Assistant Vehicle Localization Based on Three Collaborative Base Stations via SBL-Based Robust DOA Estimation

As a promising research area in Internet of Things (IoT), Internet of Vehicles (IoV) has attracted much attention in wireless communication and network. In general, vehicle localization can be achieved by the global positioning systems (GPSs). However, in some special scenarios, such as cloud cover, tunnels or some places where the GPS signals are weak, GPS cannot perform well. The continuous and accurate localization services cannot be guaranteed. In order to improve the accuracy of vehicle localization, an assistant vehicle localization method based on direction-of-arrival (DOA) estimation is proposed in this paper. The assistant vehicle localization system is composed of three base stations (BSs) equipped with a multiple input multiple output (MIMO) array. The locations of vehicles can be estimated if the positions of the three BSs and the DOAs of vehicles estimated by the BSs are known. However, the DOA estimated accuracy maybe degrade dramatically when the electromagnetic environment is complex. In the proposed method, a sparse Bayesian learning (SBL)-based robust DOA estimation approach is first proposed to achieve the off-grid DOA estimation of the target vehicles under the condition of nonuniform noise, where the covariance matrix of nonuniform noise is estimated by a least squares (LSs) procedure, and a grid refinement procedure implemented by finding the roots of a polynomial is performed to refine the grid points to reduce the off-grid error. Then, according to the DOA estimation results, the target vehicle is cross-located once by each two BSs in the localization system. Finally, robust localization can be realized based on the results of three-time cross-location. Plenty of simulation results demonstrate the effectiveness and superiority of the proposed method

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

Sparse Array Signal Processing

This dissertation details three approaches for direction-of-arrival (DOA) estimation or beamforming in array signal processing from the perspective of sparsity. In the first part of this dissertation, we consider sparse array beamformer design based on the alternating direction method of multipliers (ADMM); in the second part of this dissertation, the problem of joint DOA estimation and distorted sensor detection is investigated; and off-grid DOA estimation is studied in the last part of this dissertation. In the first part of this thesis, we devise a sparse array design algorithm for adaptive beamforming. Our strategy is based on finding a sparse beamformer weight to maximize the output signal-to-interference-plus-noise ratio (SINR). The proposed method utilizes ADMM, and admits closed-form solutions at each ADMM iteration. The algorithm convergence properties are analyzed by showing the monotonicity and boundedness of the augmented Lagrangian function. In addition, we prove that the proposed algorithm converges to the set of Karush-Kuhn-Tucker stationary points. Numerical results exhibit its excellent performance, which is comparable to that of the exhaustive search approach, slightly better than those of the state-of-the-art solvers, and significantly outperforms several other sparse array design strategies, in terms of output SINR. Moreover, the proposed ADMM algorithm outperforms its competitors, in terms of computational cost. Distorted sensors could occur randomly and may lead to the breakdown of a sensor array system. In the second part of this thesis, we consider an array model in which a small number of sensors are distorted by unknown sensor gain and phase errors. With such an array model, the problem of joint DOA estimation and distorted sensor detection is formulated under the framework of low-rank and row-sparse decomposition. We derive an iteratively reweighted least squares (IRLS) algorithm to solve the resulting problem. The convergence property of the IRLS algorithm is analyzed by means of the monotonicity and boundedness of the objective function. Extensive simulations are conducted in view of parameter selection, convergence speed, computational complexity, and performance of DOA estimation as well as distorted sensor detection. Even though the IRLS algorithm is slightly worse than the ADMM in detecting the distorted sensors, the results show that our approach outperforms several state-of-the-art techniques in terms of convergence speed, computational cost, and DOA estimation performance. In the last part of this thesis, the problem of off-grid DOA estimation is investigated. We develop a method to jointly estimate the closest spatial frequency (the sine of DOA) grids, and the gaps between the estimated grids and the corresponding frequencies. By using a second-order Taylor approximation, the data model under the framework of joint-sparse representation is formulated. We point out an important property of the signals of interest in the model, namely the proportionality relationship. The proportionality relationship is empirically demonstrated to be useful in the sense that it increases the probability of the mixing matrix satisfying the block restricted isometry property. Simulation examples demonstrate the effectiveness and superiority of the proposed method against several state-of-the-art grid-based approaches

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

Sparsity based methods for target localization in multi-sensor radar

In this dissertation, several sparsity-based methods for ground moving target indicator (GMTI) radar with multiple-input multiple-output (MIMO) random arrays are proposed. MIMO random arrays are large arrays that employ multiple transmitters and receivers, the positions of the transmitters and the receivers are randomly chosen. Since the resolution of the array depends on the size of the array, MIMO random arrays obtain a high resolution. However, since the positions of the sensors are randomly chosen, the array suffers from large sidelobes which may lead to an increased false alarm probability. The number of sensors of a MIMO random array required to maintain a certain level of peak sidelobes is studied. It is shown that the number of sensors scales with the logarithm of the array aperture, in contrast with a ULA where the number of elements scales linearly with the array aperture. The problem of sparse target detection given space-time observations from MIMO random arrays is presented. The observations are obtained in the presence of Gaussian colored noise of unknown covariance matrix, but for which secondary data is available for its estimation. To solve the detection problem two sparsity-based algorithms, the MP-STAP and the MBMP-STAP algorithms are proposed that utilizes knowledge of the upper bound on the number of targets. A constant false alarm rate (CFAR) sparsity based detector that does not utilize any information on the number of targets referred to as MP-CFAR and MBMP-CFAR are also developed. A performance analysis for the new CFAR detector is also derived, the metrics used to describe the performance of the detector are the probability of false alarm and the probability of detection. A grid refinement procedure is also proposed to eliminate the need for a dense grid which would increase the computational complexity significantly. Expressions for the computational complexity of the proposed CFAR detectors are derived. It is shown that the proposed CFAR detectors outperforms the popular adaptive beamformer at a modest increase in computational complexity

Towards the Next Generation of Location-Aware Communications

This thesis is motivated by the expected implementation of the next generation mobile networks (5G) from 2020, which is being designed with a radical paradigm shift towards millimeter-wave technology (mmWave). Operating in 30--300 GHz frequency band (1--10 mm wavelengths), massive antenna arrays that provide a high angular resolution, while being packed on a small area will be used. Moreover, since the abundant mmWave spectrum is barely occupied, large bandwidth allocation is possible and will enable low-error time estimation. With this high spatiotemporal resolution, mmWave technology readily lends itself to extremely accurate localization that can be harnessed in the network design and optimization, as well as utilized in many modern applications. Localization in 5G is still in early stages, and very little is known about its performance and feasibility. In this thesis, we contribute to the understanding of 5G mmWave localization by focusing on challenges pertaining to this emerging technology. Towards that, we start by considering a conventional cellular system and propose a positioning method under outdoor LOS/NLOS conditions that, although approaches the Cram\'er-Rao lower bound (CRLB), provides accuracy in the order of meters. This shows that conventional systems have limited range of location-aware applications. Next, we focus on mmWave localization in three stages. Firstly, we tackle the initial access (IA) problem, whereby user equipment (UE) attempts to establish a link with a base station (BS). The challenge in this problem stems from the high directivity of mmWave. We investigate two beamforming schemes: directional and random. Subsequently, we address 3D localization beyond IA phase. Devices nowadays have higher computational capabilities and may perform localization in the downlink. However, beamforming on the UE side is sensitive to the device orientation. Thus, we study localization in both the uplink and downlink under multipath propagation and derive the position (PEB) and orientation error bounds (OEB). We also investigate the impact of the number of antennas and the number of beams on these bounds. Finally, the above components assume that the system is synchronized. However, synchronization in communication systems is not usually tight enough for localization. Therefore, we study two-way localization as a means to alleviate the synchronization requirement and investigate two protocols: distributed (DLP) and centralized (CLP). Our results show that random-phase beamforming is more appropriate IA approach in the studied scenarios. We also observe that the uplink and downlink are not equivalent, in that the error bounds scale differently with the number of antennas, and that uplink localization is sensitive to the UE orientation, while downlink is not. Furthermore, we find that NLOS paths generally boost localization. The investigation of the two-way protocols shows that CLP outperforms DLP by a significant margin. We also observe that mmWave localization is mainly limited by angular rather than temporal estimation. In conclusion, we show that mmWave systems are capable of localizing a UE with sub-meter position error, and sub-degree orientation error, which asserts that mmWave will play a central role in communication network optimization and unlock opportunities that were not available in the previous generation