Compressive Sensing for Sampling Multidimensional RF Signals - Architectures and Algorithms

近年来，随着移动设备数量的大幅增加和无线覆盖范围的显著改善，互联网几乎随时随地都在我们的手中。这导致了前所未有的服务类型的创建，这些服务永久地向我们提供信息和多媒体内容。对于移动运营商来说，这带来了与此类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，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。MIMO系统利用了两个位置之间电磁波传播的空间特性。由于周围环境对信号的反射和散射，在发射机和接收机之间通常存在大量的传播路径。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，从而大幅提高可实现的数据速率。显然，对空间传播特性的深入了解对于规划、建设和运营这样的(大规模)MIMO系统至关重要。因此，无线传输通道的精确测量已经在其开发的早期阶段具有非常重要的意义。通道测深仪是一种测量设备，它允许在其相关的多个维度(例如，空间、时间和频率)上观察时变多径通道脉冲响应。为了实现这一任务，声道探测仪需要对多维射频信号进行高精度采样。这是一个巨大的挑战，因为现有的测量原理在测量速率方面基本上是受限的(例如，受探测所有发射/接收天线对所花费的时间的限制)，并且导致必须记录和处理非常大量的数据。最近，压缩传感(CS)被广泛地研究用于表现出一定冗余(稀疏性)的采样信号，以在不丢失信息的情况下将采样率降低到奈奎斯特速率以下。对于我们在MIMO信道探测中需要采样的多维RF信号，也存在这样的冗余。因此，该项目的目标是从理论(例如，数学恢复保证)和实践(例如，实现CS概念的硬件架构)的角度将CS应用于此类RF信号。特别是，我们认为弥合最近关于CS的理论结果和数学界的稀疏恢复之间的差距(通常假设过于简化的代数模型)和工程师对现实波传播的理解(包括天线阵列和非镜面(例如漫射)波传播的现实的、基于测量的极化模型)，以便使理论结果能够实际使用。

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.