  A new methodology for the design of isophoric thinned arrays with a priori
controlled pattern features is introduced. A fully analytical and general
(i.e., valid for any lattice and set of weights) relationship between the
autocorrelation of the array excitations and the power pattern samples is first
derived. Binary 2-D sequences with known autocorrelation properties, namely the
difference sets (DSs), are then chosen as a representative benchmark to prove
that it is possible to deduce closed-form synthesis formulas that a priori
guarantee to fit requirements on the sidelobe level (SLL), the directivity, the
half-power beamwidth, and the power pattern in user-defined directions. The
selected results from a wide numerical assessment, which also includes
full-wave simulations with realistic radiators, are illustrated to validate the
reliability and the accuracy of the proposed design equations and the
associated performance bounds.
