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A simple methodology is presented for the estimation and compensation of mutual coupling in antenna systems of arbitrary geometries, including antenna arrays in the vicinity of scatterers. The methodology includes both theoretical and experimental schemes, while also, does not resort to assumptions often encountered in previous mutual coupling estimation approaches. In particular, our methodology uses a matrix representation for the antenna system and is based on a new concept, the antenna current Green's function which uses the recently proven inverse reciprocity theorem, or more intuitively, a relation of the transfer function for the transmitting mode of the antenna system to the corresponding transfer function for the receiving mode. Validation is performed by comparing calculated predictions to measurements and simulations of a practical antenna system as well as a two- and four-element array. An algorithm using matrix interpolation, that aims at exploiting the antenna transfer function, is also developed and experimentally demonstrated for practical array calibrations and coupling compensation techniques in array signal processing. The developed procedures are non-specific and can also be applied to a diversity of antenna systems and other complex scattering problems.