Proceedings of the Institute of Acoustics

 

Mitigation of decoherence effects in passive sonar: Application to a scaled tank experiment

 

G Real, DGA Techniques Navales, Toulon, France

X Cristol, Thales Underwater Systems, Sophia Antipolis, France

D Habault, LMA, Aix-Marseille Université, CNRS, Centrale Marseille, Marseille, France

D Fattaccioli, DGA Techniques Navales, Toulon, France

 

 

1 INTRODUCTION

 

The authors focus on the topic of acoustic wave propagation through fluctuating media. Especially, sonar applications are subject to the variations of the speed of sound in the ocean^1,2, itself related to oceanographic phenomena (i.e. internal waves inducing temperature and salinity fluctuations)³. The performance of sonar arrays can be mitigated by these phenomena. In fact, distortion of the received acoustic wavefronts can be observed and lead to degradation of the detection capability^4,5. In particular, very large arrays, classically used to increase the array gain, are very sensitive to the fluctuations of the propagation medium^6,7. This paper explores the capability to reenact the aforedescribed situation under controlled laboratory conditions. A small-scale experimental protocol aiming to reproduce the effect of a random ocean on acoustic wave propagation is presented in section 2. A scaling procedure was developed in order to relate the water configuration to what can be observed in a realistic ocean medium. It is presented in section 2 as well. The degradation of sonar performance is evaluated in terms of decrease of the radius of coherence and of the array gain. Corrective signal processing techniques are investigated with the ultimate goal to retrieve the full detection capability. The first results of these studies are shown in section 3.

 

 

2 EXPERIMENTAL STUDY AT SMALL SCALE

 

2.1 Experimental protocol

 

This experimental setup was presented in multiple publications^6-10. It consists in transmitting an ultrasonic wave from a transducer through a slab named RAndom Faced Acoustic Lens (RAFAL). The latter is characterized by a plane input face and a randomly rough output face. This random roughness is chosen as a Gaussian normal process with a zero mean and a standard deviation ξ₀. A mobile hydrophone records the acoustic field while moving along a vertical axis. It is expected that the experimental configuration would induce acoustic perturbations comparable to what can be obtained in an oceanic case. The transducer’s depth changes as well in order to acoustically highlight statistically independent zones of the RAFAL and to obtain independent realizations of the same stochastic process. A diagram of the experimental configuration is shown in Figure 1.

 

 

 

Figure 1: Experimental configuration diagram

 

2.1.1 The equipment

 

The measurements were conducted in a 3 m long, 1m wide and 1 m deep water tank, filled with fresh water. The dimensions of the random slab are 15x15x0.2 cm³. The slab was located in the middle of the tank depth and it was possible to minimize the influence of the bottom and the surface. The transmitted signal was a continuous wave (CW) chirp at f = 2.25 MHz with a duration of 22.2 µs (N p = 50 periods) and an amplitude of 5V. At this frequency and at a temperature of 20° C, the wavelength λ is equal to 0.658 mm. The signal was generated with a HP 33120A Arbitrary Waveform Generator and sent through a Panametrics V306 transducer after x10 amplitude amplification by a NF 4005 High Speed Power Amplifier. The receiver was an Acoustic Precision Needle hydrophone. The signal was received on the control computer after high-pass filtering and amplification by a Sofranel Pulse Receiver Model 5055PR. The acoustical equipment was placed on motorized rails driven by a computer interface allowing automatic displacements of the source and the receiver. The number of RAFALs that needed to be manufactured was determined by the number of independent realizations which could be performed on a specific slab. The displacement of the hydrophone on a vertical axis was used to simulate vertical arrays of 64 hydrophones separated by a distance of 0.3 mm. This value was chosen in order to satisfy the sampling criterion (s < λ=2).

 

2.1.2 Dimensional analysis

 

A scaling procedure was developed in order to find a direct correspondence between the tank experiment configurations and realistic oceanic setups. Based on the dimensional analysis developed by Flatté¹, we adapted the calculation of the strength (Φ) and diffraction (Λ) parameters to our problem. An analytical study of the acoustic propagation based on the small-slope approximation and the parabolic approximation was carried out in the Fourier domain. An expression for Flatté’s parameters in our setup was obtained. The details of these calculations can be found in Real’s PhD dissertation^7,10. Table 1 gathers the expressions for the dimensional parameters in both cases:

 

       

 

Table 1: Dimensional parameters in the oceanic and small-scale experiment cases.

 

The main parameters involved in the oceanic case are the propagation distance 𝑅, the wavenumber 𝑘0, and the environment-related features such as the vertical and horizontal correlation length of the sound speed fluctuations 𝐿_𝑉𝑠, 𝐿_𝐻𝑠 and their standard deviation 𝛿_𝑐0. On the other hand, in our experimental setup, the dimensional analysis is carried out with the wavenumber in water 𝑘₁, the sound speeds in water and in the RAFAL 𝑐₁, 𝑐₂, the Fresnel radius 𝑅_𝐹, the propagation distance 𝑥 and parameters related to the random roughness of the RAFAL’s output face: its standard deviation 𝜉₀ and vertical/horizontal correlation length 𝐿_𝑉, 𝐿_𝐻. Combinations of the aforementioned parameters are involved in the calculation of 𝐿^𝑙_𝑧 (the complete expression for 𝑏, 𝐹, 𝑞 and 𝜌 is given in Real’s work⁷. From Table 1, we observe that a set of environmental parameters in an oceanic configuration can correspond to a set of experimental parameters in the tank experiment setup. The direct correspondence is obtained by equating the dimensional parameters calculated in both cases. Our objective is to study a large range of configurations translating into various regimes of fluctuations in the Λ-Φ plane. The parameters of the small-scale experiment were tuned in order to be representative of configurations in the unsaturated, partially saturated and fully saturated regimes. The configurations are listed from 1 to 7 and given in Figure 2:

 

 

 

Figure 2: Λ-Φ plane for the studied configurations.

 

2.2 Experimental results

 

In this section, we present the results associated with the measurements conducted in the water tank. Various metrics are used to demonstrate the validity of our experimental scheme. First the mutual coherence function (MCF)^11,12 is calculated: it accounts for the spatial correlation of the acoustic wavefront along the vertical linear array. Especially, the radius of coherence is evaluated and compared in various configurations (different regimes of fluctuations) using measured signals, synthetic data (at small and real scales) and theoretical values. This parameter is related to the array and a degradation of the gain due to the fluctuations of the propagation medium can be deduced from its calculation. These studies are presented in the following:

 

2.2.1 Mutual Coherence Function (MCF)

 

The MCF is calculated following:

 

 

where 𝛱 is the complex received pressure in the Fourier domain (at frequency f₀). The shape of the MCF was fully described and analyzed^7,10. A good agreement was found between the measurements, the simulations and the theoretical analysis (based on the simplified MCF¹²). The radius of coherence is an accurate metric to quantitatively evaluate the effects of fluctuations on the signal correlation along the array. It can also be compared to the dimensional parameter analytically defined in Table 1 noted L_z. We define the radius of coherence¹³ as follows:

 

 

Figure 3 displays the radii of coherence calculated for each configuration. A good agreement is found between the results based on synthetic and measured data, as well as with theoretical results. As an example, the case of PS1 shows an excellent correspondence between the experimental value (5.2), the synthetic data (5.19 in the small scale case, 5.22 in the oceanic case) and the theory (5.3). The pattern of evolution of the radius of coherence is consistent throughout all the studied configuration. Note that a “less saturated” region is not necessarily characterized by a greater radius of coherence (i.e. the theoretical ρ is approximately 5.9 in the US2 case and 7.1 in the FS1 case). This highlights the fact that an analysis of the coherence function is not fully sufficient to understand the effect of medium fluctuation on acoustic propagation: this study has to be coupled with dimensional analysis (qualitative understanding of the acoustic saturation). Overall the coherence study tends to validate the representativeness of our experimental scheme.

 

 

 

Figure 3: Radii of coherence calculated for each studied configuration. Comparison betweennumerical, theoretical and experimental results^7,10.

 

2.2.2 Degradation of the Array Gain (AG)

 

The array gain is related to the MCF. Therefore a decrease in coherence translates into a degradation of the AG. A parameter accounting for this degradation can be expressed as a function of the MCF. It is noted δ AG and defined as follows:

 

 

δ_AG is calculated using the measurements, the simulations and the theoretical results. It is also compared to a semi-empirical formula obtained after a linear regression on Monte Carlo simulations outputs¹⁴.

 

Figure 4 displays the comparison between these calculations in all the studied configurations. The influence of the array size is also highlighted: four sizes of linear array have been studied: 8, 16, 32 and 64-sensor arrays. A remarkably good agreement is found throughout all the sub-figures in Figure 4 : the various calculations are in excellent correspondence in all the studied cases, for each considered array size. Moreover, the match between the results presented here and the semi- empirical formula is also spectacular. Finally, an intuitive observation can be confirmed: the array size plays a critical role in the sensitivity to the medium fluctuations. In fact, the greater the array, the more important the degradation of the array gain.

 

 

Figure 4: Array gain degradation parameter δ AG for all studied configurations. Comparison between semi-empirical, numerical, theoretical and experimental results

 

 

3 TOWARDS CORRECTIVE SIGNAL PROCESSING TECHNIQUES

 

The results presented in this paper enhance the fact that classical signal processing techniques cannot handle the issue of fluctuations of the propagation medium. Not only, as shown earlier, a phenomenon of de-coherence is noticed, but also, qualitative features related to phase only or phase and amplitude fluctuations of the received acoustic data lead to strong limitations of the sonar performance. Especially, these conclusions hold when very large arrays are involved. Since the need for large array is not to be mitigated, it is more towards corrective signal processing techniques that the bulk must be provided.

 

A state of art of techniques potentially interesting for passive sonar application can be found in the work of Real 7. We present the results associated with a method called GLR¹⁵. The likelihood ratio of the probability density function under the hypothesis H₁ (noise and signal are contained in the studied data) and H₀ (only noise is contained in the studied data) is used to perform the detection.

 

 

Where

  

is the pdf under the i hypothesis. The maximization of L is a multi-dimension optimization problem (the unknown are the de-coherence rate, the radius of coherence, the angle of arrival, the noise level and the SNR).

 

Rather than the classical array gain, the deflection 16,17 is used as the detection criterion. It is defined as:

 

 

Where E_i is the mathematical expectation under the i hypothesis (i=1 for signal +noise, i=0 for noise only), V_i is the variance under the i hypothesis and Ḿ is the maximum at the output of the algorithm, averaged over N_R realizations.

 

3.1 Application to experimental data

 

We present in this section the results associated with the techniques described earlier. Three cases of saturation were studied (US1, PS2 and FS3) with various input SNRs (from -10 to 0 dB).

 

 

Figure 5: LR method performance in the US1 case.

 

 

Figure 6: LR method performance in the PS2 case.

 

 

Figure 7: LR method performance in the FS3 case.

 

 

4 CONCLUDING REMARKS AND FUTURE WORK

 

The objective of this paper was twofold: first, the relevance of an experimental protocole at small-scale allowing to faithfully reproduce the effects of sound field decoherence was demonstrated. Then the impact of these decoherence effects on sonar processing and especially detection capability was shown. Our study reveals that for large arrays, the effects of medium fluctuations on the array gain can be extremely important (up to 6 dB loss in the worst case scenario). Nevertheless, some signal processing techniques can be used to mitigate these array gain degradation. The example of the GLR technique is successfully applied to our set of experimental data. The range of techniques showing promising results in this domain is however non limited to this one. Lefort et al 18 presented some studies towards an enhancement of the localization performance. The authors will work on applying techniques similar to those presented here to field-acquired data (ALMA experiment⁷).

 

 

5 REFERENCES

 

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