Vector sensors can make use of more available acoustic information than the scalar pressure sensors (e.g., hydrophones), because they can measure the components of particle velocity and the acoustic pressure at the same point simultaneously.^[1–3] Consequently, the performance of a vector sensor array in terms of signal-to-noise ratio (SNR) enhancement, directivity, and localization accuracy, will be superior to that of the same aperture array consisting of scalar pressure sensors. Because the advantages are attractive, the vector sensor technology has grown rapidly in recent decades and it has been applied in many fields such as communication, geo-acoustic inversion, underwater imaging, and so on.^[4–7] As the signal processing techniques of the vector sensor array can be included into the classical theoretical framework of scalar pressure sensor array, the existing beamforming methods and direction-of-arrival (DOA) estimation algorithms can be extended to vector sensor arrays.^[1,8–11]

Array gain (AG) is defined as the difference between SNR of the output signal and SNR of the input signal of an array, which is an important parameter for measuring the detection performance of the array. When the source signal is a plane wave and the noise field is isotropic, the AG reduces to the directivity factor (DF). Cray and Nuttall^[12] provided detailed calculations of the DFs of vector sensors and vector-sensing linear arrays and they also presented some comparisons with the scalar-sensing linear arrays. D’Spain et al.^[13] analyzed the optimal AG and detection performance of vector sensor line arrays in a homogeneous, isotropic noise field. It is shown that vector sensors and vector sensor arrays can also provide superdirectivity or supergain in constraint of miniaturized aperture, but the basic principle is different from that for scalar pressure sensor arrays.^[14–16] Actually, the knowledge of the correlation structure of the noise always plays an important role in evaluating AG for a sensor array in a practical environment. Some models of the correlation structure under various environment assumptions have been developed for vector sensor arrays, which are useful to analyze the system performance before deployment.^[17] However, the assumptions of the environment noise are not always in accordance with practical situation and the theoretical calculations will be sometimes not suitable, even degrade the performance of beamforming methods. For a specific array, the experimental measure is still an essential and direct way to evaluate its capability. In Ref. [18], the results of the minimum variance distortionless response (MVDR) method applying to process the actual data collected by the DIFAR array are presented. Wettergren and Traweek^[19] studied the detection performance of a conformal velocity sonar array using a method of optimizing shading weights of the conventional beamformer. Some experimental results are also presented to demonstrate the feasibility of the proposed method. However, most of the previous works in relation to vector sensor arrays are limited to linear configurations, and the researches on the other type of vector sensor arrays are not sufficient.

This paper presents a detailed study of an experimental conformal acoustic vector sensor array in a practical environment, with particular focus on its AG. First, the manifold vector is calculated using the real measured data so that the effects of array mismatches can be minimized. Second, an optimal beamformer with a specific spatial response is designed using a direct optimization method, which can effectively suppress the ambient noise and improve SNR. The delay-and-sum (DAS) and MVDR beamformers are also designed for comparison. The weighting vectors of these beamformers are all calculated using the obtained manifold vector. The AGs of these different methods are calculated using experimental data and a detailed comparison is provided.

An acoustic vector sensor simultaneously measures the components of pressure and two or three orthogonal particle velocities at the same point, which can be written as

Let w be the weighting vector, then, the beampattern will be

The experimental conformal array shown in Fig. 1(a) consists of 22 vector sensors and each vector sensor contains a pressure channel and two horizontal velocity channels. Unfortunately, three sensors (which are red in Fig. 1(b)) are not working in the experiment and only the data received by the remaining 19 vector sensors (57 channels) are used.

Fig. 1.

	Figure Option ViewDownloadNew Window
	Fig. 1. Experimental conformal vector sensor array and configuration of experiment. (a) The photograph of the experimental conformal vector sensor array. (b) Top view of the conformal vector sensor array and coordinates. (c) Configuration of experiment. (d) Experiment location.

The experiment was carried out in a lake located at east China. As shown in Fig. 1(c), both the conformal vector sensor array and the projector were put at a depth of 9.4 m below the lake surface. The signals transmitted by the projector were rectangular window modulated single frequency continuous-wave pulses, which can be used to obtain the real manifold vector. The frequency is 3 kHz and the impulse repetition period was 10 ms. Note that there is a dam located in the southwest of the experiment ship and it will generate some noise, see Fig. 1(d). Some more detailed analyses of the ambient noise will be given below.

In the experiment, the array was rotated from 0° to 360° with a step of 3° in the horizontal plane to receive the signals, which is equivalent to the situation in which the signals were incident from these different directions. After the pre-processing, the received signals were sampled by A/D converters and the sample frequency was 16 kHz. The data from A/D converters were saved to a computer and processed off-line. The real manifold vectors P(ϕ) are calculated using the methods presented in Ref. [20], and they will be used to compute the weighting vectors of different beamformers. Because the real manifold vectors are obtained from the experimental data, the shadowing, scattering, and the near-field effects are all considered in this process. In other words, the weighting vectors computed using the real manifold vectors will be more accurate and efficient than that computed using the theoretical manifold vectors. This is also the reason why the real manifold vectors are always used in many applications, even though the measuring procedure is time-consuming.

The amplitude responses of the 8th and 19th sensors at a frequency of 3 kHz are shown in Figs. 2 and 3, respectively. Theoretically, the pressure channel is omnidirectional and both of the two orthogonal velocity channels are the same with a dipole contour. However, the practical directivity responses are roughly in accordance with the ideal ones. Because the wavelength of the signal is analogous to the size of platform, and the apparent acoustic impedance contrast between water and materials of platform and vector hydrophone itself, the shadowing and scattering effects of these structures will inevitably cause some distortions. Specifically, it is seen that the amplitude responses in the direction of the vertical pole (see Fig. 1(a)) are clearly smaller than those in other directions due to the shadowing and scattering effects of this vertical pole. The amplitude responses of the other sensors also have the same properties which are not shown here for compactness.

Fig. 2.

	Figure Option ViewDownloadNew Window
	Fig. 2. Theoretical (dotted line) and practical (solid line) amplitude responses of the 8th sensor. (a) Pressure channel. (b) Velocity channel 1. (c) Velocity channel 2.

Fig. 3.

	Figure Option ViewDownloadNew Window
	Fig. 3. Theoretical (dotted line) and practical (solid line) amplitude responses of the 19th sensor. (a) Pressure channel. (b) Velocity channel 1. (c) Velocity channel 2.

The directivity of ambient noise can be estimated using the MVDR method. The spatial spectrum is calculated using the following equation:^[1]

The noise covariance matrix R_n is estimated using the received noise data, which is expressed as

The obtained noise spatial directivity is shown in Fig. 4, in which only the narrow band noise with the center frequency of 3 kHz in six different time frames is used. The diagonal loading value ζ_DL is set to 0. Because there is a dam located in the southwest of the experiment ship, its noise will affect the directivity of ambient noise. As shown in Fig. 1(d), the dam is long and its noise that is generated from releasing water is stable in the experiment. Consequently, the directivity spectrum in ϕ ∈ [150°,210°] which is a relatively wide region is apparently larger than that in other angular regions and it was almost unchanging in the experiment, which means the ambient noise field was always not isotropic.

Fig. 4.

	Figure Option ViewDownloadNew Window
	Fig. 4. Actual noise spatial directivity.

One of the methods than can reduce the effect of this anisotropic ambient noise field in the experiment is to design a suitable beamformer that can minimize the responses in ϕ ∈ [150°,210°] subject to some other constraints. The desired beamformer in this paper can be formulated as the following direct optimization problem:

The beampatterns in Fig. 5 are obtained using the DAS, MVDR, and the proposed direct optimization methods, where the weighting vectors of the DAS and MVDR methods are expressed as

Fig. 5.

	Figure Option ViewDownloadNew Window
	Fig. 5. Actual beampatterns of different beamformers.

The mainlobes of the three beampatterns in Fig. 5 are almost the same, whereas the sidelobe levels (SLs) in Ω_SL2 are clearly different from each other. The SLs of the direct optimization method are all below −8 dB, which satisfy the sidelobe constraint. By contrast, the highest SLs of the DAS and MVDR methods are approximately −5.2 dB and −3.4 dB, respectively, which are higher than that of the proposed method. Moreover, the SLs of the direct optimization in Ω_SL1 are minimized to −32 dB, which is much lower than those of the DAS and MVDR methods. The performance of the direct optimization method in terms of the noise suppression and signal enhancement are better than the DAS and MVDR methods.

Three LFM signals with different input SNRs (which are spaced by 10 dB in turn) were transmitted for the purpose of evaluating the potential for AG enhancement of this conformal vector sensor array, and these signals were all incident from the direction of (90°,0°) in the experiment. Since the center frequency is 2.9 kHz and bandwidth is 200 Hz, the transmitted signals can be regarded as narrow-band signals. The beampatterns can be obtained using the weighting vectors calculated at the frequency of 3 kHz using the above-mentioned methods. Although this frequency is a little different from the signal center frequency, the effects are limited which are neglected. The signals received by the pressure channel of the 12th vector sensor are shown in Fig. 6(a), in which the actual SNRs of the three signals are 0.50 dB, 5.99 dB, 17.91 dB, respectively. Because the ambient noise was time-varying in the experiment, the SNRs of the received signals are not exactly spaced by 10 dB, but this difference will not affect the following AG results. Additionally, because the signal pulse width is a little large, some multipath signals will be included in experimental data. However, this work mainly focuses on comparing the performance of the DAS, MVDR, and the proposed direct optimization methods in terms of improving the AG under identical conditions. The effects of these multipath signals are just the same to these methods, and therefore they will not affect the final conclusions. A detailed study of the effects of multipath signals to the performance of different beamforming methods is needed but it is not the purpose of this work.

Fig. 6.

	Figure Option ViewDownloadNew Window
	Fig. 6. Experimental results. (a) Signals received by the pressure channel of the 12th vector sensor. (b) Output signals of different beamformers corresponding to signal 1.

After the beamforming procedure, the output SNRs of different beamforming methods can be calculated using the following equation:

Table 1.

Table 1.

Table 1. AGs of different methods. . Methods DAS-pressure channels only/dB DAS/dB MVDR/dB Direct optimization/dB Signal 1 9.20 11.19 17.97 15.91 Signal 2 10.78 15.38 21.48 17.59 Signal 3 9.33 13.78 19.21 16.32

Table 1. AGs of different methods. .

Because more information from the velocity channels is used, the DAS AGs computed using the data of three channels are larger than those obtained only using the data of pressure channels. Therefore, the vector sensor array can achieve higher AGs than the scalar sensor array with the same array size. As shown in Table 1, AGs of the DAS method are the smallest whereas AGs of the MVDR method are the largest among the results. Since the noise data that were used to obtain the noise covariance matrix were selected from the vicinity time of the signal pulses, they can be thought of as good estimations of the real noise data that were added to the signals. Consequently, the AGs of the MVDR method can be considered as the optimal ones that can be obtained in the corresponding circumstances. However, the performance of the MVDR method may degrade when the noise data used to estimate the noise covariance matrix contain the desired signal and the steering direction is different from the signal incident direction. Moreover, because the three signals were received in different time and the environment was time varying, the corresponding AGs achieved using the same method in the three cases are also different. However, the AG improvements of the MVDR method in comparison to the DAS method are all approximately equal to 6 dB. By contrast, the AGs of the direct optimization are enhanced by more than 2 dB over the DAS method, especially the AG enhancement in relation to signal 1 approaches 4.7 dB. Although the improvement is smaller than that of the MVDR method, the direct optimization method has no need to compute the noise covariance matrix so that it has no limitation when the noise data contain desired signals. In other words, the weighting vector of the proposed method is fixed whereas the weighting vector of the MVDR method should be adjusted when the noise covariance matrix is changed. Thus, the implementation of the direct optimization method is simpler than the MVDR method.

An experimental conformal array consisting of 22 vector sensors is designed, and its AG in a practical environment is studied in this paper. The manifold vector is calculated using the real measured data in the experiment so that the effects of array mismatches can be minimized. Then, the direct optimization, DAS, and MVDR beamformers are designed, and their weighting vectors are all calculated using the above-obtained manifold vector. Because the ambient noise shows a stable directivity, the direct optimization beamformer is deliberately designed to have a specific responese so that it can effectively suppress the ambient noise and improve SNR. The AGs of these different methods are calculated using experimental data and the results show that the direct optimization beamformer provides good SNR enhancement and has more advantages than the DAS and MVDR beamformers.