14,487 research outputs found

    Analysing Convergence through the Distribution Dynamics Approach: Why and how?

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    The convergence hypothesis has stimulated a heated debate within the growth literature. The present paper compares the two most commonly adopted empirical approaches, the regression approach and the distribution dynamics approach, and argues that the former fails to uncover important features of the dynamics that might characterise the convergence process. Next, it provides an in depth description of the features and underlying assumptions of the distribution dynamics approach as well as a detailed discussion of some important aspects related to the estimate of stochastic kernels via kernel density estimators. Finally, the empirical section allows to emphasises the interpretational advantages stemming from the use of stochastic kernels to capture the evolution of the entire cross-sectional income distribution. Incidentally, through a comparison between the results obtained from alternative sets of Italian regions, it suggest that the use of administrative regions could lead to ambiguous results.Distribution Dynamics, Stochastic Kernel, Kernel Density Estimation, beta-convergence, Regions

    A Methodological Investigation of Cost of Carbon Sequestration

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    Increased attention by policy makers to the threat of global climate change has brought with it considerable attention to the possibility of encouraging the growth of forests as a means of sequestering carbon dioxide. This approach has, in fact, become an explicit element of both U.S. and international climate policies. This paper develops a methodology whereby estimates of the costs of carbon sequestration can be developed on the basis of evidence from observations of landowners' behavior when confronted with the opportunity costs of alternative land uses. The analytical model takes account of silvicultural understanding of the intertemporal linkages between deforestation and carbon emissions, on the one hand and between forestation and carbon sequestration, on the other. The results support the efficacy and potential value of this analytical approach. The paper is intended to be illustrative of how econometric analyses of land use, which already exist for a number of countries, can be used to develop better region-specific estimates of the marginal costs of carbon sequestration.

    Joint Communication and Positioning based on Channel Estimation

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    Mobile wireless communication systems have rapidly and globally become an integral part of everyday life and have brought forth the internet of things. With the evolution of mobile wireless communication systems, joint communication and positioning becomes increasingly important and enables a growing range of new applications. Humanity has already grown used to having access to multimedia data everywhere at every time and thereby employing all sorts of location-based services. Global navigation satellite systems can provide highly accurate positioning results whenever a line-of-sight path is available. Unfortunately, harsh physical environments are known to degrade the performance of existing systems. Therefore, ground-based systems can assist the existing position estimation gained by satellite systems. Determining positioning-relevant information from a unified signal structure designed for a ground-based joint communication and positioning system can either complement existing systems or substitute them. Such a system framework promises to enhance the existing systems by enabling a highly accurate and reliable positioning performance and increased coverage. Furthermore, the unified signal structure yields synergetic effects. In this thesis, I propose a channel estimation-based joint communication and positioning system that employs a virtual training matrix. This matrix consists of a relatively small training percentage, plus the detected communication data itself. Via a core semi- blind estimation approach, this iteratively includes the already detected data to accurately determine the positioning-relevant parameter, by mutually exchanging information between the communication part and the positioning part of the receiver. Synergy is created. I propose a generalized system framework, suitable to be used in conjunction with various communication system techniques. The most critical positioning-relevant parameter, the time-of-arrival, is part of a physical multipath parameter vector. Estimating the time-of-arrival, therefore, means solving a global, non-linear, multi-dimensional optimization problem. More precisely, it means solving the so-called inverse problem. I thoroughly assess various problem formulations and variations thereof, including several different measurements and estimation algorithms. A significant challenge, when it comes to solving the inverse problem to determine the positioning-relevant path parameters, is imposed by realistic multipath channels. Most parameter estimation algorithms have proven to perform well in moderate multipath environments. It is mathematically straightforward to optimize this performance in the sense that the number of observations has to exceed the number of parameters to be estimated. The typical parameter estimation problem, on the other hand, is based on channel estimates, and it assumes that so-called snapshot measurements are available. In the case of realistic channel models, however, the number of observations does not necessarily exceed the number of unknowns. In this thesis, I overcome this problem, proposing a method to reduce the problem dimensionality via joint model order selection and parameter estimation. Employing the approximated and estimated parameter covariance matrix inherently constrains the estimation problem’s model order selection to result in optimal parameter estimation performance and hence optimal positioning performance. To compare these results with the optimally achievable solution, I introduce a focused order-related lower bound in this thesis. Additionally, I use soft information as a weighting matrix to enhance the positioning algorithm positioning performance. For demonstrating the feasibility and the interplay of the proposed system components, I utilize a prototype system, based on multi-layer interleave division multiple access. This proposed system framework and the investigated techniques can be employed for multiple existing systems or build the basis for future joint communication and positioning systems. The assessed estimation algorithms are transferrable to all kinds of joint communication and positioning system designs. This thesis demonstrates their capability to, in principle, successfully cope with challenging estimation problems stemming from harsh physical environments

    Thirty Years of Machine Learning: The Road to Pareto-Optimal Wireless Networks

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    Future wireless networks have a substantial potential in terms of supporting a broad range of complex compelling applications both in military and civilian fields, where the users are able to enjoy high-rate, low-latency, low-cost and reliable information services. Achieving this ambitious goal requires new radio techniques for adaptive learning and intelligent decision making because of the complex heterogeneous nature of the network structures and wireless services. Machine learning (ML) algorithms have great success in supporting big data analytics, efficient parameter estimation and interactive decision making. Hence, in this article, we review the thirty-year history of ML by elaborating on supervised learning, unsupervised learning, reinforcement learning and deep learning. Furthermore, we investigate their employment in the compelling applications of wireless networks, including heterogeneous networks (HetNets), cognitive radios (CR), Internet of things (IoT), machine to machine networks (M2M), and so on. This article aims for assisting the readers in clarifying the motivation and methodology of the various ML algorithms, so as to invoke them for hitherto unexplored services as well as scenarios of future wireless networks.Comment: 46 pages, 22 fig

    Robust Positioning in the Presence of Multipath and NLOS GNSS Signals

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    GNSS signals can be blocked and reflected by nearby objects, such as buildings, walls, and vehicles. They can also be reflected by the ground and by water. These effects are the dominant source of GNSS positioning errors in dense urban environments, though they can have an impact almost anywhere. Non- line-of-sight (NLOS) reception occurs when the direct path from the transmitter to the receiver is blocked and signals are received only via a reflected path. Multipath interference occurs, as the name suggests, when a signal is received via multiple paths. This can be via the direct path and one or more reflected paths, or it can be via multiple reflected paths. As their error characteristics are different, NLOS and multipath interference typically require different mitigation techniques, though some techniques are applicable to both. Antenna design and advanced receiver signal processing techniques can substantially reduce multipath errors. Unless an antenna array is used, NLOS reception has to be detected using the receiver's ranging and carrier-power-to-noise-density ratio (C/N0) measurements and mitigated within the positioning algorithm. Some NLOS mitigation techniques can also be used to combat severe multipath interference. Multipath interference, but not NLOS reception, can also be mitigated by comparing or combining code and carrier measurements, comparing ranging and C/N0 measurements from signals on different frequencies, and analyzing the time evolution of the ranging and C/N0 measurements

    Higher dimensional time-energy entanglement

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    Judging by the compelling number of innovations based on taming quantum mechanical effects, such as the development of transistors and lasers, further research in this field promises to tackle further technological challenges in the years to come. This statement gains even more importance in the information processing scenario. Here, the growing data generation and the correspondingly higher need for more efficient computational resources and secure high bandwidth networks are central problems which need to be tackled. In this sense, the required CPU minituarization makes the design of structures at atomic levels inevitable, as foreseen by Moore's law. From these perspectives, it is necessary to concentrate further research efforts into controlling and manipulating quantum mechanical systems. This enables for example to encode quantum superposition states to tackle problems which are computationally NP hard and which therefore cannot be solved efficiently by classical computers. The only limitation affecting these solutions is the low scalability of existing quantum systems. Similarly, quantum communication schemes are devised to certify the secure transmission of quantum information, but are still limited by a low transmission bandwidth. This thesis follows the guideline defined by these research projects and aims to further increase the scalability of the quantum mechanical systems required to perform these tasks. The method used here is to encode quantum states into photons generated by spontaneous parametric down-conversion (SPDC). An intrinsic limitation of photons is that the scalability of quantum information schemes employing them is limited by the low detection efficiency of commercial single photon detectors. This is addressed by encoding higher dimensional quantum states into two photons, increasing the scalability of the scheme in comparison to multi-photon states. Further on, the encoding of quantum information into the emission-time degree of freedom improves its applicability to long distance quantum communication schemes. By doing that, the intrinsic limitations of other schemes based on the encoding into the momentum and polarization degree of freedom are overcome. This work presents results on a scalable experimental implementation of time-energy encoded higher dimensional states, demonstrating the feasibility of the scheme. Further tools are defined and used to characterize the properties of the prepared quantum states, such as their entanglement, their dimension and their preparation fidelity. Finally, the method of quantum state tomography is used to fully determine the underlying quantum states at the cost of an increased measurement effort and thus operation time. It is at this point that results obtained from the research field of compressed sensing help to decrease the necessary number of measurements. This scheme is compared with an adaptive tomography scheme designed to offer an additional reconstruction speedup. These results display the scalability of the scheme to bipartite dimensions higher than 2x8, equivalent to the encoding of quantum information into more than 6 qubits.Es ist in den letzten Jahren immer deutlicher geworden, dass weitere Forschung zur Untersuchung von quantenmechanischen Systemen durchgefĂŒhrt werden muss um die wachsenden Probleme in der heutigen Informationstechnologie zu adressieren. Insbesondere sticht hier die exponentiell wachsende Nachfrage nach Computerressourcen und nach sicheren Kommunikationsprotokollen mit hoher Bandbreite hervor, um der weiter wachsenden Datengenerationsrate standzuhalten. Dies stösst auf fundamentale Grenzen, wie die erforderliche Miniaturisierung von Prozessorstrukturen (CPUs) auf atomare Dimensionen demonstriert. Von dieser Perspektive her ist es erforderlich weitere Forschung zur Kontrolle und Manipulation von QuantenzustĂ€nden durchzufĂŒhren, wie sie zum Beispiel im Feld der Quanteninformation erfolgt ist. Diese Strategie ermöglicht es von weiteren Eigenschaften der Quantenmechanik, wie zum Beispiel der PrĂ€paration von SuperpositionszustĂ€nden, Gebrauch zu machen. Dies ist insbesondere relevant, da es ermöglicht NP harte Probleme zu lösen, die durch klassische Computer nicht effizient gelöst werden können. Allerdings sind bisher experimentell realisierte quantenmechanische Systeme noch nicht skalierbar genug um den Anforderungen der klassischen Technologie gerecht zu werden. Ähnlichen Argumenten folgend sind Quantenkommunikationssysteme, die die Sicherheit von Kommunikationsprotokolle zertifizieren können, noch nicht in der Lage angemessene Bandbreiten zu gewĂ€hrleisten. Diese Doktorarbeit gliedert sich diesen Forschungsprojekten an, mit dem Ziel die Skalierbarkeit von quantenmechanischen Systemen zu vergrössern und entsprechend den genannten Anforderungen gerecht zu machen. Die Strategie die hier verfolgt wird basiert auf die Kodierung von QuantenzustĂ€nden in Photonenpaare, die durch den Prozess der Spontanen Parametrischen Down-conversion (SPDC) erzeugt werden. Dieses Verfahren bringt allerdings eine limitierte Skalierbarkeit der Quantensysteme mit sich, da die Detektionseffizienz von kommerziell erhĂ€ltlichen Einzelphotonendetektoren limitiert ist. Dieses Problem wird in dieser Arbeit umgangen indem die QuantenzustĂ€nde in höher dimensionale HilbertrĂ€ume eines Zweiphotonenzustands kodiert werden, was einen deutlichen Vorteil gegenĂŒber der Kodierung in einen Mehrphotonenzustand darstellt. DarĂŒber hinaus ermöglicht die Kodierung der QuantenzustĂ€nde in den Emissionszeit Freiheitsgrad der Photonen intrinsische Vorteile bei ihrer Anwendung auf die Quantenkommunikation. Hier ist insbesondere der Vorteil gegenĂŒber der Kodierung in den Impuls- und Polarisationsfreiheitsgrad gemeint, die durch deutliche EinschrĂ€nkungen bei der Transmission ĂŒber lange Strecken gekennzeichnet sind. Mit einem Augenmerk auf diese Ziele wird in dieser Arbeit die experimentelle Umsetzbarkeit des beschriebenen Schemas gezeigt. Dies wurde durch die Anwendung von geeigneten Maßen wie die VerschrĂ€nkung, Dimension und PrĂ€parationsfidelity auf die generierten ZustĂ€nde quantifiziert. Insbesondere bei der AbschĂ€tzung der Fidelity wurde von Forschungsergebnissen rund um Compressed Sensing Gebrauch gemacht und weiter mit einem adaptiven Messschema kombiniert, um die effektive Betriebszeit dieser Systeme zu verringern. Dies ist fĂŒr die weitere skalierbare Anwendung zur Quanteninformationsverarbeitung von Vorteil. Die Ergebnisse verdeutlichen, dass eine Skalierbarkeit der Dimension des Systems auf grösser als 2x8 Dimensionen, Ă€quivalent zur Dimension eines 6-Qubit Zustands, in der Reichweite einer experimentellen Umsetzung liegt

    Estimation of Radio Channel Parameters

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    Kurzfassung Diese Dissertation behandelt die SchĂ€tzung der Modellparameter einer Momentanaufnahme des Mobilfunkkanals. Das besondere Augenmerk liegt zum einen auf der Entwicklung eines generischen Datenmodells fĂŒr den gemessenen Funkkanal, welches fĂŒr die hochauflösende ParameterschĂ€tzung geeignet ist. Der zweite Schwerpunkt dieser Arbeit ist die Entwicklung eines robusten ParameterschĂ€tzers fĂŒr die Bestimmung der Parameter des entworfenen Modells aus Funkkanalmessdaten. Entsprechend dieser logischen Abfolge ist auch der Aufbau dieser Arbeit. Im ersten Teil wird ausgehend von einem aus der Literatur bekannten strahlenoptischen Modell eine algebraisch handhabbare Darstellung von beobachteten Wellenausbreitungspfaden entwickelt. Das mathematische Modell erlaubt die Beschreibung von SISO (single-input-single-output)- Übertragungssystemen, also von Systemen mit einer Sendeantenne und einer Empfangsantenne, als auch die Beschreibung von solchen Systemen mit mehreren Sende- und/oder Empfangsantennen. Diese Systeme werden im Allgemeinen auch als SIMO- (single-input-multiple-output), MISO- (multiple-input-single-output) oder MIMO-Systeme (multiple-input-multiple-output) bezeichnet. Im Gegensatz zu bekannten Konzepten enthĂ€lt das entwickelte Modell keine Restriktionen bezĂŒglich der modellierbaren Antennenarrayarchitekturen. Dies ist besonders wichtig in Hinblick auf die möglichst vollstĂ€ndige Erfassung der rĂ€umlichen Struktur des Funkkanals. Die FlexibilitĂ€t des Modells ist eine Grundvoraussetzung fĂŒr die optimale Anpassung der Antennenstruktur an die Messaufgabe. Eine solche angepasste Antennenarraystruktur ist zum Beispiel eine zylindrische Anordnung von Antennenelementen. Sie ist gut geeignet fĂŒr die Erfassung der rĂ€umlichen Struktur des Funkkanals (Azimut und Elevation) in so genannten Outdoor- Funkszenarien. Weiterhin wird im ersten Teil eine neue Komponente des Funkkanaldatenmodells eingefĂŒhrt, welche den Beitrag verteilter (diffuser) Streuungen zur FunkĂŒbertragung beschreibt. Die neue Modellkomponente spielt eine SchlĂŒsselrolle bei der Entwicklung eines robusten ParameterschĂ€tzers im Hauptteil dieser Arbeit. Die fehlende Modellierung der verteilten Streuungen ist eine der Hauptursachen fĂŒr die begrenzte Anwendbarkeit und die oft kritisierte fehlende Robustheit von hochauflösenden FunkkanalparameterschĂ€tzern, die in der Literatur etabliert sind. Das neue Datenmodell beschreibt die so genannten dominanten Ausbreitungspfade durch eine deterministische Abbildung der Pfadparameter auf den gemessenen Funkkanal. Der Beitrag der verteilten Streuungen wird mit Hilfe eines zirkularen mittelwertfreien Gaußschen Prozesses beschrieben. Die Modellparameter der verteilten Streuungen beschreiben dabei die Kovarianzmatrix dieses Prozesses. Basierend auf dem entwickelten Datenmodell wird im Anschluss kurz ĂŒber aktuelle Konzepte fĂŒr FunkkanalmessgerĂ€te, so genannte Channel-Sounder, diskutiert. Im zweiten Teil dieser Arbeit werden in erster Linie AusdrĂŒcke zur Bestimmung der erzielbaren Messgenauigkeit eines Channel-Sounders abgeleitet. Zu diesem Zweck wird die untere Schranke fĂŒr die Varianz der geschĂ€tzten Modellparameter, das heißt der Messwerte, bestimmt. Als Grundlage fĂŒr die VarianzabschĂ€tzung wird das aus der ParameterschĂ€tztheorie bekannte Konzept der CramĂ©r-Rao-Schranke angewandt. Im Rahmen der Ableitung der CramĂ©r-Rao-Schranke werden außerdem wichtige Gesichtspunkte fĂŒr die Entwicklung eines effizienten ParameterschĂ€tzers diskutiert. Im dritten Teil der Arbeit wird ein SchĂ€tzer fĂŒr die Bestimmung der Ausbreitungspfadparameter nach dem Maximum-Likelihood-Prinzip entworfen. Nach einer kurzen Übersicht ĂŒber existierende Konzepte zur hochauflösenden FunkkanalparameterschĂ€tzung wird die vorliegende SchĂ€tzaufgabe analysiert und in Hinsicht ihres Typs klassifiziert. Unter der Voraussetzung, dass die Parameter der verteilten Streuungen bekannt sind, lĂ€sst sich zeigen, daß sich die SchĂ€tzung der Parameter der Ausbreitungspfade als ein nichtlineares gewichtetes kleinstes Fehlerquadratproblem auffassen lĂ€sst. Basierend auf dieser Erkenntnis wird ein generischer Algorithmus zur Bestimmung einer globalen Startlösung fĂŒr die Parameter eines Ausbreitungspfades vorgeschlagen. Hierbei wird von dem Konzept der Structure-Least-Squares (SLS)-Probleme Gebrauch gemacht, um die KomplexitĂ€t des SchĂ€tzproblems zu reduzieren. Im folgenden Teil dieses Abschnitts wird basierend auf aus der Literatur bekannten robusten numerischen Algorithmen ein SchĂ€tzer zur genauen Bestimmung der Ausbreitungspfadparameter abgeleitet. Im letzten Teil dieses Abschnitts wird die Anwendung unterraumbasierter SchĂ€tzer zur Bestimmung der Ausbreitungspfadparameter diskutiert. Es wird ein speichereffizienter Algorithmus zur SignalraumschĂ€tzung entwickelt. Dieser Algorithmus ist eine Grundvoraussetzung fĂŒr die Anwendung von mehrdimensionalen ParameterschĂ€tzern wie zum Beispiel des R-D unitary ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) zur Bestimmung von Funkkanalparametern aus MIMO-Funkkanalmessungen. Traditionelle Verfahren zur SignalraumschĂ€tzung sind hier im Allgemeinen nicht anwendbar, da sie einen zu großen Speicheraufwand erfordern. Außerdem wird in diesem Teil gezeigt, dass ESPRIT-Algorithmen auch zur ParameterschĂ€tzung von Daten mit so genannter versteckter Rotations-Invarianzstruktur eingesetzt werden können. Als Beispiel wird ein ESPRIT-basierter Algorithmus zur RichtungsschĂ€tzung in Verbindung mit multibeam-Antennenarrays (CUBA) abgeleitet. Im letzten Teil dieser Arbeit wird ein Maximum-Likelihood-SchĂ€tzer fĂŒr die neue Komponente des Funkkanals, welche die verteilten Streuungen beschreibt, entworfen. Ausgehend vom Konzept des iterativen Maximum-Likelihood-SchĂ€tzers wird ein Algorithmus entwickelt, der hinreichend geringe numerische KomplexitĂ€t besitzt, so dass er praktisch anwendbar ist. In erster Linie wird dabei von der Toeplitzstruktur der zu schĂ€tzenden Kovarianzmatrix Gebrauch gemacht. Aufbauend auf dem SchĂ€tzer fĂŒr die Parameter der Ausbreitungspfade und dem SchĂ€tzer fĂŒr die Parameter der verteilten Streuungen wird ein Maximum-Likelihood-SchĂ€tzer entwickelt (RIMAX), der alle Parameter des in Teil I entwickelten Modells der Funkanalmessung im Verbund schĂ€tzt. Neben den geschĂ€tzten Parametern des Datenmodells liefert der SchĂ€tzer zusĂ€tzlich ZuverlĂ€ssigkeitsinformationen. Diese werden unter anderem zur Bestimmung der Modellordnung, das heißt zur Bestimmung der Anzahl der dominanten Ausbreitungspfade, herangezogen. Außerdem stellen die ZuverlĂ€ssigkeitsinformationen aber auch ein wichtiges SchĂ€tzergebnis dar. Die ZuverlĂ€ssigkeitsinformationen machen die weitere Verarbeitung und Wertung der Messergebnisse möglich.The theme of this thesis is the estimation of model parameters of a radio channel snapshot. The main focus was the development of a general data model for the measured radio channel, suitable for both high resolution channel parameter estimation on the one hand, and the development of a robust parameter estimator for the parameters of the designed parametric radio channel model, in line with this logical work flow is this thesis. In the first part of this work an algebraic representation of observed propagation paths is developed using a ray-optical model known from literature. The algebraic framework is suitable for the description of SISO (single-input-single-output) radio transmission systems. A SISO system uses one antenna as the transmitter (Tx) and one antenna as the receiver (Rx). The derived expression for the propagation paths is also suitable to describe SIMO (single-input-multiple-output), MISO (multiple-input-single-output), and MIMO (multiple-input-multiple-output) radio channel measurements. In contrast to other models used for high resolution channel parameter estimation the derived model makes no restriction regarding the structure of the antenna array used throughout the measurement. This is important since the ultimate goal in radio channel sounding is the complete description of the spatial (angular) structure of the radio channel at Tx and Rx. The flexibility of the data model is a prerequisite for the optimisation of the antenna array structure with respect to the measurement task. Such an optimised antenna structure is a stacked uniform circular beam array, i.e., a cylindrical arrangement of antenna elements. This antenna array configuration is well suited for the measurement of the spatial structure of the radio channel at Tx and/or Rx in outdoor-scenarios. Furthermore, a new component of the radio channel model is introduced in the first part of this work. It describes the contribution of distributed (diffuse) scattering to the radio transmission. The new component is key for the development of a robust radio channel parameter estimator, which is derived in the main part of this work. The ignorance of the contribution of distributed scattering to radio propagation is one of the main reasons why high-resolution radio channel parameter estimators fail in practice. Since the underlying data model is wrong the estimators produce erroneous results. The improved model describes the so called dominant propagation paths by a deterministic mapping of the propagation path parameters to the channel observation. The contribution of the distributed scattering is modelled as a zero-mean circular Gaussian process. The parameters of the distributed scattering process determine the structure of the covariance matrix of this process. Based on this data model current concepts for radio channel sounding devices are discussed. In the second part of this work expressions for the accuracy achievable by a radio channel sounder are derived. To this end the lower bound on the variance of the measurements i.e. the parameter estimates is derived. As a basis for this evaluation the concept of the CramĂ©r-Rao lower bound is employed. On the way to the CramĂ©r-Rao lower bound for all channel model parameters, important issues for the development of an appropriate parameter estimator are discussed. Among other things the coupling of model parameters is also discussed. In the third part of this thesis, an estimator, for the propagation path parameters is derived. For the estimator the 'maximum-likelihood' approach is employed. After a short overview of existing high-resolution channel parameter estimators the estimation problem is classified. It is shown, that the estimation of the parameters of the propagation paths can be understood as a nonlinear weighted least squares problem, provided the parameters of the distributed scattering process are known. Based on this observation a general algorithm for the estimation of raw parameters for the observed propagation paths is developed. The algorithm uses the concept of structured-least-squares (SLS) and compressed maximum likelihood to reduce the numerical complexity of the estimation problem. A robust estimator for the precise estimation of the propagation path parameters is derived. The estimator is based on concepts well known from nonlinear local optimisation theory. In the last part of this chapter the application of subspace based parameter estimation algorithms for path parameter estimation is discussed. A memory efficient estimator for the signal subspace needed by, e.g., R-D unitary ESPRIT is derived. This algorithm is a prerequisite for the application of signal subspace based algorithms to MIMO-channel sounding measurements. Standard algorithms for signal subspace estimation (economy size SVD, singular value decomposition) are not suitable since they require an amount of memory which is too large. Furthermore, it is shown that ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) based algorithms can also be employed for parameter estimation from data having hidden rotation invariance structure. As an example an ESPRIT algorithm for angle estimation using circular uniform beam arrays (circular multi-beam antennas) is derived. In the final part of this work a maximum likelihood estimator for the new component of the channel model is developed. Starting with the concept of iterative maximum likelihood estimation, an algorithm is developed having a low computational complexity. The low complexity of the algorithm is achieved by exploiting the Toeplitz-structure of the covariance matrix to estimate. Using the estimator for the (concentrated, dominant, specular-alike) propagation paths and the parametric estimator for the covariance matrix of the process describing the distributed diffuse scattering a joint estimator for all channel parameter is derived (RIMAX). The estimator is a 'maximum likelihood' estimator and uses the genuine SAGE concept to reduce the computational complexity. The estimator provides additional information about the reliability of the estimated channel parameters. This reliability information is used to determine an appropriate model for the observation. Furthermore, the reliability information i.e. the estimate of the covariance matrix of all parameter estimates is also an important parameter estimation result. This information is a prerequisite for further processing and evaluation of the measured channel parameters

    Virtual metrology for plasma etch processes.

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    Plasma processes can present dicult control challenges due to time-varying dynamics and a lack of relevant and/or regular measurements. Virtual metrology (VM) is the use of mathematical models with accessible measurements from an operating process to estimate variables of interest. This thesis addresses the challenge of virtual metrology for plasma processes, with a particular focus on semiconductor plasma etch. Introductory material covering the essentials of plasma physics, plasma etching, plasma measurement techniques, and black-box modelling techniques is rst presented for readers not familiar with these subjects. A comprehensive literature review is then completed to detail the state of the art in modelling and VM research for plasma etch processes. To demonstrate the versatility of VM, a temperature monitoring system utilising a state-space model and Luenberger observer is designed for the variable specic impulse magnetoplasma rocket (VASIMR) engine, a plasma-based space propulsion system. The temperature monitoring system uses optical emission spectroscopy (OES) measurements from the VASIMR engine plasma to correct temperature estimates in the presence of modelling error and inaccurate initial conditions. Temperature estimates within 2% of the real values are achieved using this scheme. An extensive examination of the implementation of a wafer-to-wafer VM scheme to estimate plasma etch rate for an industrial plasma etch process is presented. The VM models estimate etch rate using measurements from the processing tool and a plasma impedance monitor (PIM). A selection of modelling techniques are considered for VM modelling, and Gaussian process regression (GPR) is applied for the rst time for VM of plasma etch rate. Models with global and local scope are compared, and modelling schemes that attempt to cater for the etch process dynamics are proposed. GPR-based windowed models produce the most accurate estimates, achieving mean absolute percentage errors (MAPEs) of approximately 1:15%. The consistency of the results presented suggests that this level of accuracy represents the best accuracy achievable for the plasma etch system at the current frequency of metrology. Finally, a real-time VM and model predictive control (MPC) scheme for control of plasma electron density in an industrial etch chamber is designed and tested. The VM scheme uses PIM measurements to estimate electron density in real time. A predictive functional control (PFC) scheme is implemented to cater for a time delay in the VM system. The controller achieves time constants of less than one second, no overshoot, and excellent disturbance rejection properties. The PFC scheme is further expanded by adapting the internal model in the controller in real time in response to changes in the process operating point
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