Optimal synthesis of wideband shaped-beam array antenna through convex optimization

A linear-programming (LP) framework is introduced for the synthesis of wideband shaped-beam patterns produced by uniform linear arrays (ULAs). The single-frequency feasibility-based LP formulation is extended to a multi-frequency power mask by sampling the normalized spatial frequency on a joint frequency-angle grid. Two hybrid escalation-bisection algorithms are then proposed to identify, with a small number of LP solves, the maximum fractional bandwidth (FBW) compliant with arbitrary upper/lower mask bounds. The non-uniqueness of the spectral factorization recovering the excitations from the synthesized autocorrelation polynomial is exploited: among the admissible solutions, the candidate minimizing the dynamic range ratio (DRR) is selected, yielding a hardware-friendly excitation taper at no additional optimization cost. Numerical results, including flat-top and cosecant-squared masks, are reported to validate and assess the proposed synthesis method.