Compressive Sensing and Its Applications in Automotive Radar Systems

Die Entwicklung in Richtung zu autonomem Fahren verspricht, künftig einen sicheren Verkehr ohne tödliche Unfälle zu ermöglichen, indem menschliche Fahrer vollständig ersetzt werden. Dadurch entfällt der Faktor des menschlichen Fehlers, der aus Müdigkeit, Unachtsamkeit oder Alkoholeinfluss resultiert. Um jedoch eine breite Akzeptanz für autonome Fahrzeuge zu erreichen und es somit eines Tages vollständig umzusetzen, sind noch eine Vielzahl von Herausforderungen zu lösen. Da in einem autonomen Fahrzeug kein menschlicher Fahrer mehr in Notfällen eingreifen kann, müssen sich autonome Fahrzeuge auf leistungsfähige und robuste Sensorsysteme verlassen können, um in kritischen Situationen auch unter widrigen Bedingungen angemessen reagieren zu können. Daher ist die Entwicklung von Sensorsystemen erforderlich, die für Funktionalitäten jenseits der aktuellen advanced driver assistance systems eingesetzt werden können. Dies resultiert in neuen Anforderungen, die erfüllt werden müssen, um sichere und zuverlässige autonome Fahrzeuge zu realisieren, die weder Fahrzeuginsassen noch Passanten gefährden. Radarsysteme gehören zu den Schlüsselkomponenten unter der Vielzahl der verfügbaren Sensorsysteme, da sie im Gegensatz zu visuellen Sensoren von widrigen Wetter- und Umgebungsbedingungen kaum beeinträchtigt werden. Darüber hinaus liefern Radarsysteme zusätzliche Umgebungsinformationen wie Abstand, Winkel und relative Geschwindigkeit zwischen Sensor und reflektierenden Zielen. Die vorliegende Dissertation deckt im Wesentlichen zwei Hauptaspekte der Forschung und Entwicklung auf dem Gebiet der Radarsysteme im Automobilbereich ab. Ein Aspekt ist die Steigerung der Effizienz und Robustheit der Signalerfassung und -verarbeitung für die Radarperzeption. Der andere Aspekt ist die Beschleunigung der Validierung und Verifizierung von automated cyber-physical systems, die parallel zum Automatisierungsgrad auch eine höhere Komplexität aufweisen. Nach der Analyse zahlreicher möglicher Compressive Sensing Methoden, die im Bereich Fahrzeugradarsysteme angewendet werden können, wird ein rauschmoduliertes gepulstes Radarsystem vorgestellt, das kommerzielle Fahrzeugradarsysteme in seiner Robustheit gegenüber Rauschen übertrifft. Die Nachteile anderer gepulster Radarsysteme hinsichtlich des Signalerfassungsaufwands und der Laufzeit werden durch die Verwendung eines Compressive Sensing-Signalerfassungs- und Rekonstruktionsverfahrens in Kombination mit einer Rauschmodulation deutlich verringert. Mit Compressive Sensing konnte der Aufwand für die Signalerfassung um 70% reduziert werden, während gleichzeitig die Robustheit der Radarwahrnehmung auch für signal-to-noise-ratio-Pegel nahe oder unter Null erreicht wird. Mit einem validierten Radarsensormodell wurde das Rauschradarsystem emuliert und mit einem kommerziellen Fahrzeugradarsystem verglichen. Datengetriebene Wettermodelle wurden entwickelt und während der Simulation angewendet, um die Radarleistung unter widrigen Bedingungen zu bewerten. Während eine Besprühung mit Wasser die Radomdämpfung um 10 dB erhöht und Spritzwasser sogar um 20 dB, ergibt sich die eigentliche Begrenzung aus der Rauschzahl und Empfindlichkeit des Empfängers. Es konnte bewiesen werden, dass das vorgeschlagene Compressive Sensing Rauschradarsystem mit einer zusätzlichen Signaldämpfung von bis zu 60 dB umgehen kann und damit eine hohe Robustheit in ungünstigen Umwelt- und Wetterbedingungen aufweist. Neben der Robustheit wird auch die Interferenz berücksichtigt. Zum einen wird die erhöhte Störfestigkeit des Störradarsystems nachgewiesen. Auf der anderen Seite werden die Auswirkungen auf bestehende Fahrzeugradarsysteme bewertet und Strategien zur Minderung der Auswirkungen vorgestellt. Die Struktur der Arbeit ist folgende. Nach der Einführung der Grundlagen und Methoden für Fahrzeugradarsysteme werden die Theorie und Metriken hinter Compressive Sensing gezeigt. Darüber hinaus werden weitere Aspekte wie Umgebungsbedingungen, unterschiedliche Radararchitekturen und Interferenz erläutert. Der Stand der Technik gibt einen Überblick über Compressive Sensing-Ansätze und Implementierungen mit einem Fokus auf Radar. Darüber hinaus werden Aspekte von Fahrzeug- und Rauschradarsystemen behandelt. Der Hauptteil beginnt mit der Vorstellung verschiedener Ansätze zur Nutzung von Compressive Sensing für Fahrzeugradarsysteme, die in der Lage sind, die Erfassung und Wahrnehmung von Radarsignalen zu verbessern oder zu erweitern. Anschließend wird der Fokus auf ein Rauschradarsystem gelegt, das mit Compressive Sensing eine effiziente Signalerfassung und -rekonstruktion ermöglicht. Es wurde mit verschiedenen Compressive Sensing-Metriken analysiert und in einer Proof-of-Concept-Simulation bewertet. Mit einer Emulation des Rauschradarsystems wurde das Potential der Compressive Sensing Signalerfassung und -verarbeitung in einem realistischeren Szenario demonstriert. Die Entwicklung und Validierung des zugrunde liegenden Sensormodells wird ebenso dokumentiert wie die Entwicklung der datengetriebenen Wettermodelle. Nach der Betrachtung von Interferenz und der Koexistenz des Rauschradars mit kommerziellen Radarsystemen schließt ein letztes Kapitel mit Schlussfolgerungen und einem Ausblick die Arbeit ab.Developments towards autonomous driving promise to lead to safer traffic, where fatal accidents can be avoided after making human drivers obsolete and hence removing the factor of human error. However, to ensure the acceptance of automated driving and make it a reality one day, still a huge amount of challenges need to be solved. With having no human supervisors, automated vehicles have to rely on capable and robust sensor systems to ensure adequate reactions in critical situations, even during adverse conditions. Therefore, the development of sensor systems is required that can be applied for functionalities beyond current advanced driver assistance systems. New requirements need to be met in order to realize safe and reliable automated vehicles that do not harm passersby. Radar systems belong to the key components among the variety of sensor systems. Other than visual sensors, radar is less vulnerable towards adverse weather and environment conditions. In addition, radar provides complementary environment information such as target distance, angular position or relative velocity, too. The thesis ad hand covers basically two main aspects of research and development in the field of automotive radar systems. One aspect is to increase efficiency and robustness in signal acquisition and processing for radar perception. The other aspect is to accelerate validation and verification of automated cyber-physical systems that feature more complexity along with the level of automation. After analyzing a variety of possible Compressive Sensing methods for automotive radar systems, a noise modulated pulsed radar system is suggested in the thesis at hand, which outperforms commercial automotive radar systems in its robustness towards noise. Compared to other pulsed radar systems, their drawbacks regarding signal acquisition effort and computation run time are resolved by using noise modulation for implementing a Compressive Sensing signal acquisition and reconstruction method. Using Compressive Sensing, the effort in signal acquisition was reduced by 70%, while obtaining a radar perception robustness even for signal-to-noise-ratio levels close to or below zero. With a validated radar sensor model the noise radar was emulated and compared to a commercial automotive radar system. Data-driven weather models were developed and applied during simulation to evaluate radar performance in adverse conditions. While water sprinkles increase radome attenuation by 10 dB and splash water even by 20 dB, the actual limitation comes from noise figure and sensitivity of the receiver. The additional signal attenuation that can be handled by the proposed compressive sensing noise radar system proved to be even up to 60 dB, which ensures a high robustness of the receiver during adverse weather and environment conditions. Besides robustness, interference is also considered. On the one hand the increased robustness towards interference of the noise radar system is demonstrated. On the other hand, the impact on existing automotive radar systems is evaluated and strategies to mitigate the impact are presented. The structure of the thesis is the following. After introducing basic principles and methods for automotive radar systems, the theory and metrics of Compressive Sensing is presented. Furthermore some particular aspects are highlighted such as environmental conditions, different radar architectures and interference. The state of the art provides an overview on Compressive Sensing approaches and implementations with focus on radar. In addition, it covers automotive radar and noise radar related aspects. The main part starts with presenting different approaches on making use of Compressive Sensing for automotive radar systems, that are capable of either improving or extending radar signal acquisition and perception. Afterwards the focus is put on a noise radar system that uses Compressive Sensing for an efficient signal acquisition and reconstruction. It was analyzed using different Compressive Sensing metrics and evaluated in a proof-of-concept simulation. With an emulation of the noise radar system the feasibility of the Compressive Sensing signal acquisition and processing was demonstrated in a more realistic scenario. The development and validation of the underlying sensor model is documented as well as the development of the data-driven weather models. After considering interference and co-existence with commercial radar systems, a final chapter with conclusions and an outlook completes the work

Efficient algorithms and data structures for compressive sensing

Wegen der kontinuierlich anwachsenden Anzahl von Sensoren, und den stetig wachsenden Datenmengen, die jene produzieren, stößt die konventielle Art Signale zu verarbeiten, beruhend auf dem Nyquist-Kriterium, auf immer mehr Hindernisse und Probleme. Die kürzlich entwickelte Theorie des Compressive Sensing (CS) formuliert das Versprechen einige dieser Hindernisse zu beseitigen, indem hier allgemeinere Signalaufnahme und -rekonstruktionsverfahren zum Einsatz kommen können. Dies erlaubt, dass hierbei einzelne Abtastwerte komplexer strukturierte Informationen über das Signal enthalten können als dies bei konventiellem Nyquistsampling der Fall ist. Gleichzeitig verändert sich die Signalrekonstruktion notwendigerweise zu einem nicht-linearen Vorgang und ebenso müssen viele Hardwarekonzepte für praktische Anwendungen neu überdacht werden. Das heißt, dass man zwischen der Menge an Information, die man über Signale gewinnen kann, und dem Aufwand für das Design und Betreiben eines Signalverarbeitungssystems abwägen kann und muss. Die hier vorgestellte Arbeit trägt dazu bei, dass bei diesem Abwägen CS mehr begünstigt werden kann, indem neue Resultate vorgestellt werden, die es erlauben, dass CS einfacher in der Praxis Anwendung finden kann, wobei die zu erwartende Leistungsfähigkeit des Systems theoretisch fundiert ist. Beispielsweise spielt das Konzept der Sparsity eine zentrale Rolle, weshalb diese Arbeit eine Methode präsentiert, womit der Grad der Sparsity eines Vektors mittels einer einzelnen Beobachtung geschätzt werden kann. Wir zeigen auf, dass dieser Ansatz für Sparsity Order Estimation zu einem niedrigeren Rekonstruktionsfehler führt, wenn man diesen mit einer Rekonstruktion vergleicht, welcher die Sparsity des Vektors unbekannt ist. Um die Modellierung von Signalen und deren Rekonstruktion effizienter zu gestalten, stellen wir das Konzept von der matrixfreien Darstellung linearer Operatoren vor. Für die einfachere Anwendung dieser Darstellung präsentieren wir eine freie Softwarearchitektur und demonstrieren deren Vorzüge, wenn sie für die Rekonstruktion in einem CS-System genutzt wird. Konkret wird der Nutzen dieser Bibliothek, einerseits für das Ermitteln von Defektpositionen in Prüfkörpern mittels Ultraschall, und andererseits für das Schätzen von Streuern in einem Funkkanal aus Ultrabreitbanddaten, demonstriert. Darüber hinaus stellen wir für die Verarbeitung der Ultraschalldaten eine Rekonstruktionspipeline vor, welche Daten verarbeitet, die im Frequenzbereich Unterabtastung erfahren haben. Wir beschreiben effiziente Algorithmen, die bei der Modellierung und der Rekonstruktion zum Einsatz kommen und wir leiten asymptotische Resultate für die benötigte Anzahl von Messwerten, sowie die zu erwartenden Lokalisierungsgenauigkeiten der Defekte her. Wir zeigen auf, dass das vorgestellte System starke Kompression zulässt, ohne die Bildgebung und Defektlokalisierung maßgeblich zu beeinträchtigen. Für die Lokalisierung von Streuern mittels Ultrabreitbandradaren stellen wir ein CS-System vor, welches auf einem Random Demodulators basiert. Im Vergleich zu existierenden Messverfahren ist die hieraus resultierende Schätzung der Kanalimpulsantwort robuster gegen die Effekte von zeitvarianten Funkkanälen. Um den inhärenten Modellfehler, den gitterbasiertes CS begehen muss, zu beseitigen, zeigen wir auf wie Atomic Norm Minimierung es erlaubt ohne die Einschränkung auf ein endliches und diskretes Gitter R-dimensionale spektrale Komponenten aus komprimierten Beobachtungen zu schätzen. Hierzu leiten wir eine R-dimensionale Variante des ADMM her, welcher dazu in der Lage ist die Signalkovarianz in diesem allgemeinen Szenario zu schätzen. Weiterhin zeigen wir, wie dieser Ansatz zur Richtungsschätzung mit realistischen Antennenarraygeometrien genutzt werden kann. In diesem Zusammenhang präsentieren wir auch eine Methode, welche mittels Stochastic gradient descent Messmatrizen ermitteln kann, die sich gut für Parameterschätzung eignen. Die hieraus resultierenden Kompressionsverfahren haben die Eigenschaft, dass die Schätzgenauigkeit über den gesamten Parameterraum ein möglichst uniformes Verhalten zeigt. Zuletzt zeigen wir auf, dass die Kombination des ADMM und des Stochastic Gradient descent das Design eines CS-Systems ermöglicht, welches in diesem gitterfreien Szenario wünschenswerte Eigenschaften hat.Along with the ever increasing number of sensors, which are also generating rapidly growing amounts of data, the traditional paradigm of sampling adhering the Nyquist criterion is facing an equally increasing number of obstacles. The rather recent theory of Compressive Sensing (CS) promises to alleviate some of these drawbacks by proposing to generalize the sampling and reconstruction schemes such that the acquired samples can contain more complex information about the signal than Nyquist samples. The proposed measurement process is more complex and the reconstruction algorithms necessarily need to be nonlinear. Additionally, the hardware design process needs to be revisited as well in order to account for this new acquisition scheme. Hence, one can identify a trade-off between information that is contained in individual samples of a signal and effort during development and operation of the sensing system. This thesis addresses the necessary steps to shift the mentioned trade-off more to the favor of CS. We do so by providing new results that make CS easier to deploy in practice while also maintaining the performance indicated by theoretical results. The sparsity order of a signal plays a central role in any CS system. Hence, we present a method to estimate this crucial quantity prior to recovery from a single snapshot. As we show, this proposed Sparsity Order Estimation method allows to improve the reconstruction error compared to an unguided reconstruction. During the development of the theory we notice that the matrix-free view on the involved linear mappings offers a lot of possibilities to render the reconstruction and modeling stage much more efficient. Hence, we present an open source software architecture to construct these matrix-free representations and showcase its ease of use and performance when used for sparse recovery to detect defects from ultrasound data as well as estimating scatterers in a radio channel using ultra-wideband impulse responses. For the former of these two applications, we present a complete reconstruction pipeline when the ultrasound data is compressed by means of sub-sampling in the frequency domain. Here, we present the algorithms for the forward model, the reconstruction stage and we give asymptotic bounds for the number of measurements and the expected reconstruction error. We show that our proposed system allows significant compression levels without substantially deteriorating the imaging quality. For the second application, we develop a sampling scheme to acquire the channel Impulse Response (IR) based on a Random Demodulator that allows to capture enough information in the recorded samples to reliably estimate the IR when exploiting sparsity. Compared to the state of the art, this in turn allows to improve the robustness to the effects of time-variant radar channels while also outperforming state of the art methods based on Nyquist sampling in terms of reconstruction error. In order to circumvent the inherent model mismatch of early grid-based compressive sensing theory, we make use of the Atomic Norm Minimization framework and show how it can be used for the estimation of the signal covariance with R-dimensional parameters from multiple compressive snapshots. To this end, we derive a variant of the ADMM that can estimate this covariance in a very general setting and we show how to use this for direction finding with realistic antenna geometries. In this context we also present a method based on a Stochastic gradient descent iteration scheme to find compression schemes that are well suited for parameter estimation, since the resulting sub-sampling has a uniform effect on the whole parameter space. Finally, we show numerically that the combination of these two approaches yields a well performing grid-free CS pipeline

利用块稀疏特性的压缩感知麦克风阵列声源定位

与传统声源定位算法如相位变换加权、时延累加定位不同,压缩感知麦克风阵列声源定位算法可将声源定位转化为稀疏重构问题从而获得较高的性能。但在实际应用环境下,由于远场声源自身指向性、空间混响等原因,声源方向向量往往呈现块稀疏度结构,导致采用传统稀疏恢复算法如正交匹配追踪算法(Orthogonal matching pursuit,OMP)等进行压缩感知定位性能下降。本文在压缩感知声源定位算法中引入块稀疏似零范数,以压缩感知为基本框架,采用块稀疏似零范数稀疏恢复进行声源方向向量的重构,获取声源的方位。实验结果表明,相较于传统声源定位算法和基于OMP的压缩感知声源定位算法,本文算法具有更高的定位精度。国家自然科学基金（11574258）资助项目;;\n福建省高校产学合作（2015H6019）资助项目;;\n重点实验室基金一般项目（6142109180303）资助项

Millimeter wave MIMO communications : high-resolution angle acquisition and low-resolution time-frequency synchronization

Knowledge of the propagation channel is critical to exploit the full benefit of multiple-input multiple-output (MIMO) techniques in millimeter wave (mmWave) cellular systems. Obtaining accurate channel state information in mmWave systems, however, is challenging due to high estimation overhead, high computational complexity and on-grid setting. It is also desirable to reduce the analog-to-digital converters (ADCs) resolution at mmWave frequencies to reduce power consumption and implementation costs. The use of low-precision ADCs, though, brings new design challenges to practical cellular networks. In the first part of this dissertation, we develop several new methods to estimate and track the mmWave channel's angle-of-departure and angle-of-arrival with high accuracy and low overhead. The key ingredient of the proposed strategies is custom designed beam pairs, from which there exists an invertible function of the angle to be estimated. We further extend the proposed algorithms to dual-polarized MIMO in wideband channels, and angle tracking design for fast-varying environments. We derive analytical angle estimation error performance of the proposed methods in single-path channels. We also use numerical examples to characterize the robustness of the proposed approaches to various transceiver settings and channel conditions. In the second part of this dissertation, we focus on improving the low-resolution time-frequency synchronization performance for mmWave cellular systems. In our system model, the base station uses analog beams to send the synchronization signal with infinite-resolution digital-to-analog converters (DACs). The user equipment employs a fully digital front end to detect the synchronization signal with low-resolution ADCs. For low-resolution timing synchronization, we propose a new multi-beam probing based strategy, targeting at maximizing the minimum received synchronization signal-to-quantization-plus-noise ratio among all serving users. Regarding low-resolution frequency synchronization, we construct new sequences for carrier frequency offset (CFO) estimation and compensation. We use both analytical and numerical examples to show that the proposed sequences and the corresponding metrics used for retrieving the CFOs are robust to the quantization distortion.Electrical and Computer Engineerin

Sensor Signal and Information Processing II

In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing

Colocated MIMO radar using compressive sensing

We propose the use of compressive sensing (CS) in the context of a multi-input multioutput (MIMO) radar system that is implemented by a small scale network. Each receive node compressively samples the incoming signal, and forwards a small number of samples to a fusion center. At the fusion center, all received data are jointly processed to extract information on the potential targets via the CS approach. Since CS-based MIMO radar would require many fewer measurements than conventional MIMO radar for reliable target detection, there would be power savings during the data transmission to the fusion center, which would prolong the life of the wireless network. First, we propose a direction of arrival (DOA)-Doppler estimation approach. Assuming that the targets are sparsely located in the DOA-Doppler space, based on the samples forwarded by the receive nodes, the fusion center formulates an ℓ1-optimization problem, the solution of which yields the target DOA-Doppler information. The proposed approach achieves the superior resolution of MIMO radar with far fewer samples than required by conventional approaches. Second, we propose the use of step frequency to CS-based MIMO radar, which enables high range resolution, while transmitting narrowband pulses. For slowly moving targets, a novel approach is proposed that achieves significant complexity reduction by successively estimating angle-range and Doppler in a decoupled fashion and by employing initial estimates to further reduce the search space. Numerical results show that the achieved complexity reduction does not hurt resolution. Finally, we investigate optimal designs for the measurement matrix that is used to linearly compress the received signal. One optimality criterion amounts to decorrelating the bases that span the sparse space of the incoming signal and simultaneously enhancing signal-to-interference ratio (SIR). Another criterion targets SIRimprovement only. It is shown via simulations that, in certain cases, the measurement matrices obtained based on the aforementioned criteria can improve detection accuracy as compared to the typically used Gaussian random measurement matrix.Ph.D., Electrical Engineering -- Drexel University, 201

Embedded systems and advanced signal processing for Acousto- Ultrasonic Inspections

Non Destructive Testing (NDT) and Structural Health Monitoring (SHM) are becoming essential in many application contexts, e.g. civil, industrial, aerospace etc., to reduce structures maintenance costs and improve safety. Conventional inspection methods typically exploit bulky and expensive instruments and rely on highly demanding signal processing techniques. The pressing need to overcome these limitations is the common thread that guided the work presented in this Thesis. In the first part, a scalable, low-cost and multi-sensors smart sensor network is introduced. The capability of this technology to carry out accurate modal analysis on structures undergoing flexural vibrations has been validated by means of two experimental campaigns. Then, the suitability of low-cost piezoelectric disks in modal analysis has been demonstrated. To enable the use of this kind of sensing technology in such non conventional applications, ad hoc data merging algorithms have been developed. In the second part, instead, imaging algorithms for Lamb waves inspection (namely DMAS and DS-DMAS) have been implemented and validated. Results show that DMAS outperforms the canonical Delay and Sum (DAS) approach in terms of image resolution and contrast. Similarly, DS-DMAS can achieve better results than both DMAS and DAS by suppressing artefacts and noise. To exploit the full potential of these procedures, accurate group velocity estimations are required. Thus, novel wavefield analysis tools that can address the estimation of the dispersion curves from SLDV acquisitions have been investigated. An image segmentation technique (called DRLSE) was exploited in the k-space to draw out the wavenumber profile. The DRLSE method was compared with compressive sensing methods to extract the group and phase velocity information. The validation, performed on three different carbon fibre plates, showed that the proposed solutions can accurately determine the wavenumber and velocities in polar coordinates at multiple excitation frequencies

Regularized Estimation of High-dimensional Covariance Matrices.

Many signal processing methods are fundamentally related to the estimation of covariance matrices. In cases where there are a large number of covariates the dimension of covariance matrices is much larger than the number of available data samples. This is especially true in applications where data acquisition is constrained by limited resources such as time, energy, storage and bandwidth. This dissertation attempts to develop necessary components for covariance estimation in the high-dimensional setting. The dissertation makes contributions in two main areas of covariance estimation: (1) high dimensional shrinkage regularized covariance estimation and (2) recursive online complexity regularized estimation with applications of anomaly detection, graph tracking, and compressive sensing. New shrinkage covariance estimation methods are proposed that significantly outperform previous approaches in terms of mean squared error. Two multivariate data scenarios are considered: (1) independently Gaussian distributed data; and (2) heavy tailed elliptically contoured data. For the former scenario we improve on the Ledoit-Wolf (LW) shrinkage estimator using the principle of Rao-Blackwell conditioning and iterative approximation of the clairvoyant estimator. In the latter scenario, we apply a variance normalizing transformation and propose an iterative robust LW shrinkage estimator that is distribution-free within the elliptical family. The proposed robustified estimator is implemented via fixed point iterations with provable convergence and unique limit. A recursive online covariance estimator is proposed for tracking changes in an underlying time-varying graphical model. Covariance estimation is decomposed into multiple decoupled adaptive regression problems. A recursive recursive group lasso is derived using a homotopy approach that generalizes online lasso methods to group sparse system identification. By reducing the memory of the objective function this leads to a group lasso regularized LMS that provably dominates standard LMS. Finally, we introduce a state-of-the-art sampling system, the Modulated Wideband Converter (MWC) which is based on recently developed analog compressive sensing theory. By inferring the block-sparse structures of the high-dimensional covariance matrix from a set of random projections, the MWC is capable of achieving sub-Nyquist sampling for multiband signals with arbitrary carrier frequency over a wide bandwidth.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86396/1/yilun_1.pd