Compressive Sensing for Sampling Multidimensional RF Signals - Architectures and Algorithms

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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.