Optimal Synthesis of Sum and Difference Patterns with Arbitrary Sidelobes

A new approach to the power synthesis of fixed-geometry reconfigurable linear arrays radiating sum and difference patterns via uniformly spaced arrays with a number of common excitations is presented and assessed. The proposed technique makes use of the property that an inverse Fourier transform relationship exists between the array factor and the element excitations for a linear array with periodic spacing of the elements. This property is used in an iterative way to derive the array element excitations from the prescribed array factor to manage arbitrary and different bounds concerning radiation performance (field slope, amplitude, or even directivity) of the couple of patterns while sharing part of the feeding network. A set of numerical examples are reported and discussed to support the underlying theory and to show potentialities and features of the arising procedure.