Steering Vector Estimation Research Articles

Robust Adaptive Beamforming Algorithm Based on Complex Gauss–Legendre Integral

This study addresses the poor robustness of the current beamforming algorithm for covariance matrix reconstruction and the high computational complexity in the covariance matrix reconstruction process. A robust beamforming algorithm based on the Complex Gauss–Legendre integral is proposed. The method firstly partitions the neighborhood of the interference signal and constructs the interference signal space using the complex Gauss-Legendre integral, then projects the received signal into the interference signal space to filter out the desired signal and complete the reconstruction of the interference noise covariance matrix, before finally correcting the steering vector mismatch using the improved optimal steering vector estimation method. The simulation results show that the method has good robustness and a low sidelobe in the presence of the steering vector mismatch and the presence of array perturbation. Compared with the previous works, the proposed CGL-ISV method provides a better beamforming performance.

New convex approaches to general MVDR robust adaptive beamforming problems

AbstractConsider general minimum variance distortionless response (MVDR) robust adaptive beamforming problems based on the optimal estimation for both the desired signal steering vector and the interference‐plus‐noise covariance (INC) matrix. The optimal robust adaptive beamformer design problem is an array output power maximization problem, subject to three constraints on the steering vector, namely, a (convex or nonconvex) quadratic constraint ensuring that the direction‐of‐arrival (DOA) of the desired signal is separated from the DOA region of all linear combinations of the interference steering vectors, a double‐sided norm constraint, and a similarity constraint; as well as a ball constraint on the INC matrix, which is centered at a given data sample covariance matrix. To tackle the nonconvex problem, a new tightened semidefinite relaxation (SDR) approach is proposed to output a globally optimal solution; otherwise, a sequential convex approximation (SCA) method is established to return a locally optimal solution. The simulation results show that the MVDR robust adaptive beamformers based on the optimal estimation for the steering vector and the INC matrix have better performance (in terms of, e.g., the array output signal‐to‐interference‐plus‐noise ratio) than the existing MVDR robust adaptive beamformers by the steering vector estimation only.

Sequenced Steering Vector Estimation for Eigen-Subspace Projection-Based Robust Adaptive Beamformer

Robust adaptive beamforming (RAB) is essential in many applications to ensure signal-receiving quality when model errors exist. Eigen-subspace projection (ESP), one of the most popular RAB methods, can be used when there are arbitrary model errors. However, a major challenge of ESP is projection subspace selection. Traditional ESP (TESP) treats the signal subspace as the projection subspace; thus, source enumeration is required to obtain prior information. Another inherent defect is its poor performance at low signal-to-noise ratios (SNRs). To overcome these drawbacks, two improved ESP-based RAB methods are proposed in this study. Considering that a reliable signal-of-interest steering vector needs to be obtained via the subspace projection, the main idea underlying the proposed methods is to use sequenced steering vector estimation to invert the subspace dimension estimate for an arranged eigenvector matrix. As the proposed methods do not require source enumeration, they are simple to implement. Numerical examples demonstrate the effectiveness and robustness of the proposed methods in terms of output signal-to-interference-plus-noise ratio performance. Specifically, compared with TESP, the proposed methods present at least a 2.6 dB improvement at low SNRs regardless of the error models.

Deep Complex-Valued Neural Network-Based Triple-Path Mask and Steering Vector Estimation for Multichannel Target Speech Separation

Deep Complex-Valued Neural Network-Based Triple-Path Mask and Steering Vector Estimation for Multichannel Target Speech Separation

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.

A Priori Knowledge Based Ground Moving Target Indication Technique Applied to Distributed Spaceborne SAR System

Through formation flying, the distributed spaceborne SAR(synthetic aperture radar) system can increase the number of spatial degree of freedoms (DOFs) and provide flexible multi-baselines for SAR-GMTI (ground moving target indication), which improves the system performance. This paper proposes an a priori knowledge-based adaptive clutter cancellation and moving target detection technique applied to the distributed spaceborne SAR-GMTI systems. Firstly, the adaptive clutter cancellation technique is exploited to suppress the ground clutter. A priori knowledge, such as road network information, is integrated to the adaptive clutter cancellation processor to reduce any moving target steering vector mismatch. Secondly, adaptive matched filter (AMF) and adaptive beamformer orthogonal rejection test (ABORT) are exploited as adaptive detection techniques for moving target detection. Due to the dense road network, the moving target steering vector estimation may be ambiguous for the different position and orientation of the roads. The multiple hypothesis testing (MHT) technique is proposed to detect the moving targets and resolve the potential ambiguities. A scheme is exploited to detect, classify, and relocate the moving targets. Finally, simulation experiments and performance analysis have demonstrated the effectiveness and robustness of the proposed technique.

Robust adaptive beamforming based on zone orthogonal constraint and steering vector estimation

This Letter solves steering vector estimation under mismatch for adaptive beamforming. The proposed beamformer implements a stepwise estimation of steering vector, and zone orthogonal constraint is added first based on adaptive constraint framework from Khabbazibasmenj [IEEE Trans. Signal Process. 60(6), 2974-2987 (2012)], which ensures that the estimated steering vector does not converge to an interference steering vector outside the predefined sector, even if the sector deviates from the central observation area of arrays. Then uncertainty set error constraint is used to improve the estimation accuracy. The numerical simulation and experimental results verify the effectiveness of the proposed method.

Robust blind space‐time adaptive processing for measurement error mitigation in GNSS receivers

AbstractThe measurement errors induced by the space‐time adaptive processing (STAP) is gaining attention for its significant detriment to the precision of the global navigation satellite system (GNSS) receiver positioning. To mitigate measurement errors, the steering vector (SV) estimation method based on spreading is widely employed in measurement error mitigation algorithms. However, the hazard of the SV estimation fluctuation problem is ignored in these algorithms. In this paper, the specific harm of such SV estimation fluctuation problem is analysed. To alleviate such problem and to eliminate the measurement errors as much as possible, a robust STAP beamformer for GNSS receivers is proposed. First, to acquire a series of robust SVs in different integration times, a desired signal covariance (DSC) matrix is iteratively reconstructed to remove the disturbance from thermal noise and the residual jamming signals. Second, to eliminate measurement errors, a replacement matrix is formed to help guarantee the phase linearities of the tapped delay lines (TDLs). Numerical examples demonstrate that the method can achieve a set of stable SV estimations and linear phase TDLs, leading to a carrier‐to‐noise‐power ratio () of more than 50 dBHz and a code phase bias of less than 3.4 m, which outperform the methods used for comparison.

Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction via Steering Vector Estimation

The performance of the sample matrix inverse (SMI) beamformer degrades greatly when the signal-to-noise ratio (SNR) increases because the signal of interest (SOI) is mistaken as interferences and suppressed. To avoid this situation, the interference-plus-noise covariance matrix (INCM) is introduced via steering vector (SV) estimation for robust adaptive beamforming (RAB). To avoid the convex optimization for the SV estimation, a vertical error vector is constructed based on the property of subspace in the proposed method, and the SV error neighborhood table is built in advance to lower the computational complexity. Through the Capon spectrum search, the initial directions of the SOI and interference signals are estimated, and more accurate SVs are confirmed through neighborhood optimization in the table. Next, the interference covariance matrix (ICM) is generated by the estimated SVs and the noise covariance matrix (NCM) is obtained by the least-square (LS) solution based on the corrected SVs. Finally, INCM is reconstructed and the weight vector is computed for RAB. The main advantage of the proposed method is robust against unknown arbitrary-type mismatches. Simulation results demonstrate the effectiveness and robustness of the proposed method.

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.

Coherent receiver design and aperture expansion beamforming for frequency diverse array radar

Frequency diverse array (FDA) radar has attracted considerable attention in interference suppression due to its range-angle dependent beampattern property. However, the full-band coherent receiver design is sophisticated and expensive. Furthermore, prior research on FDA radar adaptive beamforming failed to suppress adjacent-target interference because of insufficient beam resolution. This paper aims to develop a receiver architecture based on fractional domain signal separation and to investigate aperture expansion adaptive beamforming based on interference-noise covariance matrix reconstruction and signal of interest steering vector estimation. The proposed receiver design not only simplifies the structure and saves resources, but it can also effectively separate the received signals, particularly for the FDA radar's overlapping linear frequency modulated baseband emission waveforms. The proposed aperture expansion beamforming approach improves beam resolution of beamforming and effectiveness in adjacent-target interference suppression.

Robust Adaptive Beamforming Based on Subspace Decomposition, Steering Vector Estimation and Correction

Considering that the performance of adaptive arrays is sensitive to any type of mismatches, an innovative robust adaptive beamforming method based on covariance matrix reconstruction, subspace decomposition, steering vector estimation and correction is proposed. Based on Capon spatial spectrum, a group of angle sets containing all interfering signals are determined, and the interference covariance matrix can be reconstructed with a smaller integration interval. On the other hand, the sample covariance matrix can be decomposed into signal subspace and interference-plus-noise by using the principle of maximum correlation. Based on the interference-plus-noise subspace and the reconstructed signal-plus-noise covariance matrix, a new convex optimization model is built to estimate the steering vector of the desired signal. Then, an improved projection approach based on signal subspace is designed for correction to improve the robustness against the nominal direction vector mismatches. Simulation results demonstrate that the proposed method achieves better overall performance under multiple mismatches over a wide range of input signal-to-noise ratios.

Null broadened–deepened array antenna beamforming for GNSS jamming mitigation in moving platforms

Abstract Steering vector and covariance matrix estimation mismatch along with moving jammer/platform, can affect the performance of null-steering beamformer. In this paper, by utilizing null-widening, null-deepening and diagonal loading shrinkage in space–time adaptive processing (STAP) structure, two methods for nullifying GNSS (global navigation satellite system) jamming/interference in cruise moving platforms are introduced. The enhanced performance of the proposed methods is investigated through numerical simulations. The results indicate improvement in the number of acquired GNSS satellites, in heavy jamming (GNSS denied) scenario, by reconstructing and acquiring at least 87% of satellites.

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.

A Robust Digital Beamforming on Receive in Elevation for Airborne MIMO SAR System

The echo separation issue for multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) is usually regarded as a more technical challenge. Spotlighted as a promising solution to the echo separation, the well-known short-term shift-orthogonal (STSO) beamforming scheme has become increasingly popular. However, for airborne MIMO SAR systems, the digital beamforming (DBF) involved in the STSO scheme usually encounters more issues, e.g., the direction of arrival (DOA) mismatch induced by topography variation. Up to now, relatively less research on robust DBF processing has been conducted for airborne MIMO SAR systems. In this respect, an adaptive DBF technique, based on interference plus noise covariance matrix (IPNCM) reconstruction and desired signal steering vector estimation, has been proposed in this paper. IPNCM reconstruction and steering vector estimation can not only cope with the DOA mismatch problem, but also remove the desired signal component in the training data cells to increase the beamformer convergence rates. Consequently, the proposed approach really improves the array output signal-to-interference-plus-noise ratio (SINR). Moreover, numerous discussions and simulations are carried out to prove the effectiveness of proposed DBF technique under various disturbance environments. Compared with the current DBF techniques, the proposed method provides a bright application prospect for the STSO scheme.

Low-Complexity Robust Adaptive Beamforming Based on INCM Reconstruction via Subspace Projection.

Adaptive beamforming is sensitive to steering vector (SV) and covariance matrix mismatches, especially when the signal of interest (SOI) component exists in the training sequence. In this paper, we present a low-complexity robust adaptive beamforming (RAB) method based on an interference–noise covariance matrix (INCM) reconstruction and SOI SV estimation. First, the proposed method employs the minimum mean square error criterion to construct the blocking matrix. Then, the projection matrix is obtained by projecting the blocking matrix onto the signal subspace of the sample covariance matrix (SCM). The INCM is reconstructed by replacing part of the eigenvector columns of the SCM with the corresponding eigenvectors of the projection matrix. On the other hand, the SOI SV is estimated via the iterative mismatch approximation method. The proposed method only needs to know the priori-knowledge of the array geometry and angular region where the SOI is located. The simulation results showed that the proposed method can deal with multiple types of mismatches, while taking into account both low complexity and high robustness.

Covariance matrix reconstruction with iterative mismatch approximation for robust adaptive beamforming

The covariance matrix reconstruction based robust adaptive beamforming (RAB) methods overcome the performance degradation due to the imprecise knowledge of the steering vector and the covariance matrix. However, high complexity limits the application of them. In this paper, we proposed a new RAB method based on interference plus noise covariance (INC) matrix reconstruction and desired signal steering vector estimation. In this method, nominal interference steering vectors are estimated by the Capon spatial spectrum, as well as noise power. Subsequently, the iterative mismatch approximation algorithm based on maximizing the beamformer output power is proposed to estimate all the incident signal steering vectors and powers, and the INC matrix is reconstructed. Finally, the beamformer is determined by the estimated INC matrix and desired signal steering vector. Simulation results indicate that the proposed method obtains better performance than other existed methods at both the high signal to noise ratio (SNR) and the complexity.

Covariance matrix reconstruction and steering vector estimation for robust adaptive transmit/receive beamforming in full phased‐MIMO radar

Covariance matrix reconstruction and steering vector estimation for robust adaptive transmit/receive beamforming in full phased‐MIMO radar

Convolutional Maximum-Likelihood Distortionless Response Beamforming With Steering Vector Estimation for Robust Speech Recognition

Beamforming has been one of the most successful approaches using multi-microphones for robust speech recognition. Although a beamforming method, called the “maximum-likelihood distortionless response (MLDR)” beamformer, was recently presented to achieve promising performance, it requires an accurate steering vector for a target speaker in advance like many kinds of beamformers. In this paper, we present a method for steering vector estimation (SVE) by replacing the noise spatial covariance matrix estimate with a normalized version of the variance-weighted spatial covariance matrix estimate for the observed noisy speech signal obtained by the iterative update rule in the MLDR beamforming framework. In addition, an MLDR beamforming method without a steering vector for a target speaker given in advance is presented where the SVE and the beamforming are alternately repeated. Furthermore, an online algorithm based on recursive least squares (RLS) is derived to cope with various practical applications including time-varying situations, and the power method is introduced for further efficient online processing. We also present batch and online convolutional MLDR beamforming with SVE for simultaneous beamforming and dereverberation where the weighted prediction error (WPE) dereverberation and the MLDR beamforming with the SVE were jointly optimized based on the maximum-likelihood estimation (MLE) for a zero-mean complex Gaussian signal with time-varying variances. Moreover, input signals masked by a neural network (NN) for estimating target speech or noise components can be used to further improve the presented beamformers. Experimental results on the CHiME-4 and REVERB challenge datasets demonstrate the effectiveness of the presented methods.

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.