Compressive Sensing for Sampling Multidimensional RF Signals - Architectures and Algorithms

近年来，随着移动的设备数量的大量增长和无线覆盖的显著改善，互联网几乎在任何时间和任何地点都在我们的范围内。这导致了前所未有的服务类型的创建，永久地向我们提供信息和多媒体内容。对于移动的运营商来说，这导致了与这种服务所需的越来越大的数据速率保持同步的挑战。可以预见的是，这种增长只有在进行基本技术变革的情况下才能持续，例如探索更高的频带和采用多输入多输出（MIMO）系统。MIMO系统利用了两个位置之间电磁波传播的空间特性。由于周围环境反射和散射信号，因此在发射器和接收器之间通常存在大量传播路径。MIMO系统可以利用这一事实，通过在不同的路径上同时传输独立的数据流，从而大大提高可实现的数据率。显然，对空间传播特性的深刻了解对于规划，构建和操作这样的（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已经非常重要。“信道探测器”是允许在其相关的多个维度（例如，空间、时间和频率）。为了实现这一任务，通道探测器需要以高精度对多维RF信号进行采样。这是一个重大的挑战，因为现有的测量原理在其测量速率方面基本上是有限的（例如，最近，压缩感知（CS）已经被广泛地研究用于对表现出一定冗余（稀疏性）的信号进行采样，以将采样速率降低到奈奎斯特速率以下而不丢失信息。这种冗余也存在于我们在MIMO信道探测中需要采样的多维RF信号。因此，该项目旨在将CS应用于这种RF信号，从理论上（例如，数学恢复保证）以及实际的观点（例如，实现CS概念的硬件架构）。特别是，我们认为重要的是弥合数学界最近关于CS和稀疏恢复的理论结果（通常假设过度简化的代数模型）与工程师对现实波传播的理解（包括天线阵列的现实的基于测量的极化模型以及非镜面反射（例如，扩散）波传播），以便使理论结果实际上可用。

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.