Robust Low Sidelobe Synthesis for Arbitrary Arrays Based on Gradient Ascent With Min-Oracle

This article studies the robust pattern synthesis of a narrow main beam and low sidelobes of arbitrary arrays, which represents a classical but challenging problem for array antennas. In addition, pattern synthesis for a given sidelobe envelope is discussed. The synthesis problem is formulated as a nonconvex–nonconcave minimax problem with nonconvex constraints, which avoids the design of the optimal desired pattern and ensures the robustness of pattern synthesis for arbitrary arrays by nonconvex constraints. An algorithm named gradient ascent with min-oracle (GAmin) is proposed to address the considered minimax problem. Furthermore, the majorization–minimization algorithmic framework is used to reduce computational complexity. It is shown that for arbitrary linear and planar arrays, the proposed GAmin-based pattern synthesis method can perform well for pattern synthesis both without and with a given sidelobe envelope. A variety of numerical examples are provided to demonstrate the superior performance of the proposed method.