Extension of the Orchard-Elliott synthesis method to pure real non-symmetrical shaped patterns

The Orchard-Elliott (Orchard et al., 1985) method for the synthesis of linear antenna arrays is extended to enable the synthesis of pure real radiation patterns for non-symmetrical shaped beams. It is shown that an array of N elements, with 2M root off the unit circle, grouped in pairs, will result in a pure real pattern (field synthesis), satisfying the centre-fed constraint.