Applications of compressive sensing to direction of arrival estimation

Die Schätzung der Einfallsrichtungen (Directions of Arrival/DOA) mehrerer ebener Wellenfronten mit Hilfe eines Antennen-Arrays ist eine der prominentesten Fragestellungen im Gebiet der Array-Signalverarbeitung. Das nach wie vor starke Forschungsinteresse in dieser Richtung konzentriert sich vor allem auf die Reduktion des Hardware-Aufwands, im Sinne der Komplexität und des Energieverbrauchs der Empfänger, bei einem vorgegebenen Grad an Genauigkeit und Robustheit gegen Mehrwegeausbreitung. Diese Dissertation beschäftigt sich mit der Anwendung von Compressive Sensing (CS) auf das Gebiet der DOA-Schätzung mit dem Ziel, hiermit die Komplexität der Empfängerhardware zu reduzieren und gleichzeitig eine hohe Richtungsauflösung und Robustheit zu erreichen. CS wurde bereits auf das DOA-Problem angewandt unter der Ausnutzung der Tatsache, dass eine Superposition ebener Wellenfronten mit einer winkelabhängigen Leistungsdichte korrespondiert, die über den Winkel betrachtet sparse ist. Basierend auf der Idee wurden CS-basierte Algorithmen zur DOA-Schätzung vorgeschlagen, die sich durch eine geringe Rechenkomplexität, Robustheit gegenüber Quellenkorrelation und Flexibilität bezüglich der Wahl der Array-Geometrie auszeichnen. Die Anwendung von CS führt darüber hinaus zu einer erheblichen Reduktion der Hardware-Komplexität, da weniger Empfangskanäle benötigt werden und eine geringere Datenmenge zu verarbeiten und zu speichern ist, ohne dabei wesentliche Informationen zu verlieren. Im ersten Teil der Arbeit wird das Problem des Modellfehlers bei der CS-basierten DOA-Schätzung mit gitterbehafteten Verfahren untersucht. Ein häufig verwendeter Ansatz um das CS-Framework auf das DOA-Problem anzuwenden ist es, den kontinuierlichen Winkel-Parameter zu diskreditieren und damit ein Dictionary endlicher Größe zu bilden. Da die tatsächlichen Winkel fast sicher nicht auf diesem Gitter liegen werden, entsteht dabei ein unvermeidlicher Modellfehler, der sich auf die Schätzalgorithmen auswirkt. In der Arbeit wird ein analytischer Ansatz gewählt, um den Effekt der Gitterfehler auf die rekonstruierten Spektra zu untersuchen. Es wird gezeigt, dass sich die Messung einer Quelle aus beliebiger Richtung sehr gut durch die erwarteten Antworten ihrer beiden Nachbarn auf dem Gitter annähern lässt. Darauf basierend wird ein einfaches und effizientes Verfahren vorgeschlagen, den Gitterversatz zu schätzen. Dieser Ansatz ist anwendbar auf einzelne Quellen oder mehrere, räumlich gut separierte Quellen. Für den Fall mehrerer dicht benachbarter Quellen wird ein numerischer Ansatz zur gemeinsamen Schätzung des Gitterversatzes diskutiert. Im zweiten Teil der Arbeit untersuchen wir das Design kompressiver Antennenarrays für die DOA-Schätzung. Die Kompression im Sinne von Linearkombinationen der Antennensignale, erlaubt es, Arrays mit großer Apertur zu entwerfen, die nur wenige Empfangskanäle benötigen und sich konfigurieren lassen. In der Arbeit wird eine einfache Empfangsarchitektur vorgeschlagen und ein allgemeines Systemmodell diskutiert, welches verschiedene Optionen der tatsächlichen Hardware-Realisierung dieser Linearkombinationen zulässt. Im Anschluss wird das Design der Gewichte des analogen Kombinations-Netzwerks untersucht. Numerische Simulationen zeigen die Überlegenheit der vorgeschlagenen kompressiven Antennen-Arrays im Vergleich mit dünn besetzten Arrays der gleichen Komplexität sowie kompressiver Arrays mit zufällig gewählten Gewichten. Schließlich werden zwei weitere Anwendungen der vorgeschlagenen Ansätze diskutiert: CS-basierte Verzögerungsschätzung und kompressives Channel Sounding. Es wird demonstriert, dass die in beiden Gebieten durch die Anwendung der vorgeschlagenen Ansätze erhebliche Verbesserungen erzielt werden können.Direction of Arrival (DOA) estimation of plane waves impinging on an array of sensors is one of the most important tasks in array signal processing, which have attracted tremendous research interest over the past several decades. The estimated DOAs are used in various applications like localization of transmitting sources, massive MIMO and 5G Networks, tracking and surveillance in radar, and many others. The major objective in DOA estimation is to develop approaches that allow to reduce the hardware complexity in terms of receiver costs and power consumption, while providing a desired level of estimation accuracy and robustness in the presence of multiple sources and/or multiple paths. Compressive sensing (CS) is a novel sampling methodology merging signal acquisition and compression. It allows for sampling a signal with a rate below the conventional Nyquist bound. In essence, it has been shown that signals can be acquired at sub-Nyquist sampling rates without loss of information provided they possess a sufficiently sparse representation in some domain and that the measurement strategy is suitably chosen. CS has been recently applied to DOA estimation, leveraging the fact that a superposition of planar wavefronts corresponds to a sparse angular power spectrum. This dissertation investigates the application of compressive sensing to the DOA estimation problem with the goal to reduce the hardware complexity and/or achieve a high resolution and a high level of robustness. Many CS-based DOA estimation algorithms have been proposed in recent years showing tremendous advantages with respect to the complexity of the numerical solution while being insensitive to source correlation and allowing arbitrary array geometries. Moreover, CS has also been suggested to be applied in the spatial domain with the main goal to reduce the complexity of the measurement process by using fewer RF chains and storing less measured data without the loss of any significant information. In the first part of the work we investigate the model mismatch problem for CS based DOA estimation algorithms off the grid. To apply the CS framework a very common approach is to construct a finite dictionary by sampling the angular domain with a predefined sampling grid. Therefore, the target locations are almost surely not located exactly on a subset of these grid points. This leads to a model mismatch which deteriorates the performance of the estimators. We take an analytical approach to investigate the effect of such grid offsets on the recovered spectra showing that each off-grid source can be well approximated by the two neighboring points on the grid. We propose a simple and efficient scheme to estimate the grid offset for a single source or multiple well-separated sources. We also discuss a numerical procedure for the joint estimation of the grid offsets of closer sources. In the second part of the thesis we study the design of compressive antenna arrays for DOA estimation that aim to provide a larger aperture with a reduced hardware complexity and allowing reconfigurability, by a linear combination of the antenna outputs to a lower number of receiver channels. We present a basic receiver architecture of such a compressive array and introduce a generic system model that includes different options for the hardware implementation. We then discuss the design of the analog combining network that performs the receiver channel reduction. Our numerical simulations demonstrate the superiority of the proposed optimized compressive arrays compared to the sparse arrays of the same complexity and to compressive arrays with randomly chosen combining kernels. Finally, we consider two other applications of the sparse recovery and compressive arrays. The first application is CS based time delay estimation and the other one is compressive channel sounding. We show that the proposed approaches for sparse recovery off the grid and compressive arrays show significant improvements in the considered applications compared to conventional methods

Near-Field Communications: A Comprehensive Survey

Multiple-antenna technologies are evolving towards large-scale aperture sizes, extremely high frequencies, and innovative antenna types. This evolution is giving rise to the emergence of near-field communications (NFC) in future wireless systems. Considerable attention has been directed towards this cutting-edge technology due to its potential to enhance the capacity of wireless networks by introducing increased spatial degrees of freedom (DoFs) in the range domain. Within this context, a comprehensive review of the state of the art on NFC is presented, with a specific focus on its 1) fundamental operating principles, 2) channel modeling, 3) performance analysis, 4) signal processing, and 5) integration with other emerging technologies. Specifically, 1) the basic principles of NFC are characterized from both physics and communications perspectives, unveiling its unique properties in contrast to far-field communications. 2) Based on these principles, deterministic and stochastic near-field channel models are investigated for spatially-discrete (SPD) and continuous-aperture (CAP) antenna arrays. 3) Rooted in these models, existing contributions on near-field performance analysis are reviewed in terms of DoFs/effective DoFs (EDoFs), power scaling law, and transmission rate. 4) Existing signal processing techniques for NFC are systematically surveyed, encompassing channel estimation, beamforming design, and low-complexity beam training. 5) Major issues and research opportunities associated with the integration of NFC and other emerging technologies are identified to facilitate NFC applications in next-generation networks. Promising directions are highlighted throughout the paper to inspire future research endeavors in the realm of NFC.Comment: 56 pages, 23figures; submit for possible journa

Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented

Millimeter wave link configuration with hybrid MIMO architectures

The use of multiple antennas, widely known as MIMO technology, is a key feature to deploy mmWave communication systems enabling high-data-rate applications. With more than two decades of global experience in deploying Wi-Fi and cellular communication using sub-6 GHz frequency bands, simply repurposing these designs for mmWave bands would fail to account for additional propagation impairments and circuit design constraints at these higher frequencies. A solution to overcome the propagation challenges is the use of multiple directional communication beams, whereby proper alignment between transceivers provides sufficient link quality to enable reliable decoding of the transmitted data. In this dissertation, efficient link configuration solutions suitable for mmWave cellular communications are developed. To gain some insight into the achievable performance of mmWave systems, two broadband channel-estimation-based link configuration solutions are proposed for MIMO-OFDM systems, in which both the transmitter and receiver are assumed to be perfectly synchronized. The proposed solution exploits the spatially common sparsity in the mmWave channel and enables efficient acquisition of the CSI while allowing the use of multiple RF chains on both the transmitter and receiver sides. In a simplified scenario, the CRLB for the channel estimation problem is derived, and the proposed channel estimation algorithms are shown to both outperform prior work in communication performance and exhibit excellent estimation performance. Furthermore, the proposed algorithms are assessed in a more challenging scenario with realistic channel parameters, and it is shown that both near-optimal spectral efficiency and low BER can be attained with lower overhead and computational complexity than prior solutions. Next, the impact of imperfect CFO synchronization on the channel estimation problem is analyzed under a narrowband channel model. The CRLB for the estimation of the different unknown parameters involved in the problem is theoretically analyzed, and closed-form expressions are provided for the estimation of the different parameters. Under a joint estimation-theoretic and CS framework, a low-complexity multi-stage solution is proposed to estimate both the different unknown synchronization parameters and the large-dimensional mmWave MIMO channel. Different trade-offs between estimation, spectral efficiency, and overhead performance are exposed, and the proposed estimators are shown to be asymptotically optimal in the low SNR regime. The proposed solution is assessed under a channel model with several clusters and rays per cluster, and is shown to attain near-optimal spectral efficiency values in both the low and high SNR regimes. The computational complexity of the proposed solution is also analyzed, in which it is shown to achieve a marginal increase in computational complexity with respect to the solution proposed in the previous contribution. Finally, the impact of TO, CFO, and PN impairments on the channel estimation problem is analyzed under a broadband channel model. The problem of time-frequency synchronization under PN impairments is theoretically analyzed, and the proposed solutions to the synchronization problem are exploited to estimate the frequency-selective mmWave MIMO channel. The hybrid CRLB for the estimation of the different synchronization impairments is analyzed, and closed-form expressions leveraging the information coupling between the different impairments are provided. The previously proposed joint estimation-theoretic and CS framework is extended to frequency-selective scenarios, and two low-complexity multi-stage solutions are proposed to estimate both the different synchronization impairments and the large-dimensional mmWave MIMO channel. The first solution relies on a batch-processing LMMSE-based EM algorithm to estimate the different synchronization impairments, while the second solution uses a sequential-processing EKF-RTS-based EM algorithm, thereby reducing computational complexity. Thereafter, both the hybrid CRLB for the estimation of the equivalent beamformed complex channels and the estimates for these parameters are exploited to estimate the large-dimensional frequency-selective mmWave MIMO channel. Finally, a joint PN and data detection algorithm is proposed for data transmission under the 5G NR frame structure. The proposed solutions are evaluated using a 5G NR-based channel model, and different trade-offs between estimation performance, computational complexity, overhead, achievable spectral efficiency and BER are exposed, and comparisons with prior work are also provided. The results show that mmWave link configuration using hybrid MIMO architectures can be established with low overhead without assuming synchronization, even in the low SNR regime.Electrical and Computer Engineerin

Compressive Sensing of Multiband Spectrum towards Real-World Wideband Applications.

PhD Theses.Spectrum scarcity is a major challenge in wireless communication systems with their rapid evolutions towards more capacity and bandwidth. The fact that the real-world spectrum, as a nite resource, is sparsely utilized in certain bands spurs the proposal of spectrum sharing. In wideband scenarios, accurate real-time spectrum sensing, as an enabler of spectrum sharing, can become ine cient as it naturally requires the sampling rate of the analog-to-digital conversion to exceed the Nyquist rate, which is resourcecostly and energy-consuming. Compressive sensing techniques have been applied in wideband spectrum sensing to achieve sub-Nyquist-rate sampling of frequency sparse signals to alleviate such burdens. A major challenge of compressive spectrum sensing (CSS) is the complexity of the sparse recovery algorithm. Greedy algorithms achieve sparse recovery with low complexity but the required prior knowledge of the signal sparsity. A practical spectrum sparsity estimation scheme is proposed. Furthermore, the dimension of the sparse recovery problem is proposed to be reduced, which further reduces the complexity and achieves signal denoising that promotes recovery delity. The robust detection of incumbent radio is also a fundamental problem of CSS. To address the energy detection problem in CSS, the spectrum statistics of the recovered signals are investigated and a practical threshold adaption scheme for energy detection is proposed. Moreover, it is of particular interest to seek the challenges and opportunities to implement real-world CSS for systems with large bandwidth. Initial research on the practical issues towards the real-world realization of wideband CSS system based on the multicoset sampler architecture is presented. In all, this thesis provides insights into two critical challenges - low-complexity sparse recovery and robust energy detection - in the general CSS context, while also looks into some particular issues towards the real-world CSS implementation based on the i multicoset sampler

A survey on 5G massive MIMO Localization

Massive antenna arrays can be used to meet the requirements of 5G, by exploiting different spatial signatures of users. This same property can also be harnessed to determine the locations of those users. In order to perform massive MIMO localization, refined channel estimation routines and localization methods have been developed. This paper provides a brief overview of this emerging field