Signal Of Interest Steering Vector Research Articles

Robust adaptive beamforming for cylindrical uniform conformal arrays based on low-rank covariance matrix reconstruction

Recently, conformal arrays have attracted considerable interest because such arrays can provide reduced radar cross-section and increased angle coverage. In this article, we devise a robust adaptive beamforming (RAB) approach using cylindrical uniform conformal array (CUCA). Firstly, we derive the minimum variance distortionless response (MVDR) beamformer for the CUCA by utilizing the noise subspace of interference covariance matrix (ICM) and steering vector (SV) of the signal-of-interest (SOI). Subsequently, the ICM is reconstructed by estimating the noise-free covariance matrix of the CUCA outputs and the interference projection matrix. Specifically, the noise-free covariance matrix can be regarded as multiple low-rank covariance matrices, and each low-rank matrix is reconstructed by formulating a nuclear norm minimization (NNM) problem. With the reconstructed covariance matrix, the 2-D DOAs of sources are determined by employing 2-D MUSIC spectrum to form the interference projection matrix. In addition, the SOI SV is estimated by solving a quadratically constrained quadratic programming (QCQP) problem. Numerical results demonstrate that the proposed approach is obviously superior to the existing RAB techniques.

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.

Robust and Efficient Adaptive Beamforming Using Nested Subarray Principles

In this paper, we propose an adaptive beamforming algorithm for large uniform linear arrays (ULAs), where only a nested subarray is utilized to calculate the beamforming coefficients for the original ULA. In this algorithm, the steering vectors and powers of the signal-of-interest (SOI) and interferences are firstly estimated using the Capon spatial spectrum and known array structure, and the interference-plus-noise covariance matrix (INCM) is then constructed. Subsequently, an augmented INCM is formed via vectorization and spatial smoothing operations. Finally, the beamformer weight vector is determined by the augmented INCM and the estimated SOI steering vector. Our proposed algorithm exploits the enhanced degrees of freedom of the nested array, and thus can be applied to a large ULA to reduce the implementation complexity. Moreover, it fundamentally eliminates the SOI component. Numerical results demonstrate that the proposed algorithm performs better than the existing approaches.

Robust beamforming via alternating iteratively estimating the steering vector and interference-plus-noise covariance matrix

To develop an adaptive beamformer against the steering vector mismatch of the signal of interest (SOI), a novel robust algorithm is proposed to estimate the steering vector of the SOI and interference- plus-noise covariance matrix (INCM) in an alternative and iterative way. That is, via determining a convex optimization problem, which forces the steering vector moving towards the signal-plus- interference subspace (SIS) but getting away from the interference subspace (IS), the actual steering vector of the SOI is estimated. To proceed, the suitable SIS is easy to obtain through applying eigendecomposition on the sample covariance matrix while the appropriate IS is hard to estimate because of the array perturbations. Given this, a novel INCM reconstruction method, which utilizes a blocking matrix to eliminate the SOI from the training samples, is provided to realize the preferable estimate of the IS. More specifically, the abovementioned processes are carried out in an alternative iteration scheme, which leads to the SOI steering vector and INCM converging to the theoretical ones sufficiently, respectively. Unlike the conventional algorithms which are vulnerable to the various mismatches, the proposed beamforming algorithm is insensitive to the SOI steering vector mismatch arisen from the DOA error and array perturbations, numerous theoretical analysis and simulation experiments are presented to demonstrate the superiority of the proposed adaptive beamformer.

Robust adaptive beamforming using a novel signal power estimation algorithm

Recently, many robust adaptive beamforming (RAB) methods based on covariance matrix reconstruction have been proposed. Motivated by the idea, in this paper, a novel and efficient signal power estimator is devised to reconstruct the interference-plus-noise covariance (INC) matrix, with the corresponding RAB algorithm proposed. Firstly, the steering vectors of the incoming sources are derived using the Capon spatial spectrum and known array geometry. Secondly, a set of linear equations is established based on the signal subspace projection, from which the powers of the incoming sources are estimated. Based on the presumed angular sector of the signal-of-interest (SOI), the steering vectors and powers of the SOI and interferences are distinguished, and the INC matrix is then reconstructed. Finally, the beamformer is determined by the estimated INC matrix and SOI steering vector. The proposed algorithm is computationally more efficient than other reconstruction-based methods because there are closed-form solutions for the signal powers. Simulation results indicate that our proposed algorithm performs better than the existing methods at high signal-to-noise ratios (SNRs), and achieves nearly optimal performance across a wide range of SNR.

Non‐circularity coefficient estimation of the SOI for narrowband widely linear beamforming

In widely linear beamforming, the second-order non-circularity property exhibited by the signal-of-interest (SOI) can be exploited to improve interference and noise suppression. Assuming known SOI steering vector and spatially white noise, several algebraic schemes for estimating the SOI non-circularity coefficient are proposed in the context of narrowband widely linear beamforming without training/reference signal. These new estimators are based on signal purification, pseudoinverse, oblique projection, and pre-processed subspace separation. Simulation results are included to illustrate the performances of the proposed methods.

New Designs on MVDR Robust Adaptive Beamforming Based on Optimal Steering Vector Estimation

The robust adaptive beamforming design problem based on estimation of the signal of interest steering vector is considered in the paper. In this case, the optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the signal of interest steering vector. The common criteria to find the best estimate of the steering vector are the beamformer output SINR and output power, while the constraints assume as little as possible prior inaccurate knowledge about the signal of interest, the propagation media, and the antenna array. Herein, a new beamformer output power maximization problem is formulated and solved subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint that guarantees that the direction-of-arrival (DOA) of the signal of interest is away from the DOA region of all linear combinations of the interference steering vectors. In the new robust design, the prior information required consists of some allowable error norm bounds, the approximate knowledge of the antenna array geometry, and the angular sector of the signal of interest. It turns out that the array output power maximization problem is a non-convex QCQP problem with inhomogeneous constraints. However, we show that the problem is still solvable, and develop efficient algorithms for finding globally optimal estimate of the signal of interest steering vector. The results are generalized to the case where an ellipsoidal constraint is considered, and sufficient conditions for the global optimality are derived. In addition, a new quadratic constraint on the actual signal steering vector is proposed in order to improve the array performance. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformers in terms of the output SINR as well as the output power.

Biquaternion Capon beamformer using four-component vector-sensor arrays

A hypercomplex variant of Capon beamformer, called biquaternion Capon (BQ-Capon), is herein proposed for signal strengthening with four-component vector-sensor arrays. This BQ-Capon beamformer extracts the signal-of-interest (SOI) while rejecting interferences plus noise in a multiple-input-multiple-output (MIMO) fashion. Simulation results show that BQ-Capon beamformer outperforms the standard long-vector counterpart in convergence and sensitivity to mismatch in SOI steering vector.

Robust Adaptive Array Beamforming With Subspace Steering Vector Uncertainties

In this letter, the steering vector of the signal-of-interest (SOI) is assumed to belong to a given linear subspace but the associated coordinates are otherwise unknown. In the case where the signal subspace is poorly estimated, a rank-constrained optimization problem is formulated in which the signal subspace is forced to intersect with the known linear subspace (where the SOI steering vector is located). Such problem can be reformulated as two subproblems via the variable alternation method. Also, the analytical solutions of these two subproblems can be found. Numerical results demonstrate that the proposed method can be regarded as an improved subspace-based method, which lowers the requirements in terms of snapshot number or signal-to-noise ratio (SNR) to outperform the diagonal-loading-type methods as compared with the traditional signal-subspace projection method.

On robust Capon beamforming and diagonal loading

The Capon (1969) beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. We show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches, but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance for SOI power estimation is demonstrated via a number of numerical examples.

Robust Capon beamforming

The Capon beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. We present a natural extension of the Capon beamformer to the case of uncertain steering vectors. The proposed robust Capon beamformer can no longer be expressed in a closed form, but it can be efficiently computed. Its excellent performance is demonstrated via a number of numerical examples.