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We study the characteristics and radiation mechanism of antenna superstrates based on closely located periodical grids of loaded wires. An explicit analytical method based on the local field approach is used to study the reflection and transmission properties of such superstrates. It is shown that as a result of proper impedance loading there exists a rather wide frequency band over which currents induced to the grids cancel each other, leading to a wide transmission maximum. In this regime radiation is produced by the magnetic dipole moments created by circulating out-of-phase currents flowing in the grids. An impedance matrix representation is derived for the superstrates, and the analytical results are validated using full-wave simulations. As a practical application example we study numerically the radiation characteristics of dipole antennas illuminating finite-size superstrates.