Robust adaptive beamforming using iterative adaptive approach

Forest height is an essential input parameter for forest biomass estimation, ecological modeling, and the carbon cycle. Tomographic synthetic aperture radar (TomoSAR), as a three-dimensional imaging technique, has already been successfully used in forest areas to retrieve the forest height. The nonparametric iterative adaptive approach (IAA) has been recently introduced in TomoSAR, achieving a good compromise between high resolution and computing efficiency. However, the performance of the IAA algorithm is significantly degraded in the case of a small tomographic aperture. To overcome this shortcoming, this paper proposes the robust IAA (RIAA) algorithm for SAR tomography. The proposed approach follows the framework of the IAA algorithm, but also considers the noise term in the covariance matrix estimation. By doing so, the condition number of the covariance matrix can be prevented from being too large, improving the robustness of the forest height estimation with the IAA algorithm. A set of simulated experiments was carried out, and the results validated the superiority of the RIAA estimator in the case of a small tomographic aperture. Moreover, a number of fully polarimetric L-band airborne tomographic SAR images acquired from the ESA BioSAR 2008 campaign over the Krycklan Catchment, Northern Sweden, were collected for test purposes. The results showed that the RIAA algorithm performed better in reconstructing the vertical structure of the forest than the IAA algorithm in areas with a small tomographic aperture. Finally, the forest height was estimated by both the RIAA and IAA TomoSAR methods, and the estimation accuracy of the RIAA algorithm was 2.01 m, which is more accurate than the IAA algorithm with 3.25 m.

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.

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.

The performance of adaptive beamforming degrades in presence of signal model mismatches. In particular, when the desired signal is present in training snapshots, the adaptive beamforming is quite sensitive to desired signal steering vector mismatch. Therefore, a robust adaptive beamforming for actual system is proposed based on the reconstruction of interference covariance matrix and mismatched steering vector compensation. In the proposed method, the interference covariance matrix is firstly reconstructed by using Root-MUSIC method to estimate Direction-of-Arrival (DOA) of signals, where the desired signal component is removed from the training snapshots. Subsequently, the mismatched desired signal steering vector is compensated by solving a quadratically constrained quadratic programming problem. Simulation results show that the performance of proposed algorithm outperforms the existing robust adaptive beamforming, and the output signal-to-interference-plus-noise ratio (SINR) is close to optimal values. Therefore, the proposed algorithm could be significantly effective for actual system.

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.

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.

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.

When sensor position errors exist, the performance of recently proposed interference-plus-noise covariance matrix (INCM)-based adaptive beamformers may be severely degraded. In this paper, we propose a weighted subspace fitting-based INCM reconstruction algorithm to overcome sensor displacement for linear arrays. By estimating the rough signal directions, we construct a novel possible mismatched steering vector (SV) set. We analyze the proximity of the signal subspace from the sample covariance matrix (SCM) and the space spanned by the possible mismatched SV set. After solving an iterative optimization problem, we reconstruct the INCM using the estimated sensor position errors. Then we estimate the SV of the desired signal by solving an optimization problem with the reconstructed INCM. The main advantage of the proposed algorithm is its robustness against SV mismatches dominated by unknown sensor position errors. Numerical examples show that even if the position errors are up to half of the assumed sensor spacing, the output signal-to-interference-plus-noise ratio is only reduced by 4 dB. Beam patterns plotted using experiment data show that the interference suppression capability of the proposed beamformer outperforms other tested beamformers.

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 quasi-signal subspace estimation for covariance matrix reconstruction

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

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.

Consider an optimal design problem of robust adaptive beamforming of minimum variance distortionless response, based on estimation of steering vector. The optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the desired signal steering vector. The common criteria to select a best estimate include high performance in terms of output signal-to-noise-plus-interference ratio (SINR) and array output power, but less prior knowledge. However there is often a trade-off between the two criteria. Herein, in order to find an optimal steering vector estimate, a beamformer output power maximization problem is formulated subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint to guarantee the desired source direction-of-arrival (DOA) to get away from the DOA region of all linear combinations of the interference steering vectors. In the new robust design, all the prior information includes some allowable error norm bounds, besides the antenna array geometry and angular sector of the desired signal. It turns out that the optimization problem is a non-convex quadratically constrained quadratic program with inhomogeneous constraints, but we show that it is still solvable, and propose how to efficiently get an optimal estimate, via a semidefinite programming relaxation technique. To validate our results, simulation examples are presented to demonstrate the improved performance of the new robust beamformer in terms of the output SINR as well as the output power.

ABSTRACTThis paper proposes a super-resolution Doppler beam sharpening (DBS) imaging method in the wide-area surveillance mode based on the iterative adaptive approach (IAA). DBS imaging is an effective technique to improve the azimuth resolution in the wide-area surveillance mode. However, the conventional DBS imaging, which is realized by fast Fourier transform (FFT) method, suffers from poor resolutions and high sidelobes. In this paper, the IAA algorithm is introduced to replace the FFT method in the DBS imaging, in order to enhance resolution and reduce sidelobe levels. Both simulation and real data processing have validated the effectiveness of the proposed method.

In signal processing applications such as wideband beamforming or multiple-input multiple-output systems, the parameters we wish to estimate can occur in groups. These groups are defined by the system design and known a priori. However, the parameters within the group are often not phase coherent, therefore the standard method is to non-coherently integrate the appropriate groups to maximize signal power. In this paper, we modify the iterative adaptive approach (IAA) algorithm to the Group IAA algorithm to improve the estimation of the noncoherent parameters. The performance improvement is measured via numerical simulations.