Robust array pattern synthesis with uncertain manifold vector

The knowledge of the array manifold vectors of an acoustic array can be imprecise, which is often the case in practice. This may cause undesirably high sidelobes for a nominal optimal beamformer where the array manifold vectors are assumed to be known exactly. Although the norm constraint on beamformer weights can be imposed to improve the robustness of the optimal beamformer, it is not clear how to choose the optimal constrained parameter based on the known level of uncertainty of the array manifold vectors. A pattern synthesis approach to arbitrary arrays with robustness against array manifold vectors errors is developed. Our technique optimizes the worst-case performance by minimizing the worst-case sidelobe level while maintaining a distortionless response to the worst-case signal steering vector. The parameters can be optimally chosen based on the uncertainty of the array manifold vector. The robust beamformer problem is shown to be convex, which can be efficiently solved using second-order cone programming. A simple lower bound on how much worse the robust optimal beamformer will be compared to the nominal one is also derived. Computer simulations show better performance of the proposed robust beamformer.