Revisiting Goto's Method: Stable Hexagonal Array Pattern Synthesis Via Recursive Spatial Mapping

Hexagonal planar arrays are widely utilized in radar and satellite communications due to their efficient aperture tiling and six-fold rotational symmetry. While the technique of Goto provides a theoretical framework to map 1D linear tapers onto hexagonal grids, its traditional implementation relies on closed-form binomial expansions that suffer from numerical instability for large-scale arrays. This letter proposes a robust alternative using Recursive Spatial Mapping. By treating the hexagonal mapping kernel as a discrete six-point spatial operator, the aperture excitations are synthesized via successive 2D convolutions. This approach improves efficiency eliminating factorial-based computations, ensures numerical stability for high-order arrays, and naturally preserves the triangular lattice geometry.