Closed-form solution for integral operators applied to the calculation of radiated fields from parabolic reflector antennas

An approach based on the well-known aperture method is employed to develop a closed-form (asymptotic) solution for integral operators related to the radiation from parabolic reflector antennas. Such operators, expressed in the time domain (step and impulse responses), allow the determination of the antenna radiated fields for a source with an arbitrary temporal behavior and can be very useful in the analysis of parabolic reflector antennas designed for operation in high capacity (digital) communication systems. In order to show the applicability of the method introduced in this work, numerical results have been obtained for antennas designed to radiate a 4-PSK signal.