Synthesis of Sparse Planar Antenna Arrays Using a Matrix Constraints Method

Sparse arrays have gained increasing research attention due to their potential to reduce system cost and weight. However, current studies on sparse array synthesis often overlook the physical dimensions of the antennas and only consider the distance constraints of antenna centers. In this communication, we propose a novel matrix constraints (MCs) method for the sparse planar array synthesis, taking into account the actual area occupied by each antenna unit. The proposed method introduces a matrix that relates the aperture lattices to each candidate antenna; this matrix is then used as a spatial constraint for the antennas. The synthesis problem, aimed at achieving a low sidelobe level, is formulated as a mixed-integer optimization problem under this MC. To obtain the array layouts efficiently, the synthesis problem is relaxed to a compressed sensing (CS) problem and subsequently solved using a combination of reweighted
$l_{1}$
minimization convex optimization and the integer genetic algorithm (IGA). Numerical experiments and full-wave simulations were conducted, verifying the effectiveness of the proposed method.