Huijun Xia

Study of robust and high-gain beamforming based on diagonal reducing

Ocean ambient noise mainly includes uncorrelated noise and correlated noise. The uncorrelated noise only affects the diagonal elements in the noise covariance matrix, and it can be suppressed by subtracting a value on the diagonal elements. Utilizing this feature, a high array-gain beamforming based on diagonal reducing is presented. Meanwhile, the robustness becomes poor. So, the array weight norm constraint is used to ensure the robustness of this method, and the threshold is selected by some criterions. Then, the diagonal reducing value is calculated by the newton iteration method. After subtracting the diagonal reducing value, the covariance matrix is used in the minimum variance distortionless response (MVDR) beamformer. Both the numerical simulations and experimental results show that the proposed method can improve the array gain and the resolution capacity of multi-targets and it also can provide a tradeoff between array gain and robustness by chanOcean ambient noise mainly includes uncorrelated noise and correlated noise. The uncorrelated noise only affects the diagonal elements in the noise covariance matrix, and it can be suppressed by subtracting a value on the diagonal elements. Utilizing this feature, a high array-gain beamforming based on diagonal reducing is presented. Meanwhile, the robustness becomes poor. So, the array weight norm constraint is used to ensure the robustness of this method, and the threshold is selected by some criterions. Then, the diagonal reducing value is calculated by the newton iteration method. After subtracting the diagonal reducing value, the covariance matrix is used in the minimum variance distortionless response (MVDR) beamformer. Both the numerical simulations and experimental results show that the proposed method can improve the array gain and the resolution capacity of multi-targets and it also can provide a tradeoff between array gain and robustness by changing the diagonal reducing value.ging the diagonal reducing value.

Noise Reduction Method for Acoustic Sensor Arrays in Underwater Noise

Noise reduction capacity in sensor array signal processing is derived under the assumption of white noise, where the noise reduction is defined as the difference between the input noise power and the output noise power in this paper. However, the underwater noise mainly includes white noise and correlated noise. In this situation, the noise reduction capacity may be deteriorated considerably in actual underwater environment. To tackle this problem, a new noise reduction method, which is named imaginary delay-and-sum beamforming method, is proposed. First, the noise signals received by a sensor array are decomposed into symmetrical and asymmetrical components. Theoretically, the symmetrical component can only affect the real parts of the noise covariance matrix. Then, the real parts of the data covariance matrix are eliminated to reduce the symmetrical noise, and the beamforming is completed by using only imaginary parts. The output signal-to-noise ratio is improved and the root mean square error of the direction-of-arrival estimation is decreased. Theoretical analyses and experimental results show that the proposed method can be easily implemented to improve the noise reduction capacity in sensor array signal processing.

A Noise Removal Method for Uniform Circular Arrays in Complex Underwater Noise Environments with Low SNR

Generally, many beamforming methods are derived under the assumption of white noise. In practice, the actual underwater ambient noise is complex. As a result, the noise removal capacity of the beamforming method may be deteriorated considerably. Furthermore, in underwater environment with extremely low signal-to-noise ratio (SNR), the performances of the beamforming method may be deteriorated. To tackle these problems, a noise removal method for uniform circular array (UCA) is proposed to remove the received noise and improve the SNR in complex noise environments with low SNR. First, the symmetrical noise sources are defined and the spatial correlation of the symmetrical noise sources is calculated. Then, based on the preceding results, the noise covariance matrix is decomposed into symmetrical and asymmetrical components. Analysis indicates that the symmetrical component only affect the real part of the noise covariance matrix. Consequently, the delay-and-sum (DAS) beamforming is performed by using the imaginary part of the covariance matrix to remove the symmetrical component. However, the noise removal method causes two problems. First, the proposed method produces a false target. Second, the proposed method would seriously suppress the signal when it is located in some directions. To solve the first problem, two methods to reconstruct the signal covariance matrix are presented: based on the estimation of signal variance and based on the constrained optimization algorithm. To solve the second problem, we can design the array configuration and select the suitable working frequency. Theoretical analysis and experimental results are included to demonstrate that the proposed methods are particularly effective in complex noise environments with low SNR. The proposed method can be extended to any array.

Gain analysis for vertical linear array in deep ocean

A formula is developed in this paper to calculate array gain when the plane-wave assumption is not applied. The formula is developped based on the assumption that the noise in the deep water is Gassian white and isotropic. The performance of a vertical linear is analyzed in the range-independent ocean, and also in a weak range-dependent ocean perturbed by random internal waves. Simulation results illustrate that the array gain is influenced by signal and environment features in the real ocean, and the array gain cannot keep increasing with the increasing of element numbers. It should be tested and simulated to decide the array length and the number of array elements.

Superdirective beamforming for dual concentric circular hydrophone arrays

This paper proposes a superdirective beamforming method for dual concentric circular hydrophone arrays based on the previously established eigenbeam decomposition and synthesis model. The optimal solutions of superdirectivity, including the optimal beampattern, the global directivity factor, and the total sensitivity function, are all decomposed into corresponding sub-solutions termed eigenbeams, their directivity factors, and their sensitivity functions, respectively, based on the block matrix inversion lemma and the properties of the circulant matrix. The eigenbeams possess different directivities and robustness, and a robust scheme called the reduced-rank technique is then applied to achieve robust superdirective results based on these solutions. The feasibility and good performance of the proposed method are demonstrated in simulations.

Direction-of-arrival estimation using high-order superdirective beamforming for a circular hydrophone array

This paper presents a method of direction-of-arrival estimation using the high-order superdirective beamforming for a circular hydrophone array. The weighting vectors with different orders used for DOA estimation can be obtained using the previously proposed eigenbeam decomposition and synthesis theory, which can provide frequency-invariant beampatterns in a wide frequency band. The DOA estimation result of this method is the sum of estimations with different orders and the robustness decreases with an increase of the number of order. The reduced-rank technique is applied to achieve robust DOA estimations by truncating some error-intolerable high order estimation results and reserving the low order ones. Simulation results show that the DOA method proposed in this paper can improve the angular resolution (when the sensor space to wavelength ratio is smaller than 1/2) compared to the conventional beamforming (CBF) method. An experiment was conducted in the South China Sea with a 12-hydrophone circular array, and the results show effectiveness and validity of the proposed method.

Numerical modeling of sound propagation through the internal soliton waves over continental slope

The internal solitary waves propagating over the shelf slope fluctuating the acoustic energy in shallow water has been widely studied. In this paper, this process is broadened into the continental slope with different gradient at different range which is linked with the shallow water and the deep water. The temporal and spatial structures of the acoustic field with the internal solitary wave passing through continental shelf to the deep region are analyzed. The variation of signal intensity at the receiver, which is caused by the moving soliton and space dependent bathymetry, shows the coupling between low modes and high modes. The location of the internal soliton waves relative to the source and the gradient of the continental slope are considered as the dominant factors fluctuating the acoustic energy received at a range of 15km by simulating the individual and joint effect of the soliton and bathymetry on the coupling coefficients.

Delay-and-sum beamforming based on the diagonal reducing method

The delay-and-sum beamforming method (DAS) is robust, as a consequence, it is widely used in the underwater array signal processing. However, the array gain of the DAS method is limited, and is restricted to the array aperture. To tackle this problem, we propose a DAS method based on the diagonal reducing method in the data covariance matrix. Firstly, a reducing value is subtracted from the diagonal elements of the covariance matrix, so as to reduce the noise. As a consequence, a new covariance matrix includes less noise component. Then, the DAS method is applied using this new covariance matrix to obtain the beam output, and we can obtain high array gain when compared with the traditional DAS method. The analytic solution and approximate solution of reducing value are obtained under the constraint condition that the output signal-to-noise ratio (SNR) attains its maximum. The simulation and the experimental results show that the diagonal reducing method reduces some ambient noise, the output array gain is increased.

Model-independent depth classification of transient acoustic signal in deep water

A method of estimating the source depth of wideband underwater acoustic pulses in deep water is proposed in this paper. The method is based on the characteristic of frequency domain interference oscillation of broadband signals received at a single stationary hydrophone. The oscillation period is related to the Lloyds Mirror effect (LME) and can be transformed into the information of source depth with the known source range. If the source range is uncertain, one can distinguish the submerged source from the near-surface one according to the sensitivity of estimated source depth versus source range. Experimental results confirm this source depth classification method.

Spatial coherence of sub-arrays in spherically isotropic noise

A Close-form solution of spatial coherence for collinear sub-arrays in spherically isotropic noise is proposed in this paper. By utilizing beamforming techniques, sub-array outputs can be expressed in a combination of the fixed weight vector, the steering vector and the frequency domain sequence received by the first sensor. Then the formulations of the power spectrum density and cross-power spectrum density of two sub-arrays will be simplified to those with summations instead of integrals, which can be analytically computed. It is shown that the half power beam width of sub-array determines the amplitude of spatial coherence, and the angle between the beam steering direction and the line across two acoustical centers of sub-arrays affects the frequency of curves fluctuation. Numerical simulations demonstrated the accuracy of the analytical solution and the validity of the related theoretical analyses.