Low-Sidelobe Shaped-Beam Pattern Synthesis With Amplitude Constraints

The paper deals with the low-sidelobe shaped-beam pattern synthesis (SBPS) problem under amplitude constraints, including the controllable dynamic range ratio (DRR) and the predetermined excitation amplitude. The formulated problem is nonconvex owning to the existing nonconvex constraints. To this end, a set of auxiliary variables are introduced to reformulate the original problem, and then a double-loop iterative algorithm based on the penalty dual decomposition method (PDD) framework is proposed. The proposed approach solves the reformulated problem by updating primal variables with block successive upper-bound maximization (BSUM) algorithm in the inner loop and updating the dual variables and penalty parameter with the constraint violation strategy in the outer loop. One important advantage of the proposed approach is that all of its subproblems have closed-form solutions, which guarantees that the reformulated problem can be effectively solved. Numerical simulations are carried out to validate the proposed approach’s superiority with both isotropic element pattern and active element pattern. The results show that the proposed approach can obtain a lower sidelobe level (SLL) and a smaller DRR when compared with the state-of-art approaches.