draft. HZ: Conceptualization, Supervision, Writing – review & editing. WH: Conceptualization, Formal Analysis, Methodology, Resources, Supervision, Writing – review & editing. XC: Methodology, Supervision, Writing – review & editing. NT: Data curation, Supervision, Writing – review & editing. YA: Data curation, Methodology, Writing – review & editing.