Sensing Strategies for Spherical Phaseless Antenna Measurements (S³PAM)

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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. Furthermore, in order to compute the spherical wave coefficients from the near-field measurements, both amplitude and phase are necessary. However, phase measurements imply the use of expensive equipment, e.g., network analyzer, and rely on the assumption of having access to the reference phase, which is, for example, not the case in over the air measurement scenarios. For these reasons, there is a great interest in the development of phaseless measurement setups.The project aims to bring together mathematical methods of phase retrieval and compressed sensing with the theory of spherical near- to far-field transformation to enable phase-less (subsampled) antenna measurements on the sphere with minimal loss of accuracy. To this end, we extend theory on existing sampling strategies to respect all involved rotation angles and to obtain improved sampling patterns. We suggest phase-less antenna measurements operable in practice and relate them to theoretical developments on signal recovery from phase-less measurements by established algorithms. This connection is used to obtain in context of spherical near- to far-field transformation the first reconstruction guarantees for a number of sampling points close to information theoretical limits, hence, proving reliability of the method. We compare the new measurement procedure to established concepts like holography. In extensive numerical simulations, we will also test its applicability under additional structural assumptions like sparsity.The research results should answer the question how antenna characteristics can be reliably extracted from phase-less measurements.