Robust Adaptive Beamforming with Sparse Constraint via Semidefinite Relaxation

This paper proposes a robust adaptive beamforming method based on the l
1
norm sparse constraint. The solution of this algorithm involves introducing the l
1
norm to find better beamforming weight vectors. To control the sidelobe level, the power constraint in the Direction of Arrival (DOA) of the Signal of Interest (SOI) is relaxed. We reformulate the adaptive beamforming problem as a Quadratic Constraint Quadratic Programming (QCQP) with an l
1
norm constraint, achieving better sparsity. The QCQP problem is solved using semi-definite relaxation. The beam pattern generated by the proposed algorithm exhibits low sidelobes and excellent robustness. Simulation results validate the effectiveness of the proposed adaptive beamforming algorithm.