Robust beamforming with quadratically constrained array directivity

To improve the robustness of the Minimum Variance Distortionless Response (MVDR) beamforming to the array steering vector,a quadratic constraint method is proposed.The weighted least squared error between the actual beam pattern and the desired beam pattern over a small region around the array steering direction is constrained.As a result,the signals coming from the directions near the steering angle will suffer the least distortion,and the interferences outside the constrained area can still be suppressed.Numerical results show that whether there are array perturbations or not,the array output Signal-to-Interference-Plus-Noise-Ratio (SINR) using our proposed method and the recently occurred spherical constraint robust Capon's beamforming (RCB-Sphere) is close to each other,but when exists look direction mismatch,our method outperforms the latter.