Pattern synthesis of sparse linear arrays based on the atomic norm minimization and alternating direction method of multipliers approach

Abstract

To address the mesh mismatch issue and enhance array performance, this paper proposes a design algorithm for sparse reconfigurable linear arrays based on the ANM-ADMM framework. Initially, the algorithm formulates a meshless sparse optimization model grounded on the low-dimensional semidefinite programming theory of atomic norm minimization. This model simultaneously optimizes the quantity of array elements, their placements, and their excitations. Subsequently, an efficient iterative algorithm solves the low-rank Toeplitz matrix using the alternating direction method of multipliers (ADMM). Finally, the Root-MUSIC algorithm is employed to determine the locations and excitations of the array components in the sparsely reconfigurable linear array, which is designed using the ANM-ADMM approach. Since the proposed algorithm operates in a continuous domain, it effectively addresses the mesh mismatch problem, thereby enhancing the matching accuracy of reconstructed linear array beampatterns. Simulation results demonstrate that compared to existing algorithms, the proposed method requires fewer array elements while achieving higher matching accuracy and better fitting performance.