Shaped Beam Synthesis of Real Antenna Arrays via Finite-Element Method, Floquet Modal Analysis, and Convex Programming

A shaped beam synthesis methodology for planar arrays with control of the ripple amplitude in the shaped region, and constraints on the sidelobe and cross-polar levels, is proposed in this paper. A previously developed synthesis formulation for designing finite impulse response (FIR) filters by transforming a nonconvex synthesis problem to a convex optimization scheme enforcing conjugate symmetric excitation weights, is extended to real and coupled radiating elements of complex geometry, taking into account mutual coupling effects. The optimization procedure is integrated with a finite array approach simulating different array environments. This approach is based on the infinite array model through a Floquet modal- and general scattering matrix (GSM)-based analysis, where the periodic radiating element is characterized from a hybrid and full-wave analysis procedure combining the FEM, modal analysis, and domain decomposition technique. Numerical results of different synthesized beam patterns are presented for arrays of open-ended apertures and microstrip antennas.