Coping with spectrum and energy scarcity in Wireless Networks: a Stochastic Optimization approach to Cognitive Radio and Energy Harvesting

In the last decades, we have witnessed an explosion of wireless communications and networking, spurring a great interest in the research community. The design of wireless networks is challenged by the scarcity of resources, especially spectrum and energy. In this thesis, we explore the potential offered by two novel technologies to cope with spectrum and energy scarcity: Cognitive Radio (CR) and Energy Harvesting (EH). CR is a novel paradigm for improving the spectral efficiency in wireless networks, by enabling the coexistence of an incumbent legacy system and an opportunistic system with CR capability. We investigate a technique where the CR system exploits the temporal redundancy introduced by the Hybrid Automatic Retransmission reQuest (HARQ) protocol implemented by the legacy system to perform interference cancellation, thus enhancing its own throughput. Recently, EH has been proposed to cope with energy scarcity in Wireless Sensor Networks (WSNs). Devices with EH capability harvest energy from the environment, e.g., solar, wind, heat or piezo-electric, to power their circuitry and to perform data sensing, processing and communication tasks. Due to the random energy supply, how to best manage the available energy is an open research issue. In the second part of this thesis, we design control policies for EH devices, and investigate the impact of factors such as the finite battery storage, time-correlation in the EH process and battery degradation phenomena on the performance of such systems. We cast both paradigms in a stochastic optimization framework, and investigate techniques to cope with spectrum and energy scarcity by opportunistically leveraging interference and ambient energy, respectively, whose benefits are demonstrated both by theoretical analysis and numerically. As an additional topic, we investigate the issue of channel estimation in UltraWide-Band (UWB) systems. Due to the large transmission bandwidth, the channel has been typically modeled as sparse. However, some propagation phenomena, e.g., scattering from rough surfaces and frequency distortion, are better modeled by a diffuse channel. We propose a novel Hybrid Sparse/Diffuse (HSD) channel model which captures both components, and design channel estimators based on it

Sparse channel estimation based on compressed sensing theory for UWB systems

Català: L'estimació de canal en receptors wireless esdevé un factor determinant a l'hora de incrementar les prestacions dels sistemes sense fils per tal de satisfer les exigències cada vegades més elevades dels consumidors en quant a velocitats de transmissió i qualitat. En aquesta tesi es proposa explotar la "sparsity" que mostren els canals wireless per tal de millorar els clàssics sistemes d'estimació de canal mitjançant les noves teòries de Compressed Sensing. Així doncs, es proposa un nou model freqüencial de senyal on el canal i un nou algoritme de reconstrucció de senyals sparse que redueix la probabilitat de detecció de falsos camins de propagació millorant d'aquesta manera l'estimació de temps d'arribada.Castellano: En los últimos años, la revolución inalámbrica se ha convertido en una realidad. Wi-fi está en todas partes, impactando significativamente en nuestro estilo de vida. Sin embargo, las comunicaciones inalámbricas nunca tendrán las condiciones de propagación igual que los cables debido a las duras condiciones de la propagación inalámbricas. El canal de radio móvil se caracteriza por la recepción múltiple, eso es que la señal recibida no sólo contiene una camino de propagación, sino también un gran número de ondas reflejadas. Estas ondas reflejadas interfieren con la onda directa, lo que provoca una degradación significativa del rendimiento del enlace. Un sistema inalámbrico debe estar diseñado de tal manera que el efecto adverso del desvanecimiento multicamino sea reducido al mínimo. Afortunadamente, el multipath puede ser visto como diversidad de información dependiendo de la cantidad de Channel State Information (CSI) disponible para el sistema. Sin embargo, en la práctica CSI rara vez se dispone a priori y debe ser estimado. Por otro lado, un canal inalámbrico a menudo puede ser modelado como un canal sparse, en la que el retraso de propagación puede ser muy grande, pero el número de caminos de propagación es normalmente muy pequeño. El conocimiento previo de la sparsity del canal se puede utilizar eficazmente para mejorar la estimación de canal utilizando la nueva teoría de Compressed Sensing (CS). CS se origina en la idea de que no es necesario invertir una gran cantidad de energía en la observación de las entradas de una señal sparse porque la mayoría de ellas será cero. Por lo tanto, CS proporciona un marco sólido para la reducción del número de medidas necesarias para resumir señales sparse. La estimación de canal sparse se centra en este trabajo en Ultra-Wideband (UWB) porque la gran resolución temporal que proporcionan las señales UWB se traduce en un número muy grande de componentes multipath que se pueden resolver. Por lo tanto, UWB mitiga significativamente la distorsión de trayectoria múltiple y proporciona la diversidad multicamino. Esta diversidad junto con la resolución temporal de las señales UWB crear un problema de estimación de canal muy interesante. En esta tesis se estudia el uso de CS en la estimación de canal altamente sparse por medio de un nuevo enfoque de estimación basado en el modelo de frecuencial de la señal UWB. También se propone un nuevo algoritmo llamado extended Orthogonal Matching Pursuit (eOMP) basado en los mismos principios que el clásico OMP, con el fin de mejorar algunas de sus característica.English: In recent years, the wireless revolution has become a reality. Wireless is everywhere having significant impact on our lifestyle. However, wireless will never have the same propagation conditions as wires due to the harsh conditions of the wireless propagation. The mobile radio channel is characterized by multipath reception, that is the signal offered to the receiver contains not only a direct line-of-sight radio wave, but also a large number of reflected radio waves. These reflected waves interfere with the direct wave, which causes significant degradation of the performance of the link. A wireless system has to be designed in such way that the adverse effect of multipath fading is minimized. Fortunately, multipath can be seen as a blessing depending on the amount of Channel State Information (CSI) available to the system. However, in practise CSI is seldom available a priori and needs to be estimated. On the other hand, a wireless channel can often be modeled as a sparse channel in which the delay spread could be very large, but the number of significant paths is normally very small. The prior knowledge of the channel sparseness can be effectively use to improve the channel estimation using the novel Compressed Sensing (CS) theory. CS originates from the idea that is not necessary to invest a lot of power into observing the entries of a sparse signal because most of them will be zero. Therefore, CS provides a robust framework for reducing the number of measurement required to summarize sparse signals. The sparse channel estimation here is focused on Ultra-WideBand (UWB) systems because the very fine time resolution of the UWB signal results in a very large number of resolvable multipath components. Consequently, UWB significantly mitigates multipath distortion and provides path diversity. The rich multipath coupled with the fine time resolution of the UWB signals create a challenging sparse channel estimation problem. This Master Thesis examines the use of CS in the estimation of highly sparse channel by means of a new sparse channel estimation approach based on the frequency domain model of the UWB signal. It is also proposed a new greedy algorithm named extended Orthogonal Matching Pursuit (eOMP) based on the same principles than classical Orthogonal Matching Pursuit (OMP) in order to improve some OMP characteristics. Simulation results show that the new eOMP provides lower false path detection probability compared with classical OMP, which also leads to a better TOA estimation without significant degradation of the channel estimation. Simulation results will also show that the new frequency domain sparse channel model outperforms other models presented in the literature

Ultra-Wideband Relay Communication Systems

Impulse-radio ultra-wide-band (IR-UWB) signaling is a promising technique for high-speed, short-range relay communications networks. Depending on how the relay node retransmits the signal, there are two main relay schemes: conventional one-directional (one-way) relay model, and bi-directional (two-way) relay model. In bi-directional relay communications, wireless network coding (WNC), also called physical-layer network coding (PNC), could be applied to overcome the spectral efficiency limitation of the conventional one-way relay. In the first part of this work, we propose asynchronous, differential, and bidirectional decode and forward (ADBDF) and asynchronous, differential, and bidirectional denoise and forward (ADBDNF) UWB relay methods, where the relay node (RN) does not need to be synchronized with the end nodes (ENs). The proposed schemes are attractive for networks in which stringent/complicated synchronization between the RN and the ENs may not be feasible. The second part of this work focuses on UWB channel classification. We propose a 2-dimensional (2-D) LOS/NLOS classification scheme that uses skewness of the channel impulse/pulse response. The proposed channel classification decreases the complexity of existing channel classification methods and can be used in a variety of areas such as localization, relay communications, and cooperative communications. The final part of this work deals with compressive sensing (CS) algorithms that employ sub-Nyquist sampling for UWB communications. We develop coarse graining (CG) for the proposed CS sub-Nyquist sampling technique, which leads to: (1) reduced sampling rate at the receiver, and hence reduced use of analog-to-digital converters (ADCs) resources; and (2) low-complexity channel estimation

Remote Sensing

This dual conception of remote sensing brought us to the idea of preparing two different books; in addition to the first book which displays recent advances in remote sensing applications, this book is devoted to new techniques for data processing, sensors and platforms. We do not intend this book to cover all aspects of remote sensing techniques and platforms, since it would be an impossible task for a single volume. Instead, we have collected a number of high-quality, original and representative contributions in those areas

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

Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github