Adaptive beamforming with sidelobe control: a second-order cone programming approach

A new approach to adaptive beamforming with sidelobe control is developed. The proposed beamformer represents a modification of the popular minimum variance distortionless response (MVDR) beamformer. It minimizes the array output power while maintaining the distortionless response in the direction of the desired signal and a sidelobe level that is strictly guaranteed to be lower than some given (prescribed) threshold value. The resulting modified MVDR problem is shown to be convex, and its second-order cone (SOC) formulation is obtained that facilitates a computationally efficient way to implement our beamformer using the interior point method.