Compressed Sensing in the Spherical Near-Field to Far-Field Transformation

Abstract

AbstractA way to improve the measurement speed of spherical near-field antenna measurements is by reducing the number of acquisition samples, since the typical sampling scheme used for such measurements is heavily oversampled. However, several problems arise when reducing the sampling points, since the lack of a priori knowledge of the radiation characteristics complicates the choice of the points that do, in fact, contain information. Additionally, the consideration of sparsity of the spherical mode coefficients, the coefficients containing the information about the radiation characteristics of the antenna, is done, which allows using techniques from compressed sensing. Considering compressed sensing as the tool to address these problems requires a transformation of the problem into a linear system of equations and the construction of a sensing matrix from the sampled basis functions that are used in spherical near field, which are spherical harmonics and Wigner D-functions. Still, the reduction of measurement points does not automatically guarantee a reduction in measurement time, since considerations on the mechanical speed at which the data points can be acquired come into play. For this reason, a geometrical constraint is introduced for the resulting sampling scheme, and its reconstructability is evaluated in terms of the mutual coherence of the sensing matrix. In the end, the implementation of the proposed method in real antenna measurements is presented and extended to arbitrary surfaces, while the possibilities of application of similar approaches to the domain of phaseless near-field measurements are discussed.