Comparison of the Quadratic U and Inverse Quadratic U Sum-Difference Beampatterns

This work examines and compares the radiative behavior of the quadratic U and vertically-inverted quadratic U distribution, both unique convex quadratic functions for the application of distributed antenna arrays. The comparison of the two analogous distributions demonstrated that the beamwidth of the random array relies on how the element population is either clustered or dispersed. Furthermore, this behavior occurs for both characteristic modal solutions in which element radiators are used independently to deliver both sum and difference beams. The quadratic U distribution raises sidelobe levels, and its inverse lowers sidelobe levels. By the same token this applies to a tapered aperture distribution where energy is seen to be removed by the mainbeam, increasing sidelobe levels or oppositely lowering sidelobe levels, but increasing mainbeam width. Thus, a trade-off applies to mainbeam width and its corresponding sidelobe levels. Simulated results for the quadratic U and inverted quadratic U with comparison on beamwidth and sidelobe levels conclude this paper.