Quaternion-valued robust adaptive beamformer based on widely linear processing

The quaternion-valued robust adaptive beamforming (QRAB) problem with electromagnetic vector-sensor arrays is investigated based on the widely linear processing (WLP) model, which can fully exploit the second-order statistics of array quaternionic outputs to guarantee a versatile ability to tackle the steering vector mismatch problem in the context of both proper and improper signals. In detail, two QRAB algorithms are presented by adopting the well-known criterions of worst-case performance optimization and principal eigenspace projection. The former one formulates the augmented steering vector as belonging to a quaternion-valued uncertainty set and then involves a constrained optimization problem, which can be transformed into a solvable real-valued convex form; while the latter one just needs to apply the quaternionic eigenvalue decomposition (QEVD) to the augmented covariance matrix with reduced computational complexity. Simulation results verify the effectiveness of the proposed schemes and show their superior performance as compared to the conventional QRAB schemes.