Low-Complexity Robust Adaptive Beamforming Based on Covariance Matrix Reconstruction

Traditional adaptive beamformers are sensitive to model mismatch and they have poor performances when the input signal-to-noise ratio (SNR) is close to or more than interference-to-noise ratio (INR). In this letter, a novel robust adaptive beamforming (RAB) algorithm based on twice interference-plus-noise covariance (INC) matrix reconstruction is proposed. Firstly, the desired signal (DS) steering vector is estimated by the alternating projection algorithm based on the antenna array geometry and angular sector prior information. Then, the proposed method obtains the eigenvalue corresponding to DS by correlation coefficient and takes the place of it by noise power to obtain the first INC matrix. Furthermore, the second precise covariance matrix is reconstructed based on the theoretical INC matrix expression. The interferences powers are estimated by the theoretical formulation of the interference covariance matrix (ICM), which is derived from the first INC matrix. The simulation results demonstrate that the proposed algorithm achieves good performance especially when the input SNR is high, and its performance is close to the optimal beamformer in the case of look direction error.

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.

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

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.

Robust adaptive beamforming (RAB) based on interference-plus-noise covariance (INC) matrix reconstruction can experience performance degradation when model mismatch errors exist, particularly when the input signal-to-noise ratio (SNR) is large. In this work, we devise an efficient RAB technique for dealing with covariance matrix reconstruction issues. The proposed method involves INC matrix reconstruction using an idea in which the power and the steering vector of the interferences are estimated based on the power method. Furthermore, spatial match processing is computed to reconstruct the desired signal-plus-noise covariance matrix. Then, the noise components are excluded to retain the desired signal (DS) covariance matrix. A key feature of the proposed technique is to avoid eigenvalue decomposition of the INC matrix to obtain the dominant power of the interference-plus-noise region. Moreover, the INC reconstruction is carried out according to the definition of the theoretical INC matrix. Simulation results are shown and discussed to verify the effectiveness of the proposed method against existing approaches.

Radar networks can provide spatial diversity by observing targets from different perspectives with adequately separated receiving stations. This article proposes a mainlobe interference suppression approach for radar networks based on covariance matrix reconstruction. First, we formulate the mainlobe interference suppression under multiradar configuration as a multichannel signal enhancement problem and perform range and Doppler equalization to improve interferences’ spatial correlation. Then, we estimate the signal and interference covariance matrix from the sampling covariance matrix by solving a robust principal component analysis (RPCA) model. After that, we devise a time-domain-constrained (TDC) linear estimator dependent on the reconstructed covariance matrices to enhance target echo. To remove those duplicate false targets caused by signal enhancement and estimate the state of the physical targets, we establish and solve a generalized multiple measurement vector (GMMV) model based on the fact that targets have unique locations in the state space. Finally, we confirm the effectiveness of the proposed approach with numerical experiments and demonstrate better performance in comparison with the subspace projection method.

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.

Robust adaptive beamforming (RAB) has became a popular research topic, with various RAB techniques being proposed in the past decades. However, because the sample covariance matrix rather than the interference-plus-noise co-variance matrix is used to calculate the weight vector, the performance of the previously developed RAB techniques is not optimal. In this paper, a novel RAB algorithm, which uses the reconstructed interference-plus-noise covariance matrix, is developed. First, the interference-plus-noise covariance matrix and the desired signal covariance matrix are reconstructed by matched spectrum processing. Then, the weight vector of RAB is directly obtained using the general-rank minimum variance distortionless response method. A significant advantage of the proposed RAB is that only little prior information is required. The imprecise knowledge of the antenna array geometry and the angular sectors (in which the desired signal and interferences are located) is sufficient for the proposed RAB algorithm. Simulation results demonstrate that the proposed method outperforms other previously developed RAB techniques.

Adaptive beamforming methods are sensitive to underlying assumptions on the environment, sources, or sensor array violation, especially when interferences are moving fast. In this study, the non-stationary interference source is estimated during the period in which snapshots are taken. Then, a new interference-plus-noise covariance matrix reconstruction is introduced which is derived from a simplified power spectral density function that can be used to shape the directional response of the beamformer. Finally, the beamformer is designed to impose nulls towards the regions of the moving interference based on the reconstructed covariance matrix. The essence of the proposed method is to express the inverse of the reconstructed covariance matrix which needs less computational complexity calculation. The effectiveness of the proposed method is demonstrated by numerical results.

A mainlobe interference suppression method is proposed based on eigen-projection processing and covariance matrix reconstruction. In the proposed method, the eigen-projection matrix is calculated based on the eigenvector of mainlobe interference to suppress the mainlobe interference in received echo data. The interference covariance matrix is reconstructed after the eigenvalue of mainlobe interference is replaced by the average value of noise eigenvalues to eliminate the effect of mainlobe interference to adaptive weight vector. Finally, the output of adaptive beamforming is calculated by processed echo data and adaptive weight vector obtained based on reconstructed covariance matrix. Simulation results show that the proposed method can suppress the mainlobe interference effectively and achieve excellent performance .

The presence of mutual coupling usually causes space-time steering vector distortion for space-time adaptive processing (STAP) in airborne radar, thereby causing significant performance degradation. In this paper, a robust STAP approach was proposed against mutual coupling based on middle subarray clutter covariance matrix reconstruction. To address the space-time steering vector distortion caused by the mutual coupling, the training snapshots of middle subarray were obtained using the spatial-temporal selection matrix, and they were collected to compute the sample covariance matrix (SCM). Thus, the clutter-plus-noise covariance matrix (CNCM) of middle subarray was reconstructed by utilizing the clutter Capon spectrum of middle subarray to integrate over the possible clutter spatial-temporal domain. Moreover, the target covariance matrix of middle subarray was calculated by employing the target Capon spectrum of middle subarray to integrate over the possible target region, and the space-time steering vector of the target was estimated with the eigenvector corresponding to its maximum eigenvalue. Finally, the proposed robust STAP weight vector of middle subarray was built. The proposed method is capable of simultaneously mitigating the mutual coupling, target components in the SCM, and target space-time steering vector mismatch. The simulation results verified the effectiveness of the proposed approach.

Because the maximum radiation direction of the end-fire array antenna points to the axis of the array and the small element spacing required to suppress the grating lobes, the mutual coupling effect between the arrays is more serious than that of the broadside array. The article first established the end-fire array antenna pattern model and clutter signal model with the effect of mutual coupling. The clutter signal model includes two cases, ideal mutual coupling effect and mutual coupling error. On this basis, we take a ten-element uniform linear array using CST Microwave Studio to validate our model. Then we analyze the clutter distribution characteristics of the end-fire array airborne radar and the effect of mismatch on the spatial steering vector. Finally, an adaptive mutual coupling compensation method based on covariance matrix reconstruction is proposed. In general, clutter suppression methods with end-fire array take no account of the mutual coupling error changing over time, but the proposed method first adaptively estimates the mutual coupling error based on the airborne radar echo data and uses the estimated normalized impedance matrix to compensate the spatial steering vector, then combines the system parameters to construct the clutter covariance matrix. The simulations indicate that this method accurately estimate the impedance matrix, and it eliminates the clutter power reduction and spatial steering vector mismatch caused by mutual coupling error. Moreover, it also solves the serious non-stationary clutter problem of the end-fire array airborne radar.

In recent years, some iterative robust beamforming (RAB) algorithms using a fixed adaptive uncertainty level (Fu-IRAB) are proposed to overcome the SINR performance deterioration of the conventional RAB methods in the presence of large array steering vector (ASV) errors. However, more iteration steps are consumed before the actual steering vector is reached. This paper introduces a new adaptive beamformer based on the traditional DCRCB (doubly constrained robust capon beamformer using adaptive uncertainty level), by means of updating the uncertainty level adaptively that is proportional to the amount of the mismatch in each step, resulting in a faster convergence rate in comparison with the Fu-IRAB. In addition, a new robustness is provided to against the initial uncertainty level in the first iteration.

Acoustic environment has a low signal-to-noise ratio (SNR); hence, array signal processing is widely used for noise reduction and signal enhancement. The actual ambient noise includes uncorrelated noise and correlated noise. The received noises of the two arbitrary array elements are correlated. Consequently, the performance of array signal processing method decreases obviously. Aiming at this problem, the real-part elimination of covariance matrix method is proposed. Firstly, from a physical point of view, the noise signals can be generated by using a number of uncorrelated noise sources: the more the noise sources, the less the error between the noise from the model and the actual noise will be. Theoretically, the noise field is decomposed into the symmetrical noise field and the asymmetrical noise field. A number of noise sources generate the symmetrical noise fields; the directions of these noise sources are symmetric, and the powers of two arbitrary symmetric sources are the same. Secondly, the symmetry of the ambient noise is analyzed, as a result, the symmetrical noise can only affect the real part of the covariance matrix. Thirdly, the real part of covariance matrix is eliminated in order to reduce the noise, and then the delay-and-sum beamforming is achieved by using only the imaginary part. The advantages are that the output signal-to-noise ratio is increased and the noise output power is reduced obviously; the disadvantage is that it produces a false target. The azimuth of the actual target differs from that of the false target by 180, and the false target cannot be distinguished. Finally, to eliminate the false target, the real part of the signal covariance matrix is reconstructed by establishing a constrained optimization problem, which is solved by using the particle swarm algorithm. Then, the reconstructed covariance matrix composed of the imaginary part and the reconstruction of real part is applied to delay-and-sum beamforming, as a result, the false target is eliminated. The simulation results show that the real-part elimination of covariance matrix method reduces the symmetrical ambient noise, the noise output power is reduced, the output signal-to-noise ratio is increased, and this method improves the performance of array signal processing. The experimental results show that the output SNRs of two targets with using the imaginary part of covariance matrix are increased by 3.57 dB and 3.149 dB, respectively, and the output SNRs of two targets with using the reconstructed covariance matrix are increased by 7.027 dB and 6.985 dB, respectively. The real-part elimination of covariance matrix method is easy to implemente, and has a definite value for engineering application.

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.