ROBUST LCMP BEAMFORMER WITH NEGATIVE LOADING

The adaptive linearly constrained minimum power (LCMP) beamformer can improve the robustness of the Capon beamformer. And quadratic constraints on the weighting vector of the LCMP beamformer can improve the robustness to pointing errors and to random perturbations in sensor parameters. But how to solve it and how to select the constraint parameters are its key problems. In this paper, the Lagrange multiplier method is proposed to solve the LCMP beamformer under quadratic inequality constraint (QIC). The problem of finding the optimal weight vector is solved, and the choice of the quadratic constraint parameter is analyzed and the selected bound is also given. Since the quadratic equality constraint (QEC) is stronger than the quadratic inequality constraint (QIC), the performance of the QECLCMP beamformer is more robust than that of the QICLCMP beamformer. Therefore, the QECLCMP beamformer is proposed and is solved effectively. Numerical examples attest the correctness and the efficiency of the proposed algorithms. And the results show that the QECLCMP beamformer has the advantage of overcoming the steering vector mismatch, namely the optimal negative loading has the preferable robustness.