Response Vector Constrained Robust LCMV Beamforming Based on Semidefinite Programming

Although linearly constrained minimum variance (LCMV) beamforming is robust against imprecise target information, it usually leads to relatively high sidelobe and distorted mainlobe which would induce a high false alarm probability. To circumvent this problem, this work devises a novel robust LCMV beamforming approach by utilizing response vector optimization. It intends to find the optimal response vector in lieu of the all-one response vector in traditional LCMV beamformer. The proposed robust beamformer is first formulated as a nonconvex quadratically constrained quadratic programming problem, and then transformed into a semidefinite programming problem which can be efficiently and exactly solved. The proposed beamformer not only improves the performance in terms of signal-to-interference-plus-noise ratio substantially, but also possesses low sidelobe and well-maintained mainlobe. Moreover, since the response vector is quite small in size, the complexity of calculating the optimal response vector is negligible. Additionally, the proposed beamformer is also extended to two-dimensional space-time adaptive processing. Simulation results are presented to demonstrate the superiority of the proposed approach.