Flat-Top Footprint Pattern Synthesis Through the Design of Arbitrary Planar-Shaped Apertures

The problem of generating a flat-top main beam with an arbitrary footprint for array elements placed in an arbitrary planar aperture is considered in this paper. Some simplifying properties of the Bessel functions, encourages the general framework of the paper to encompass patterns produced by circular aperture and eventually generalize it to arbitrary aperture geometries. In this regard two synthesis methods are presented. The first method is based on the use of the Rayleigh quotient to obtain constant phase array patterns, hence, a class of generally linear phase patterns can be considered. The second approach is based on power pattern synthesis where there is no restriction on the phase of the pattern, hence, it provides us with greater flexibility. The nonlinear problem is appropriately modeled and formulated for amenable performance. These two new methods can exhibit a significant reduction in the number of unknown parameters, and high flexibility in shaping the desired main beam by arbitrary lattice geometry.