Many of the available array synthesis procedures require the prescription of bath amplitude and phase of the sought pattern and therefore can be labelled as field synthesis procedures, in contrast to the power synthesis ones, in which Only the field amplitude is prescribed. If the array is formed by equal elements with a fixed geometry, only the excitations must be determined. Aim of this work is to find an efficient solution to the array power synthesis involving null field constraints in the near-field (NF) region. The null field constraints in near-field are introduced in the synthesis process to avoid the interaction between the array and the surrounding environment and to prevent electromagnetic (em) compatibility troubles. In a recent mock [1], the solution of the considered problem was found as intersection between a subset of the set B of all far-field patterns which can be radiated by the array and the set M of all functions fulfilling the patters requirements. The alternating projection method was employed to this end in analogous way as in [2]. In particular, in [1] the null field constraints in the volume were imposed at the sampling points fixed according to the results relevant to the 3-D sampling representations of em fields. This allowed a considerable reduction of their number with respect to the classical λ/2 spacing. Now the null field constraints are imposed on the spherical surface enclosing the considered volume (see Fig. 1). In fact, as a consequence of the uniqueness theorem, if the tangential components of the em field on a closed surface external to the sources are zero, the field is null in the enclosed volume. It is clear that the number of constraints can be remarkably reduced by imposing the annulment of the field tangential components at the sampling points fixed by the nonredundant field representation on a spherical surface external to the sources [3].
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