A linear aperture radiating maximum power within prescribed angular constraints

For fixed aperture size, the aperture taper which maximizes the power radiated into a specified interval (-\theta_{0},\theta_{0}) is determined, and the properties of the corresponding pattern are compared to the ideal space pattern introduced by Taylor [1]. We consider the case of the linear aperture with no supergaining, although the results are directly applicable to the principal plane patterns of the two dimensional rectangular aperture. It is shown that for an aperture of widtha, as (\pi\alpha/\lambda)sin \theta_{0}increases, one can not only maximize the power radiated into (-\theta_{0},\theta_{0}), but also constrain the sidelobe ratio outside (-\theta_{0},\theta_{0}) below a specified value.