<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The formulation of the generalized scattering matrix (GSM) of a finite array is revised to take into account the feeding network effects in the calculation of the external mutual coupling. It allows the analysis of finite arrays of externally coupled elements whose radiated field can be described by means of spherical waves on a ground plane, such as apertures, monopoles, cavity-backed patch antennas, or dielectric resonator antennas (DRAs), including rigorously the mismatching and internal coupling effects because of the feeding network. </para>