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A proposed definition of antenna efficiency for contoured coverages

The efficiency of an antenna designed for maximum radiation towards a single direction (ie, pencil beam) is defined as the ratio between the antenna gain in that direction and the directivity, in that same direction, of an uniformly illuminated aperture with the same projected area. This definition indicates how well the performance of an actual design approaches an ideal antenna. However, antennas for contoured coverage currently do not have an associated ideal design. Therefore, the efficiency of contoured beams is often estimated by comparison to previous designs using some figure of merit (e.g., the gain integrated over the coverage area). However, this approach is subjective and non-rigorous, leaving the assessment of the antenna performance on uneasy ground. In this work we propose a rigorous method to determine the efficiency of contoured coverage antennas.