A robust beamformer with main beam control

In this paper, a new robust beamforming approach which is capable of accurately controlling the main beam response is proposed. In this method, steering vector uncertainties are taken into account in the beamformer design problem with array magnitude response constraints. This allows us to control the main beam as prescribed. However, the resultant non-convex problem has a different formulation from that of the existing methods for robust beamforming with magnitude response constraints. Thus, existing techniques cannot be applied directly. To cope with this problem, the lower and upper norm bounds of the beamformer weight vector are first derived. The semidefinite relaxation technique is then employed as an approximate solver ending up with a grid search solution. Simulation results show that the proposed method is able to accurately control the main beam magnitude response in the presence of steering vector uncertainties.