CHANG Hao，YANG Li-bo，SHI Yu-xuan，HOU Jin-chao

(Department of Computer Science and Engineering，Taiyuan University，Taiyuan 030032, China)

Abstract：In the exploration, tracking and positioning of underwater targets, it is necessary to perform frequency domain analysis and correlation calculation on the underwater acoustic signals of the target radiation.In a strong noise environment, the target signal may be overwhelmed by noise, resulting in an inability to effectively identify the target.Aiming at this problem, this paper presents a method of signal-noise separation by combining Fourier denoising with wavelet transform to realize underwater acoustic signal extraction in a strong noise environment.The combination algorithm of Fourier coefficient threshold adjustment and wavelet threshold transform is designed, and performance of the algorithm is tested.Simulation results show that the combination algorithm can effectively extract underwater acoustic signals when signal-to-noise ratio(SNR)is-15 dB, which can improve the SNR to 8.2 dB.

Key words：underwater acoustic signal; signal-to-noise ratio(SNR)；wavelet transform；signal-noise separation；threshold

0 Introduction

With the development of underwater acoustic technology and ocean engineering, underwater acoustic detection has become a key development area, and passive sonar has achieved rapid development due to low energy consumption and difficulty in exposing its position[1].The use of hydrophones to obtain sound field information and the use of new underwater signal reception and processing technology based on underwater acoustic sensing technology to construct a new type of passive sonar have important research significance in the field of underwater acoustics[2].Hydrophone technology has been greatly developed in recent years.On the one hand, research on scalar hydrophones using piezoelectric materials still occupies a certain position.Teng et al.developed a hydrophone with a piezoelectric tube structure in the frequency band, and a high receiving sensitivity was achieved[3].Lu et al.developed a slotted ring hydrophone with a hydrostatic pressure resistance of 30 MPa, which can meet the needs of deep sea exploration[4].On the other hand, the industry is gradually shifting its attention to the field of vector hydrophone technology, focusing on the development of related vector hydrophones and signal processing methods, and vector hydrophones based on optical fiber sensing, MEMS, etc.have emerged.Zhang et al.developed a silicon microcapacitive one-dimensional vector hydrophone to achieve the perception of underwater acoustic signals[5].Xu et al.produced a standard vector integrated hydrophone to achieve simultaneous measurement of the standard and vector acoustic signals[6].Pyo et al.developed a vector hydrophone with a diameter of only 23 mm by improving the sensor structure[7].Despite the rapid development of hydrophones and related technologies, due to the complexity of the actual underwater acoustic testing environment, the collected underwater acoustic information often contains a lot of noise, and the signal is sometimes completely submerged by noise, therefore the effective noise reduction of the signal is very important.The commonly used Fourier transform signal processing method is not obvious in the background of strong noise with a signal-to-noise ratio(SNR)lower than-10 dB[8], therefore it is necessary to select a signal processing method suitable for the actual strong noise environment.

Here, the combination of Fourier transform based on noise and signal cross-validation and wavelet denoising is used to denoise the signal, and the performance of the combined algorithm is compared.The simulation results show that the combined algorithm is feasible.It breaks through the limitation of the traditional method in the strong noise background and non-stationary noise environment, and reduces the minimum applicable SNR to-15 dB, which can effectively realize the underwater acoustic signal extraction.

1 Noise reduction principle and combination algorithm

Here, the line spectrum of the known frequency of the underwater acoustic signal is measured, and the frequency band is 20-2 000 Hz.In this frequency band, the ambient sound is very sensitive, therefore the obtained underwater acoustic signal includes both the target signal and environmental noise.Since detection and orientation of the target are only interested in the target signal of the study, but environmental noise and interference need to be filtered out, therefore it is extremely important to separate the desired signal from the noise.

The SNR refers to the proportional relationship between the active component and the noise component in the signal.It is a major indicator to measure the noise reduction performance of the algorithm and can be expressed as[1]

(1)

whereδSNRis the signal-to-noise ratio;Sis the target signal power, andNis the noise energy power in dB.The larger the SNR, the stronger the anti-interference ability of the system, the higher the target resolution, and the better the noise reduction performance of the algorithm.

Root mean square error is very sensitive to the extra large or very small error in a set of measurements.Therefore, it can well reflect the precision of the measurement and can be expressed as

(2)

The SNR gain(G)refers to the difference between the input SNR and the output SNR.It is mainly used to measure the performance of the system or processing algorithm and can be expressed as

(3)

1.1 Basic principle of Fourier transform

For any successively measured timing or signal, it can be represented as an infinite superposition of sinusoidal signals with different frequencies.As one of the most important algorithms in the field of digital signals, the Fourier transform algorithm can directly calculate the frequency, amplitude and phase of different sinusoidal signals contained in the measured original signal directly.The Fourier transform has a good analytical effect on the continuous stationary signal, which can reflect the time domain characteristics and frequency characteristics of the signal.The Fourier transform can transform the time domain signals that are difficult to process into the frequency domain signals that are easy to analyze and understand.Then, the transformed frequency domain signals can be further processed by some existing software toolboxes.After the processing is completed, the processed frequency domain signals can be converted into new time domain signals by using the inverse Fourier transform, thus the time-frequency domain processing of the signals is completed.The core function of Fourier filtering is frequency domain filtering.The operation of filtering out the specific band frequency in the signal is an important measure to suppress and prevent interference.Supposing there is a square integrable periodic signal, and its Fourier transform relationship is expressed as[4]

(4)

However, when the signal is masked by noise, the direct Fourier analysis is less than ideal, which requires further processing.

1.2 Principle analysis of wavelet threshold denoising

As a unique analysis method, wavelet analysis is developed based on Fourier transform.The multi-scale refinement analysis of signals can be performed through the functions of stretching and translation[9].A continuous wavelet transform of any signal can be defined as the inner product of the signal and the wavelet basis function.From the perspective of signal processing, wavelet denoising is a signal filtering problem.Wavelet transform can extract the correlation of the signal, and the processed noise is close to white noise, therefore denoising in wavelet domain is more convenient than in time domain.Since wavelet transform can flexibly select the basis function, the suitable wavelet can be selected according to the signal characteristics and denoising requirements.

The key is to find the appropriate wavelet base and wavelet threshold.Different wavelet bases and thresholds have different processing effects on the signal.At present, the sinusoidal signal is mainly used as the target signal, and “db4” and “sym8” wavelet basis functions are selected in combination with the research.The wavelet threshold denoising algorithm processes the coefficients of the layer coefficients after wavelet decomposition, especially according to the modulu which is greater than or less than a certain threshold.

The adaptive threshold selection rules include the following four types: “rigrsure” adaptive threshold selection uses Stein’s unbiased risk estimation principle; “heursure” uses heuristic threshold selection; “sqtwolog” threshold selection rule is sqrt(2log(length(X))); and “minimaxi” uses the mininum principle to select a threshold.Simulation studies have found that the difference between the output SNR and the mean square error under different threshold rules is not too large, therefore the next step is to select the “heursure” threshold rule for signal processing.

1.3 Algorithm for underwater acoustic signal extraction

Combining the characteristics of Fourier transform and wavelet transform, a new combination algorithm is obtained and its flow block diagram is shown in Fig.1.

Fig.1 Flow block diagram of combination algorithm

The algorithm steps are as follows:

1)Extract the original input signal.After Fourier transform on the input signal, narrow-band filter adjustment on the transformed frequency domain signal and selection of the target frequency band of interest, a processed signal is obtained.

2)Select the wavelet basis.Based on threshold rule, wavelet denoising is performed and the signal after the secondary processing is obtained.

3)Fourier threshold processing.Fourier threshold processing is performed on the secondary output signal again(choose a suitable threshold), and all the amplitudes of the frequency domain coefficients below the threshold are reset to be zero, with all the above thresholds being retained.The final output is the best estimate of the useful signal.Fourier transform is combined with wavelet processing and both are nested for processing, thereby a useful estimate of the signal is obtained, which prepares for subsequent algorithm processing.

2 Simulation and analysis

Here we use Matlab software to simulate the proposed algorithm.The original observation signal is superimposed by Gaussian white noise and useful signals.The target signal except noise is the part of the signal we need, therefore it is necessary to extract this part of the signal efficiently.

First of all, we simulate and verify the influence of different wavelet basis functions on signal processing.Here, the two wavelet base functions “db4” and “sym8” are used for verification.The time domain and frequency domain results are shown in Fig.2.

Fig.2 Different wavelet basis processing results

The left side of Fig.2 is the time domain signal, the abscissa axis is the sampling time, and the vertical axis is the voltage amplitude.The right side is the frequency domain diagram of the signal.

SNR and RMSE are compared and the results are shown in Table 1.

Table 1 Performance comparison of different wavelet bases under different noise conditions

Based on the results inFig.2 and Table 1, it can be seen that under the two wavelets of “db4” and “sym8”, the RMSE and SNR errors are very small, and the signal calculation results are not much different.Thus in the next simulation and calculation, the “db4” wavelet basis is selected.

Then-10 dB noise is used to verify the effectivess of the proposed combination algorithm.The time domain diagrams of the original signal and the noise signal are shown in Fig.3.

Fig.3 Original signal and noise signal

Finally, the proposed combination algorithm is used for signal processing.

At first, Fourier transform is performed on the noise signal and narrow-band filtering is completed.Then“db4” wavelet function and “heursure” wavelet threshold are selected to continue the signal processing.Fourier transform is performed again, and the appropriate amplitude coefficient threshold is selected(here the threshold is 50), especially all of the values below the threshold are replaced by zero.By means of inverse transform, the final time domain signal is obtained.The processing is shown in Fig.4, the horizontal axis refers to the time, and the vertical axis represents the voltage amplitude.It can be seen from the amplitude that the noise is significantly reduced and the signal tends to be stable.

Fig.4 Time domain diagram of signal processing

Fig.5 shows the comparison of time domain signal and frequency domain signal before and after noise reduction.

In Fig.5, the horizontal axis refers to sampling time and the vertical axis is voltage value.Figs.5(a)and(b)are the time domain and frequency domain diagrams of noise signals, respectively.It can be seen that it is difficult to distinguish the useful signal in the frequency domain diagrams, and the noise is distributed in the whole frequency range.Random noise is filtered by Fourier transform and wavelet transform, and the single frequency information of 315 Hz is retained.It can be seen from Figs.5(c)and(d)that most of the noise has been filtered by the combination algorithm, and the time domain waveform of the signal is obtained.

Fig.5 Time-frequency signal comparison before and after noise denosing

Through Monte Carlo analysis, experiment is repeated for 200 times at each SNR, and signal denoising performance is analyzed and compared with all the results.

It can be seen that the smaller the root mean square error of the signal, the better the denoising effect of the algorithm; the higher the output SNR, the higher the SNR gain, and the higher the similarity.This means better denoising performance of the algorithm.After multiple simulation verifications, a SNR of-25 dB is selected as strong noise background.As we know, the higher the SNR, the stronger the signal and the weaker the noise.The experimental SNR can be selected from-25 to 0 dB, increasing at a interval of 5 dB.

The different performance values for different SNR ratios are shown in Table 2.

Table 2 Performance comparison under different noise conditions

It can be obtained from the results of Table 2.In the background of strong noise, the proposed combination algorithm has a good denoising effect, whereas the traditional Fourier filter can only be practically limited in the stationary case above 0 dB.However, when the noise becomes stronger, the mean square error increases sharply at-25 dB, thus the algorithm is not suitable.The wavelet algorithm is not very good when the signal frequency is high, and the useful signal and its noise are filtered together, which has a certain range limitation on the signal frequency.For a specific target signal and its noise characteristics, we can choose the appropriate signal processing algorithm to get higher output SNR and lower RMSE.

3 Conclusion

In this study, the combination algorithm is used to denoise the signal in the known strong noise environment.By means of the proposed algorithm signal processing is completed by selecting different wavelet functions and combining them with threshold value, the signal is processed.The simulation results show that the effective the correspond and it can provide some help for the processing of subsequent directional algorithm.However, due to the time-varying and complexity of the actual underwater acoustic environment, the performance of the proposed algorithm under complex hydrological conditions needs further verification and improvement.