Multi-level spherical wave expansion for fast near-field to far-field transformation

Abstract

Traditional near-field to far-field transformation algorithms based on modal expansion are unable to deal with arbitrary measurement surfaces. To approach these problems, a matrix inversion method can be used to retrieve the spherical wave expansion (SWE) of the antenna under test (AUT) fields. Modeling the antenna with a set of multiple SWEs centered at arbitrary points over its surface offers a flexible approach for the solution of field transformation problems over arbitrary surfaces. The coefficients of each SWE are obtained using an iterative inversion approach where the matrix-vector products can be replaced by multilevel operators based on recursive aggregations and interpolations of the partial SWE fields, reducing the computational complexity from ?(?) to ? ? ? . The proposed algorithm is tested using synthetic data and measurements showing good scalability and reduced transformation error.