Performance Of Adaptive Beamformer Research Articles

Adaptive Beamforming with Hydrophone Arrays Based on Oblique Projection in the Presence of the Steering Vector Mismatch

In sonar systems, the performance of adaptive beamformers severely degrades when mismatches occur between the actual and presumed steering vectors of the desired signal, mainly due to hydrophone position errors, amplitude-phase errors, and the scattered effect of arrays. Similarly, an inadequate number of “training” samples can lead to performance degradations similar to those caused by mismatches. In this paper, an adaptive beamforming algorithm based on oblique projection (OP-ABF) mismatch compensation is proposed to remove the degradation caused by the arbitrary-type steering vector mismatch of the desired signal. The proposed algorithm is motivated by the fact that the weight vector of adaptive beamforming can be represented as a linear combination of the optimal one and the oblique projection (OP) vector, which is generated by the steering vector mismatch and does not exist without this. Our algorithm was developed by constructing the oblique projection mismatch compensation vector (OPMCV) to provide the minimum variance distortionless response (MVDR) beamformer. Then, the algorithm could be implemented by the solution of the OP matrix with the formulation of the covariance matrix loading (CML). The simulation results of a uniform linear array (ULA) and a half-cylindrical conformal array (HCCA) show that the OP-ABF can optimize the original weight vector as much as possible without sacrificing the output signal-to-interference-plus-noise ratio (SINR) under different conditions. Experimental results for the HCCA also confirm the effectiveness of this algorithm.

基于低管秩张量分解的互质阵列自适应波束成形算法

The coprime array (CPA) has attracted extensive attention in the field of adaptive beamforming (ABF) because of its large array aperture and high degree of freedom. To make full use of this characteristic, several algorithms based on hole filling have been proposed to improve the performance of ABF. However, these algorithms have disadvantages in computation and noise robustness, which are difficult to adapt to complex and changeable environments. To solve this problem, this paper proposes a CPA-ABF algorithm based on low-tubal-rank tensor decomposition. First, the multi-sampling virtual signal matrix of the CPA is rearranged into a tensor form, and the missing cross-correlation information is completed using its low tubal rank. Then, signal parameters are extracted from the completed tensor data and matched with the target a priori. Finally, the ABF weight vector is obtained. The algorithm uses ADMM and Tucker decomposition to improve the efficiency of tensor completion and decomposition. The designed target matching scheme also effectively controls the algorithm error. The simulation results show the advantages of the algorithm in performance and computational complexities compared with existing methods, especially in the case of low signal-to-noise ratios and a small number of samples.

Fast Wideband Beamforming Using Convolutional Neural Network

With the wideband beamforming approaches, the synthetic aperture radar (SAR) could achieve high azimuth resolution and wide swath. However, the performance of conventional adaptive wideband time-domain beamforming is severely affected as the received signal snapshots are insufficient for adaptive approaches. In this paper, a wideband beamformer using convolutional neural network (CNN) method, namely, frequency constraint wideband beamforming prediction network (WBPNet), is proposed to obtain a satisfactory performance in the circumstances of scanty snapshots. The proposed WBPNet successfully estimates the direction of arrival of interference with scanty snapshots and obtains the optimal weights with effectively null for the interference by utilizing the uniqueness of CNN to extract potential nonlinear features of input information. Meanwhile, the novel beamformer has an undistorted response to the wideband signal of interest. Compared with the conventional time-domain wideband beamforming algorithm, the proposed method can fast obtain adaptive weights because of using few snapshots. Moreover, the proposed WBPNet has a satisfactory performance on wideband beamforming with low computational complexity because it avoids the inverse operation of covariance matrix. Simulation results show the meliority and feasibility of the proposed approach.

Robust adaptive beamforming based on covariance matrix reconstruction using Gauss–Legendre quadrature and steering vector estimation

The performance of adaptive beamforming is considerably affected by system errors in the gain and phase perturbation errors, direction of arrival mismatch, and incoherent local scattering, especially when the sample data contains the signal of interest (SOI) component. In this study, a robust adaptive beamforming approach based on interference plus noise covariance matrix (INCM) reconstruction using Gauss–Legendre quadrature (GLQ) and steering vector (SV) estimation is developed. The proposed algorithm incorporates the GLQ with the integral over the spherical uncertainty set and uses a linear combination of the integral at several angular nodes to substitute the integral of the entire interference region; consequently, the computational efficiency of reconstructing the INCM is enhanced. The SV of the SOI is represented as a linear combination of several principal eigenvectors of the SOI covariance matrix; thus, the double-constrained problem corresponding to the noise subspace is transformed into a single-constrained model, and its solution can be gained by utilizing the Lagrange multiplier method. Subsequently, the weight vector of the proposed beamformer can be calculated. Numerical simulations indicate that the proposed approach can effectively suppress interferences and exhibits superior overall performance under system errors.

Investigation on improving performance of adaptive beamformer by statistical analysis of ultrasonic echoes

Minimum variance (MV) beamformers have been introduced in medical ultrasound imaging to improve image quality. In most cases, the MV beamformers have been investigated in terms of resolution improvement. However, the contrast-to-noise ratio (CNR) is also a clinically important metrics and gathers attention recently. In this study, we examined the diagonal loading parameter σ in MV beamforming and determined its appropriate value by evaluating image quality evaluation metrics including CNR. In order to further improve the image quality, a method for determining the value of σ based on the difference in statistical properties of received ultrasonic echo signals was also investigated. The phantom experimental results showed that the proposed method achieved a better CNR than the conventional MV beamformer while keeping resolution significantly better than that in delay-and-sum beamforming.

Robust adaptive beamforming based on virtual sensors using low-complexity spatial sampling

The performance of robust adaptive beamforming (RAB) based on interference-plus-noise covariance (IPNC) matrix reconstruction can be degraded seriously in the presence of random mismatches (look direction and array geometry), particularly when the input signal-to-noise ratio (SNR) is high. In this work, we present a RAB technique to address covariance matrix reconstruction problems. The proposed RAB technique involves IPNC matrix reconstruction using a low-complexity spatial sampling process (LCSSP) and employs a virtual received array vector. In particular, the power spectrum sampling is realized by a proposed projection matrix in a higher dimension. The essence of the proposed technique is to avoid reconstruction of the IPNC matrix by integrating over the angular sector of the interference-plus-noise region. Simulation results are presented to verify the effectiveness of the proposed RAB approach.

Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction With Annular Uncertainty Set and Vector Space Projection

The performance of adaptive beamforming will degrade dramatically in practical application due to system errors including signal direction error, array geometry error, gain, and phase errors. Besides, the performance will further deteriorate when the desired signal is contained in the sample data. Therefore, a robust adaptive beamforming method based on the covariance matrix reconstruction with annular uncertainty set (AUS) and vector space projection (VSP) is proposed in this letter. By integrating the corresponding Capon spectrum over the surface of AUS, the interference-plus-noise covariance matrix (INCM) and the desired signal covariance matrix are reconstructed, respectively. Because the steering vector (SV) of desired signal lies in the intersection of the signal subspaces of the sample covariance matrix and the reconstructed desired signal covariance matrix, it can be estimated by the VSP method. Finally, the adaptive weight vector is calculated based on the reconstructed INCM and the estimated SV. Simulation and experiment results show that the proposed method can effectively suppress the interference and achieve excellent performance under system errors.

Neighborhood Singular Value Decomposition Filter and Application in Adaptive Beamforming for Coherent Plane-Wave Compounding

Coherent plane-wave compounding (CPWC) is widely used in medical ultrasound imaging, in which plane-waves tilted at multiple angles are used to reconstruct ultrasound images. CPWC helps to achieve a balance between frame rate and image quality. However, the image quality of CPWC is limited due to sidelobes and noise interferences. Filtering techniques and adaptive beamforming methods are commonly used to suppress noise and sidelobes. Here, we propose a neighborhood singular value decomposition (NSVD) filter to obtain high-quality images in CPWC. The NSVD filter is applied to adaptive beamforming by combining with adaptive weighting factors. The NSVD filter is advantageous because of its singular value decomposition (SVD) and smoothing filters, performing the SVD processing in neighboring regions while using a sliding rectangular window to filter the entire imaging region. We also tested the application of NSVD in adaptive beamforming. The NSVD filter was combined with short-lag spatial coherence (SLSC), coherence factor (CF), and generalized coherence factor (GCF) to enhance performances of adaptive beamforming methods. The proposed methods were evaluated using simulated and experimental datasets. We found that NSVD can suppress noise and achieve improved contrast (contrast ratio (CR), contrast-to-noise ratio (CNR) and generalized CNR (gCNR)) compared to CPWC. When the NSVD filter is used, adaptive weighting methods provide higher CR, CNR, gCNR and speckle signal-to-noise ratio (sSNR), indicating that NSVD is able to improve the imaging performance of adaptive beamforming in noise suppression and speckle pattern preservation.

An uncertainty-set-shrinkage-based covariance matrix reconstruction algorithm for robust adaptive beamforming

This paper presents an uncertainty-set-shrinkage (USS) algorithm that aims to reconstruct a precise interference-plus-noise covariance matrix (INCM) and improve the performance of adaptive beamformers when steering vector (SV) mismatch exists. Both of the interference covariance matrix (ICM) and the desired signal covariance matrix (DSCM) can be divided into two parts, namely the nominal matrix reconstructed using the nominal SVs and the error matrix consisting of the residual component of the covariance matrix. By using a two-step uncertainty set shrinkage method, the proposed beamformer constructs the error matrices by integrating the estimated spatial spectrum over the shrinked uncertainty set at a cost of low computational complexity. After extracting the principal component of the reconstructed ICM and DSCM, the INCM and the SV of the source of interest (SOI) can be estimated without solving any optimization problem. Both of numerical simulations and experimental results demonstrate that the performance of the proposed algorithm is robust with several categories of SV mismatches.

Experimental study of robust acoustic beamforming for speech acquisition in reverberant and noisy environments

The performance of adaptive beamformers may suffer from significant degradation in the presence of steering vector errors, statistics estimation errors, and reverberation. To address this issue, robust beamforming methods, which were originally studied in the narrow-band cases, are studied and compared in this paper for processing acoustic and speech signals, which are broadband in nature. We study two types of methods. In the first type, the robustness of the beamformer is improved by adding a norm constraint and/or a steering vector uncertainty constraint to the optimization problem. It is worth noticing that the norm constraint also helps to control the sidelobes of the beampattern, which makes the beamformers able to suppress interference and multipath effect, thereby improving the robustness of the beamformers with respect to reverberation. Another type of methods improve the robustness using the spatial smoothing technique in which the noise covariance matrix is implicitly estimated first by subtracting an estimate of the desired signal covariance matrix with a delay-and-sum beamformer from the observation signal covariance matrix. Simulations and experiments are performed to investigate the performance of the studied robust adaptive beamformers in acoustic environments. The results show that the robust beamformers outperform their non-robust counterparts in terms of: (1) better performance in reverberation and different noise levels; (2) resilience against steering vector and noisy signal covariance matrix estimation errors; and (3) better predicted speech quality and intelligibility measured using the PESQ and STOI measures.

Accessibility and Convergence Analysis of the Beamformer Design Based on Fibonacci Branch Search

An approach toward beamforming for uniform linear array (ULA) based on a novel optimization algorithm, designated as Fibonacci branch search (FBS), is presented in this paper. The proposed FBS search strategy inspired from Fibonacci sequence principle used fundamental branch structure and interactive searching rules to obtain the global optimal solution in the search space. The structure of FBS is established by two types of multidimensional points on the basis of shortening fraction formed by the Fibonacci sequence; in this mode, interactive global searching and local optimization rules are implemented alternately to reach global optima, avoiding stagnating in local optimum. At the same time, the rigorous mathematical proof for the accessibility and convergence of FBS toward the global optimum is presented to further verify the validity of our theory and support our claim. Taking advantage of the global search ability and high convergence rate of this technique, a robust adaptive beamformer technique is also constructed here by FBS as a real-time implementation to improve the beamforming performance by preventing loss of optimal trajectory. The performance of the FBS is compared with the five typical heuristic optimization algorithms, and the reported simulation results demonstrate the superior of the proposed FBS algorithm in locating the optimal solution with higher precision and reveal the further improvement in the adaptive beamforming performance.

Fast‐time STAP based on BSS for heterogeneous ionospheric clutter mitigation in HFSWR

High-frequency surface-wave radar (HFSWR) is widely used in vessel and aircraft detection, sea-state sensing and wind-field mapping. Target detection suffers from the ionospheric clutter, which is reflected by the ionosphere. Adaptive beamforming (ABF) has been used for ionospheric clutter mitigation. However, the performance of ABF is limited by the heterogeneous ionospheric clutter and degrees of freedom (DOF) of the antennas array. In order to improve the performance, here, the one-dimensional ABF is expanded to two-dimensional fast-time space–time adaptive processing (STAP), which combines beam and range domains to obtain more DOFs than that in the ABF. In addition, the blind sources separation (BSS) method is also used to improve the spatial covariance matrix estimation accuracy of STAP in the heterogeneous ionospheric clutter background. The simulation and real data results demonstrate the effectiveness of the proposed BSS-STAP method in HFSWR.

다기능레이다에 적용 가능한 적응빔 형성 알고리듬 간 성능 비교 연구

In a multi-function radar, the adaptive beamforming algorithm is one of the several methods that can be applied to restore the degraded SINR(Signal-to-Interference Noise Ratio) to its original level. This algorithm is employed for the regular operation of radars in jamming situations, when unwanted high-power signals are received. In this paper, we introduce a few adaptive beamforming algorithms that can be applied to a multi-function digital radar in jamming situations. Furthermore, we compare and analyze the adaptive beamforming performance in terms of SINR and sidelobe level characteristics by applying each algorithm to a specific planar array comprising optimized subarray structures.

Implementation of a novel Fibonacci branch search optimizer for the design of the low sidelobe and deep nulling adaptive beamformer

AbstractIn this work, we proposed an adaptive beamformer based on a novel heuristic optimization algorithm. The novel optimization technique inspired from Fibonacci sequence principle, designated as Fibonacci branch search (FBS), used new tree's branches fundamental structure and interactive searching rules to obtain the global optimal solution in the search space. The branch structure of FBS is selected using two types of multidimensional points on the basis of shortening fraction formed by Fibonacci sequence; in this mode, interactive global and local searching rules are implemented alternately to obtain the optimal solutions, avoiding stagnating in local optimum. The proposed FBS is also used here to construct an adaptive beamforming (ABF) technique as a real-time implementation to achieve near-optimal performance for its simplicity and high convergence rate, then, the performance of the FBS is compared with the five typical heuristic optimization algorithms. Simulation results demonstrate the superiority of the proposed FBS approach in locating the optimal solution with higher precision and reveal further improvement in the ABF performance.

Robust Adaptive Beamforming via Simplified Interference Power Estimation

Adaptive beamformer is very sensitive to model mismatch, especially when the signal-of-interest is present in the training data. In this paper, we focus on the topic of robust adaptive beamforming (RAB) based on interference-plus-noise covariance matrix (INCM) reconstruction. First, we analyze the effectiveness of several INCM reconstruction schemes, and particularly analyze the impacts of interference power estimation on RAB. Second, according to the analysis results, we develop a simplified algorithm to estimate the interference powers, and a RAB algorithm based on INCM reconstruction is then presented. Compared with some existing methods, the proposed algorithm simplifies the interference power estimation of INCM reconstruction. Aligned with our analysis, simulation results demonstrate that the overestimation of interference powers hardly degrades the performance of adaptive beamforming, and our proposed algorithm achieves nearly optimal performance across a wide range of signal-to-noise ratios.

New BSS‐based ABF for heterogeneous ionospheric clutter mitigation in HFSWR

Ionospheric clutter is detrimental to target detection in high-frequency surface-wave radar (HFSWR). Adaptive beamforming (ABF) has been adopted to suppress the ionospheric clutter in recent years. Unfortunately, the performance of ABF degrades due to the heterogeneity of the ionospheric clutter. In this study, a new approach is proposed to suppress the ionospheric clutter. A novel heterogeneous ionospheric clutter model based on the mixture of mutually independent ionospheric clutter sources is established. The blind source separation (BSS) approach is used to separate the clutter sources first. Then the separated components are exploited to estimate the spatial covariance matrix (SCM) of the cell under test. The SCM estimation based on BSS is more accurate than the classical sample matrix inversion method under the heterogeneous ionospheric clutter. Therefore, the ABF performance improves due to the better SCM estimation. The simulation and real data results demonstrated the effectiveness of the new BSS-based ABF method in HFSWR. The signal-to-clutter-plus-noise ratio of the new method improved compared with the traditional ABF based on the SMI method. The new method can help to detect targets under the heterogeneous ionospheric clutter. It may also be a promising methodology in other ABF applications.

Modified Eigenspace Based Iterative Robust Capon Beamformer

To improve the performance of adaptive beamformer with large steering vector mismatch, a modified eigenspace based iterative robust capon beamformer (ME-IRCB) is proposed. The approach iteratively implements the robust Capon beamformer (RCB) with an adaptively adjusted uncertainty set. Based on the modified eigenspace method, the desired signal subspace is given, whereafter the size of the uncertainty set is adaptively adjusted according to the mismatch between the estimated and presumed steering vector of the desired signal at each iteration. The proposed approach gives two estimation methods about the uncertainty size, and both of them contribute to the robustness improving of the beamformer. Moreover, unlike other robust beamformers, the proposed approach does not take the integration of the steering vector’s outer product over the adjacent direction of the desired signal, and it works well with the adjacent directions of the desired signal and interference. This merit is due to that, the proposed approach only uses the fundamental sample covariance matrix during the subspace construction, therefore the influence of imprecise steering vector on the subspace is overcame. Simulation results show that the proposed approach performs better than the existing robust beamformers under different evaluation criteria.

An improved algorithm for radar adaptive beamforming based on machine learning

In the field of radar digital signal processing, adaptive beamforming is a widely used technique for suppressing interference and noise. The Least Mean Square Algorithm (LMS) is a simple and easy algorithm for adaptive digital beamforming. However, it has the disadvantage of not achieving a balance between convergence speed and stability. In order to improve the performance of adaptive beamforming, this paper firstly reviews the classical LMS algorithm and then the machine learning optimization algorithm. Improvement effects of the three machine learning methods on the LMS algorithm are analyzed. The results show that the improved LMS algorithm based on AdaGrad exhibits the best performance. The algorithm can independently adjust the adaptive learning rate of different parameter components, making the iterative process of the adaptive beamforming more stable, efficient, and suitable for both theoretical research and engineering practice.

Robust adaptive beamforming method based on desired signal steering vector estimation and interference‐Plus‐noise covariance matrix reconstruction

Here, the authors propose a robust adaptive beamforming method based on desired signal steering vector estimation and interference-plus-noise covariance matrix reconstruction, so as to attenuate the influences of the desired signal steering vector mismatch and the limited training snapshots on the performance of adaptive beamformer. More precisely, the desired signal steering vector is estimated by minimising the sine value of the angle between the presumed desired signal steering vector and the eigenvectors of sample covariance matrix. Besides, the sample covariance matrix is reconstructed by reducing the dispersion extent of the noise eigenvalues and eliminating the desired signal component from the sample covariance matrix. The proposed method can not only accelerate the convergence speed of adaptive beamforming algorithm, but also avoid the desired signal cancellation phenomenon when the desired signal is present in the training snapshots. Simulation results demonstrate the superiority of the proposed method.

A Robust Eigenanalysis Interference Canceler Using Sensitivity-Based Number of Sources Estimation

When the estimation of the number of sources is inaccurate and the expected signal is mixed in the training data, the conventional eigenanalysis interference canceler (EC) will result in the expected signal cancelation, which leads the performance of adaptive beamforming to be degraded significantly. In this paper, a robust eigenanalysis interference canceler (REC) algorithm is proposed to resolve this problem by using the minimum sensitivity-based number of sources estimation. In the proposed method, the number of sources is first pre-estimated by effectively using the minimum sensitivity function. Then, based on the eigenvalue decomposition of the array covariance matrix, the expected signal in the training data is determined and eliminated, so that the corresponding impact of the adaptive weight calculation can be avoided. Finally, the adaptive weight vector is obtained by orthogonally projecting the quiescent weight vector into the interference subspace. Simulation results show that the performance of the output signal-to-interference-plus-noise ratio (SINR) of the proposed algorithm has improved significantly when compared with the conventional adaptive beamforming methods.