Multiscale analysis of array and antenna farm problems

To keep explicit information about the multi-scale nature of the solution directly into the representation of the unknown fields/currents, two techniques are discussed in this paper: the synthetic basis function expansion (SFX); and the vector multi-resolution (MR) expansion. Both the SFX and MR approaches are applicable to general array geometries, e.g. for "printed" arrays with (possibly) different radiators, and general space layouts. With the use of MR, complexity is reducing by "thinning" (sparsifying) a (large) matrix. In an opposite way, SFX implements the multi-scale paradigm via a two-step procedure that results in reducing the number of unknowns, and thus "compressing" the MoM matrix into a much smaller size. These methods had been, in their basic traits, presented elsewhere and therefore in the next two sections they will be described only briefly, focusing on the common origins of the multi-scale issue and paradigm.