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In antenna array design, low dynamic range ratio (DRR) of excitation coefficients is important because it simplifies array’s feeding network and enables better control of mutual coupling. Optimization-based synthesis of pencil beams allows explicit control of DRR. However, incorporating DRR into an optimization problem leads to nonconvex constraints, making its solving challenging. In this paper, a framework for global optimization of linear pencil beams with constrained DRR is presented. By using this framework, the methods for synthesis of pencil beams with minimum sidelobe level and minimum sidelobe power are developed. Both methods utilize convex problems suitable for the synthesis of pencil beams whose coefficients’ signs are known in advance. By incorporating these problems into a branch and bound algorithm, the procedures for global optimizations are formed which systematically search the space of all coefficient signs. The method for minimization of sidelobe power is further analyzed in the context of beam efficiency. It is shown that this method can be utilized in an approximate and at the same time global design of pencil beam arrays with maximum beam efficiency and constrained DRR. Based on this approach, a method for the design of pencil beam arrays with minimum DRR and specified beam efficiency is proposed.

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