An antenna system , comprising: an antenna array including: a substantially conically-shaped face ; a plurality of radiating elements formed in the substantially conically-shaped face; a plurality of feed delay lines coupled respectively to each of the plurality of radiating elements in the substantially conically-shaped face; a phase shifter associated with each feed delay line; an array aperture face ; a plurality of radiating elements formed in the array aperture face, each respectively coupled to one of the feed delay lines; and a phase shifter controller and algorithm configured to produce a non-periodic phase modulation across the antenna array; wherein: the array aperture face is a substantially flat array aperture face opposite to the substantially conically-shaped face; one of the plurality of radiating elements is formed in the array aperture face for each of the feed delay lines such that each feed delay line connects one of the plurality of radiating elements formed in the substantially conically-shaped face to one of the plurality of radiating elements formed in the array aperture face to form a radiating element pair ; and the plurality of feed delay lines each have an effective dielectric constant and length configured to provide a progressive phase delay to each radiating elements pair. a substantially conically-shaped face ; a plurality of radiating elements formed in the substantially conically-shaped face; a plurality of feed delay lines coupled respectively to each of the plurality of radiating elements in the substantially conically-shaped face; a phase shifter associated with each feed delay line; an array aperture face ; a plurality of radiating elements formed in the array aperture face, each respectively coupled to one of the feed delay lines; and a phase shifter controller and algorithm configured to produce a non-periodic phase modulation across the antenna array; wherein: the array aperture face is a substantially flat array aperture face opposite to the substantially conically-shaped face; one of the plurality of radiating elements is formed in the array aperture face for each of the feed delay lines such that each feed delay line connects one of the plurality of radiating elements formed in the substantially conically-shaped face to one of the plurality of radiating elements formed in the array aperture face to form a radiating element pair ; and the plurality of feed delay lines each have an effective dielectric constant and length configured to provide a progressive phase delay to each radiating elements pair. the array aperture face is a substantially flat array aperture face opposite to the substantially conically-shaped face; one of the plurality of radiating elements is formed in the array aperture face for each of the feed delay lines such that each feed delay line connects one of the plurality of radiating elements formed in the substantially conically-shaped face to one of the plurality of radiating elements formed in the array aperture face to form a radiating element pair ; and the plurality of feed delay lines each have an effective dielectric constant and length configured to provide a progressive phase delay to each radiating elements pair. <EOS>