Efficient implementation of robust adaptive beamforming based on worst-case performance optimisation

Traditional adaptive beamforming methods undergo serious performance degradation when a mismatch between the presumed and the actual array responses to the desired source occurs. Such a mismatch can be caused by desired look direction errors, distortion of antenna shape, scattering due to multipath, signal fading as well as other errors. This mismatch entails robust design of the adaptive beamforming methods. Here, the robust minimum variance distortionless response (MVDR) beamforming based on worst-case (WC) performance optimisation is efficiently implemented using a novel ad hoc adaptive technique. A new efficient implementation of the robust MVDR beamformer with a single WC constraint is developed. Additionally, the WC optimisation formulation is generalised to include multiple WC constraints which engender a robust linearly constrained minimum variance (LCMV) beamformer with multiple-beam WC (MBWC) constraints. Moreover, the developed LCMV beamformer with MBWC constraints is converted to a system of nonlinear equations and is efficiently solved using a Newton-like method. The first proposed implementation requires low computational complexity compared with the existing techniques. Furthermore, the weight vectors of the two developed adaptive beamformers are iteratively updated using iterative gradient minimisation algorithms which eliminate the estimation of the sample matrix inversion. Several scenarios including angle-of-incidence mismatch and multipath scattering with small and large angular spreads are simulated to study the robustness of the developed algorithms.