Synthesis of $L_{1}$ Pencil Beams with Constrained Sidelobe Level and Dynamic Range Ratio

Optimization-based methods for pencil-beam design often incorporate controlling the dynamic range ratio (DRR) of excitation coefficients. However, constraining the DRR causes the deterioration of sidelobe region, in which some lobes may rise and even exceed design specifications. To prevent such behavior, additional requirement can be specified to constrain maximum sidelobe level (SLL). This paper presents a global design of pencil beams with specified DRR and SLL. The design is based on branch and bound method that utilizes convex optimization and feasibility analysis for tree pruning. As a case study, the paper considers design of pencil beams optimum in
$L_{1}$
-sense to which DRR and SLL constraints are added. The resulting beam patterns exhibit low DRRs and decreasing side lobes.