Design of multiply constrained beamformer via alternating direction method of multipliers

Design of high array gain beamformer with norm constraints on weight vectors and peak constraints on sidelobes is studied. In view of the difficulties in hardware implementation and high computational complexity of the traditional interior-point based optimization techniques, an alternating iterative method with multiple constraints is proposed. By introducing auxiliary variables to decouple norm constraints and sidelobe constraints, the multiply constrained optimization is transformed into two groups of singly constraint optimization problems. The analytical or approximate solutions of the optimization subproblem are provided. Theoretical analysis shows that the proposed method requires less computation since the computational complexity in one iteration is only quadratic polynomial compared with the existing interior point optimization algorithms. The proposed method is verified by both simulated and measured array manifold. The results show that the proposed method can provide the reasonable tradeoff among the sidelobe level, the array gain and the robustness of the sensor arrays.