Direct radiating array design via convex aperture synthesis, pareto front theory, and deterministic sampling [antenna designer's notebook

Abstract

A deterministic method for the design of direct radiating arrays for multibeam satellite applications is presented in the current work. The method embodies the following steps: First, we consider the problem of continuous aperture synthesis, subject to directivity-pattern mask constraints. We succeed in stating the problem as a convex magnitude antenna design that exhibits a second-order cone program form. The solution provides the optimum continuous aperture current-density distribution. Second, exploiting the optimum solution, analytical formulas, in the form of the Pareto front, are presented through which the proposed method determines the minimum number of radiating elements that must be used in the process of transforming the continuous aperture to an antenna array. Third, an effective deterministic sampling approach is contributed to produce a discrete array with the desired characteristics. Armed with the above, the current work provides a generalized framework for the design of direct radiating arrays for multibeam satellite applications. The method is validated by the provided design examples.