Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch

It is well known that the performance of the minimum variance distortionless response (MVDR) beamformer is very sensitive to steering vector mismatch. Such mismatches can occur as a result of direction-of-arrival (DOA) errors, local scattering, near-far spatial signature mismatch, waveform distortion, source spreading, imperfectly calibrated arrays and distorted antenna shape. In this paper, an adaptive beamformer that is robust against the DOA mismatch is proposed. This method imposes two quadratic constraints such that the magnitude responses of two steering vectors exceed unity. Then, a diagonal loading method is used to force the magnitude responses at the arrival angles between these two steering vectors to exceed unity. Therefore, this method can always force the gains at a desired range of angles to exceed a constant level while suppressing the interferences and noise. A closed-form solution to the proposed minimization problem is introduced, and the diagonal loading factor can be computed systematically by a proposed algorithm. Numerical examples show that this method has excellent signal-to-interference-plus-noise ratio performance and a complexity comparable to the standard MVDR beamformer

A Robust Beamformer Based on Weighted Sparse Constraint

Applying a sparse constraint on the beam pattern has been suggested to suppress the sidelobe level of a minimum variance distortionless response (MVDR) beamformer. In this letter, we introduce a weighted sparse constraint in the beamformer design to provide a lower sidelobe level and deeper nulls for interference avoidance, as compared with a conventional MVDR beamformer. The proposed beamformer also shows improved robustness against the mismatch between the steering angle and the direction of arrival (DOA) of the desired signal, caused by imperfect estimation of DOA.Comment: 4 pages, 2 figure

Sidelobe Suppression for Capon Beamforming with Mainlobe to Sidelobe Power Ratio Maximization

High sidelobe level is a major disadvantage of the Capon beamforming. To suppress the sidelobe, this paper introduces a mainlobe to sidelobe power ratio constraint to the Capon beamforming. it minimizes the sidelobe power while keeping the mainlobe power constant. Simulations show that the obtained beamformer outperforms the Capon beamformer.Comment: 8 pages, 2 figure

Performance analysis of beamformers using generalized loading of the covariance matrix in the presence of random steering vector errors

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. In this paper, we present a theoretical analysis of the signal-to-interference-plus-noise ratio (SINR) for the class of beamformers based on generalized (i.e., not necessarily diagonal) loading of the covariance matrix in the presence of random steering vector errors. A closed-form expression for the SINR is derived that is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR

Performance analysis for a class of robust adaptive beamformers

Robust adaptive beamforming is a key issue in array applications where there exist uncertainties about the steering vector of interest. Diagonal loading is one of the most popular techniques to improve robustness. Recently, worst-case approaches which consist of protecting the array's response in an ellipsoid centered around the nominal steering vector have been proposed. They amount to generalized (i.e. non necessarily diagonal) loading of the covariance matrix. In this paper, we present a theoretical analysis of the signal to interference plus noise ratio (SINR) for this class of robust beamformers, in the presence of random steering vector errors. A closed-form expression for the SINR is derived which is shown to accurately predict the SINR obtained in simulations. This theoretical formula is valid for any loading matrix. It provides insights into the influence of the loading matrix and can serve as a helpful guide to select it. Finally, the analysis enables us to predict the level of uncertainties up to which robust beamformers are effective and then depart from the optimal SINR

Quaternion-valued robust adaptive beamformer for electromagnetic vector-sensor arrays with worst-case constraint

A robust adaptive beamforming scheme based on two-component electromagnetic (EM) vector-sensor arrays is proposed by extending the well-known worst-case constraint into the quaternion domain. After defining the uncertainty set of the desired signal׳s quaternionic steering vector, two quaternion-valued constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the so-called second-order cone (SOC) programming method. It is also demonstrated that the proposed algorithms can be classified as a specific type of the diagonal loading scheme, in which the optimal loading factor is a function of the known level of uncertainty of the desired steering vector. Numerical simulations show that our new method can cope with the steering vector mismatch problem well, and alleviate the finite sample size effect to some extent. Besides, the proposed beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) and the quaternion Capon (Q-Capon) beamformers in all the scenarios studied, and achieves a better performance than the traditional diagonal loading scheme, in the case of smaller sample sizes and higher SNRs