Estimation of the radiation pattern of finite arrays of waveguide-fed apertures from the transmitting characteristics of an isolated element

This work presents a simple method to estimate the radiation pattern of finite arrays of waveguide-fed apertures on an infinite ground plane. This method is based on the theory of Minimum-Scattering Antennas and the Generalized Scattering Matrix of a finite array in terms of spherical modes. Waveguide-fed apertures can be considered as short-circuited minimum-scattering antennas just in the aperture. This way, the scattering characteristics of an isolated aperture can be deduced from its transmitting properties if the reflection coefficient is known. Therefore, the generalized scattering matrix in terms of spherical modes of an isolated aperture can be obtained. Finally, the generalized scattering matrix of the finite array can be calculated by applying translation and rotation of spherical modes.