Robust Adaptive Beamforming Algorithm Research Articles

Efficient and Robust Adaptive Beamforming Based on Coprime Array Interpolation

Unlike uniform linear arrays (ULAs), coprime arrays require fewer physical sensors yet provide higher degrees of freedom (DOF) and larger array apertures. However, due to the existence of “holes” in the differential co-array, the target detection performance deteriorates, especially in adaptive beamforming. To address these challenges, this paper proposes an efficient and robust adaptive beamforming algorithm leveraging coprime array interpolation. The algorithm eliminates unwanted signals and uses the Gauss–Legendre quadrature method to reconstruct an Interference-plus-Noise Covariance Matrix (INCM), thereby obtaining the beamforming coefficients. Unlike previous techniques, we utilize a virtual interpolated ULA to expand the aperture, enabling the acquisition of a high-dimensional covariance matrix. Additionally, a projection matrix is constructed to eliminate unwanted signals from the received data, greatly enhancing the accuracy of INCM reconstruction. To address the high computational complexity of integral operations used in most INCM reconstruction algorithms, we propose an approximation based on the Gauss–Legendre quadrature, which reduces the computational load while maintaining accuracy. This algorithm avoids the array aperture loss caused by using only the ULA segment in the difference co-array and improves the accuracy of INCM reconstruction. Simulation and experimental results show that the performance of the proposed algorithm is superior to the compared beamformers and is closer to the optimal beamformer in various scenarios.

A New Robust Adaptive Beamforming Algorithm Based on GSC

A New Robust Adaptive Beamforming Algorithm Based on GSC

Virtual covariance matrix reconstruction-based adaptive beamforming for small aperture array.

Recently, many robust adaptive beamforming (RAB) algorithms have been proposed to improve beamforming performance when model mismatches occur. For a uniform linear array, a larger aperture array can obtain higher array gain for beamforming when the inter-sensor spacing is fixed. However, only the small aperture array can be used in the equipment limited by platform installation space, significantly weakening beamforming output performance. This paper proposes two beamforming methods for improving beamforming output in small aperture sensor arrays. The first method employs an integration algorithm that combines angular sector and gradient vector search to reconstruct the interference covariance matrix (ICM). Then, the interference-plus-noise covariance matrix (INCM) is reconstructed combined with the estimated noise power. The INCM and ICM are used to optimize the desired signal steering vector (SV) by solving a quadratically constrained quadratic programming (QCQP) problem. The second method proposes a beamforming algorithm based on a virtual extended array to increase the degree of freedom of the beamformer. First, the virtual conjugated array element is designed based on the structural characteristics of a uniform linear array, and received data at the virtual array element are obtained using a linear prediction method. Then, the extended INCM is reconstructed, and the desired signal SV is optimized using an algorithm similar to the actual array. The simulation results demonstrate the effectiveness of the proposed methods under different conditions.

Robust adaptive beamforming algorithm for coherent signals based on virtual array

Robust adaptive beamforming algorithm for coherent signals based on virtual array

A Novel Robust Adaptive Beamforming Algorithm Based on Subspace Orthogonality and Projection

Recently, it has been extensively researched about designing robust adaptive beamforming (RAB) algorithms to deal with model mismatch issues. In this paper, a RAB algorithm is proposed to estimate the steering vectors (SVs) of the incident sources and reconstruct the interference-plus-noise covariance matrix (INCM). First, we construct the error SVs in the noise subspace, which correct the nominal SVs by iterative updates to obtain more accurate estimation of SVs. Then the projection matrix is constructed utilizing the estimated SV of the signal of interest (SOI), and the interference powers are estimated by projecting the sampled covariance matrix (SCM). Furthermore, two virtual interferences are added on both sides of each estimated interference direction to widen the nulls in the corresponding directions of the interferences. Finally, the INCM can be constructed and utilize the estimated SV of the SOI to calculate the weight vector of the beamformer. The proposed method has less computational complexity and the simulation results show that the proposed method is more robust to various types of mismatches in comparison to previous algorithms.

Null Broadening Robust Adaptive Beamforming Algorithm Based on Power Estimation.

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.

Adaptive Null Widening Beamforming Algorithm in Spatially Correlated Color Noise

Under the background of spatially correlated color noise, the incidence angle of a jamming signal in a high-speed moving platform rapidly changes, which leads to the degradation of the anti-interference performance and the waveform distortion of the adaptive beamformer. In this paper, a projection-constrained null broadening beamforming algorithm based on the Toeplitz matrix structure is proposed. The algorithm first extracts the subspace of the covariance matrix of the steering vector of the pre-determined extended angle interval and constructs the constraint matrix and the projection transformation matrix. The received signal covariance matrix with a Toeplitz structure is then constructed using the correlation number between each array element and the pre-set reference array element. Finally, the constructed covariance matrix is transformed through projection, and the weight of each array element is constrained by the constraint matrix. The theoretical optimal solution of adaptive wide null beamforming in spatially correlated color noise is obtained. The simulation results show that, compared with the existing robust adaptive beamforming algorithms, the proposed algorithm can efficiently improve the distortion of adaptive anti-jamming beams, and can achieve null broadening in the jamming direction under the condition of spatially correlated color noise, which improves the output signal to the interference-plus-noise ratio (SINR) of the adaptive beamformer.

Robust Adaptive Beamforming Algorithm for Sparse Subarray Antenna Array Based on Hierarchical Weighting

Sparse antenna arrays based on subarrays have more and more broad application prospects for the limitation of array space, real-time algorithm and hardware costs. Aiming at the beamforming technology of sparse antenna arrays based on subarrays, this paper proposes a robust adaptive beamforming algorithm based on hierarchical weighting. The algorithm performs conventional beamforming to calculate the weights of each element in the subarray, then the synthetic signals output by each subarray are used as sparse array metadata. The Interference-plus-Noise Covariance Matrix (INCM) is reconstructed by integration in two-dimensional space, and a convex optimization model of a multi-constraint array containing the signal pointing error was established to estimate the real guide vector. Finally, using the reconstructed INCM and the estimation of the guide vector, we obtain a weighted vector between the subarrays and output signal for the whole array. The simulation results show that the proposed algorithm has better Signal-to-Interference-and-Noise Ratio (SINR) and robustness compared with other algorithms for sparse subarray antenna array beamforming.

Covariance Matrix Reconstruction via a Subspace Method and Spatial Spectral Estimation for Robust Adaptive Beamforming

Several robust adaptive beamforming (RAB) algorithms based on interference plus noise covariance matrix (INCM) reconstruction have been recently proposed, which can enhance the robustness of beamforming algorithms when certain mismatches occur in the model. However, some approaches ignore the resolution of the Capon spectral estimator (CSE), leading to reconstruction errors. This paper proposes a novel RAB algorithm formulated using the subspace projection method and spatial spectral estimation (SSE), which is named INCM-SSE. First, without using the CSE, the subspace projection matrix (SPM) is obtained through the integral of the angular sector where the signal of interest (SOI) is located. Subsequently, after estimating the direction of arrival (DOA) of incident signals using the multiple signal classification (MUSIC) algorithm, we project the sample covariance matrix (SCM) onto the SPM to eliminate the SOI influence. Then, the estimation method of interference powers is derived. Moreover, the INCM is reconstructed based on the estimated powers and steering vector (SV) of interferences. The SV of the SOI is optimized by solving a quadratic convex optimization problem. The INCM-SSE algorithm not only employs SSE to improve the angular resolution but also reduces the influence of the SOI component by using SPM. Simulation results indicate that the proposed method is robust against various types of mismatches, thus achieving superior overall performance.

Robust adaptive beamforming based on covariance matrix reconstruction with RCB principle

In this paper, a novel robust adaptive beamforming (RAB) technique based on the covariance matrix reconstruction is proposed to solve the array model mismatch. The proposed technique provides an alternative method to reconstruct the interference-plus-noise covariance matrix (IPNCM) and estimate the steering vector (SV) of the desired signal. In particular, an unknown error exists in the SV of the considered array. The proposed RAB algorithm adopts the robust Capon beamformer (RCB) principle to roughly estimate the SVs of the desired and interference signals. Based on those preliminary estimated SVs, an improved Capon power spectrum is constructed. Then the interference covariance matrix is reconstructed by utilizing the modified Capon power spectrum integrated over the union of several disjoint angular sectors. Then, the reconstructed covariance matrix is further refined by exploring the low rank property. Meanwhile, the SV of the desired signal is estimated by solving a modified quadratically constrained quadratic programming (QCQP) problem. The simulation results show that the RCB principle provides an accurate IPNCM reconstruction, and the proposed RAB algorithm outperforms the existing RAB techniques over a wide range of input signal-to-noise ratio (SNR) region under various mismatch conditions.

Spatial deception suppression for wideband linear frequency modulation signals based on fractional Fourier transform with robust adaptive beamforming

Wideband linear frequency modulation (LFM) signal is popular for target detection and imaging in wideband array radar systems. In this paper, a novel and robust adaptive wideband digital beamforming (DBF) algorithm is proposed for suppressing the deception jamming of wideband LFM signals. Firstly, wideband LFM echoes are treated as narrowband signals using fractional Fourier transform (FrFT) with a specific order. Secondly, a robust and adaptive narrowband DBF method based on steering vector estimation, covariance matrix reconstruction, and low-pass filtering are applied to suppress deception jamming. Finally, the inverse FrFT is performed to transform the processing results back to the time-domain wideband signals. Compared with the conventional time- and frequency-domain wideband beamformers, the proposed algorithm significantly reduces the amount of calculation and computational complexity. The simulation results indicate that the proposed algorithm can effectively suppress deception jamming, and its interference suppression capability is approximately like that of an optimal beamformer. Furthermore, the validity and effectiveness of the proposed algorithm are verified with the experimental data in a microwave anechoic chamber.

Robust Beamforming Based on Covariance Matrix Reconstruction in FDA-MIMO Radar to Suppress Deceptive Jamming.

Frequency diverse array (FDA)-multiple-input multiple-output (MIMO) radars can generate a range-angle two-dimensional transmit steering vector (SV), which is capable of suppressing mainbeam deceptive jamming in the transmit–receive frequency domain by utilizing additional degrees of freedom (DOFs) in the range dimension. However, when there are target SV mismatch, covariance matrix estimation error and target contamination, the jamming suppression performance degrades severely. In this paper, a robust adaptive beamforming algorithm for anti-jammer application based on covariance matrix reconstruction is proposed in FDA-MIMO radar. In this method, the residual noise is further determined by using the spatial power spectrum estimation approach, which results in improved estimation accuracy of the signal covariance matrix and the desired target SV. The jamming SV is obtained from vectors in the intersection of two subspaces (namely, the signal-jamming subspace derived from the sample covariance matrix (SCM) and the jamming subspace generated from the jamming covariance matrix) by an alternating projection algorithm. Furthermore, the jamming power is obtained by exploiting the orthogonality between the different SVs. With the obtained parameters of target and jamming, the optimal adaptive beamformer weight vector is calculated. Simulation results demonstrate that the proposed algorithm can cope with the mainbeam deceptive jamming suppression under various model mismatches and has excellent performance over a wide range of signal-to-noise ratios (SNRs).

Robust adaptive beamforming algorithm based on damped singular value decomposition regularization

When adaptive beamformers are applied to actual problems, various model mismatches are present in the sample covariance matrix and signal steering vector, which severely deteriorates the performance of the beamformer. To address this issue, we develop a novel adaptive beamforming algorithm in which the weight vector is a linear combination of the presumed steering vector and basis vectors of the orthogonal supplement subspace of the steering vector. Then, we convert the common constrained optimization problem into an unconstrained one to establish the new beamformer. Moreover, we use damped singular value decomposition regularization, which employs the L-curve method to adaptively determine the regularized factor (loading level), for suppressing the effects of model mismatches. In addition, we perform simulations of the proposed algorithm and other existing beamforming algorithms by considering several commonly encountered mismatches (e.g., the direction-of-arrival mismatch, sensor gain, phase error and location perturbation, coherent local scattering, and mutual coupling) and demonstrate the superior performance of the new beamforming algorithm.

Adaptive beamforming algorithm for coprime array based on interference and noise covariance matrix reconstruction

Compared with the uniform linear array (ULA) under the same physical array element, the coprime array can obtain a higher degree of freedom and a larger array aperture, so it has received extensive attention from scholars in recent years. Based on the idea of interference plus noise covariance matrix (INCM) reconstruction, this study proposed a robust adaptive beamforming algorithm using the coprime array. In the virtual array generated by the coprime array, the authors prove from the perspective of virtual signals that the constructed Toeplitz matrix is equivalent to a virtual ULA with more array elements. Subsequently, a high-resolution subspace algorithm is used to estimate the direction of arrival (DOA) of the signals, and the estimated DOA is used to reconstruct the direction vector (DV) of the coprime array. Through the eigenvalue decomposition of the reconstructed Toeplitz matrix, the corresponding relationship between the eigenvalue and the power is deduced, and the signals and noise power are estimated using the eigenvalue. Finally, combine the DV of the desired signal and the reconstructed INCM to calculate the weight vector of the proposed algorithm. The simulation results prove the superiority and effectiveness of the algorithm.

Fast and robust adaptive beamforming algorithms for large-scale arrays with small samples

The adaptive beamformer of large-scale sensor array mainly suffers from two limits. One limit is an insufficient number of training snapshots, which usually results in an ill-posed sample covariance matrix in many real applications. The other limit is the high computation complexity of the beamformer that severely restricts its online processing. To overcome these two limits, two fast and robust adaptive beamforming algorithms are proposed in this paper, which refers to the linear kernel approaches and formulates the weight vector as a linear combination of the training samples and the signal steering vector. The proposed algorithms only need to calculate a low-dimensional combination vector instead of the high-dimensional adaptive weight vector, which remarkably reduces the computation complexity. Moreover, regularization techniques are utilized to suppress the excessive variation of the combination vector caused by an underdetermined estimation of the Gram matrix. Experimental results show that the proposed algorithms achieve better performance and lower computation complexity than algorithms in the literature. Especially, like the kernel approaches, the proposed algorithms achieve good performance under the small sample case.

Fast and accurate covariance matrix reconstruction for adaptive beamforming using Gauss-Legendre quadrature

Most of the reconstruction-based robust adaptive beamforming (RAB) algorithms require the covariance matrix reconstruction (CMR) by high-complexity integral computation. A Gauss-Legendre quadrature (GLQ) method with the highest algebraic precision in the interpolation-type quadrature is proposed to reduce the complexity. The interference angular sector in RAB is regarded as the GLQ integral range, and the zeros of the three-order Legendre orthogonal polynomial is selected as the GLQ nodes. Consequently, the CMR can be efficiently obtained by simple summation with respect to the three GLQ nodes without integral. The new method has significantly reduced the complexity as compared to most state-of-the-art reconstruction-based RAB techniques, and it is able to provide the similar performance close to the optimal. These advantages are verified by numerical simulations.

Robust adaptive beamforming based on a method for steering vector estimation and interference covariance matrix reconstruction

Robustness is an important factor in adaptive beamforming because various mismatches that exist in reality will lead to considerable performance degradation. In this paper, a robust adaptive beamforming (RAB) algorithm is proposed based on a novel method for estimating the steering vectors (SVs). The interference-plus-noise covariance matrix (INCM) is then reconstructed by the SVs and their corresponding power estimates. As we know, the Capon power spectrum is actually a function of the SV defined in a high-dimensional domain, in which the actual SVs correspond to the highest peaks. The nominal SVs may lead to relatively lower power amplitude points around the peaks when mismatches exist, and these peaks are located in the directions of gradient vectors at the lower power points obtained by the nominal SVs. Therefore, to obtain the actual SVs, we first construct a subspace for each nominal SV in a small neighborhood of angles. Then we get the gradient vector, which is orthogonal to the corresponding nominal SV neighborhood, using a subspace-based method. Finally, we search along the gradient vector to obtain the adjusted SV that generates the highest Capon power amplitude. The interference covariance matrix (ICM) is reconstructed by the adjusted interference SVs and corresponding Capon power amplitudes. The actual SV of the signal of interest (SOI) is estimated as the adjusted SV of the SOI. Simulation results demonstrate that the proposed method is robust against various types of mismatch and is superior to other existing reconstruction-based beamforming algorithms.

A Robust Beamforming Algorithm Based on Covariance Matrix Reconstruction and Steering Vector Estimation

Adaptive beamforming algorithms often suffer from performance degradation due to the presence of the desired signal component in the interference-plus-noise covariance matrix (IPNCM) and mismatch of steering vector. In order to improve the robustness of the beamforming algorithm performance, a new robust adaptive beamforming algorithm is proposed in this paper. In the proposed algorithm, Capon spatial spectrum is first used to reconstruct the IPNCM. Then, based on the robust Capon beamforming algorithm based on the steering vector uncertain set, new constraints are added so that the steering vector does not converge to the interference direction. The proposed beamforming algorithm is a non-convex quadratic constraint quadratic programming (QCQP) problem that is solved using semidefinite programming (SDP) relaxation. Simulation results show that the proposed algorithm is more robust than some other existing algorithms and is closest to the optimal solution.

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.

Multi-Operator Minimum Variance Adaptive Beamforming Algorithms Accelerated With GPU.

The goal of this work is to design high-resolution, high-contrast and robust MV adaptive beamforming algorithms, which are also implemented in real-time frame rate. Multi-operator optimization is introduced into MV adaptive beamforming in this work to propose a multi-operator MV adaptive beamforming algorithmic optimization framework. Based on the proposed algorithmic optimization framework, the algorithm optimization can be either conducted by activating a single optimization operator, or conducted by activating multiple optimization operators. The multi-operator MV (MOMV) adaptive beamforming algorithms are then derived from this framework. Moreover, in order to promote the real-time imaging capability of MOMV beamforming, a GPU-based parallel acceleration framework is proposed along with the algorithmic optimization framework by exploring the image-level coarse-grained parallelization and pixel-level fine-grained parallelization. GPU computing resource allocation strategy and memory access strategy are both explored to better design the acceleration framework. Comprehensive quantitative simulation evaluations and qualitative in vivo experiments of imaging performance are studied, and the results demonstrate that the proposed MOMV adaptive beamforming algorithms significantly improve the imaging performance as compared with other MV beamforming algorithms, which have high resolution, high contrast, good robustness, and real-time imaging capability with thousands of acceleration speedup. Furthermore, the MOMV beamforming algorithm without eigen-decomposition and projection optimization operator achieves much higher beamforming frame rate with little downgrade of image quality as compared with the MOMV beamforming algorithm with all optimization operators.