Pulsed and Continuous Signal Enhancement Based on Improved Noise Power Spectrum Density Estimation in the Passive Underwater Acoustic Data

Yun Zhong Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education Southeast University, Nanjing, China Email:220200912@seu.edu.cn

Qisong Wu Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education Southeast University, Nanjing, China Email:qisong.wu@seu.edu.cn

ABSTRACT

The pulsed and continuous narrow-band signal enhancement is quite important for the target detection and recognition in a passive sonar system. In this paper, a novel signal enhancement approach is proposed for both pulsed and continuous narrow-band components in the passive underwater acoustic data. The short time Fourier transform (STFT) method is firstly used in the time-domain radiated noise data, and then an improved noise power spectrum density (PSD) estimation is proposed to obtain the accurate noise power by using a two-dimension (2-D) sliding window. Finally, the improved PSD is utilized to enhance both pulsed and continuous narrow-band components. The proposed method has the capability of enhancing pulsed and continuous narrow-band components with avoiding the annoying tuning of the window length. Both simulation and experimental results verify the effectiveness and robustness of the proposed method.

1. INTRODUCTION

Signal enhancement technique based on time-frequency analysis in a passive sonar system is a hot topic in underwater acoustic signal processing and has been paid much attention by researchers. According to the generating mechanism of the underwater acoustic radiated noise, it generally involves three kinds of noise components, including the hydrodynamic noises, the propeller noises and the mechanical vibration noises [1]. The statistic model of its spectrum generally contains wideband spectra caused by the hydrodynamic noises, and narrow-band spectra from the rotation of the propeller and the vibration of mechanical components like diesel generators and air conditioning

_________________________________________________________ The work was supported in part by National Natural Science Foundation under Grants No. 61701109 and 91938203, in part by Science and Technology on Sonar Laboratory under Grant No. 6142109180202, and in part by National Defense Basis Scientific Research program of China under Grant No. JCKY2019110C143 Q. Wu and Z. Lai are with Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing, 210096, China, and Dr. Wu is also with Purple Mountain Laboratories, Nanjing, 211111, China. (Correspondence email: qisong.wu@seu.edu.cn)

inter.noise | 21-24 AUGUST SCOTTISH EVENT cans

equipment [2,3]. The wideband spectra can be modelled by the three parameters model, which can be achieved by the Gaussian white noise into autoregressive model, and the narrow-band spectra are often modelled by the superposition of multiple sinusoid signals [3]. In the real passive sonar system, the narrow-band spectra components generated from the inevitable vibration of mechanical equipment are quite important and useful features for the target detection and recognition. Therefore, it is quite requisite for the narrow-band spectra components enhancement [4].

A number of efforts have been paid to narrow-band signal enhancement techniques. The least mean square error (LMS) algorithm was developed for adaptive narrow-band signal enhancement [5-7]. The adaptive line spectrum enhancement (ALE) algorithm can be used to improve the narrow-band components [8,9]. The approaches mentioned above are able to effectively enhance the continuous narrow-band signals, and they seem to fail in the pulsed narrow-band signal enhancement. The Wigner Ville Distribution (WVD) method based on time-frequency analysis was used for pulsed signal enhancement; however, it has poor performance for complex signals [10-11] . A noise power spectrum density (PSD) estimation algorithm based on minimum statistics was proposed for the pulsed speech enhancement [12]. These methods above were generally developed for the pulsed signal enhancement, whereas they are not suitable for continuous signal enhancement.

In this paper, a novel both continuous and pulsed narrow-band signal enhancement approach is proposed. The short time Fourier transform (STFT) method is firstly applied to the radiated noise signal, and then an improved noise power spectrum density (PSD) estimation is proposed to acquire the accurate noise power by exploiting a two-dimension sliding window. Finally, the improved PSD is used for the enhancement of both continuous and pulsed narrow-band components. Both simulation and experimental results demonstrate the effectiveness of the proposed method.

2. PROPOSED MODEL

2.1. Signal Model According to the statistical model of underwater acoustic radiated noise, the spectrum � � ( � ) of radiated noise involves three kinds of components including the wideband spectrum component, the narrow-band spectrum component and the periodic modulation spectrum component, and can be expressed by [1],

� � �= � � �+ � � �+ � � ( � ) , (1)

where � � � represents the narrow-band spectrum component, � � � denotes the stationary wideband spectrum component and � � ( � ) represents periodic modulation spectrum component. The corresponding time-domain �� is

��= 1 + ����+ �(�) , (2)

where �� is the stationary wideband signal in time domain, which is often modelled by the three parameters model, and �� represents the periodic modulation signal. The �(�) component denotes the narrow-band signal, which is given by the superposition of multiple sinusoid signals. Generally, this narrow-band signal can be written by,

��= �(�) + �(�) , (3)

where �(�) represents a periodic pulsed narrow-band signal and �(�) is a continuous narrow-band signal. �(�) can be expressed as

��= �rect[

� � ]sin 2�� 0 �+ � 0 , 0,1, m   (4)

�−�� �

where � is the signal amplitude of �(�) , and � 0 is the center frequency, � 0 is the initial phase. � � is the pulse width, � � is the pulse period, and rect( )  is the rectangular window function. �(�) can be expressed as

��= �=1 � � � σ sin 2�� � �+ � � , (5)

where � is the number of continuous narrow-band components. � � , � � and � � represent the amplitude, frequency and initial phase of the � th continuous narrow-band component respectively.

Without loss of generality, the additive noise is considered in the model, and we obtain the underwater acoustic radiated noise signal �� in the discrete domain,

� ( � ) = � ( � ) + � ( � ), 1,2, , i N   (6)

where s N f T  denotes the total sample number with the sampling rate of s f and the observation interval of T . The short-time Fourier transform is subsequently performed on the noisy signal � . The window function ℎ(�) with the length of � and the overlapped sample number of �−� , is applied to the noisy signal �(�) , and the time-frequency �(�, �) can be written as

� ( �, � ) = �=0 �−1 �(��+ �)ℎ(�)� −�2���/� σ . (7)

�(�, �) 2 is the periodogram of the noisy signal, where � is the subsampling time index. � is the frequency bin index, �∈{0,1, . . . , �−1} , which is related to the normalized center frequency � � by � � = 2��/� .

2.2. Improved Noise PSD Estimation

Inspired by the minimum statistics noise PSD estimation method that is suitable for pulsed speech enhancement, we proposed an enhanced noise PSD estimation method for both pulsed and continuous narrow-band components in the passive underwater acoustic data

According to minimum statistics noise PSD estimation, a recursively smoothed periodogram ��, � is introduced [10]

��, �= �ෝ � (�, �)��−1, �+ (1 −�ෝ � (�, �)) ��, � 2 , (8)

where �(�, �) 2 is the periodogram of the noisy signal (�∈{� 1 , . . . , � 1 −�, . . . , � 1 −�+ 1}, 0 ≤ �< �) with the length of subframe of � . ��, � is the smoothed periodogram, which is considered as an estimate of the noisy signal PSD. � ��� �, �= min [��, �] represents the minimum value of ��, � . The scale �ෝ � (�, �) is a quite important final smoothing factor and would be estimated in the model which is given by

�ෝ � (�, �) =

� max � � (�)

1+(��−1,�/� ෠ � (�−1,�)−1) 2 , (9)

where we replace the true noise PSD � � (�, �) with its latest estimated value � ෠ � (�−1, �) . To avoid deadlock in the case of ��−1, �/� ෠ � (�−1, �) = 1 , the empirical smoothing parameter is often limited to a maximum value � ��� [10]. � � (�) is a smoothing parameter. According to the reference [10], the resulting correction factor is limited to values larger than 0.7 and smoothed over time, and � � (�) is given by

� � (�) = 0.7� � (�−1) + 0.3max(�෥ � (�), 0.7) , (10)

where the max( )  function represents the maximum value between the initial smoothing parameter �෥ � (�) and 0.7. �෥ � (�) is given by

�෥ � (�) =

1

1+( �=0 �−1 ��−1,� σ / �=0 �−1 �(�,�) 2 σ −1) 2 . (11)

When tracking � ��� �, � in the subframe, a deviation between the real noise PSD and the estimated noise PSD called the deviation compensation parameter � ���

−1 is induced. The unbiased noise PSD estimation � � (�, �) can be obtained by compensating � ��� �, � . It is found that the deviation compensation parameter � ���

−1 is a function of ���[��, � ] (variance of ��, � ) and the subframe length of � .

Finally, the unbiased noise PSD estimation � ෠ � (�, �) is given by

� ෠ � (�, �) = � ��� (�, ���[��, �])� ��� �, �� � (�) , (12)

where � � (�) is a parameter proportional to the normalized standard deviation of ��, � .

� � (�) = 1 + � � (1/�) �=0 �−1 2�෠ �

2 (�, �)/���[��, �] σ , (13)

where the empirical value � � = 2.12 [10] .

In general, the noise PSD estimation method was only suitable for the pulsed narrow-band components enhancement [10]. Since continuous narrow-band components always maintain a high-energy state within subframe, the noise PSD estimation based on the method [10] will take the high-energy narrow-band components instead of the true noise power spectrum density. Therefore, the continuous narrow-band components will be drastically suppressed. To overcome this issue, a 2-D sliding window � � of size 2�× � is introduced to modify the noise PSD estimation in � ෠ � (�, �) . For the estimation of the � ෠ � (�, �) at the frequency point � , the range of the two-dimensional sliding window � � is � ෠ � �, � � , 0 ≤�< �, �−�≤� � < �+ � , as is shown in the Figure 1.

Figure 1: The two-dimensional sliding window � � in � ෠ � (�, �) .

For the estimation of � ෠ � ( �, �) at the frequency point � , the cost function Φ �

� , 0 ≤�< � is calculated in turn for judgement. The cost function Φ �

� is given by

Φ �

� = log 10 (

�1=�−� �+� � ෠ � (�,� 1 ) σ − �1=�−1 �+1 � ෠ � (�,� 1 ) σ ), 0 ≤�< �, 0 ≤�< � , (14)

� ෠ � (�,�)

where � is the range of the noise PSD estimation. When the condition is satisfied by cost function Φ �

� , replace the original value of �෠ � (�, �) with the minimum noise PSD estimation � � within � � ; if the condition is not satisfied, keep the original value of � ෠ � (�, �) . The judgement is described as

� ෠ �� (�, �) = � � , Φ �

� > Φ 0 � ෠ � (�, �), otherwise . (15)

Φ 0 is the significant value, usually, Φ 0 ≥1 . When all the � values of � ෠ � (�, �) at frequency point � are revised, the frequency point is updated from � to �+ 1 , as well as the sliding window. The above process is repeated until all the values of � ෠ � (�, �), 0 ≤�< �, 0 ≤�< � is modified to obtain a complete � ෠ �� (�, �) . The entire process is summarized as Figure 2.

Input: � ෠ � (�, �), 0 ≤�< �, 0 ≤�< � Output: � ෠ �� (�, �), 0 ≤�< �, 0 ≤�< � for �= 0: �−1 do

Initialize two-dimensional sliding window � � Find the minimum value � � in the sliding window � � Calculate the cost function Φ �

� of the results � of the �෠ � (�, �) at the frequency point �

Complete the revision to � ෠ � (�, �) through judgement end for Return: � ෠ �� (�, �), 0 ≤�< �, 0 ≤�< �

Figure 2: Improved Noise PSD estimation algorithm.

2.3. Signal Enhancement

As long as the noise PSD estimation process is obtained, the subsequent step is to enhance the pulsed and continuous narrow-band components. The minimum mean square error (MMSE) signal enhancement algorithm essentially gives a system gain equation from the input noisy signal to the output signal estimation, which can be expressed as [11],

� ෡ (�, �) = � log���� [�(�, �), �(�, �)]�(�, �) , (16)

where � ෡ (�, �) and �(�, �) represent the amplitude of enhanced signal and original signal after short-time Fourier transform respectively. �(�, �) and �(�, �) represent a priori signal-to-noise ratio and a posteriori signal-to-noise ratio respectively.

Following the reference [11], the classical log MMSE PSD enhancer is used, and the gain equation is given by

� log���� [�(�, �), �(�, �)] = [

1+�(�,�) ���[

� ׬ ��]] 2 , (17)

∞ � −�

�(�,�)

1

2 �(�,�)

and �(�, �) is defined as

�(�, �) =

1+��,� ��, � . (18)

��,�

�(�, �) is estimated using the “decision guidance” method,

�(�, �) = � �

� ෠ �� (�−1,�) + (1 −� � )max[�(�, �) −1,0] , (19)

�(�−1,�) 2

where � � represents the smoothing parameter of �(�, � ) , and the posteriori signal-to-noise ratio �(�, �) can be expressed as:

�(�, �) =

�(�,�) 2

� ෠ �� (�,�) . (20)

Therefore, the enhanced signal is obtained by inputting the noise PSD estimation � ෠ �� (�, �) and the noisy signal PSD �(�, �) 2 .

3. PERFORMANCE EVALUATION

3.1. Simulation Experiments To verify the effectiveness of the proposed method, three types of signals including pulsed narrow-band signal, pulsed chirp signal and continuous narrow-band signal are considered in simulations. A pulsed narrow-band signal is at the frequency of 200 Hz with the pulse width of 1 second and a period of 2 seconds; the pulsed chirp signal is 700Hz -1000 Hz, with a pulse width of 0.5s and a period of 2 seconds, and the frequency of the continuous narrow-band signal is 1500 Hz. The observation interval T is 10 s, sampling frequency fs=8000 Hz. Without loss of generality, an additive noise is considered with the input signal-to-noise ratio (SNR) of -5 dB.

The STFT method is firstly performed on the radiated noise data, and we obtain the time-frequency periodogram, as shown in Figure 3(a). It is observed that the periodic pulsed chirp signals disappear due to low SNR. All types of signals including pulsed signals and continuous signals are perfectly enhanced in the proposed method, compared to these in the R Martin’s method and LMS method. It is obvious that the proposed method has superior performance over other methods.

(a) (b)

(c) (d) Figure 3: Performance comparisons (a) Time-frequency periodogram based on STFT method. (b) Proposed method. (c) R Martin’s method. (d) LMS method.

The quantitative performance with respect to the gains of three signals are provided through 50 Monte Carlo experiments, as shown in Figure 4(a) – Figure 4(c). It can be concluded that the proposed method not only implements the enhancement of the three types of signals, but also eliminates the dependence on the subframe length during pulse signal enhancement. Furthermore, the proposed method has the highest gains among these methods.

= = = =

(a) (b)

(c)

Figure 4: Performance comparisons. (a) Gain of the continuous narrow-band signal. (b) Gain of the pulsed chirp signal. (c) Gain of the pulsed narrow-band signal with the subframe length of 0.768s.

3.2. Real Data Experiments In this section, experimental data will be used to verify the effectiveness of the proposed method. In the experiment, the ship with the power amplifier as the acoustic source actively transmits several signals in 15 meters underwater, including a pulsed narrow-band signal with a frequency of 190 Hz, a period of 140 seconds, a pulsed narrow-band signal with an initial frequency of 380 Hz and a period of 80 seconds, a chirp signal with an initial frequency of 200 Hz, and two continuous narrow-band signals with frequencies of 223 Hz and 306 Hz. The output spectrum of Short Time Fourier Transform based on the original signal and the signal enhanced by proposed method during 300 seconds are shown in Figure 5(a) – Figure 5(d). It is obvious that the proposed method has the capability of enhancing both pulsed and continuous narrow-band signals, and has the superior performance over other methods.

(a) (b)

(c) (d) Figure 5: Performance comparisons. (a) Time-frequency periodogram based on the STFT method. (b) Result based on the proposed method. (c) R Martin’s method. (d) LMS’s method.

4. CONCLUSION

This paper focused on the enhancement of pulsed and continuous narrow-band signals. An improved noise PSD estimation was proposed to obtain the accurate noise power by using a 2-D sliding window. We also analyzed the reason why this method implements robust filtering in detail. Simulation and experiments demonstrated the effectiveness of the proposed method.

5. REFERENCES

1. Ross D, Kuperman W A. Mechanics of underwater noise. J. Acoust. Soc. Amer., 86(4) ,

pp.1626–1626(1989). 2. Wales S C, Heitmeyer R M. An ensemble source spectra model for merchant ship-radiated

noise. J. Acoust. Soc. Amer., 111(3) , pp.1211–1231(2002). 3. Urick R J. Principles of Underwater Sound, 3rd ed.; McGraw-Hill Book Company: New York,

NY, USA, (1983). 4. LI Qihu. Advances of research work in some areas of underwater acoustics signal processing.

Applied Acoustics, 20(1) , 1–5 (2001). 5. KWONG R H and JOHNSTON E W. A variable step size LMS algorithm. IEEE Transactions

on Signal Processing, 40(7) ,1633–1642 (1992). 6. EVANS J B, XUE P, and LIU B. Analysis and implementation of variable step size adaptive

algorithms. IEEE Transactions on Signal Processing, 41(8) , 2517–2535 (1993). 7. MAYYAS M. A variable step-size selective partial update LMS algorithm. Digital Signal

Processing, 23(1) , 75–85 (2013). 8. SHI Min, XU Xi, and YUE Jianping. Detection of ship radiated noise line spectra based on

two-level adaptive line enhancement. Ship Science and Technology, 34(8) , 79–82 (2012). 9. LUO Bin, WANG Maofa, and WANG Shichuang. A highly efficient weak target line-spectrum

detection algorithm. Technical Acoustics, 36(2) , 171–176 (2017). 10. Martin w, Flandrin P. Wigner-Ville spectral analysis of nonstationary processes. IEEE

Transactions on Acoustics, Speech, and Signal Processing, 33(6) , 1461-1470 (1985). 11. Boashash B ， Black P. An efficient real-time implementation of the Wigner-Ville distribution.

IEEE Transactions on Acoustics, Speech, and Signal Processing, 35(11) ,1611-1618 (1987). 12. Martin R ． Noise power spectral density estimation based on optimal smoothing and minimum

statistics[J]. IEEE Transactions on Speech & Audio Processing, 9(5) , 504–512 (2001). 13. Ephraim Y, Malah D. Speech enhancement using a minimum mean-square error log-spectral

amplitude estimator. IEEE Transactions on Acoustics, Speech, and Signal Processing, 33(2) , 443–445 (1984).

14. Cappe O. Elimination of the musical noise phenomenon with the Ephraim and Malah noise

suppressor[J]. IEEE Transactions on Speech & Audio Processing, 2 , 345-349 (1994).