Steering Vector Mismatch Research Articles

Robust Widely Linear Beamforming With Multiple Uncertainty Sets

The widely linear minimum variance distortionless response (WL-MVDR) beamformer has a better performance than the conventional MVDR beamformer when the received signals are potentially noncircular. However, it is sensitive to the extended steering vector (ESV) mismatches which can be caused by direction of arrival (DOA) errors, noncircularity coefficient errors, array imperfections and so on. To improve the robustness against large ESV mismatches, a robust WL beamformer based on the worst-case performance optimization (WCPO) method with multiple uncertainty sets is proposed. The resultant beamformer has the mathematical form of a nonconvex optimization problem, which can be converted into a semidefinite programming (SDP) problem and solved iteratively. Simulation results show that, in comparison with several representative robust WL beamformers, the proposed method can achieve better performances, especially under large ESV mismatch conditions.

Design of Customized Adaptive Radar Detectors in the CFAR Feature Plane

The paper addresses the design of adaptive radar detectors having desired behavior, in Gaussian disturbance with unknown statistics. Specifically, given detection probability specifications for chosen signal-to-noise ratios and steering vector mismatch levels, a methodology for the optimal design of customized CFAR detectors is devised in a suitable feature plane based on maximal invariant statistics. To overcome the analytical and numerical intractability of the resulting optimization problem, a novel general reduced-complexity algorithm is developed, which is shown to be effective in providing a close approximation of the desired detector. The proposed approach solves the open problem of ensuring a prefixed false alarm probability while controlling the behavior under both matched and mismatched conditions, so enabling the design of fully customized adaptive CFAR detectors.

Robust beamforming for non-circular signals in uniform linear arrays with unknown mutual coupling

The performance of widely linear beamformer (WLB) is seriously degraded by any uncalibrated mutual coupling between antenna elements. In this paper, we propose an architecture to mitigate the unknown mutual coupling mismatch in uniform linear arrays and design a robust WLB for non-circular signals. We exploit the fourth-order cumulants method and the steering vector property of a uniform linear array to estimate the directions of incident signals as well as the mutual coupling coefficients. We decouple the received signals by using the mutual coupling matrix so that the powers and non-circularity coefficients of incident signals can be estimated appropriately. This allows us to reconstruct a so-called decoupled augmented interference-plus-noise covariance matrix (AINCM). We minimize the variance of beamformer with the subspace constraint to estimate the steering vector mismatch. Meanwhile, the extended steering vector (ESV) mismatch is estimated by minimizing the variance of WLB with the extended subspace constraint. Therefore, the ESV of signal-of-interest can be estimated accurately. Numerical simulations illustrate that the proposed WLB is robust against the unknown mutual coupling mismatch and significantly outperforms some of the state-of-the-art WLBs.

A Two-Stage STAP Method Based on Fine Doppler Localization and Sparse Bayesian Learning in the Presence of Arbitrary Array Errors.

In the presence of unknown array errors, sparse recovery based space-time adaptive processing (SR-STAP) methods usually directly use the ideal spatial steering vectors without array errors to construct the space-time dictionary; thus, the steering vector mismatch between the dictionary and clutter data will cause a severe performance degradation of SR-STAP methods. To solve this problem, in this paper, we propose a two-stage SR-STAP method for suppressing nonhomogeneous clutter in the presence of arbitrary array errors. In the first stage, utilizing the spatial-temporal coupling property of the ground clutter, a set of spatial steering vectors with array errors are well estimated by fine Doppler localization. In the second stage, firstly, in order to solve the model mismatch problem caused by array errors, we directly use these spatial steering vectors obtained in the first stage to construct the space-time dictionary, and then, the constructed dictionary and multiple measurement vectors sparse Bayesian learning (MSBL) algorithm are combined for space-time adaptive processing (STAP). The proposed SR-STAP method can exhibit superior clutter suppression performance and target detection performance in the presence of arbitrary array errors. Simulation results validate the effectiveness of the proposed method.

Robust Minimum Variance Beamforming With Sidelobe-Level Control Using the Alternating Direction Method of Multipliers

Adaptive beamforming with sidelobe-level control in the presence of signal steering vector uncertainty is investigated. Unlike the traditional multiconstrained optimization strategy using the interior point method, iterative optimization algorithms with the aid of the alternating direction method of multipliers (ADMM) framework are proposed. The uncertainty set constraint and the sidelobe constraint are formulated into two optimization subproblems and handled with the Lagrange multiplier method. By introducing matrix decomposition techniques, subproblem 1 is transformed into a polynomial root-finding problem that can be solved with low computational complexity. For subproblem 2, a closed-form solution can be obtained directly. Furthermore, for the continuously receiving snapshots case, iterative gradient minimization is introduced and embedded into the ADMM iterations to give an approximate solution free from matrix decompositions. Theoretical analyses and simulations verify the low complexities and performance advantages of the proposed algorithms in the low sample support, steering vector mismatch, and real-time snapshot update scenarios.

Deep-Learning-Based Phase-Only Robust Massive MU-MIMO Hybrid Beamforming

Conventional hybrid beamforming (BF) techniques encounter high computational complexity (CC) and performance loss due to array steering vector mismatches. Therefore, in this letter, a joint robust adaptive BF (RAB) method based on the diagonal loading technique along with phase-only digital beamformer design is proposed. In addition, with the aim of reducing the CC of the system, a novel deep-learning model is proposed to estimate the digital weights. Simulations demonstrated that the proposed deep neural network (DNN) model can have similar performance for digital BF weights estimation as a metaheuristic-based one with significantly lower CC.

Robust Range Ambiguous Deceptive Target Suppression Based on Covariance Matrix Reconstruction

When the deceptive targets are in the ambiguious range bin but are received at the same range gate with the desired target by the array, the traditional multiple-input multiple-output (MIMO) radar is not able to discriminate between them. Based on the unique range-dependent beampattern of the frequency diverse array (FDA)-MIMO radar, we propose a novel robust mainlobe deceptive target suppression method based on covariance matrix reconstruction to form nulls at the frequency points of the transmit–receive domain where deceptive targets are located. First, the proposed method collects the deceptive targets and noise information in the transmit–receive frequency domain to reconstruct the jammer-noise covariance matrix (JNCM). Then, the covariance matrix of the desired target is constructed in the desired target region, which is assumed to already be known. The transmit–receive steering vector (SV) of the desired target is estimated to be the dominant eigenvector of the desired target covariance matrix. Finally, the weighting vector of the receive beamformer is calculated by combining the reconstructed JNCM and the estimated desired target SV. By implementing the weighting vector at the receiving end, the deceptive targets can be effectively suppressed. The simulation results demonstrate that the proposed method is robust to SV mismatches and provides a signal-to-jamming-plus-noise ratio (SJNR) output that is close to the optimal.

Steering vector optimization using subspace-based constraints for robust adaptive beamforming

To address the issue of steering vector mismatch, a robust adaptive beamforming design via steering vector optimization is proposed in this paper. Different from conventional studies, this paper resolves the exact desired signal (DS) steering vector through formulating an array output power maximization problem subjected to noise subspace (NS) based and interference subspace (IS) based constraints. Under the condition that the NS is ready to be attained while the IS is hard to be got, two efficient interference-plus-noise covariance matrix (INCM) reconstruction means, i.e. direct DS matrix removal from sample covariance matrix and indirect DS blocking from training data and matrix transition, are derived to estimate the IS with high accuracy. Herein, after resolving DS steering vector, the weight vectors are thereby extracted with orthogonal projection (OP) criterion. Numerical simulations verify that the devised methods can outperform the existing ones and obtain almost optimal performance across a wide range of DS power.

Passive Radar STAP Detection and DoA Estimation Under Antenna Calibration Errors

This article addresses the problem of clutter cancelation for slowly moving target detection and localization in multichannel passive radar onboard mobile platforms. A post-Doppler space-time adaptive processing (STAP) approach is exploited in the case of an angle-dependent imbalance affecting the receiving channels. While the clutter suppression capability is ensured by the adaptivity of space-time filtering, different solutions are compared, aimed at recovering the detection performance losses associated with channel calibration errors. A space-time generalized-likelihood ratio test (GLRT) scheme is considered, where the steering vector is not specified in the spatial domain, resulting in a noncoherent integration of target echoes across the receiving channels. This is compared with a fully coherent GLRT scheme where echoes from the stationary scene are exploited for the proper calibration of spatial steering vector mismatch. The first scheme proves to be a simple solution for target detection in the passive radar case, offering comparable clutter cancelation capability. The second scheme, at the expense of an additional stage, offers slightly better detection performance and preserves target direction-of-arrival (DoA) estimation capability. Finally, the STAP scheme is employed for the maximum-likelihood estimation of target DoA, evaluating the role of the steering vector calibration against the negative impact of channel imbalance. The effectiveness of the proposed approaches is tested against both simulated and experimental data from a DVB-T-based mobile passive radar.

Robust Beamforming Based on Weighted Vector Norm Regularization

Steering vector mismatch rapidly degrades the performance of the minimum variance distortionless response beamformer. To solve this problem, a robust beamforming method based on weighted vector norm regularization is proposed. First, the factors affecting the robustness of the beamformer are analyzed. Second, by introducing the weighted vector norm, an optimization problem is constructed to increase the robustness of the beamformer. Furthermore, the regularization coefficient is provided to achieve a balance between the output power and the robustness of the beamformer. Meanwhile, a method of finding the appropriate regularization coefficient is provided. Then, simulations of an irregular arc array are carried out, showing that the proposed method is robust to the snapshot number. Finally, the results and data analysis indicate the effectiveness of the proposed method.

An RCB-Like Steering Vector Estimation Method Based on Interference Matrix Reduction

To develop an adaptive beamformer against the signal of interest (SOI) steering vector mismatch, a robust Capon beamformer (RCB) like steering vector estimation method based on the interference matrix reduction is proposed. Different from the RCB and its modified versions that optimize the SOI steering vector with the Capon power estimator, this article designs an SOI power estimator to formulate the steering vector optimization problem with an uncertainty set constraint. In terms of that, the unknown SOI covariance matrix is needed to realize the SOI power estimator, an efficient interference matrix reconstruction way via SOI blocking and matrix eigen-transition is exploited to reduce the interference component from the sample covariance matrix. Herein, after solving the given steering vector optimization problem and adding the noise component to the aforesaid interference matrix, the weight vector of the derived algorithm is, thereby, computed using the estimated SOI steering vector and interference covariance matrix. The proposed method only requires the source number and prior direction of the SOI. The numerical simulations show that the proposed approach can outperform the compared ones with reduced complexity in the situation of various steering vector mismatches.

An Improved Sub-Array Adaptive Beamforming Technique Based on Multiple Sources of Errors

In this paper, a new robust adaptive beamforming method is proposed in order to improve the robustness against steering vector (SV) mismatches that arise from multiple types of array errors. First, the sub-array technique is applied in order to obtain the decoupled sample covariance matrix (DSCM), in which the auxiliary sensors are selected to decouple the array. The decoupled interference-plus-noise covariance matrix (DINCM) is reconstructed with the estimated interference SV and maximum eigenvalue of the DSCM. Furthermore, the desired signal SV is estimated as the corresponding eigenvector determined by the correlation coefficients of the assumed SV and eigenvectors. Finally, the optimal weighting vector is obtained by combining the reconstructed DINCM and the estimated desired signal SV. Our simulation results show significant signal-to-interference-plus-noise ratio (SINR) enhancement of the proposed method over existing methods under multiple types of array errors.

Robust adaptive beamforming for coprime array with steering vector estimation and covariance matrix reconstruction

Coprime array exhibits many advantages over the uniform linear array (ULA) with the same number of physical sensors in resolution performance and interference suppression capability. In this study, the authors take the advantages of coprime array to improve the robustness of adaptive beamformer. In the coprime virtual ULA (CV-ULA), they prove that a constructed Toeplitz matrix can be taken as the sample covariance matrix from the perspective of virtual signal characteristics. The CV-ULA Capon spectrum estimator is modified to obtain the directions and powers of all impinging signals. Since the real directions of all impinging signals are located at different angular sectors, they form independent signal subspace for each impinging signal. They also assign independent steering vector mismatches for different impinging signals to obtain their real steering vectors. The steering vector mismatch of each impinging signal is independently obtained by solving its own convex optimisation problem. They reconstruct the interference-plus-noise covariance matrix (INCM) with precise steering vectors and powers of interference signals. The proposed weight vector is computed by combining the desired signal steering vector and the reconstructed INCM. Extensive simulations show that the proposed algorithm provides robustness against many types of model mismatches.

Robust detection of distributed targets based on Rao test and Wald test

We consider the problem of detecting distributed targets in Gaussian noise with unknown covariance matrix. To make the signal-plus-noise hypothesis more plausible in the mismatched case, we model the received signal under the signal-plus-noise hypothesis as the sum of noise, useful target echoes and fictitious signals. Two adaptive detectors are designed according to the Rao test and Wald test. We prove the proposed Rao test and Wald test exhibit constant false alarm rate properties against the covariance matrix. Numerical examples show that the proposed Rao test has strong robustness against the steering vector mismatches.

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.

Adaptive Beamforming via Desired Signal Robust Removal for Interference-Plus-Noise Covariance Matrix Reconstruction

To tackle the problem of the desired signal (DS) steering vector mismatch, especially in the situation of direction-of-arrival error and array perturbations, a robust interference-plus-noise covariance matrix (INCM) reconstruction method based upon DS removal is presented. Unlike previous studies, this paper proposes to remove the DS component from the training data by building a blocking matrix, which is computed as the inverse of the DS-plus-noise covariance matrix (DSNCM). More specifically, to increase the robustness against arbitrary mismatches, the DS steering vector estimated as the prime eigenvector of the DS matrix, which is attained through integrating the Capon spectrum estimator over the annulus uncertainty sets of the mainlobe region in advance, is adopted to give a faithful blocking matrix. After that, utilizing the obtained blocking matrix to process the training data, the quasi INCM is computed indeed. Finally, a precise INCM is reconstructed by projecting the principal components of the quasi INCM onto the aforesaid DSNCM. Numerical simulations have illustrated that the proposed adaptive beamformer can outperform the existing ones and gain almost optimal performance under different scenarios.

Persymmetric adaptive detection with improved robustness to steering vector mismatches

We exploit persymmetry to study the adaptive detection problem with multiple observations in partially homogeneous environments where noise shares the same covariance matrix up to different power levels between the test and training data. A persymmetric subspace model is designed for taking into account steering vector mismatches. Based on the persymmetric subspace model, we propose adaptive detectors in partially homogeneous environments, according to the criteria of two-step generalized likelihood ratio test (GLRT), Wald test, and Rao test. It is found that the proposed GLRT and Wald test coincide, while the Rao test does not exist. The proposed detector is proved to exhibit a constant false alarm rate property against both the covariance matrix structure and the scaling factor. Numerical examples show that the proposed detector, compared to its counterparts, is more robust to steering vector mismatches.

Robust Target Detection and Estimation for Airborne STAP Radar with Arbitrary Array Errors and Target Uncertainty

In the presence of arbitrary array errors and angle mismatch, performance on target detection and angle estimation will be degraded due to steering vector mismatch. Thus, a robust target detection and estimation algorithm for airborne STAP radar is developed. First, utilizing the spatial-temporal coupling property of the ground clutter, array steering vectors are well estimated by fine Doppler localization of the mainlobe clutter. Then, the robust subspace detector spanned by these estimated array steering vectors is developed, which can improve the detection performance for the targets not located in the look direction. Finally, target angle estimation using subspace coefficients, which implements the ML estimator in a reduced-dimensional version, is presented to reduce the computational complexity of the ML estimator. Numerical examples are given to demonstrate the effectiveness of the presented algorithm.

A robust STAP beamforming algorithm for GNSS receivers in high dynamic environment

In high dynamic environment, the output performance of the space-time adaptive processing (STAP) beamformer can be degraded dramatically since directions of arrival (DOAs) corresponding to interferences change rapidly. A novel robust STAP beamforming algorithm is proposed for global navigation satellite system (GNSS) receivers to broaden the nulls towards interferences and meanwhile fight against the steering vector (SV) mismatch caused by DOA estimation errors. Firstly, the received signal model in high dynamic environment is established for the STAP architecture. Then, the spatial-temporal interference plus noise covariance (INC) matrix is obtained by reconstructing the interference covariance matrix and noise covariance matrix respectively to avoid DOA estimation of GNSS signals, which can also remove the signal of interest (SOI) component from the sample covariance matrix (SCM). Furthermore, the spatial-temporal spectrum estimates around interferences are respectively reset to be the same as those of interferences, due to which the nulls towards interferences in the space domain can be widened in high dynamic environment. Finally, the constraints to solve weight vector is specially designed for GNSS signals. Simulation results show that the proposed algorithm can broaden the nulls effectively and also has a better output carrier-to-noise (C/No) ratio performance than the other involving algorithms.

Robust adaptive beamforming against large steering vector mismatch based on minimum dispersion

Many efforts have been recently devoted to adaptive beamformers based on the minimum dispersion (MD) criterion for non-Gaussian signals, which results in improved signal-to-noise ratio performance. However, large steering vector mismatch and inappropriate choice of uncertainty set will cause performance degradation to the existing MD-based methods. To address these issues, we develop a robust MD-based beamformer against large steering vector mismatch, which utilizes multiple small uncertainty sets to cover the whole uncertainty region. The ℓp−norm (p≥1) minimization problem turns to be nonlinear and nonconvex because of these multi-uncertainty-set constraints. To solve the problem, a projected gradient algorithm is utilized to transform the original problem into a nonconvex quadratically constrained quadratic programming (QCQP) problem. The semidefinite programming relaxation technique is then employed in each iteration to deal with the nonconvex QCQP problem. Numerical results demonstrate that the proposed beamformer offers a significant performance improvement in case of large steering vector mismatch for non-Gaussian signals compared with the conventional schemes.