Sensing Strategies for Spherical Phaseless Antenna Measurements (S³PAM)

由于天线在带宽（例如，用于超宽带天线）、辐射特性（例如，用于可重构天线）和高工作频率（例如，用于汽车领域中的雷达系统）方面的多样化和不断增长的需求，天线的复杂性以及它们的测量工作近年来大大增加。为了节省时间，通常只进行具有少量频率和天线配置选择的部分测量。特别是在近场，长的测量周期是一个很强的限制因素。其原因在于，为了以令人满意的精度确定天线的传输特性，必须采集大量的测量点。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中。此外，为了从近场测量计算球面波系数，振幅和相位都是必要的。然而，相位测量意味着使用昂贵的设备，例如，网络分析器，并且依赖于能够访问参考相位的假设，这例如不是空中测量场景中的情况。由于这些原因，人们对无相位测量装置的发展产生了极大的兴趣。该项目旨在将相位恢复和压缩传感的数学方法与球面近场到远场变换的理论结合起来，以使球面上的无相位（二次采样）天线测量具有最小的精度损失。为此，我们扩展理论现有的采样策略，尊重所有涉及的旋转角度，并获得改进的采样模式。我们建议在实践中可操作的无相天线测量，并将它们与理论发展的信号恢复从无相测量建立的算法。该连接用于在球形近场到远场变换的上下文中获得第一重建保证接近信息理论极限的采样点的数量，从而证明该方法的可靠性。我们比较了新的测量程序，如全息摄影的既定概念。在大量的数值模拟中，我们还将在稀疏性等额外的结构假设下测试其适用性。研究结果应该回答如何从无相位测量中可靠地提取天线特性的问题。

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.