Robust Beamforming with Sidelobe Suppression for Impulsive Signals

Beamforming is a fundamental technique in array signal processing. Many existing approaches are based on second-order statistics. However, their performance degrades significantly due to outliers in the received signal. In this letter, we propose an outlier-resistant beamformer design criterion based on minimizing the expectation of the modulus of the array output with an ${\ell _1}$-regularization term being added for sidelobe suppression. By using the ${\ell _1}$-modulus of complex numbers instead of the standard modulus, the resulting optimization problem can be efficiently solved by a simple iterative algorithm or linear programming. Simulation results in the presence of impulsive signals are provided to demonstrate its robustness and accuracy compared to existing techniques.