Multiscale analysis of array and antenna farm problems

Large, complex arrays and antennas mounted on complex platforms are among the most challenging modeling issues, since they involve both large structures (in terms of wavelength) and fine details that require much smaller than wavelength discretizations, and that dominate the frequency response of input parameters. The integral equation-method of moments (IE-MoM) approach cannot be used to attack these problems directly, since standard MoM techniques are severely limited by the matrix size and condition number involved in the problems of interest. A number of techniques have been presented in the past to overcome the these difficulties. We focus on two of these techniques that attempt to keep explicit information about the multiscale nature of the solution directly into the representation of the unknown fields/currents: 1) synthetic basis function expansion (SFX); 2) vector multiresolution (MR) expansion. Both the SFX and MR approaches are applicable to general array geometries, e.g. for "printed" or 3D arrays with (possibly) different radiators, and general space layouts. In addition, the SFX technique has recently been rendered efficient for the analysis of scattering problems as typically encountered in antenna farm issues aboard satellites or other complex platforms.