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

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