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Beamforming technology is very important for passive sonar to detect targets. However, the performance of a beamformer is seriously degraded in practical applications due to the complex and changeable underwater environment. In this paper, a null broadening algorithm for passive sonar based on a weighted similarity vector is proposed for underwater fast-moving strong interference signals. First, the covariance matrix was reconstructed through the correlation between the steering vector and the subspace eigenvector, which was used to calculate the similarity vector. Then, the maximum power in the interference angle sector was used as the virtual interference source power to broaden the null in the angle sector. Next, the difference between the optimal weight vector and the similar vector was minimized, the interference-plus-noise power constraints and norm constraints were added, and the equation was written as a quadratic constrained quadratic programming (QCQP) problem, which was converted into a convex optimization problem by using the semidefinite relaxation technique. Finally, the optimal solution was calculated by using eigen decomposition. The simulation results show that the algorithm can guarantee deep nulling and effectively suppress sidelobe height under various error conditions, which shows that the proposed algorithm has a good suppression effect and strong robustness for fast strong interference. [ABSTRACT FROM AUTHOR]

When the rapid moving interference exists, especially in the presence of look direction mismatch, coherent local scattering and so on, the output performance of beamformer will degrade dramatically. To solve this problem, a novel robust adaptive null broadening beamforming method based on subspace projection is proposed. First, the proposed beamformer requires a priori information, that is, the spatial sector where the desired signal and interference may locate, so as to construct the signal-plus-noise covariance matrix (SPNCM) and interference-plus-noise covariance matrix (IPNCM). Then, the desired signal steering vector (SV) is calibrated twice. The desired signal SV is estimated from the SPNCM and subsequently calibrated by using the uncertainty set optimisation method. Next, we construct the null broadening projection matrix by tapering the interference subspace got from IPNCM. Finally, the sample covariance matrix is processed by projection technology and diagonal loading technology. The optimal weight vector is obtained by the new covariance matrix and calibrated desired signal SV. Simulation results show that the proposed method can form wide null in the incident direction of interference and prevent interference from moving out of the null when the rapid moving interference exists. The proposed method outperforms other existing methods. [ABSTRACT FROM AUTHOR]

To solve the problem that the performance of adaptive beamformer degrades severely in the presence of steering vector mismatch or non-stationary interference, a null broadening robust beamforming based on decomposition and iterative second-order cone programming (SOCP) is proposed. The width and depth of the nulls is controlled. The magnitude response constraints are applied to control the beamwidth and ripple of mainlobe, so the SV mismatch can be overcame. Due to the decomposition of the non-convex magnitude response constraints, the proposed approach can be solved by decomposition and iterative SOCP. Simulation results show that the proposed approach can effectively broaden the null width and enhance the null depth, and it is also robust against SV mismatch, especially large SV mismatch. The proposed approach is jointly robust against the SV mismatch and non-stationary interference, and is still effective in the case of low snapshot, which enhances the robustness of adaptive beamformer in complex environments.

Beamforming technology is very important for passive sonar to detect targets. However, the performance of a beamformer is seriously degraded in practical applications due to the complex and changeable underwater environment. In this paper, a null broadening algorithm for passive sonar based on a weighted similarity vector is proposed for underwater fast-moving strong interference signals. First, the covariance matrix was reconstructed through the correlation between the steering vector and the subspace eigenvector, which was used to calculate the similarity vector. Then, the maximum power in the interference angle sector was used as the virtual interference source power to broaden the null in the angle sector. Next, the difference between the optimal weight vector and the similar vector was minimized, the interference-plus-noise power constraints and norm constraints were added, and the equation was written as a quadratic constrained quadratic programming (QCQP) problem, which was converted into a convex optimization problem by using the semidefinite relaxation technique. Finally, the optimal solution was calculated by using eigen decomposition. The simulation results show that the algorithm can guarantee deep nulling and effectively suppress sidelobe height under various error conditions, which shows that the proposed algorithm has a good suppression effect and strong robustness for fast strong interference.

In order to solve the problem of severely decreased performance under the situation of rapid moving sources and unstable array platforms, a null broadening robust adaptive beamforming algorithm based on power estimation is proposed in this paper. First of all, we estimate the interference signal power according to the characteristic subspace theory. Then, the correspondence between the signal power and steering vector (SV) is obtained based on the orthogonal property, and the interference covariance matrix (ICM) is reconstructed. Finally, with the aim of setting virtual interference sources, null broadening can be carried out. The proposed algorithm results in a deeper null, lower side lobes and higher tolerance of the desired signal steering vector mismatch under the condition of low complexity. The simulation results show that the algorithm also has stronger robustness. [ABSTRACT FROM AUTHOR]

Featured Application: Global Navigation Satellite Systems (GNSS) anti-jamming. In order to flexibly and completely suppress dynamic interference, a flexible and robust beamforming based on JADE is proposed in this paper. In addition, it is insensitive to the gain–phase errors of the array. Firstly, the actual steering vector with gain–phase errors is separated from the received snapshot data by the joint approximate diagonalization of eigenmatrix (JADE) algorithm. Secondly, the direction of arrival (DOA) of interference can be estimated from the separated actual steering vector by the correlation coefficient method. Thus, the actual interference steering vector with gain–phase errors can be selected by the correlation coefficient with the nominal steering vector constructed by the estimated DOA. Then, the interference covariance matrix can be reconstructed by the actual interference steering vector, and the interference power estimated by the Capon power spectral. Finally, according to the prior information of the interference, only the dynamic interference covariance matrix is tapered by the novel covariance matrix trap (CMT), which can flexibly broaden and deepen the null. Simulation results show that the depth of the proposed beamformer is more than 10 dB deeper than that of the traditional algorithm in the non-stationary interference. In addition, it can save at least 2 degrees of freedom compared to the traditional method. [ABSTRACT FROM AUTHOR]

To solve the problem that the performance of adaptive beamformer degrades severely in the presence of steering vector mismatch or non-stationary interference, a null broadening robust beamforming based on decomposition and iterative second-order cone programming (SOCP) is proposed. The width and depth of the nulls is controlled. The magnitude response constraints are applied to control the beamwidth and ripple of mainlobe, so the SV mismatch can be overcome. Due to the decomposition of the non-convex magnitude response constraints, the proposed approach can be solved by decomposition and iterative SOCP. Simulation results show that the proposed approach can effectively broaden the null width and enhance the null depth, and it is also robust against SV mismatch, especially large SV mismatch. The proposed approach is jointly robust against the SV mismatch and nonstationary interference, and is still effective in the case of low snapshot, which enhances the robustness of adaptive beamformer in complex environments. [ABSTRACT FROM AUTHOR]

Beamforming plays an important role in the array radar anti-interference. However, the interference targets with fast speed may move out of the narrow null area of the beampattern. A null broadening method with robust adaptive beamforming for frequency diverse array (FDA)-multiple-input and multiple-output (MIMO) systems is proposed in this paper. The projection preprocessing and windowing functions are applied to obtain stable beampatterns. Then, a novel null broadening method based on the covariance matrix reconstruction is realized by setting artificial fluctuations around each actual jammer. Finally, a new convex optimization model is established and solved to estimate the desired steering vector. Numerical simulations results verify the effectiveness of the proposed method.

In order to flexibly and completely suppress dynamic interference, a flexible and robust beamforming based on JADE is proposed in this paper. In addition, it is insensitive to the gain–phase errors of the array. Firstly, the actual steering vector with gain–phase errors is separated from the received snapshot data by the joint approximate diagonalization of eigenmatrix (JADE) algorithm. Secondly, the direction of arrival (DOA) of interference can be estimated from the separated actual steering vector by the correlation coefficient method. Thus, the actual interference steering vector with gain–phase errors can be selected by the correlation coefficient with the nominal steering vector constructed by the estimated DOA. Then, the interference covariance matrix can be reconstructed by the actual interference steering vector, and the interference power estimated by the Capon power spectral. Finally, according to the prior information of the interference, only the dynamic interference covariance matrix is tapered by the novel covariance matrix trap (CMT), which can flexibly broaden and deepen the null. Simulation results show that the depth of the proposed beamformer is more than 10 dB deeper than that of the traditional algorithm in the non-stationary interference. In addition, it can save at least 2 degrees of freedom compared to the traditional method.

Copyright of Transactions of Beijing Institute of Technology is the property of Beijing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the cases of rapidly moving interference and look-direction error, robustness and output signal to interference and noise ratio (SINR) of conventional wideband adaptive beamforming methods are degraded severely. In order to solve these problems, a robust wideband adaptive beamforming with null broadening and constant beamwidth is proposed. We first propose a taper matrix constructed by adding virtual interferences for null broadening, where the reference frequency and number of virtual interferences of taper matrix are determined based on numerical methods. This is followed by reconstructing the array covariance matrix based on taper matrix. Spatial response variation (SRV) constraint is then applied for a constant beamwidth over the entire frequency band. Finally, the adaptive weight vector for null broadening and constant beamwidth is obtained by using Lagrange multiplier method. The effectiveness of proposed method is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

When jammers move rapidly or an antenna platform travels at high speed, interference signals may move out of the null width in the array beampattern. Consequently, the interference suppression performance can be significantly degraded. To solve this problem, both the null broadening technique and robust adaptive beamforming are considered in this paper. A novel null broadening beamforming method based on reconstruction of the interference-plus-noise covariance (INC) matrix is proposed, in order to broaden the null width and offset the motion of the interfering signals. In the moving case, a single interference signal can have multiple directions of arrival, which is equivalent to the existence of multiple interference sources. In the reconstruction of the INC matrix, several virtual interference sources are set up around each of the actual jammers, such that the nulls can be broadened. Based on the reconstructed INC and signal-plus-noise covariance (SNC) matrices, the steering vector of the desired signal can be obtained by solving a new convex optimization problem. Simulation results show that the proposed beamformer can effectively broaden the null width and deepen the null depth, and its performance in interference cancellation is robust against fast-moving jammers or array platform motion. Furthermore, the null depth can be controlled by adjusting the power parameters in the reconstruction process and, if the direction of interference motion is known, the virtual interference sources can be set to achieve better performance.

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to improve the performance of antenna array beamforming in the case of jammer motion, a null broadening beamforming approach based on covariance matrix expansion is proposed in this paper. The covariance matrix of the array is expanded through the Kronecker product of an eye matrix and the sample covariance matrix. The steering vector of the array is also expanded. When the expanded covariance matrix is used for beamforming, more linear constraints can be constructed compared with the original sample covariance matrix, so wider and deeper nulls can be obtained with equal number of array elements, or similar performance can be obtained with fewer number of array elements. Necessary numerical procedures are provided and computation complexity is analyzed. The validity of the proposed approach is verified by theoretical analysis and simulation results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Beamforming is an important technology for array systems, the spatial filtering can be achieved by focusing the main beam to the target and null point to the interference. Comparing to the noise suppression method based single-channel, the signal from beamforming output shows lower distortion and higher signal-to-interference plus noise ratio. This study is to investigate the null broadening (bearing, width and depth) control of beamforming, the purpose is to overcome the bearing error between interference and null by producing a broadening null, and to improve the interference signal suppression. Considering the requirements of real-time and broadband in the acoustic system, the fixed beamforming process is chosen and combined with the convex optimization technique. There are several advantages form fixed process that are better robustness due to avoiding the signal self-cancellation from the issue of model mismatch and low-complexity computation contributes to achieving the real-time and broadband spatial filtering in the present process. In the experiment of the chirp signal, the SNR of beamformer output is increased from 2 to 10.5 dB, the correlation coefficient for target is increased from 0.52 to 0.82, and the interference is reduced from 0.54 to 0.07. In the experiment of the broadband voice signal, the SNR of beamformer output is increased from 2 to 6.5 dB, the correlation coefficient for target is increased from 0.37 to 0.68, and the interference is reduced from 0.58 to 0.19. The experimental results verify that the proposed algorithm can effectively controlled the capability of null broadening and have better interference suppression than other algorithms. [Display omitted] • CNBF is a null broadening beamforming combined with convex optimization technique. • CNBF is truly more efficient at suppressing interference. • CNBF has a better robustness due to avoid the signal self-cancellation from the issue of model mismatch. • CNBF has low-complexity computation contributes to achieving the real-time and broadband spatial filtering. [ABSTRACT FROM AUTHOR]

Adaptive beamforming algorithm can automatically optimize the array pattern by adjusting the elemental control weights until a prescribed objective function is satisfied. Unfortunately, it is possible that the mismatch occurs between adaptive weights and data, due to the perturbation of the interference location when the antenna platform vibrates or interference moves quickly. Besides, the traditional beamformers may have unacceptably high sidelobes when few samples are available. To solve these problems, an effective robust adaptive beamforming method is presented. In the proposed method, firstly, a tapered covariance matrix is constructed to broaden the width of nulls for interference signal sources. Secondly, multiple additional quadratic inequality constraints outside the mainlobe beampattern area are used to guarantee that the sidelobe level is strictly lower than the prescribed threshold value. Finally, the beamforming optimization problem is formulated as a multi-parametric quadratic programming problem, such that the optimal weight vector can be easily obtained by real-valued computation. Simulation results are shown to demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

When jammers move rapidly or an antenna platform travels at high speed, interference signals may move out of the null width in the array beampattern. Consequently, the interference suppression performance can be significantly degraded. To solve this problem, both the null broadening technique and robust adaptive beamforming are considered in this paper. A novel null broadening beamforming method based on reconstruction of the interference-plus-noise covariance (INC) matrix is proposed, in order to broaden the null width and offset the motion of the interfering signals. In the moving case, a single interference signal can have multiple directions of arrival, which is equivalent to the existence of multiple interference sources. In the reconstruction of the INC matrix, several virtual interference sources are set up around each of the actual jammers, such that the nulls can be broadened. Based on the reconstructed INC and signal-plus-noise covariance (SNC) matrices, the steering vector of the desired signal can be obtained by solving a new convex optimization problem. Simulation results show that the proposed beamformer can effectively broaden the null width and deepen the null depth, and its performance in interference cancellation is robust against fast-moving jammers or array platform motion. Furthermore, the null depth can be controlled by adjusting the power parameters in the reconstruction process and, if the direction of interference motion is known, the virtual interference sources can be set to achieve better performance. [ABSTRACT FROM AUTHOR]