Compressive Acquisition and Processing of Sparse Analog Signals

Since the advent of the first digital processing units, the importance of digital signal processing has been steadily rising. Today, most signal processing happens in the digital domain, requiring that analog signals be first sampled and digitized before any relevant data can be extracted from them. The recent explosion of the demands for data acquisition, storage and processing, however, has pushed the capabilities of conventional acquisition systems to their limits in many application areas. By offering an alternative view on the signal acquisition process, ideas from sparse signal processing and one of its main beneficiaries compressed sensing (CS), aim at alleviating some of these problems. In this thesis, we look into the ways the application of a compressive measurement kernel impacts the signal recovery performance and investigate methods to infer the current signal complexity from the compressive observations. We then study a particular application, namely that of sub-Nyquist sampling and processing of sparse analog multiband signals in spectral, angular and spatial domains.Seit dem Aufkommen der ersten digitalen Verarbeitungseinheiten hat die Bedeutung der digitalen Signalverarbeitung stetig zugenommen. Heutzutage findet die meiste Signalverarbeitung im digitalen Bereich statt, was erfordert, dass analoge Signale zuerst abgetastet und digitalisiert werden, bevor relevante Daten daraus extrahiert werden können. Jahrzehntelang hat die herkömmliche äquidistante Abtastung, die durch das Nyquist-Abtasttheorem bestimmt wird, zu diesem Zweck ein nahezu universelles Mittel bereitgestellt. Der kürzliche explosive Anstieg der Anforderungen an die Datenerfassung, -speicherung und -verarbeitung hat jedoch die Fähigkeiten herkömmlicher Erfassungssysteme in vielen Anwendungsbereichen an ihre Grenzen gebracht. Durch eine alternative Sichtweise auf den Signalerfassungsprozess können Ideen aus der sparse Signalverarbeitung und einer ihrer Hauptanwendungsgebiete, Compressed Sensing (CS), dazu beitragen, einige dieser Probleme zu mindern. Basierend auf der Annahme, dass der Informationsgehalt eines Signals oft viel geringer ist als was von der nativen Repräsentation vorgegeben, stellt CS ein alternatives Konzept für die Erfassung und Verarbeitung bereit, das versucht, die Abtastrate unter Beibehaltung des Signalinformationsgehalts zu reduzieren. In dieser Arbeit untersuchen wir einige der Grundlagen des endlichdimensionalen CSFrameworks und seine Verbindung mit Sub-Nyquist Abtastung und Verarbeitung von sparsen analogen Signalen. Obwohl es seit mehr als einem Jahrzehnt ein Schwerpunkt aktiver Forschung ist, gibt es noch erhebliche Lücken beim Verständnis der Auswirkungen von komprimierenden Ansätzen auf die Signalwiedergewinnung und die Verarbeitungsleistung, insbesondere bei rauschbehafteten Umgebungen und in Bezug auf praktische Messaufgaben. In dieser Dissertation untersuchen wir, wie sich die Anwendung eines komprimierenden Messkerns auf die Signal- und Rauschcharakteristiken auf die Signalrückgewinnungsleistung auswirkt. Wir erforschen auch Methoden, um die aktuelle Signal-Sparsity-Order aus den komprimierten Messungen abzuleiten, ohne auf die Nyquist-Raten-Verarbeitung zurückzugreifen, und zeigen den Vorteil, den sie für den Wiederherstellungsprozess bietet. Nachdem gehen wir zu einer speziellen Anwendung, nämlich der Sub-Nyquist-Abtastung und Verarbeitung von sparsen analogen Multibandsignalen. Innerhalb des Sub-Nyquist-Abtastung untersuchen wir drei verschiedene Multiband-Szenarien, die Multiband-Sensing in der spektralen, Winkel und räumlichen-Domäne einbeziehen.Since the advent of the first digital processing units, the importance of digital signal processing has been steadily rising. Today, most signal processing happens in the digital domain, requiring that analog signals be first sampled and digitized before any relevant data can be extracted from them. For decades, conventional uniform sampling that is governed by the Nyquist sampling theorem has provided an almost universal means to this end. The recent explosion of the demands for data acquisition, storage and processing, however, has pushed the capabilities of conventional acquisition systems to their limits in many application areas. By offering an alternative view on the signal acquisition process, ideas from sparse signal processing and one of its main beneficiaries compressed sensing (CS), have the potential to assist alleviating some of these problems. Building on the premise that the signal information rate is often much lower than what is dictated by its native representation, CS provides an alternative acquisition and processing framework that attempts to reduce the sampling rate while preserving the information content of the signal. In this thesis, we explore some of the basic foundations of the finite-dimensional CS framework and its connection to sub-Nyquist sampling and processing of sparse continuous analog signals with application to multiband sensing. Despite being a focus of active research for over a decade, there still remain signi_cant gaps in understanding the implications that compressive approaches have on the signal recovery and processing performance, especially against noisy settings and in relation to practical sampling problems. This dissertation aims at filling some of these gaps. More specifically, we look into the ways the application of a compressive measurement kernel impacts signal and noise characteristics and the relation it has to the signal recovery performance. We also investigate methods to infer the current complexity of the signal scene from the reduced-rate compressive observations without resorting to Nyquist-rate processing and show the advantage this knowledge offers to the recovery process. Having considered some of the universal aspects of compressive systems, we then move to studying a particular application, namely that of sub-Nyquist sampling and processing of sparse analog multiband signals. Within the sub-Nyquist sampling framework, we examine three different multiband scenarios that involve multiband sensing in spectral, angular and spatial domains. For each of them, we provide a sub-Nyquist receiver architecture, develop recovery methods and numerically evaluate their performance

Orthogonal frequency division multiplexing multiple-input multiple-output automotive radar with novel signal processing algorithms

Advanced driver assistance systems that actively assist the driver based on environment perception achieved significant advances in recent years. Along with this development, autonomous driving became a major research topic that aims ultimately at development of fully automated, driverless vehicles. Since such applications rely on environment perception, their ever increasing sophistication imposes growing demands on environmental sensors. Specifically, the need for reliable environment sensing necessitates the development of more sophisticated, high-performance radar sensors. A further vital challenge in terms of increased radar interference arises with the growing market penetration of the vehicular radar technology. To address these challenges, in many respects novel approaches and radar concepts are required. As the modulation is one of the key factors determining the radar performance, the research of new modulation schemes for automotive radar becomes essential. A topic that emerged in the last years is the radar operating with digitally generated waveforms based on orthogonal frequency division multiplexing (OFDM). Initially, the use of OFDM for radar was motivated by the combination of radar with communication via modulation of the radar waveform with communication data. Some subsequent works studied the use of OFDM as a modulation scheme in many different radar applications - from adaptive radar processing to synthetic aperture radar. This suggests that the flexibility provided by OFDM based digital generation of radar waveforms can potentially enable novel radar concepts that are well suited for future automotive radar systems. This thesis aims to explore the perspectives of OFDM as a modulation scheme for high-performance, robust and adaptive automotive radar. To this end, novel signal processing algorithms and OFDM based radar concepts are introduced in this work. The main focus of the thesis is on high-end automotive radar applications, while the applicability for real time implementation is of primary concern. The first part of this thesis focuses on signal processing algorithms for distance-velocity estimation. As a foundation for the algorithms presented in this thesis, a novel and rigorous signal model for OFDM radar is introduced. Based on this signal model, the limitations of the state-of-the-art OFDM radar signal processing are pointed out. To overcome these limitations, we propose two novel signal processing algorithms that build upon the conventional processing and extend it by more sophisticated modeling of the radar signal. The first method named all-cell Doppler compensation (ACDC) overcomes the Doppler sensitivity problem of OFDM radar. The core idea of this algorithm is the scenario-independent correction of Doppler shifts for the entire measurement signal. Since Doppler effect is a major concern for OFDM radar and influences the radar parametrization, its complete compensation opens new perspectives for OFDM radar. It not only achieves an improved, Doppler-independent performance, it also enables more favorable system parametrization. The second distance-velocity estimation algorithm introduced in this thesis addresses the issue of range and Doppler frequency migration due to the target’s motion during the measurement. For the conventional radar signal processing, these migration effects set an upper limit on the simultaneously achievable distance and velocity resolution. The proposed method named all-cell migration compensation (ACMC) extends the underlying OFDM radar signal model to account for the target motion. As a result, the effect of migration is compensated implicitly for the entire radar measurement, which leads to an improved distance and velocity resolution. Simulations show the effectiveness of the proposed algorithms in overcoming the two major limitations of the conventional OFDM radar signal processing. As multiple-input multiple-output (MIMO) radar is a well-established technology for improving the direction-of-arrival (DOA) estimation, the second part of this work studies the multiplexing methods for OFDM radar that enable simultaneous use of multiple transmit antennas for MIMO radar processing. After discussing the drawbacks of known multiplexing methods, we introduce two advanced multiplexing schemes for OFDM-MIMO radar based on non-equidistant interleaving of OFDM subcarriers. These multiplexing approaches exploit the multicarrier structure of OFDM for generation of orthogonal waveforms that enable a simultaneous operation of multiple MIMO channels occupying the same bandwidth. The primary advantage of these methods is that despite multiplexing they maintain all original radar parameters (resolution and unambiguous range in distance and velocity) for each individual MIMO channel. To obtain favorable interleaving patterns with low sidelobes, we propose an optimization approach based on genetic algorithms. Furthermore, to overcome the drawback of increased sidelobes due to subcarrier interleaving, we study the applicability of sparse processing methods for the distance-velocity estimation from measurements of non-equidistantly interleaved OFDM-MIMO radar. We introduce a novel sparsity based frequency estimation algorithm designed for this purpose. The third topic addressed in this work is the robustness of OFDM radar to interference from other radar sensors. In this part of the work we study the interference robustness of OFDM radar and propose novel interference mitigation techniques. The first interference suppression algorithm we introduce exploits the robustness of OFDM to narrowband interference by dropping subcarriers strongly corrupted by interference from evaluation. To avoid increase of sidelobes due to missing subcarriers, their values are reconstructed from the neighboring ones based on linear prediction methods. As a further measure for increasing the interference robustness in a more universal manner, we propose the extension of OFDM radar with cognitive features. We introduce the general concept of cognitive radar that is capable of adapting to the current spectral situation for avoiding interference. Our work focuses mainly on waveform adaptation techniques; we propose adaptation methods that allow dynamic interference avoidance without affecting adversely the estimation performance. The final part of this work focuses on prototypical implementation of OFDM-MIMO radar. With the constructed prototype, the feasibility of OFDM for high-performance radar applications is demonstrated. Furthermore, based on this radar prototype the algorithms presented in this thesis are validated experimentally. The measurements confirm the applicability of the proposed algorithms and concepts for real world automotive radar implementations

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

Advanced RFI detection, RFI excision, and spectrum sensing : algorithms and performance analyses

Because of intentional and unintentional man-made interference, radio frequency interference (RFI) is causing performance loss in various radio frequency operating systems such as microwave radiometry, radio astronomy, satellite communications, ultra-wideband communications, radar, and cognitive radio. To overcome the impact of RFI, a robust RFI detection coupled with an efficient RFI excision are, thus, needed. Amongst their limitations, the existing techniques tend to be computationally complex and render inefficient RFI excision. On the other hand, the state-of-the-art on cognitive radio (CR) encompasses numerous spectrum sensing techniques. However, most of the existing techniques either rely on the availability of the channel state information (CSI) or the primary signal characteristics. Motivated by the highlighted limitations, this Ph.D. dissertation presents research investigations and results grouped into three themes: advanced RFI detection, advanced RFI excision, and advanced spectrum sensing. Regarding advanced RFI detection, this dissertation presents five RFI detectors: a power detector (PD), an energy detector (ED), an eigenvalue detector (EvD), a matrix-based detector, and a tensor-based detector. First, a computationally simple PD is investigated to detect a brodband RFI. By assuming Nakagami-m fading channels, exact closed-form expressions for the probabilities of RFI detection and of false alarm are derived and validated via simulations. Simulations also demonstrate that PD outperforms kurtosis detector (KD). Second, an ED is investigated for RFI detection in wireless communication systems. Its average probability of RFI detection is studied and approximated, and asymptotic closed-form expressions are derived. Besides, an exact closed-form expression for its average probability of false alarm is derived. Monte-Carlo simulations validate the derived analytical expressions and corroborate that the investigated ED outperforms KD and a generalized likelihood ratio test (GLRT) detector. The performance of ED is also assessed using real-world RFI contaminated data. Third, a blind EvD is proposed for single-input multiple-output (SIMO) systems that may suffer from RFI. To characterize the performance of EvD, performance closed-form expressions valid for infinitely huge samples are derived and validated through simulations. Simulations also corroborate that EvD manifests, even under sample starved settings, a comparable detection performance with a GLRT detector fed with the knowledge of the signal of interest (SOI) channel and a matched subspace detector fed with the SOI and RFI channels. At last, for a robust detection of RFI received through a multi-path fading channel, this dissertation presents matrix-based and tensor-based multi-antenna RFI detectors while introducing a tensor-based hypothesis testing framework. To characterize the performance of these detectors, performance analyses have been pursued. Simulations assess the performance of the proposed detectors and validate the derived asymptotic characterizations. Concerning advanced RFI excision, this dissertation introduces a multi-linear algebra framework to the multi-interferer RFI (MI-RFI) excision research by proposing a multi-linear subspace estimation and projection (MLSEP) algorithm for SIMO systems. Having employed smoothed observation windows, a smoothed MLSEP (s-MLSEP) algorithm is also proposed. MLSEP and s-MLSEP require the knowledge of the number of interferers and their respective channel order. Accordingly, a novel smoothed matrix-based joint number of interferers and channel order enumerator is proposed. Performance analyses corroborate that both MLSEP and s-MLSEP can excise all interferers when the perturbations get infinitesimally small. For such perturbations, the analyses also attest that s-MLSEP exhibits a faster convergence to a zero excision error than MLSEP which, in turn, converges faster than a subspace projection algorithm. Despite its slight complexity, simulations and performance assessment on real-world data demonstrate that MLSEP outperforms projection-based RFI excision algorithms. Simulations also corroborate that s-MLSEP outperforms MLSEP as the smoothing factor gets smaller. With regard to advanced spectrum sensing, having been inspired by an F–test detector with a simple analytical false alarm threshold expression considered an alternative to the existing blind detectors, this dissertation presents and evaluates simple F–test based spectrum sensing techniques that do not require the knowledge of CSI for multi-antenna CRs. Exact and asymptotic analytical performance closed-form expressions are derived for the presented detectors. Simulations assess the performance of the presented detectors and validate the derived expressions. For an additive noise exhibiting the same variance across multiple-antenna frontends, simulations also corroborate that the presented detectors are constant false alarm rate detectors which are also robust against noise uncertainty