Compressive Sensing for Sampling Multidimensional RF Signals - Architectures and Algorithms

近年来，随着移动设备数量的大量增加和无线覆盖范围的显著改善，互联网几乎在任何时间、任何地点都触手可及。这导致了前所未有的服务类型的产生，这些服务永久性地向我们传递信息和多媒体内容。对于移动运营商来说，这带来了跟上此类服务所需的越来越大的数据速率的挑战。可以预见，只有进行根本性的技术变革，如探索更高的频段和采用多输入多输出（MIMO）系统，这种增长才能持续下去。MIMO系统利用电磁波在两个位置之间传播的空间特性。由于周围环境反射和散射信号，通常在发射器和接收器之间存在大量的传播路径。MIMO系统可以利用这一事实，同时在不同的路径上传输独立的数据流，从而大大提高可实现的数据速率。显然，对空间传播特性的深刻了解对于规划、建设和操作这种（大规模）MIMO系统至关重要。因此，无线传输信道的精确测量在其发展的早期阶段就具有很高的重要性。“信道测深器”是一种测量装置，它允许在其相关的多个维度（例如，空间、时间和频率）中观察时变多径信道脉冲响应。为了完成这项任务，通道测深仪需要高精度地采样多维射频信号。这是一个重大的挑战，因为现有的测量原理在测量速率方面基本上是有限的（例如，探测所有对发射/接收天线所需的时间），并且导致必须记录和处理非常大量的数据。近年来，压缩感知（CS）已被广泛研究用于具有一定冗余（稀疏）的采样信号，以便在不丢失信息的情况下将采样率降低到奈奎斯特率以下。这种冗余也存在于我们需要在MIMO信道探测中采样的多维射频信号中。因此，该项目旨在从理论（例如，数学恢复保证）和实践的角度（例如，实现CS概念的硬件架构）将CS应用于此类RF信号。特别是，我们认为重要的是要弥合最近在CS和稀疏恢复的理论结果之间的差距，在数学界（通常假设过于简化的代数模型）和工程师之间的现实波传播的理解（包括现实的，基于测量的天线阵列极化模型以及非镜面（例如，漫射）波传播），以使理论结果实际可用。

In recent years, with a massively growing number of mobile devices and significant improvements in the wireless coverage, the internet is in our reach almost at any time and any place. This has led to the creation of unprecedented types of services that deliver us information and multimedia content permanently. For mobile operators, this leads to the challenge of keeping pace with the larger and larger data rates such services require. It is foreseeable that this growth can only be sustained if fundamental technological changes are made, such as exploring higher frequency bands and employing multiple-input multiple-output (MIMO) systems.MIMO systems take advantage of the spatial characteristics of the electromagnetic wave propagation between two locations. Since the surroundings reflect and scatter the signals, there is typically a large number of propagation paths between transmitter and receiver. MIMO systems can exploit this fact by transmitting independent streams of data on different paths simultaneously, thus boosting the achievable data rate substantially.It is obvious that a profound knowledge of the spatial propagation characteristics is crucial for planning, building, and operating such (massive) MIMO systems. Therefore, precise measurements of the wireless transmission channels are of high importance already at an early stage of their development. A "channel sounder" is a measuring device which allows the observation of the time-varying multipath channel impulse response in its relevant multiple dimensions (e.g., space, time, and frequency). To achieve this task, channel sounders need to sample multidimensional RF signals with high precision. This is a significant challenge since the existing measurement principles are fundamentally limited in terms of their measurement rate (e.g., by the time it takes for probing all pairs of transmit/receive antennas) and lead to very large amounts of data that have to be recorded and processed.Recently, compressive sensing (CS) has been widely investigated for sampling signals that exhibit a certain redundancy (sparsity) to reduce the sampling rate below the Nyquist rate without loss of information. Such a redundancy exists also for the multidimensional RF signals we need to sample in MIMO channel sounding. Therefore, the project aims at applying CS to such RF signals, from a theoretical (e.g., mathematical recovery guarantees) as well as a practical point of view (e.g., hardware architectures that implement the CS concept). In particular, we consider it important to bridge the gap between the recent theoretical results on CS and sparse recovery in the mathematical community (often assuming over-simplified algebraic models) and the understanding of the realistic wave propagation among engineers (including realistic, measurement-based polarimetric models for the antenna arrays as well as non-specular (e.g., diffuse) wave propagation) in order to make the theoretical results practically usable.