A new approach to adaptive beamforming with sidelobe control is developed. The proposed technique represents a modification of the popular minimum variance distortionless response (MVDR) beamformer. It minimizes the array output power while keeping the distortionless response in the direction of the desired signal and, at the same time, maintaining the sidelobe level which is strictly guaranteed to be lower than some given (prescribed) value. Multiple quadratic inequality constraints are used outside the mainlobe beampattern area to maintain the prescribed sidelobe level. The resulting modified MV[)R problem is shown to be convex and its second-order cone (SOC) formulation is obtained which enables to implement our beamformer in a computationally efficient way using the interior point method.
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