Radiation Efficiency Cost of Optimal Current Density Generating Specific Far-Field Pattern

This paper addresses the question of how closely can a prescribed far field be generated by the current density optimal in radiation efficiency. Two types of current optimization problems are introduced and solved with the tools of convex programming. The theory is demonstrated in several examples utilizing in-house software tools. The complexity of the problems is discussed, showing that the complete problem, including an unspecified phase of the desired far field, is an NP-hard problem, requiring one of the iterative approaches known in the literature.