Robust Adaptive Beamforming with Sensor Position Errors Using Weighted Subspace Fitting-Based Covariance Matrix Reconstruction.

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.

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.

Without the response variation constraint, the main‐lobe responses of wideband beamforming usually vary with the frequencies of interest, and the beam pointing may deviate from the incident angle of the desired signal. If the interference‐plus‐noise covariance matrix (INCM) is directly replaced by the sample covariance matrix, the desired signal in the sample data may result in self‐null problem, which can lead to the degradation of the performance of wideband beamformers. Through frequency division, a novel wideband adaptive beamforming is proposed by reconstructing the INCM and solving the convex optimisation problem. Using fast Fourier transform (FFT), the time‐domain samples are transformed into the frequency field, and the covariance matrix of each subband can be obtained from the frequency‐domain data. In the spatial‐frequency domain, the INCM and signal‐plus‐noise covariance matrix can be respectively reconstructed by integrating the stacked steering vector and the Capon spatial spectrum over the corresponding angular region. Then, we establish the optimisation criteria, that is, minimising the output interference‐plus‐noise power, minimising the main‐lobe spatial response variation, and constraining the response deviation of the desired signal. A novel convex optimisation model can be established, and then the weight coefficients for time‐domain wideband beamforming can be obtained by solving the optimisation problem. The simulation and experimental results demonstrate that the proposed beamformer can provide better performance compared with other tested beamformers and maintain good robustness in various applications.

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.

Robust adaptive beamforming via quasi-signal subspace estimation for covariance matrix reconstruction

An advanced interference plus noise covariance matrix (ICM) reconstruction approach was proposed to facilitate robust adaptive beamforming for antenna sensor arrays The proposed method involves the calculation of the eigenvectors and eigenvalues of the signal of interest (SOI) and the interference through eigen-projection processing. Following this, the covariance matrix without the required signal component is formed by amending the diagonal matrix of the eigenvalue Then, the mixed ICM is constructed using the shrinkage method. A quadratically constrained quadratic programming (QCQP) dilemma can be worked out to ascertain the difference between the proposed steering vector (SV) and the true vector. The benefit of the proposed method is that the ICM can be obtained on the move and also can be obtained more precisely in the situation of high signal-to-noise ratio (SNR). Finally, the results of the theoretical analysis and simulation demonstrate the robustness and efficacy of the proposed method.

Robust adaptive beamforming via covariance matrix reconstruction with diagonal loading on interference sources covariance matrix

Robust adaptive beamforming via coprime coarray interpolation

Null broadening is an effective method to suppress the motion interference, but most methods are suitable for the uniform linear array. To solve this problem, an adaptive null broadening method based on uniform rectangular array (URA) is proposed in this paper. The method first estimates the power of interference and adds virtual interference with the same power near the real interference. Then, the method estimates the noise power and reconstructs the interference plus noise covariance matrix (INCM) which contains the null broadening information. Finally, the desired signal steering vector is corrected to obtain the optimal weighting vector. Simulation results show that the method can form wide nulls in the interference direction to suppress the motion interference and is robust to the desired signal steering vector mismatch.

Here a novel eigen-projection matrix preprocessing (EMP ) technology in view of covariance matrix rebuilding is presented. The eigenvectors of multiple mainlobe interferences are calculated via the correlation of eigenvectors between the sample covariance matrix ( SCM ) and this reconstructed mainlobe interference-plus-noise covariance matrix (IPNCM). Simulation consequents exhibit the excellence of this presented technique over this normal EMP method.

This paper is concerned with a new robust design algorithm for signal mismatch, the modified steering vector and covariance matrix are investigated. Under the correlation coefficient and norm constraints, the mismatched desired signal steering vector is estimated via output power maximization. The original design is nonconvex, and usually Np-hard. Then the relaxed semidefinite programming (SDP) is employed to solve the problem, and the relaxation is tight via analytically proven. Subsequently, the sample covariance matrix is further restructured with the shrinkage method and the subspace theorem based on the corrected steering vector in order to remove the desired signal. Finally, we provide some numerical results to show that the proposed method gives satisfactory results under different scenarios.

Amainlobe interference suppression method is proposed in this paper, which can still work when the signal of interest (SOI) is present in the training data. In this method, the iterative adaptive approach (IAA) is applied to spatial spectrum estimation at first. Then, IAA spatial spectrum is used to reconstruct the interference-plus-noise covariance matrix (INCM). Next, the eigenvector associated with mainlobe interference in INCM is determined and the eigen-projection matrix can be calculated to suppress the mainlobe interference. Meanwhile, the sidelobe-interference-plus-noise covariance matrix (SINCM) can be reconstructed. Finally, the adaptive weight vector is obtained. One main advantage is that the proposed method can deal with coherent mainlobe interference and sidelobe interferences simultaneously. Simulation results demonstrate the effectiveness of the proposed method.

Adaptive beamformers are sensitive to model mismatch, especially when the desired signal is present in training snapshots or when the training is done using data samples. In contrast to previous works, this correspondence attempts to reconstruct the interference-plus-noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix. The estimator is based on the Capon spectral estimator integrated over a region separated from the desired signal direction. This is shown to be more robust than using the sample covariance matrix. Subsequently, the mismatch in the steering vector of the desired signal is estimated by maximizing the beamformer output power under a constraint that prevents the corrected steering vector from getting close to the interference steering vectors. The proposed adaptive beamforming algorithm does not impose a norm constraint. Therefore, it can be used even in applications where gain perturbations affect the steering vector. Simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios.

Beamforming can be used for sound source localization through microphone sensor arrays. Adaptive beamforming is extremely sensitive to model mismatch, particularly when the desired signal is present in the training data, which has a significant impact on beamforming efficiency. In order to address this problem, an adaptive beamforming algorithm based on K-means clustering and INCM (interference plus noise covariance matrix) reconstruction is proposed in this paper. When the expected signal and the interfering signal have a large difference in power, the expected signal and the interfering signal are identified using the K-means clustering algorithm, and the expected signal components are extracted from the covariance matrix to reconstruct the INCM. Meanwhile, a QCQP (quadratic constrained quadratic programming model) is constructed to improve the output performance degradation of the beamformer when the steering vectors of the expected signal are not matched. The results show that the proposed algorithm suppresses interference output more effectively while retaining a high output SINR (signal to interference plus noise ratio).

Aiming at the problem of beamformer performance degradation caused by coherent signals, We propose an adaptive beamforming algorithm for interference plus noise covariance matrix (INCM) reconstruction. The idea of the proposed algorithm is that the sum of eigenvalues (SE) is not affected by coherent signals, so that the power of the eigenvalues can be used to reconstruct INCM. First, we perform eigenvalue decomposition on the covariance matrix after the forward and backward spatial smoothing, which proves that spatial smoothing does not affect SE. On this basis, a new method of signal power estimation is proposed. The estimated signal power and direction vector are then used to reconstruct INCM. Finally, the weight vector is calculated from the estimated desired signal steering vector (DSDV) and the reconstructed INCM. The innovation of this algorithm lies in the combination of coherent signal processing and beamforming, which effectively improves the output interference plus noise ratio (SINR) performance of the beamformer. Simulation analysis verifies the superiority of the algorithm and the validity of theoretical analysis.