Mask Based Array Pattern Synthesis Via Subspace Relaxation and Levenberg–Marquardt Optimization

ABSTRACT Pattern synthesis based on complex masks remains challenging for optimization algorithms due to poor conditioning and slow convergence. To address this issue, this paper proposes SRLM, a novel pattern synthesis algorithm based on subspace relaxation and the Levenberg–Marquardt (LM) algorithm. The problem is formulated as a weighted nonlinear least‐squares (LS) problem in the amplitude domain, where array excitations are represented in a reduced null space basis consistent with the mask. The resulting problem is solved using LM. A subspace relaxation mechanism progressively enlarges the solution space, enabling fast initial shaping and refined global optimization. Whitening is applied as a preconditioner to improve conditioning and computational efficiency during the LM iterations. Numerical experiments demonstrate that the proposed SRLM algorithm is competitive with representative state‐of‐the‐art (SOTA) synthesis methods. In the low‐dimensional case, it achieves comparable pattern control performance while maintaining efficient and stable convergence. For high‐dimensional planar array synthesis, the algorithm exhibits robust performance across diverse scenarios, including stochastic constraints, irregular element layouts, and cases incorporating mutual coupling. Consequently, this study establishes a unified framework for high‐fidelity radiation pattern synthesis.