Robust minimum sidelobe beamforming in mode space for circular arrays

Beamformer with low sidelobe is important in many applications, but its performance will degrade in the presence of errors in sensor array characteristics, such as position, gain and phase errors. White noise gain constraint is always used to improve the robustness, but it is not clear how to choose the related parameters according to the given level of errors. The robust method based on worst-case performance optimization can use the a priori knowledge of the error levels, but not sufficiently. The bounds of the manifold vector uncertainty set cannot be easily obtained. In this paper, a feasible way is used to derive the bounds considering the errors in sensor array characteristics together, and then a robust minimum sidelobe beamforming method based on worst-case performance optimization in mode space for circular arrays is presented. This problem can be transformed to convex optimization and solved by second-order cone programming. Simulation results show the computation load of this method is effectively reduced and the results are more reliable.