A Global-Local Synthesis Approach for Large Non-Regular Arrays

A method is proposed for the synthesis of large planar non-regular arrays assuming constant magnitude for the excitation of the elements. The approach, which combines global and local optimization, is based on distinguishing aperture-type and non-coherent parts of the array factor. The following constraints are considered: minimal separation of the antennas, maximum size of the array and fixed mainbeam width. The level of the sidelobes is reduced via the minimization of a new type of flexible averaging cost function based on an Lp-norm. Possible applications of this model lie in the field of radio astronomy, satellite communications and radar systems. The proposed optimization strategy consists of three successive steps designed to be independent of each other. Starting with an equivalent continuous aperture, the first two steps act as global transformations of the radial and azimuthal positions of the elements in the initial array, while the third step performs a local optimization of individual elements of the array. This last step heavily relies on computations of the gradient of the cost function, which can be done quickly using an FFT-based procedure. The method is illustrated for several large-scale examples by considering as inputs four different types of non-regular arrays.