An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation

In this work we design a receiver that iteratively passes soft information between the channel estimation and data decoding stages. The receiver incorporates sparsity-based parametric channel estimation. State-of-the-art sparsity-based iterative receivers simplify the channel estimation problem by restricting the multipath delays to a grid. Our receiver does not impose such a restriction. As a result it does not suffer from the leakage effect, which destroys sparsity. Communication at near capacity rates in high SNR requires a large modulation order. Due to the close proximity of modulation symbols in such systems, the grid-based approximation is of insufficient accuracy. We show numerically that a state-of-the-art iterative receiver with grid-based sparse channel estimation exhibits a bit-error-rate floor in the high SNR regime. On the contrary, our receiver performs very close to the perfect channel state information bound for all SNR values. We also demonstrate both theoretically and numerically that parametric channel estimation works well in dense channels, i.e., when the number of multipath components is large and each individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin

Exploration of a Scalable Holomorphic Embedding Method Formulation for Power System Analysis Applications

abstract: The holomorphic embedding method (HEM) applied to the power-flow problem (HEPF) has been used in the past to obtain the voltages and flows for power systems. The incentives for using this method over the traditional Newton-Raphson based nu-merical methods lie in the claim that the method is theoretically guaranteed to converge to the operable solution, if one exists. In this report, HEPF will be used for two power system analysis purposes: a. Estimating the saddle-node bifurcation point (SNBP) of a system b. Developing reduced-order network equivalents for distribution systems. Typically, the continuation power flow (CPF) is used to estimate the SNBP of a system, which involves solving multiple power-flow problems. One of the advantages of HEPF is that the solution is obtained as an analytical expression of the embedding parameter, and using this property, three of the proposed HEPF-based methods can es-timate the SNBP of a given power system without solving multiple power-flow prob-lems (if generator VAr limits are ignored). If VAr limits are considered, the mathemat-ical representation of the power-flow problem changes and thus an iterative process would have to be performed in order to estimate the SNBP of the system. This would typically still require fewer power-flow problems to be solved than CPF in order to estimate the SNBP. Another proposed application is to develop reduced order network equivalents for radial distribution networks that retain the nonlinearities of the eliminated portion of the network and hence remain more accurate than traditional Ward-type reductions (which linearize about the given operating point) when the operating condition changes. Different ways of accelerating the convergence of the power series obtained as a part of HEPF, are explored and it is shown that the eta method is the most efficient of all methods tested. The local-measurement-based methods of estimating the SNBP are studied. Non-linear Thévenin-like networks as well as multi-bus networks are built using model data to estimate the SNBP and it is shown that the structure of these networks can be made arbitrary by appropriately modifying the nonlinear current injections, which can sim-plify the process of building such networks from measurements.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

On b-bit min-wise hashing for large-scale regression and classification with sparse data

Large-scale regression problems where both the number of variables, $p$, and the number of observations, $n$, may be large and in the order of millions or more, are becoming increasingly more common. Typically the data are sparse: only a fraction of a percent of the entries in the design matrix are non-zero. Nevertheless, often the only computationally feasible approach is to perform dimension reduction to obtain a new design matrix with far fewer columns and then work with this compressed data. $b$-bit min-wise hashing is a promising dimension reduction scheme for sparse matrices which produces a set of random features such that regression on the resulting design matrix approximates a kernel regression with the resemblance kernel. In this work, we derive bounds on the prediction error of such regressions. For both linear and logistic models, we show that the average prediction error vanishes asymptotically as long as $q \|\beta^*\|_2^2 /n \rightarrow 0$, where $q$ is the average number of non-zero entries in each row of the design matrix and $\beta^*$ is the coefficient of the linear predictor. We also show that ordinary least squares or ridge regression applied to the reduced data can in fact allow us fit more flexible models. We obtain non-asymptotic prediction error bounds for interaction models and for models where an unknown row normalisation must be applied in order for the signal to be linear in the predictors.The first author was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1 and an EPSRC programme grant

Comparative study and performance evaluation of MC-CDMA and OFDM over AWGN and fading channels environment

Η απαίτηση για εφαρμογές υψηλής ταχύτητας μετάδοσης δεδομένων έχει αυξηθεί σημαντικά τα τελευταία χρόνια. Η πίεση των χρηστών σήμερα για ταχύτερες επικοινωνίες, ανεξαρτήτως κινητής ή σταθερής, χωρίς επιπλέον κόστος είναι μια πραγματικότητα. Για να πραγματοποιηθούν αυτές οι απαιτήσεις, προτάθηκε ένα νέο σχήμα που συνδυάζει ψηφιακή διαμόρφωση και πολλαπλές προσβάσεις, για την ακρίβεια η Πολλαπλή Πρόσβαση με διαίρεση Κώδικα Πολλαπλού Φέροντος (Multi-Carrier Code Division Multiple Access MC-CDMA). Η εφαρμογή του Γρήγορου Μετασχηματισμού Φουριέ (Fast Fourier Transform,FFT) που βασίζεται στο (Orthogonal Frequency Division Multiplexing, OFDM) χρησιμοποιεί τις περίπλοκες λειτουργίες βάσεως και αντικαθίσταται από κυματομορφές για να μειώσει το επίπεδο της παρεμβολής. Έχει βρεθεί ότι οι μετασχηματισμένες κυματομορφές (Wavelet Transform,W.T.) που βασίζονται στον Haar είναι ικανές να μειώσουν το ISI και το ICI, που προκαλούνται από απώλειες στην ορθογωνιότητα μεταξύ των φερόντων, κάτι που τις καθιστά απλούστερες για την εφαρμογή από του FFT. Επιπλέον κέρδος στην απόδοση μπορεί να επιτευχθεί αναζητώντας μια εναλλακτική λειτουργία ορθογωνικής βάσης και βρίσκοντας ένα καλύτερο μετασχηματισμό από του Φουριέ (Fourier) και τον μετασχηματισμό κυματομορφής (Wavelet Transform). Στην παρούσα εργασία, υπάρχουν τρία προτεινόμενα μοντέλα. Το 1ο, ( A proposed Model ‘1’ of OFDM based In-Place Wavelet Transform), το 2ο, A proposed Model ‘2’ based In-Place Wavelet Transform Algorithm and Phase Matrix (P.M) και το 3ο, A proposed Model ‘3’ of MC-CDMA Based on Multiwavelet Transform. Οι αποδόσεις τους συγκρίθηκαν με τα παραδοσιακά μοντέλα μονού χρήστη κάτω από διαφορετικά κανάλια (Κανάλι AWGN, επίπεδη διάλειψη και επιλεκτική διάλειψη).The demand for high data rate wireless multi-media applications has increased significantly in the past few years. The wireless user’s pressure towards faster communications, no matter whether mobile, nomadic, or fixed positioned, without extra cost is nowadays a reality. To fulfill these demands, a new scheme which combines wireless digital modulation and multiple accesses was proposed in the recent years, namely, Multicarrier-Code Division Multiple Access (MC-CDMA). The Fourier based OFDM uses the complex exponential bases functions and it is replaced by wavelets in order to reduce the level of interference. It is found that the Haar-based wavelets are capable of reducing the ISI and ICI, which are caused by the loss in orthogonality between the carriers. Further performance gains can be made by looking at alternative orthogonal basis functions and finding a better transform rather than Fourier and wavelet transform. In this thesis, there are three proposed models [Model ‘1’ (OFDM based on In-Place Wavelet Transform, Model ‘2’ (MC-CDMA based on IP-WT and Phase Matrix) and Model ‘3’ (MC-CDMA based on Multiwavelet Transform)] were created and then comparison their performances with the traditional models for single user system were compared under different channel characteristics (AWGN channel, flat fading and selective fading). The conclusion of my study as follows, the models (1) was achieved much lower bit error rates than traditional models based FFT. Therefore these models can be considered as an alternative to the conventional MC-CDMA based FFT. The main advantage of using In-Place wavelet transform in the proposed models that it does not require an additional array at each sweep such as in ordered Fast Haar wavelet transform, which makes it simpler for implementation than FFT. The model (2) gave a new algorithm based on In-Place wavelet transform with first level processing multiple by PM was proposed. The model (3) gave much lower bit error than other two models in additional to traditional models

Analysis of Layered Social Networks

Prevention of near-term terrorist attacks requires an understanding of current terrorist organizations to include their composition, the actors involved, and how they operate to achieve their objectives. To aid this understanding, operations research, sociological, and behavioral theory relevant to the study of social networks are applied, thereby providing theoretical foundations for new methodologies to analyze non-cooperative organizations, defined as those trying to hide their structure or are unwilling to provide information regarding their operations. Techniques applying information regarding multiple dimensions of interpersonal relationships, inferring from them the strengths of interpersonal ties, are explored. A layered network construct is offered that provides new analytic opportunities and insights generally unaccounted for in traditional social network analyses. These provide decision makers improved courses of action designed to impute influence upon an adversarial network, thereby achieving a desired influence, perception, or outcome to one or more actors within the target network. This knowledge may also be used to identify key individuals, relationships, and organizational practices. Subsequently, such analysis may lead to the identification of exploitable weaknesses to either eliminate the network as a whole, cause it to become operationally ineffective, or influence it to directly or indirectly support National Security Strategy

New approaches in statistical network data analysis

This cumulative dissertation is dedicated to the statistical analysis of network data. The general approach of combining network science with statistical methodology became very popular in recent years. An important reason for this development lies in the ability of statistical network data analysis to provide a means to model and quantify interdependencies of complex systems. A network can be comprehended as a structure consisting of nodes and edges. The nodes represent general entities that are related via the edges. Depending on the research question at hand, it is either of interest to analyze the dependence structure among the nodes or the distribution of the edges given the nodes. This thesis consists of six contributed manuscripts that are concerned with the latter. Based on statistical models, edges in different dynamic and weighted networks are investigated or reconstructed. To put the contributing articles in a general context, the thesis starts with an introductory chapter. In this introduction, central concepts and models from statistical network data analysis are explained. Besides giving an overview of the available methodology, the advantages and drawbacks of the models are given, supplemented with a discussion of potential extensions and modifications. Content-wise it is possible to divide the articles into two projects. One project is focused on the statistical analysis of international arms trade networks. Two articles are devoted to the global exchange of major conventional weapons with a focus on the dynamic structure of the system and the volume traded. A third article explores latent patterns in the international trade system of small arms and ammunition. Additionally, the arms trade data is used in a survey paper that is concerned with dynamic network models. The second project regards the reconstruction of financial networks from their marginals and includes two articles. All contributing articles are attached in the form as published as a preprint. For publications in scientific journals, the respective sources are given. Additionally, the contributions of all authors are included. All computations were done with the statistical software R and the corresponding code is available from Github.Diese kumulative Dissertation beschäftigt sich mit der statistischen Analyse von Netzwerkdaten. Der generelle Ansatz, interdependente Systeme als Netzwerke zu konzeptualisieren um sie anschließend mit statistischer Methodik zu analysieren, hat in den vergangenen Jahren deutlich an Relevanz gewonnen. Insbesondere die Flexibilität der Methodik, zusammen mit der Möglichkeit komplexe Abhängigkeitsstrukturen zu modellieren, hat zu ihrer Popularität beigetragen. Ein Netzwerk ist ein System, das sich aus Knoten und Kanten zusammensetzt. Dabei sind die Knoten generelle Einheiten, die durch die Kanten miteinander in Verbindung gebracht werden. Je nach Forschungsfrage interessieren entweder die Abhängigkeiten zwischen den Knoten oder die Verteilung der Kanten mit gegebenen Knoten. Diese Arbeit greift mit insgesamt sechs Artikeln den zweiten Ansatz auf. Unter Zuhilfenahme von statistischen Modellen werden die Kanten in verschiedenen binären und gewichteten Netzwerken analysiert, beziehungsweise rekonstruiert. Um der Arbeit einen generellen Kontext zu geben, wird den angehängten Artikeln ein Mantelteil vorangestellt. In diesem wird auf zentrale Konzepte und Modelle der statistischen Netzwerkanalyse eingegangen. Dabei werden die Vorteile als auch die Nachteile der Modelle diskutiert und potenzielle Erweiterungen und Modifikationen beschrieben. Die in dieser Dissertation enthaltenen Artikel lassen sich grob in zwei verschiedene Projekte einordnen. In einem Projekt steht die statistische Modellierung des internationalen Waffenhandels im Fokus. Zwei Artikel untersuchen den globalen Austausch von Großwaffen (Major Conventional Weapons), dabei wird sowohl die dynamische Struktur als auch das gehandelte Waffenvolumen analysiert. Ein weiterer Artikel widmet sich den latenten Strukturen im internationalen Kleinwaffenhandel (Small Arms and Ammunition). Weiterhin werden die Waffenhandelsdaten in einem Übersichtsartikel, der sich mit dynamischen Netzwerkmodellen beschäftigt, verwendet. Das zweite Projekt befasst sich, verteilt über zwei Artikel, mit der Rekonstruktion von finanziellen Netzwerken basierend auf den Randsummen von Netzwerkmatrizen. Alle in dieser Dissertation angehängten Artikel befinden sich in der Form, in der sie als Vorabversion veröffentlicht wurden. Bei Veröffentlichungen in Fachjournalen wird die jeweilige Quelle angegeben. Zudem wird vor jedem Artikel der Beitrag des jeweiligen Autors angegeben. Sämtliche Analysen wurden mit der statistischen Software R durchgeführt. Der dazugehörige Code ist über Github verfügbar

MCMC methods: graph samplers, invariance tests and epidemic models

Markov Chain Monte Carlo (MCMC) techniques are used ubiquitously for simulation-based inference. This thesis provides novel contributions to MCMC methods and their application to graph sampling and epidemic modeling. The first topic considered is that of sampling graphs conditional on a set of prescribed statistics, which is a difficult problem arising naturally in many fields: sociology (Holland and Leinhardt, 1981), psychology (Connor and Simberloff, 1979), categorical data analysis (Agresti, 1992) and finance (Squartini et al., 2018, Gandy and Veraart, 2019) being examples. Bespoke MCMC samplers are proposed for this setting. The second major topic addressed is that of modeling the dynamics of infectious diseases, where MCMC is leveraged as the general inference engine. The first part of this thesis addresses important problems such as the uniform sampling of graphs with given degree sequences, and weighted graphs with given strength sequences. These distributions are frequently used for exact tests on social networks and two-way contingency tables. Another application is quantifying the statistical significance of patterns observed in real networks. This is crucial for understanding whether such patterns indicate the presence of interesting network phenomena, or whether they simply result from less interesting processes, such as nodal-heterogeneity. The MCMC samplers developed in the course of this research are complex, and there is great scope for conceptual, analytic, and implementation errors. This motivates a chapter that develops novel tests for detecting errors in MCMC implementations. The tests introduced are unique in being exact, which allows us to keep the false rejection probability arbitrarily low. Rather than develop bespoke samplers, as in the first part of the thesis, the second part leverages a standard MCMC framework Stan (Stan Development Team, 2018) as the workhorse for fitting state-of-the-art epidemic models. We present a general framework for semi-mechanistic Bayesian modeling of infectious diseases using renewal processes. The term semi-mechanistic relates to statistical estimation within some constrained mechanism. This research was motivated by the ongoing SARS-COV-2 pandemic, and variants of the model have been used in specific analyses of Covid-19. We present epidemia, an R package allowing researchers to leverage the epidemic models. A key goal of this work is to demonstrate that MCMC, and in particular, Stan’s No-U-Turn (Hoffman and Gelman, 2014) sampler, can be routinely employed to fit a large-class of epidemic models. A second goal is to make the models accessible to the general research community, through epidemia.Open Acces

Novel Insights into Orbital Angular Momentum Beams: From Fundamentals, Devices to Applications

It is well-known by now that the angular momentum carried by elementary particles can be categorized as spin angular momentum (SAM) and orbital angular momentum (OAM). In the early 1900s, Poynting recognized that a particle, such as a photon, can carry SAM, which has only two possible states, i.e., clockwise and anticlockwise circular polarization states. However, only fairly recently, in 1992, Allen et al. discovered that photons with helical phase fronts can carry OAM, which has infinite orthogonal states. In the past two decades, the OAM-carrying beam, due to its unique features, has gained increasing interest from many different research communities, including physics, chemistry, and engineering. Its twisted phase front and intensity distribution have enabled a variety of applications, such as micromanipulation, laser beam machining, nonlinear matter interactions, imaging, sensing, quantum cryptography and classical communications. This book aims to explore novel insights of OAM beams. It focuses on state-of-the-art advances in fundamental theories, devices and applications, as well as future perspectives of OAM beams

New approaches in statistical network data analysis

This cumulative dissertation is dedicated to the statistical analysis of network data. The general approach of combining network science with statistical methodology became very popular in recent years. An important reason for this development lies in the ability of statistical network data analysis to provide a means to model and quantify interdependencies of complex systems. A network can be comprehended as a structure consisting of nodes and edges. The nodes represent general entities that are related via the edges. Depending on the research question at hand, it is either of interest to analyze the dependence structure among the nodes or the distribution of the edges given the nodes. This thesis consists of six contributed manuscripts that are concerned with the latter. Based on statistical models, edges in different dynamic and weighted networks are investigated or reconstructed. To put the contributing articles in a general context, the thesis starts with an introductory chapter. In this introduction, central concepts and models from statistical network data analysis are explained. Besides giving an overview of the available methodology, the advantages and drawbacks of the models are given, supplemented with a discussion of potential extensions and modifications. Content-wise it is possible to divide the articles into two projects. One project is focused on the statistical analysis of international arms trade networks. Two articles are devoted to the global exchange of major conventional weapons with a focus on the dynamic structure of the system and the volume traded. A third article explores latent patterns in the international trade system of small arms and ammunition. Additionally, the arms trade data is used in a survey paper that is concerned with dynamic network models. The second project regards the reconstruction of financial networks from their marginals and includes two articles. All contributing articles are attached in the form as published as a preprint. For publications in scientific journals, the respective sources are given. Additionally, the contributions of all authors are included. All computations were done with the statistical software R and the corresponding code is available from Github.Diese kumulative Dissertation beschäftigt sich mit der statistischen Analyse von Netzwerkdaten. Der generelle Ansatz, interdependente Systeme als Netzwerke zu konzeptualisieren um sie anschließend mit statistischer Methodik zu analysieren, hat in den vergangenen Jahren deutlich an Relevanz gewonnen. Insbesondere die Flexibilität der Methodik, zusammen mit der Möglichkeit komplexe Abhängigkeitsstrukturen zu modellieren, hat zu ihrer Popularität beigetragen. Ein Netzwerk ist ein System, das sich aus Knoten und Kanten zusammensetzt. Dabei sind die Knoten generelle Einheiten, die durch die Kanten miteinander in Verbindung gebracht werden. Je nach Forschungsfrage interessieren entweder die Abhängigkeiten zwischen den Knoten oder die Verteilung der Kanten mit gegebenen Knoten. Diese Arbeit greift mit insgesamt sechs Artikeln den zweiten Ansatz auf. Unter Zuhilfenahme von statistischen Modellen werden die Kanten in verschiedenen binären und gewichteten Netzwerken analysiert, beziehungsweise rekonstruiert. Um der Arbeit einen generellen Kontext zu geben, wird den angehängten Artikeln ein Mantelteil vorangestellt. In diesem wird auf zentrale Konzepte und Modelle der statistischen Netzwerkanalyse eingegangen. Dabei werden die Vorteile als auch die Nachteile der Modelle diskutiert und potenzielle Erweiterungen und Modifikationen beschrieben. Die in dieser Dissertation enthaltenen Artikel lassen sich grob in zwei verschiedene Projekte einordnen. In einem Projekt steht die statistische Modellierung des internationalen Waffenhandels im Fokus. Zwei Artikel untersuchen den globalen Austausch von Großwaffen (Major Conventional Weapons), dabei wird sowohl die dynamische Struktur als auch das gehandelte Waffenvolumen analysiert. Ein weiterer Artikel widmet sich den latenten Strukturen im internationalen Kleinwaffenhandel (Small Arms and Ammunition). Weiterhin werden die Waffenhandelsdaten in einem Übersichtsartikel, der sich mit dynamischen Netzwerkmodellen beschäftigt, verwendet. Das zweite Projekt befasst sich, verteilt über zwei Artikel, mit der Rekonstruktion von finanziellen Netzwerken basierend auf den Randsummen von Netzwerkmatrizen. Alle in dieser Dissertation angehängten Artikel befinden sich in der Form, in der sie als Vorabversion veröffentlicht wurden. Bei Veröffentlichungen in Fachjournalen wird die jeweilige Quelle angegeben. Zudem wird vor jedem Artikel der Beitrag des jeweiligen Autors angegeben. Sämtliche Analysen wurden mit der statistischen Software R durchgeführt. Der dazugehörige Code ist über Github verfügbar