The present disclosure provides system and methods for optimizing the tuning of impedance elements associate with sub-wavelength antenna elements to attain target radiation and/or field patterns. Both static and variable (tunable) antenna systems may be manufactured. Static embodiments may be entirely passive in some embodiments. A scattering matrix (S-Matrix) of field amplitudes for each of a plurality of modeled lumped ports, N, may be determined that includes a plurality of lumped antenna ports, Na, with impedance values corresponding to the impedance values of associated impedance elements and at least one modeled external port, Ne, located external to the antenna system at a specified radius vector. Impedance values may be identified through an optimization process, and the impedance elements may be tuned (dynamically or statically) to attain a specific target radiation pattern.