In recent years many techniques have been developed for the method of moments (MoM) efficient analysis of finite periodic antenna arrays. A first class of approaches is based on the infinite array solution with corrections for the truncation effects [1]-[3]. A second point of view relies on fast iterative methods in which matrix-vector products are accelerated by means of either multipole decompositions [4] or fast Fourier transforms. An alternative choice consists of assuming that the currents on a given antenna in the finite array can be decomposed in terms of a limited number of known current distributions, obtained through the solution of smaller problems. This idea has been found in many publications [5]-[6], where the "macro basis functions" (MBF) are also called "characteristic basis functions". Furthermore, macro basis functions and fast multipoles can be advantageously combined as done in [7] in order to reduce the computational cost of matrix reduction. As long as the radiating elements in the array are placed in a regular grid, we can take advantage of the aforementioned techniques. Nevertheless if the antennas are located in arbitrary positions the infinite-array approach is no longer relevant. Besides this, in this situation, multipoles have to be applied to each possible inter-element spacing, which involves much more operations than in the regular case. This paper deals with the formulation of an efficient technique for computing interactions between elements in antenna arrays with application to non-uniform antenna arrays. The approach relies on the combination of macro basis functions and on a novel interpolation technique explained in the next sections.
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