Quaternion-based worst case constrained beamformer based on electromagnetic vector-sensor arrays

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 quaternionic domain. After defining the uncertainty set of the desired signal´s quaternionic steering vector, two quaternion-based constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the second-order cone (SOC) programming approach. Numerical simulations show that our quaternion-based robust beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) beamformer and the quaternion Capon (Q-Capon) beamformer in the presence of steering vector mismatches.