Compressed Sensing for spherical near- to far-field transformation (CoSSTra)

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Due to diverse and increasing demands for antennas regarding bandwidth (e.g. for ultra-wideband antennas), radiation properties (e.g. for reconfigurable antennas) and high operating frequencies (e.g. for radar systems in the automobile sector), the complexity of antennas as well as their measurement efforts has increased greatly in recent years. In order to save time, often only partial measurements with a small selection of frequencies and antenna configurations are carried out. Particularly in the near-field, the long measurement period is a strong limiting factor. The reason for this is the high number of measurement points that have to be acquired in order to determine the transmission characteristics of an antenna with satisfactory accuracy. However, if the radiation of the antenna is described in terms of spherical waves, it turns out that in practice the relevant information is mostly concentrated in a few spherical wave coefficient.The project aims to bring together methods of compressed sensing with the theory of spherical near- to far-field transformation to enable subsampled antenna measurements on the sphere with minimal loss of accuracy. To this end, different approaches for signal reconstruction are initially considered to integrate structural properties of the spherical mode spectrum in existing solutions. Methods are developed that, based on prior knowledge about the antenna characteristics, provide information about selecting an optimal basis and restrict the search space of optimal solutions. For a reliable reconstruction of the subsampled signal, it is also necessary to select the required number of measurement points appropriately. For this purpose, it is studied which antenna characteristics lead to sparse mode spectra. Another part of the project aims at identifying appropriate sampling strategies on the sphere, enabling a robust reconstruction of the spherical modes. In this context, the as yet unexplored influence of the polarization angle on the reconstruction behavior is determined. An important part of the project aims at the identification of measurement uncertainties when using the new methods, which are determined by extensive analysis. An interesting method in this context is the so-called Bayesian Compressed Sensing which allows for obtaining confidence intervals for the calculated solutions during reconstruction. In the final step, the explored approaches will be verified on the basis of extensive measurements of various types of antennas.The research results should answer the question how compressed sensing can be used in the context of spherical near- to far-field transformation for subsampling of antenna measurements.