Planar array synthesis with prescribed pattern nulls

A novel synthesis method for planar arrays that is applicable to polygonal arrays with a general triangular lattice is presented. The method fundamentally requires specification of pattern nulls which may be arbitrary and utilizes a two-dimensional convolution process and a four-element canonical array. The design procedure is noniterative and does not require separable illumination, but bas at least the same number of degrees of freedom as those methods relying on separable illumination. The method is illustrated through several examples of synthesis which include diamond, regular hexagonal, and stretched hexagonal arrays. The aperture illumination efficiencies of the designs are computed. Although only examples of sum patterns are shown, it may be used to synthesize difference patterns as well. Also the method can be used to synthesize optimal patterns in designated planes. The null synthesis method has an important advantage over other synthesis techniques. The algorithm for determining the array excitations is trivially different for different array boundaries and lattices and can be implemented on a small computer.