Desired Signal Steering Vector Research Articles

Robust Adaptive Beamforming for Interference Suppression Based on SNR

Robust adaptive beamforming (RAB) can be used to suppress interference signals while retaining the desired signals received by a sensor array. However, desired signal self-cancellation and model mismatch can affect RAB performance. In this paper, a novel interference-plus-noise covariance matrix (INCM) reconstruction method is proposed for RAB to solve these problems. The proposed method divides the desired signal into two ranges according to the input signal-to-noise ratio (SNR), namely low SNR and high SNR. In the low SNR range, INCM reconstruction directly uses the same sample covariance matrix as the sample matrix inversion (SMI) beamformer to retain the advantages of the traditional SMI algorithm. In the high SNR range, the eigenvalues of the sample covariance matrix are used to estimate the interference power and noise power. The optimized interference steering vector (SV) is obtained by solving a quadratic convex optimization problem in an interference subspace. The INCM is reconstructed from the interference SVs, interference power, and noise power. The reconstructed INCM is then used to correct the desired signal SV via maximizing the beamformer output power. This is achieved by solving a quadratically constrained quadratic programming (QCQP) problem. Analysis and simulation results are presented which demonstrate that the proposed method performs well under a variety of mismatch conditions.

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.

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.

Robust Block Sparse Beamforming for Strictly Non-Circular Signals and Unknown Array Mutual Coupling

Widely linear beamformers (WLBs) can greatly outperform the traditional adaptive beamformers. However, the performance of WLBs is extremely susceptible to the unknown mutual coupling (MC) effects caused by the imperfectly calibrated antennas array. In this brief, we propose a block sparse representation scheme and design a robust WLB for strictly non-circular (SNC) signals to mitigate the unknown MC mismatch. We use the structural characteristics of the steering vector under MC, and derive a new augmented formulation for the observed signals which takes into account the MC mismatches. We solve a block sparse optimization problem in order to estimate the directions of illuminating signals allowing us to reconstruct the augmented interference-plus-noise covariance matrix (AINCM). We then propose to estimate the augmented desired signal steering vector using the augmented subspace projection method. Our proposed robust WLB not only avoids estimating the MC coefficients, but also prevents the signal cancellation phenomenon from reconstructing the AINCM. Our simulation results demonstrate that the proposed WLB is effective for the SNC signals, outperforms the existing methods, and is robust against unknown MC and look direction mismatches.

Digital adaptive wideband beamforming without pre-steering delay processing

Compared with the traditional frost space-time beamformer (STB) with a pre-steering delay processing (PSDP), the method without the PSDP is able to provide a more intuitive observation of the space-frequency response (SFR) for both the desired signal and interference in the beam pattern. In this paper, a new SFR constraint is proposed to guarantee the same time delay for all different frequency components in the desired signal by analyzing the desired signal process of the digital STB. Specifically, in order to make all frequencies in the desired bandwidth meet the SFR constraint, we propose a method to obtain the number of the sample frequency points of the new constraint. After that, the equivalent beamformer with lower complexity is acquired via transforming the SFR constraints into a part of the optimization objectives. On this basis, a robust wideband beamformer against the direction of arrival (DOA) mismatch of the desired signal is established. To be more concretely, in the proposed robust beamformer, the covariance matrix of the interference plus noise and the covariance matrix of the desired signal are reconstructed with the observed data containing the desired signal. Additionally, the reconstructed two matrices are used to estimate the actual desired signal steering vector by considering a maximization of the desired signal output power. Numerical results verify the effectiveness of those proposed 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.

Robust adaptive null broadening beamforming based on subspace projection

ABSTRACT When the rapid moving interference exists, especially in the presence of look direction mismatch, coherent local scattering and so on, the output performance of beamformer will degrade dramatically. To solve this problem, a novel robust adaptive null broadening beamforming method based on subspace projection is proposed. First, the proposed beamformer requires a priori information, that is, the spatial sector where the desired signal and interference may locate, so as to construct the signal-plus-noise covariance matrix (SPNCM) and interference-plus-noise covariance matrix (IPNCM). Then, the desired signal steering vector (SV) is calibrated twice. The desired signal SV is estimated from the SPNCM and subsequently calibrated by using the uncertainty set optimisation method. Next, we construct the null broadening projection matrix by tapering the interference subspace got from IPNCM. Finally, the sample covariance matrix is processed by projection technology and diagonal loading technology. The optimal weight vector is obtained by the new covariance matrix and calibrated desired signal SV. Simulation results show that the proposed method can form wide null in the incident direction of interference and prevent interference from moving out of the null when the rapid moving interference exists. The proposed method outperforms other existing methods.

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.

Subspace Based Adaptive Beamforming Algorithm with Interference Plus Noise Covariance Matrix Reconstruction

As we all know, the model mismatch, primarily when the desired signal exists in the training data, or when the sample data is used for training, will seriously affect algorithm performance. This paper combines the subspace algorithm based on direction of arrival (DOA) estimation with the adaptive beamforming. It proposes a reconstruction algorithm based on the interference plus noise covariance matrix (INCM). Firstly, the eigenvector of the desired signal is obtained according to the eigenvalue decomposition of the subspace algorithm, and the eigenvector is used as the estimated value of the desired signal steering vector (SV). Then the INCM is reconstructed according to the estimated parameters to remove the adverse effect of the desired signal component on the beamformer. Finally, the estimated desired signal SV and the reconstructed INCM are used to calculate the weight. Compared with the previous work, the proposed algorithm not only improves the performance of the adaptive beamformer but also dramatically reduces the complexity. Simulation experiment results show the effectiveness and robustness of the proposed beamforming algorithm.

Novel robust adaptive beamforming against unknown mutual coupling

Mutual coupling effects among the array elements can degrade the performance of the beamformer seriously. In this paper, we propose a novel robust adaptive beamforming method, which is robust against unknown mutual coupling. The main idea is to reconstruct the interference-plus-noise covariance matrix (IPNCM) with the estimated eigenvector and eigenvalue corresponding to the interference. The eigenvector lies in the intersection of two special subspaces. The first subspace is the signal-plus-interference (SPI) subspace got from the sample covariance matrix (SCM). The second subspace, which is interference subspace, can be obtained by integrating the conduction matrix in each interference angular sector. According to the correlation between the estimated eigenvector and SPI subspace, the eigenvalues corresponding to each interference are determined. Therefore, the IPNCM is reconstructed. The desired signal steering vector (SV) is estimated by a similar method. Simulation results show that the proposed beamformer outperforms other methods in the presence of unknown mutual coupling.

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.

Robust widely linear beamforming using estimation of extended covariance matrix and steering vector

The distribution of the received signals in many array processing applications is noncircular. Although optimal widely linear beamformer (WLB) can provide the best performance for noncircular received signals, its performance degrades severely under model mismatches in practical applications. As a remedy, we propose a robust WLB by using precise reconstruction of extended interference-plus-noise covariance matrix (EINCM) and low-complexity estimation of extended desired signal steering vector (EDSSV). We propose to first determine the steering vectors, powers, and noncircularity coefficients of all signals and the noise power. In contrast to the previous reconstruction methods using the integration over a wide angular sector, we reconstruct the interference-plus-noise covariance matrix (INCM) and the pseudo INCM accurately according to their definitions. By using INCM and pseudo INCM, we can precisely reconstruct the EINCM. We propose to estimate the EDSSV by intersecting two extended subspaces, which are respectively formed by eigendecomposing the extended sample covariance matrix and the extended desired signal covariance matrix. Unlike the convex optimization methods, the proposed EDSSV estimation does not require any optimization programming and yields a solution with closed expression in low computational complexity. Simulation results show that the proposed robust WLB provides near optimal performance under several model mismatch cases.

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 adaptive beamforming for MIMO radar in the presence of covariance matrix estimation error and desired signal steering vector mismatch

Owing to covariance matrix estimation error, desired signal steering vector mismatch, and the existence of target signal in training samples, most of adaptive beamforming algorithms suffer from a great performance degradation. Aim at this, this study proposes a robust adaptive beamforming algorithm for multiple-input-multiple-output radar. To be specific, the sample covariance matrix is replaced by the reconstructed covariance matrix, to narrow the difference between the maximum and minimum noise eigenvalues. In addition, the diagonal loading technique is applied to correct the mismatched desired signal steering vector by maximising the output signal-to-interference-plus-noise ratio of adaptive beamformer, and a simple closed-form solution to loading factor can be further obtained. Computer simulation results demonstrate that the proposed algorithm can efficiently improve the robustness of adaptive beamformer against both covariance matrix estimation error and desired signal steering vector mismatch.

Improved OP approach utilising correlated projection and eigenspace processing for robust adaptive beamforming

The capability of orthogonal projection (OP) approach degrades severely in the presence of array model mismatch, especially when the training samples are mixed with the strong desired signal. Therefore, an improved OP robust adaptive beamforming is proposed based on correlated projection and eigenspace processing in wide input signal-to-noise ratio to remove the desired signal self-null effect and improve robustness. In the proposed approach, the interference subspace is constructed combining the correlated projection and eigenspace processing first. Then, the interference-plus-noise covariance matrix is accurately reconstructed via super-resolution spatial spectrum estimator to eliminate desired signal from sample covariance matrix. Subsequently, the desired signal steering vector is corrected applying correlated projection and then the adaptive weighted vector is modified by OP approach. Simulation results demonstrate that the capability of the proposed approach is almost consistently same as the optimal beamformer in many scenarios.

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.

Low‐complexity robust adaptive beamforming method for MIMO radar based on covariance matrix estimation and steering vector mismatch correction

In this study, the authors consider a low-complexity robust adaptive beamforming problem in a collocated multiple-input multiple-output (MIMO) radar. This study is motivated by the fact that in practical applications, the conventional adaptive beamforming algorithm for MIMO radar requires a large computational complexity and suffers from a great performance degradation because of the finite number of training snapshots, the desired signal steering vector mismatch and the corruption of training data by the desired signal. Since the dimension of the virtual steering vector of the MIMO radar is relatively large, the proposed method can estimate the covariance matrix by using a low-complexity method to effectively improve the computational efficiency of the adaptive beamforming algorithm and the robustness of the beamformer against the covariance matrix uncertainty. Besides, based on the estimated covariance matrix, the proposed method can also correct the desired signal steering vector mismatch to efficiently prevent the desired signal cancellation phenomenon. Simulation results demonstrate that the performance of the proposed method is always close to that of the optimal processing in a wide range of signal-to-noise ratio or of the number of training snapshots.

Middle Subarray Interference Covariance Matrix Reconstruction Approach for Robust Adaptive Beamforming With Mutual Coupling

In this letter, a middle subarray interference-plus-noise covariance matrix (INCM) reconstruction approach is proposed to mitigate the mutual coupling problem in robust adaptive beamforming. In the proposed approach, the banded symmetric Toeplitz structure of mutual coupling matrix in the uniform linear array is employed. The INCM of middle subarray is first reconstructed by using the Capon spectrum of middle subarray to integrate over the possible interference region. Similarly, the desired signal covariance matrix of middle array is calculated over the desired signal region, and the desired signal steering vector of middle array is estimated. Finally, the proposed middle subarray beamformer weight vector is obtained. Simulation results validate the superiority and effectiveness of the proposed method.

Robust adaptive beamforming using iterative adaptive approach

ABSTRACTThe performance of traditional reconstruction-based robust adaptive beamformers may degrade when the array is not well calibrated. This performance degradation is mainly caused by the Capon spectrum estimator which can not estimate the spatial power spectrum accurately. In contrast to existing approaches, we propose two new reconstruction-based robust adaptive beamformers by using the accurate iterative adaptive approach (IAA) spectrum to combat the covariance matrix uncertainties and the steering vector mismatches. The first one employs the low-complexity IAA (IAA-LC) algorithm to obtain the interference power estimates and reconstruct the interference-plus-noise covariance matrix (INCM) with the computational complexity further reduced. The second one reconstructs the INCM by updating the power estimates corresponding to each interference steering vector with the use of knowledge-aided IAA (IAA-KA) algorithm. The desired signal steering vector is corrected by searching for the direction corresponding to the maximum power, which circumvents the use of optimization program. Simulation results show that our proposed beamformers outperform the others and can achieve the robust performance in the cases of array model mismatches.