Robust adaptive beamforming under quadratic constraint

In this paper, a adaptive weighted computation algorithm based on quadratic constraint for a robust array antenna is presented to improve the shortcoming of linearly constrained adaptive beamformer´s sensitivity to the mismatch between the prescribed and actual direction of arrival (MPDOA). The quadratic constraint is added to the weighted least squared error between the desired and the actual beam patterns over a small region near the array steering direction, which will make the array less sensitive to the steering vector errors and nonstationary data snapshots. A new efficient and accurate approximation of the continuous direction range integration is derived and an equivalent inequality constraint is given, then the Lagrange multiplier method and the Newton´s method are united to solve the equivalent equality constrained minimization problem. The computer simulation results show that the proposed beamformer in the robustness has a superior performance against MPDOA with high SINR (nearest to the optimum).