Square Kilometre Array Enhancement: A Convex Programming Approach to Optimize SKA-Low Stations in the Case of Perturbed Vogel Layout

This study presents a convex optimization framework for beam synthesis in Square Kilometre Array low-frequency radio telescope stations configured in a sunflower-like layout. The method minimizes the peak sidelobe level by computing an optimized set of beamforming weights, enabling precise control of the main beam while preserving angular resolution. The framework is validated through full-wave electromagnetic simulations based on detailed physical models of the antenna elements and station geometry. Compared to conventional beamforming employing constant unitary real weights, the optimized solutions yield a significant reduction in sidelobe levels, with only a minimal impact on directivity. These benefits are particularly evident at frequencies where mutual coupling between array elements is strong, confirming the suitability of the proposed approach for dense radio astronomy arrays.