Determination of the far-field radiation pattern of an antenna from a set of sparse near-field measurements

Abstract

This work introduces a new technique in electromagnetic antenna near-field to far-field transformation (NF/FF). The NF/FF transformation is based on the solution of an inverse problem in which the measured NF and predicted FF values are attributed to a set of equivalent electric and magnetic surface currents which lie on a convex arbitrary surface that is conformal to the antenna under test (AUT). The NF points are conformal to the AUT, reducing the number of samples and relaxing positioning requirements used in conventional spherical, cylindrical and planar NF/FF geometries. A pseudo inversion of the matrix representing the mapping of the equivalent sources into the near-field samples is obtained by using the singular value decomposition (SVD). The SVD is used to form an approximation of the inverse of the matrix. This inverse, when multiplied by the NF measurement vector, solves for the efficiently radiating components of the current, and not the essentially non-radiating components of current which are not visible in the measurements. The inversion technique used is robust in the presence of measurement noise and provides a stable solution for the unknown currents. The FF is computed from the currents in a straightforward manner. The work develops the theoretical foundation for the approach and investigates the FF reconstruction accuracy of the technique for a test case.