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

由于对天线在带宽(例如超宽带天线)、辐射特性(例如可重构天线)和高工作频率(例如汽车领域的雷达系统)方面的多样化和日益增长的需求，近年来天线及其测量工作的复杂性大大增加。为了节省时间，通常只进行频率和天线配置选择较少的部分测量。特别是在近场，较长的测量周期是一个很强的限制因素。其原因是为了以令人满意的精度确定天线的传输特性，必须获取大量的测量点。然而，如果用球面波来描述天线的辐射，实际上相关信息大多集中在几个球面波系数上，该项目旨在将压缩传感方法与球面近远场变换理论相结合，以最小的精度损失实现球面上的欠采样天线测量。为此，最初考虑了不同的信号重建方法，以在现有解中整合球面模谱的结构特性。发展了基于关于天线特性的先验知识，提供关于选择最优基的信息并限制最优解的搜索空间的方法。为了可靠地重建下采样信号，还需要适当地选择所需数量的测量点。为此，研究了天线特性导致模式谱稀疏的原因。该项目的另一部分目的是确定球面上适当的采样策略，以实现球面模式的稳健重建。在此背景下，确定了极化角度对重建行为的尚未探索的影响。该项目的一个重要部分是在使用新方法时识别测量不确定度，这些不确定度是通过广泛的分析确定的。在这种情况下，一种有趣的方法是所谓的贝叶斯压缩传感，它允许在重建过程中获得计算解的置信度区间。在最后一步，探索的方法将在各种类型天线的广泛测量的基础上进行验证。研究结果应该回答如何在球面近场到远场变换的背景下使用压缩感知来对天线测量进行二次采样。

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.