Robust Capon beamformer under norm constraint

In order to improve the robustness against the array steering vector mismatch, the norm constraint on the weight vector is used. By the complete investigation on the Capon beamformer under norm inequality constraint (NICCB), the existence of its solution is analyzed in detail, the choice of the norm inequality constraint parameter for NICCB is analyzed and the selecting range is given. In this paper, the Capon beamformer under norm equality constraint (NECCB) is also proposed and is solved effectively. At the end, numerical examples attest the correctness of the theory, and show that when the norm constraint parameter is selected in the allowable range, the performances of the optimal NICCB and NECCB vary unobvious, but for the same given norm constraint parameter, NECCB has the better performance than NICCB, namely the optimal negative loading that has the preferable robustness.