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.