This thesis focuses on the development and analysis of efficient simulation and inference techniques for Markovian pure jump processes with a view towards applications in dense communication networks. These techniques are especially relevant for modeling networks of smart devices —tiny, abundant microprocessors with integrated sensors and wireless communication abilities— that form highly complex and diverse communication networks. During 2010, the number of devices connected to the Internet exceeded the number of people on Earth: over 12.5 billion devices. By 2015, Cisco’s Internet Business Solutions Group predicts that this number will exceed 25 billion. The first part of this work proposes novel numerical methods to estimate, in an efficient and accurate way, observables from realizations of Markovian jump processes. In particular, hybrid Monte Carlo type methods are developed that combine the exact and approximate simulation algorithms to exploit their respective advantages. These methods are tailored to keep a global computational error below a prescribed global error tolerance and within a given statistical confidence level. Indeed, the computational work of these methods is similar to the one of an exact method, but with a smaller constant. Finally, the methods are extended to systems with a disparity of time scales. The second part develops novel inference methods to estimate the parameters of Markovian pure jump process. First, an indirect inference approach is presented, which is based on upscaled representations and does not require sampling. This method is simpler than dealing directly with the likelihood of the process, which, in general, cannot be expressed in closed form and whose maximization requires computationally intensive sampling techniques. Second, a forward-reverse Monte Carlo Expectation-Maximization algorithm is provided to approximate a local maximum or saddle point of the likelihood function of the parameters given a set of observations. The third part is devoted to applications in communication networks where also mean field or fluid approximations techniques, to substantially reduce the computational work of simulating large communication networks are explored. These methods aim to capture the global behaviour of systems with large state spaces by using an aggregate approximation, which is often described by means of a non-linear dynamical system.

The objective of this thesis is to review the two popular mathematical models of the financialderivatives market. The models are the classical Black–Scholes–Merton and the Continuoustime Markov chain (CTMC) model. We study the CTMC model which is illustrated by themathematician Ragnar Norberg. The thesis demonstrates how the fundamental results ofFinancial Engineering work in both models.The construction of the main financial market components and the approach used for pricingthe contingent claims were considered in order to review the two models. In addition, the stepsused in solving the first–order partial differential equations in both models are explained.The main similarity between the models are that the financial market components are thesame. Their contingent claim is similar and the driving processes for both models utilizeMarkov property.One of the differences observed is that the driving process in the BSM model is the Brownianmotion and Markov chain in the CTMC model.We believe that the thesis can motivate other students and researchers to do a deeper andadvanced comparative study between the two models.

Les amplificateurs de puissance, éléments constitutifs essentiels de tout système de télécommunication, vont jouer un rôle capital dans le développement des futurs systèmes de communication. Aujourd'hui l'amélioration des amplificateurs de puissance nécessite un progrès technologique au niveau du composant lui même mais doit aussi tenir compte d'une approche plus globale. En particulier, le progrès dans les traitements numériques permet aujourd'hui de corriger en amont certaines distorsions qui seront générées en aval de la chaîne de communication. La pré-distorsion numérique est une technique de correction des amplificateurs de puissance qui connaît un intérêt grandissant de par son intégration complètement numérique et par les gains en linéarité et en consommation. Cette technique nécessite une voie de retour dont un élément critique est le convertisseur analogique-numérique. Ce composant doit répondre à des contraintes de résolution, de bande passante et de linéarité élevées. Dans cette thèse, nous proposons une nouvelle architecture de convertisseur analogique-numérique à base de modulateurs Sigma-Delta passe-bande. Cette architecture tire partie du fonctionnement passe bande des modulateurs que nous faisons travailler en parallèle, chacun centré sur différentes fréquences, mais aussi d'un agencement en cascade particulier pour éliminer le signal utile, qui est de forte puissance, dans le but de diminuer les contraintes de dynamique.La conception haut niveau et les simulations ont été menées pour des systèmes à temps discret et aussi à temps continu et a nécessité le développement d'outils adaptés de simulation se basant sur la boîte à outils Delta Sigma Toolbox de Richard Schreier / Power amplifiers, which are essential elements of any communication system, will play a crucial role in the development of future communication systems. Today improving power amplifiers requires technological advances at the circuit device level, but one also must consider a more global approach. In particular, advances in digital processing can now correct in the early stage of the communication chain some distortions that are generated downstream in the chain. Digital pre-distortion is a correction technique for power amplifiers that has a growing interest because of its completely digital implementation and of its gains in linearity and energy consumption. This technique requires a feedback path where the analog-to-digital converter is a critical element. This component must satisfy the constraints of high resolution , wide bandwidth, and high linearity. In this thesis, we propose a new architecture of analog-to-digital converter based on bandpass Delta-Sigma modulators. This architecture takes advantage of operating bandpass modulators that are designed to work in parallel, each focusing on different frequencies, but also of a particular cascading arrangement to eliminate the useful signal, which has a high power, in order to reduce dynamics constraints. High-level design and simulations were carried out for discrete time and continuous time systems and also required the development of appropriate simulation tools.

High-performance, high-frequency operational transconductance amplifiers (OTAs) are very important elements in the design of high-frequency continuous-time integrated analog signal processing circuits, because resistors, inductors, integrators, mutators, buffers, multipliers, and filters can be built by OTAs and capacitors. The critical considerations for OTA design are linearity, tuning, frequency response, output impedance, power supply rejection (PSR) and common-mode rejection (CMR). For linearity considerations, two different methods are proposed. One uses cross-coupled pairs (CMOS or NMOS), producing OTAs with very high linearity but either the input range is relatively small or the CMR to asymmetrical inputs is poor. Another employs multiple differential pairs (current addition or subtraction), producing OTAs with high linearity over a very large input range. So, there are tradeoffs among the critical considerations. For different applications, different OTAs should be selected. For consideration of frequency response, the first reported GaAs OTA was designed for achieving very-high-frequency performance, instead of using AC compensation techniques. GaAs is one of the fastest available technologies, but it was new and less mature than silicon when we started the design in 1989. So, there were several issues, such as low output impedance, no P-channel devices, and Schottky clamp. To overcome these problems, new techniques are proposed, and the designed OTA has comparable performance to a CMOS OTA. For PSR and CMR considerations, a fully balanced circuit structure is employed with a common-mode feedback (CMF) circuit used to stabilize the DC output voltages. To reduce the interaction of the operation of CMF and tuning of OTAs, three improved versions of the CMF circuits used in operational amplifiers are proposed. With the designed OTAs, a I GHz GaAs inductor with small parasitics is designed using the proposed procedure to reduce high-frequency effects. Two CMOS high-order, high-frequency filters are designed: one in cascade structure and one in LC ladder form. Also, a 200 MHz third-order elliptic GaAs filter is designed with special consideration of very-high-frequency parasitics. All circuits were fabricated and measured. The experimental results were used to verify the designs.

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Continuous-time system identification deals with the problem of building continuous-time models of dynamical systems from sampled input and output data. In this field, there are two main approaches: indirect and direct. In the indirect approach, a suitable discrete-time model is first determined, and then it is transformed into continuous-time. On the other hand, the direct approach obtains a continuous-time model directly from the sampled data. In both approaches there exists a dichotomy between discrete-time data and continuous-time models, which can induce robustness issues and complications in the theoretical analysis of identification algorithms. These difficulties are addressed in this thesis. First, we consider the indirect approach to continuous-time system identification. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree one, independent of the relative degree of the strictly proper true system. Inspired by the indirect prediction error method, we propose an indirect-approach estimator that enforces the desired number of poles and zeros in the continuous-time transfer function estimate, and show that the estimator is consistent and asymptotically efficient. A robustification of this method is also developed, by which the estimates are also guaranteed to deliver stable models. In the second part of the thesis, we analyze asymptotic properties of the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC), which is one of the most popular direct identification methods. This algorithm applies an adaptive prefiltering to the sampled input and output that requires assumptions on the intersample behavior of the signals. We present a comprehensive analysis on the consistency and asymptotic efficiency of the SRIVC estimator while taking into account the intersample behavior of the input signal. Our results show that the SRIVC estimator is generically consistent when the intersample behavior of the input is known exactly and subsequently used in the implementation of the algorithm, and we give conditions under which consistency is not achieved. In terms of statistical efficiency, we compute the asymptotic Cramér-Rao lower bound for an output error model structure with Gaussian noise, and derive the asymptotic covariance of the SRIVC estimates. We conclude that the SRIVC estimator is asymptotically efficient under mild conditions, and that this property can be lost if the intersample behavior of the input is not carefully accounted for in the SRIVC procedure. Moreover, we propose and analyze the statistical properties of an extension of SRIVC that is able to deal with input signals that cannot be interpolated exactly via hold reconstructions. The proposed estimator is generically consistent for any input reconstructed using zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. Comparisons with the Maximum Likelihood technique and an analysis of the iterations of the method are provided, in order to reveal the influence of the intersample behavior of the output and to propose new robustifications to the SRIVC algorithm. / <p>QC 20200511</p>

Access to the large web content hosted all over the world by users of the Internet engage many hosts, routers/switches and faster links. They challenge the internet backbone to operate at its capacity to assure e±cient content access. This may result in congestion and raises concerns over various Quality of Service (QoS) issues like high delays, high packet loss and low throughput of the system for various Internet applications. Thus, there is a need to develop effective congestion control mechanisms in order to meet various Quality of Service (QoS) related performance parameters. In this paper, our emphasis is on the Active Queue Management (AQM) mechanisms, particularly Random Early Detection (RED). We propose a threshold based novel analytical model based on standard RED mechanism. Various numerical examples are presented for Internet traffic scenarios containing both the burstiness and correlation properties of the network traffic.

Ko, Chi Tung. / On t.p. "delta" and "sigma" appear as the Greek letters. / Thesis submitted in: December 2007. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references. / Abstracts in English and Chinese. / Abstract --- p.1 / 摘要 --- p.3 / Acknowledgements --- p.4 / Table of Contents --- p.5 / List of Figures --- p.8 / List of Tables --- p.13 / Chapter Chapter 1 --- Introduction --- p.14 / Chapter 1.1 --- Motivation --- p.14 / Chapter 1.2 --- Objectives --- p.17 / Chapter 1.3 --- Organization of the Thesis --- p.17 / References --- p.18 / Chapter Chapter 2 --- Fundamentals of Delta-sigma Modulators --- p.20 / Chapter 2.1 --- Delta-sigma Modulator as a Feedback System --- p.20 / Chapter 2.2 --- Quantization Noise --- p.22 / Chapter 2.3 --- Oversampling --- p.23 / Chapter 2.4 --- Noise Shaping --- p.25 / Chapter 2.5 --- Performance Parameters --- p.27 / Chapter 2.6 --- Baseband Modulators vs Bandpass Modulators --- p.27 / Chapter 2.7 --- Discrete-time Modulators vs Continuous-time Modulators --- p.28 / Chapter 2.8 --- Single-bit Modulators vs Multi-bit Modulators --- p.29 / Chapter 2.9 --- Non-linearity and Image Problems in Multi-bit Delta-sigma Modulators --- p.29 / Chapter 2.9.1 --- Non-linearity Problem --- p.29 / Chapter 2.9.2 --- Image Problem --- p.31 / Reference --- p.36 / Chapter Chapter 3 --- Image Rejection and Non-linearity Suppression Techniques for Quadrature Multi-bit Δ¡♭ Modulators --- p.38 / Chapter 3.1 --- Quadrature DEM Technique --- p.38 / Chapter 3.1.1 --- Introduction and Working Principle --- p.38 / Chapter 3.1.2 --- Behavioral Simulation Results --- p.42 / Chapter 3.2 --- IQ DWA Technique --- p.44 / Chapter 3.2.1 --- Introduction and Working Principle --- p.44 / Chapter 3.2.2 --- Behavioral Simulation Results --- p.49 / Chapter 3.3 --- DWA and Bit-wise Data-Dependent DEM --- p.52 / Chapter 3.3.1 --- Introduction and Working Principle --- p.52 / Chapter 3.3.2 --- Behavioral Simulation Results --- p.54 / Chapter 3.4 --- Image Rejection Technique for Quadrature Mixer --- p.61 / Chapter 3.5 --- Conclusion --- p.63 / Reference --- p.64 / Chapter Chapter 4 --- System Design of a Multi-Bit CT Modulator for GSM/WCDMA Application --- p.65 / Chapter 4.1 --- Objective of Design and Design Specification --- p.65 / Chapter 4.2 --- Topology Selection --- p.65 / Chapter 4.3 --- Discrete-time Noise Transfer Function Generation --- p.66 / Chapter 4.4 --- Continuous-time Loop Filter Transfer Function Generation --- p.69 / Chapter 4.5 --- Behavioral Model of Modulator --- p.69 / Chapter 4.6 --- Dynamic Range Scaling --- p.75 / Chapter 4.7 --- Behavioral Modeling of Operational Amplifiers --- p.77 / Chapter 4.8 --- Impact of RC Variation on Performance --- p.85 / Chapter 4.9 --- Loop Filter Component Values --- p.88 / Chapter 4.10 --- Summary --- p.90 / Reference --- p.90 / Chapter Chapter 5 --- Transistor-level Implementation of Modulators --- p.92 / Chapter 5.1 --- Overview of Design --- p.92 / Chapter 5.2 --- Design of Operational Transconductance Amplifiers (OTAs) --- p.94 / Chapter 5.2.1 --- First Stage --- p.94 / Chapter 5.2.2 --- Second and Third Stages --- p.98 / Chapter 5.3 --- Design of Feed-forward Transconductance (Gm) Cells --- p.101 / Chapter 5.4 --- Design of Quantizer --- p.102 / Chapter 5.4.1 --- Reference Ladder Design --- p.102 / Chapter 5.4.2 --- Comparator Design --- p.104 / Chapter 5.5 --- Design of Feedback Digital-to-Analog Converter (DAC) --- p.106 / Chapter 5.5.1 --- DWA and DEM Logic --- p.107 / Chapter 5.5.2 --- DAC Circuit --- p.109 / Chapter 5.6 --- Design of Integrated Mixers --- p.111 / Chapter 5.7 --- Design of Clock Generators --- p.112 / Chapter 5.7.1 --- Master Clock Generator --- p.112 / Chapter 5.7.2 --- LO Clock Generator --- p.114 / Chapter 5.7.3 --- Simulation Results --- p.116 / Reference --- p.125 / Chapter Chapter 6 --- Physical Design of Modulators --- p.127 / Chapter 6.1 --- Floor Planning of Modulator --- p.127 / Chapter 6.2 --- Shielding of Sensitive Signals --- p.130 / Chapter 6.3 --- Common Centroid Layout --- p.130 / Chapter 6.4 --- Amplifier Layout --- p.132 / Reference --- p.137 / Chapter Chapter 7 --- Conclusions --- p.138 / Chapter 7.1 --- Conclusions --- p.138 / Chapter 7.2 --- Future Works --- p.138 / Appendix A Schematics of Building Blocks --- p.140 / First Stage Operational Amplifier --- p.140 / First Stage Amplifier Local Bias Circuit --- p.140 / Second and Third Stage Operational Amplifier --- p.141 / Second and Third Stage Local Bias Circuit --- p.141 / CMFB Circuit (First Stage) --- p.142 / CMFB Circuit (Second Stage) --- p.142 / Gm-Feed-forward Cells --- p.143 / Gm Feed-forward Cell Bias Circuit --- p.143 / Reference Ladder Circuit --- p.144 / Pre-amplifier Circuit --- p.145 / Latch Circuit --- p.145 / DAC Circuit (Unit Cell) --- p.146 / Author's Publications --- p.147