Investigation of the Sum-Difference Beampatterns Using the Quadratic U Distribution

This work examines the quadratic U distribution, a unique convex quadratic function for the application of distributed antenna arrays. The analysis applies a fitting phase coefficient for the elements, such that the radiated signal power of each element is coherently added in the far-field region of a specified target direction with net destructive interference occurring in all other regions to suppress sidelobe behavior. The analysis also applies characteristic modal solutions in which element radiators are used independently to deliver both sum and difference beams. Sum-difference radiation patterns are generated and analyzed for suitability in applications such as amplitude monopulse scanning, the direction of arrival estimation, and target tracking. We observe that the inherent randomness of the antenna array distribution alleviates typical half-wavelength spacing requirements for grating-lobe-free scanning. Tapering of the pattern is accomplished by confining the distribution to a quadratic U or convex probability topology.