The Internet of Bodies (IoB) is a wireless network of on-body or in-body commu- nication formed by wearable, ingestible, injectable, and implantable smart devices. The vast majority of on-body communications, is typically required to be within <5 cm vicinity of the human body. The radiative nature of currently used RF devices leads to wasted energy that is radiated in unneeded off-body directions. Consequently, it degrades energy efficiency, introduces co-existence and interference problems, and imposes security threats on sensitive data. As an alternative, the capacitive body channel communication (BCC) couples the signal (between 10 kHz-100 MHZ) to the human body, which is more conductive than air. Hence, it provides lower loss, bet- ter privacy and confidentiality, and nJ/bit to pJ/bit energy efficiency. Accordingly, our work investigates orthogonal and non-orthogonal capacitive body channel access schemes for ultralow-power IoB networks with or without cooperation. We derive the closed-form optimal power allocation for uplink and downlink transmissions and the maximum number of IoB nodes satisfying a reliable and feasible network for non- cooperative schemes. The cooperative schemes necessitate joint optimization of both power and phase time allocations. We achieve this by using the Golden-Section search algorithm to minimize the power consumption in both phases.

Indiana University-Purdue University Indianapolis (IUPUI) / In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the ferroelectric phase region, we show that $Z_n=CG^nF^{n^2}(1+O(e^{-n^{1-\ep}}))$ for any $\ep>0$, and we give explicit formulae for the numbers $C, G$, and $F$. On the critical line separating the ferroelectric and disordered phase regions, we show that $Z_n=Cn^{1/4}G^{\sqrt{n}}F^{n^2}(1+O(n^{-1/2}))$, and we give explicit formulae for the numbers $G$ and $F$. In this phase region, the value of the constant $C$ is unknown. In the antiferroelectric phase region, we show that $Z_n=C\th_4(n\om)F^{n^2}(1+O(n^{-1}))$, where $\th_4$ is Jacobi's theta function, and explicit formulae are given for the numbers $\om$ and $F$. The value of the constant $C$ is unknown in this phase region. In each case, the proof is based on reformulating $Z_n$ as the eigenvalue partition function for a random matrix ensemble (as observed by Paul Zinn-Justin), and evaluation of large $n$ asymptotics for a corresponding system of orthogonal polynomials. To deal with this problem in the antiferroelectric phase region, we consequently develop an asymptotic analysis, based on a Riemann-Hilbert approach, for orthogonal polynomials on an infinite regular lattice with respect to varying exponential weights. The general method and results of this analysis are given in Chapter 5 of this dissertation.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this dissertation, we study the Sturm Liouvile's theorems for the zeros of the solutions of linear differential equations of second order. These classical theorems are applied to analysis of the monotonicity of functions involving the zeros of classical orthogonal polynomials. in particular, Gegenbauer polynomials. / Neste trabalho estudamos os Teoremas de Sturm Liouville para zeros de soluções de equações diferenciais lineares de segunda ordem. Estes teoremas clássicos são aplicados para análise do crescimento e decrescimento de certas funções que envolvem os zeros de Polinômios Ortogonais Clássicos, como os Polinômios de Gegenbauer. / Mestre em Matemática

Dans la première partie de ce travail nous considérons des problèmes hyperboliques du premier ordre linéaires où des problèmes paraboliques linéaires dégénérés en temps. En utilisant une méthode de matrice de masse singulière, nous proposons une méthode d’élément finis permettant d’avoir des estimations d’erreur en espace optimale pour l’élément fini de Lagrange P1 par exemple. Nous appliquons ces résultats au cas d’un système parabolique utilisé en electroradiologie. La seconde partie est consacrée aux polynômes Lp extrémaux à l’extérieur du cercle unité associés à une mesure de la forme générale α = βa + βs + γ, où βa est régulière, βs singulière et γ discrète. Dans un premier temps nous considérons βs = 0, et nous avons généralisé au cas Lp des résultats connus dans le cas L2. Dans le cas où βs = 0 nous montrons les mêmes résultats (formules d’optimalité) mais en utilisant d’autres fonctions de régularité. / In the first part of this work, we deal with, linear hyperbolic problems of first order or linear parabolic problems, which are degenerated with respect to the time operator. By using a singular mass matrix technique, we propose a finite element method allowing to get optimal error estimates with respect to space for the Lagrange first order finite element for example. Then our method is applied to a parabolic system degenerated with respect to time which is used in electrocardiology. The second part of this work is dedicated to extremal polynomials in Lp , outside to the unit circle associated to a measure α, with a general form given by α = βa + βs + γ. The regular part is denoted βa , the singular part βs and the discrete part γ. In a first step we take βs = 0, and we generalized to the Lp case the known results in the L2 case. When the singular part is non zero, by using different regularity functions, we get the same optimality formulae.

正交主效應計畫(Orthogonal main-effect plans)因可無相關地估計主效應，故常被應用於一般工業上作為篩選因子之用。然而，實驗通常費時耗財。因此，如何設計一個較經濟且有效的計劃是很重要的。回顧過去相關的研究，Jacroux (1992)提供了最小正交主效應計劃的充份條件及正交主效應計畫之最少實驗次數表(Jacroux 1992)，張純明(1998)針對此表提出修正與補充。在此，我們再次的補足此表。 正交主效應計畫中，如有重複實驗點，則純誤差可被估計，且據此檢定模型之適合度。Jacroux (1993)及張純明(1998)皆曾提出具最多部份重複之正交主效應計畫(Partially replicated orthogonal main-effect plans)。在此，我們討論所有三因子部份重複正交主效應計畫中，可能重複之最大次數，且具體提出建構此最大部份重複之最小正交主效應計畫之方法。 / Orthogonal main-effect plans (OMEP's), being able to estimate the main effects without correlation, are often employed in industrial situations for screening purpose. But experiments are expensive and time consuming. When an economical and efficient design is desired, a minimal orthogonal main-effect plans is a good choice. Jacroux (1992) derived a sufficient condition for OEMP's to have minimal number of runs and provided a table of minimal OMEP run numbers. Chang (1998) corrected and supplemented the table. In this paper, we try to improve the table to its perfection. A minimal OMEP with replicated runs is appreciated even more since then the pure error can be estimated and the goodness-of-fit of the model can be tested. Jacroux (1993) and Chang (1998) gave some partially replicated orthogonal main-effect plans (PROMEP's) with maximal number of replicated points. Here, we discuss minimal PROMEP's with 3 factors in detail. Methods of constructing minimal PROMEP's with replicated runs are provided, and the number of replicated runs are maximal for most cases.

In this thesis, a fairly detailed survey on the q-classical orthogonal polynomials of the Hahn class is presented. Such polynomials appear to be the bounded solutions of the so called qhypergeometric difference equation having polynomial coefficients of degree at most two. The central idea behind our study is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric difference equation by means of a qualitative analysis of the relevant q-Pearson equation. To be more specific, a geometrical approach has been used by taking into account every posssible rational form of the polynomial coefficients, together with various relative positions of their zeros, in the q-Pearson equation to describe a desired q-weight function on a suitable orthogonality interval. Therefore, our method differs from the standard ones which are based on the Favard theorem and the three-term recurrence relation.

In this thesis, space-time block codes originally developed for multiple antenna systems are extended to cooperative multi-hop networks. The designs are applicable to any wireless network setting especially cellular, adhoc and sensor networks where space limitations preclude the use of multiple antennas. The thesis first investigates the design of distributed orthogonal and quasi-orthogonal space time block codes in cooperative networks with single and multiple antennas at the destination. Numerical and simulation results show that by employing multiple receive antennas the diversity performance of the network is further improved at the expense of slight modification of the detection scheme. The thesis then focuses on designing distributed space time block codes for cooperative networks in which the source node participates in cooperation. Based on this, a source-assisting strategy is proposed for distributed orthogonal and quasi-orthogonal space time block codes. Numerical and simulation results show that the source-assisting strategy exhibits improved diversity performance compared to the conventional distributed orthogonal and quasi-orthogonal designs.Motivated by the problem of channel state information acquisition in practical wireless network environments, the design of differential distributed space time block codes is investigated. Specifically, a co-efficient vector-based differential encoding and decoding scheme is proposed for cooperative networks. The thesis then explores the concatenation of differential strategies with several distributed space time block coding schemes namely; the Alamouti code, square-real orthogonal codes, complex-orthogonal codes, and quasiorthogonal codes, using cooperative networks with different number of relay nodes. In order to cater for high data rate transmission in non-coherent cooperative networks, differential distributed quasi-orthogonal space-time block codes which are capable of achieving full code-rate and full diversity are proposed. Simulation results demonstrate that the differential distributed quasi-orthogonal space-time block codes outperform existing distributed space time block coding schemes in terms of code rate and bit-error-rate performance. A multidifferential distributed quasi-orthogonal space-time block coding scheme is also proposed to exploit the additional diversity path provided by the source-destination link.A major challenge is how to construct full rate codes for non-coherent cooperative broadband networks with more than two relay nodes while exploiting the achievable spatial and frequency diversity. In this thesis, full rate quasi-orthogonal codes are designed for noncoherent cooperative broadband networks where channel state information is unavailable. From this, a generalized differential distributed quasi-orthogonal space-frequency coding scheme is proposed for cooperative broadband networks. The proposed scheme is able to achieve full rate and full spatial and frequency diversity in cooperative networks with any number of relays. Through pairwise error probability analysis we show that the diversity gain of the proposed scheme can be improved by appropriate code construction and sub-carrier allocation. Based on this, sufficient conditions are derived for the proposed code structure at the source node and relay nodes to achieve full spatial and frequency diversity. In order to exploit the additional diversity paths provided by the source-destination link, a novel multidifferential distributed quasi-orthogonal space-frequency coding scheme is proposed. The overall objective of the new scheme is to improve the quality of the detected signal at the destination with negligible increase in the computational complexity of the detector.Finally, a differential distributed quasi-orthogonal space-time-frequency coding scheme is proposed to cater for high data rate transmission and improve the performance of noncoherent cooperative broadband networks operating in highly mobile environments. The approach is to integrate the concept of distributed space-time-frequency coding with differential modulation, and employ rotated constellation quasi-orthogonal codes. From this, we design a scheme which is able to address the problem of performance degradation in highly selective fading environments while guaranteeing non-coherent signal recovery and full code rate in cooperative broadband networks. The coding scheme employed in this thesis relaxes the assumption of constant channel variation in the temporal and frequency dimensions over long symbol periods, thus performance degradation is reduced in frequencyselective and time-selective fading environments. Simulation results illustrate the performance of the proposed differential distributed quasi-orthogonal space-time-frequency coding scheme under different channel conditions.

This thesis investigates several design problems concerning two-channel conjugate quadrature (CQ) filter banks and orthogonal wavelets, as well as orthogonal cosine-modulated (OCM) filter banks. It is well known that optimal design of CQ filters and wavelets and optimal design of prototype filters (PFs) of OCM filter banks in the least squares (LS) or minimax sense are nonconvex problems and to date only local solutions can be claimed. In this thesis, we first make some improvements over several direct design techniques for local design problems in terms of convergence and solution accuracy. By virtue of the recent progress in global polynomial optimization and the improved local design methods mentioned above, we describe an attempt at developing several design strategies that may be viewed as our endeavors towards global solutions for LS CQ filter banks, minimax CQ filter banks, and OCM filter banks. In brief terms, the proposed design strategies are based on several observations made among globally optimal impulse responses of low-order filter banks, and are essentially order-recursive algorithms in terms of filter length combined with some techniques in identifying a desirable initial point in each round of iteration. This main idea is applied to three design scenarios in this thesis, namely, LS design of orthogonal filter banks and wavelets, minimax design of orthogonal filter banks and wavelets, and design of orthogonal cosine-modulated filter banks. Simulation studies are presented to evaluate and compare the performance of the proposed design methods with several well established algorithms in the literature.

Στην παρούσα διπλωματική εργασία εξετάζεται η εκμετάλλευση της διαφορετικότητας πολλών χρηστών και της προσαρμοστικής διαμόρφωσης στα OFDMA συστήματα. Οι αλγόριθμοι που εκμεταλλεύονται αυτά τα κέρδη δεν προσδιορίζονται από το πρότυπο WiMAX, και έτσι όλοι οι κατασκευαστές WiMAX να είναι ελεύθεροι να αναπτύξουν τις δικές τους καινοτόμες διαδικασίες. Η ιδέα είναι η ανάπτυξη αλγορίθμων για την κατανομή των υποφορέων στους χρήστες, για τον προσδιορισμό των ποσοτήτων ισχύος σε αυτούς. Η μελέτη εστιάζεται στην κάτω ζεύξη (downlink) του συστήματος OFDMA, δηλαδή στη μετάδοση δεδομένων από το σταθμό βάσης της κυψέλης στους χρήστες – δέκτες. Οι διαθέσιμοι πόροι του συστήματος είναι οι ορθογώνιοι υποφορείς και η συνολική διαθέσιμη ισχύς στο σταθμό βάσης. Οι χρήστες κάνουν εκτίμηση και ανατροφοδότηση της πληροφορίας κατάστασης του καναλιού (CSI-channel state information) σε έναν κεντρικό σταθμό βάσης, όπου υποφορείς και κατανομή ισχύος προσδιορίζονται σύμφωνα με CSI των χρηστών και τη διαδικασία κατανομής των διαθέσιμων πόρων. Μόλις οι υποφορείς για κάθε χρήστη καθοριστούν, ο σταθμός βάσης πρέπει να ενημερώνει τον κάθε χρήστη για το ποιοι υποφορείς έχουν ανατεθεί στον καθένα. Συνήθως, η κατανομή των πόρων πρέπει να γίνεται σε χρονικά διαστήματα της τάξης του χρόνου συνοχής, αν και μπορεί να γίνει πιο συχνά, αν υπάρχουν πολλοί χρήστες που ανταγωνίζονται για τους πόρους που είναι διαθέσιμοι. Στην παρούσα διπλωματική εργασία εξετάζονται διαφορετικά σενάρια κατανομής των πόρων που περιλαμβάνουν αλγορίθμους για την ανάθεση των υποφορέων και το διαμοιρασμό των κατάλληλων ποσοτήτων ισχύος στους υποφορείς. Ανάλογα με το στόχο και τις ανάγκες των χρηστών του συστήματος, καθώς και με το ποσό της διαθέσιμης πληροφορίας καναλιού στο σταθμό βάσης, χρησιμοποιούνται διαφορετικοί αλγόριθμοι. Η κατανομή των διαθέσιμων πόρων συνήθως διατυπώνεται ως πρόβλημα βελτιστοποίησης με περιορισμούς, είτε (1) ελαχιστοποίηση της συνολικής εκπεμπόμενης ισχύoς με περιορισμό στο ρυθμό μετάδοσης δεδομένων στο χρήστη είτε (2) μεγιστοποίηση του συνολικού ρυθμού μετάδοσης δεδομένων με περιορισμό στην συνολική εκπεμπόμενη ισχύ. Ο αλγόριθμος με περιορισμό αναλογίας των ρυθμών μετάδοσης (Proportional Rate Constraints algorithm - PRC) έχει ως στόχο τη μεγιστοποίηση της συνολικής διεκπεραίωσης με τον περιορισμό ότι ο ρυθμός μετάδοσης δεδομένων σε κάθε χρήστη είναι ανάλογος με ένα σύνολο από προκαθορισμένες παραμέτρους του συστήματος. Ενώ ο στόχος του αλγόριθμου μέγιστου ολικού ρυθμού μετάδοσης (MSR- maximum sum rate algorithm), είναι η μεγιστοποίηση του συνόλου των ρυθμών μετάδοσης όλων των χρηστών, λαμβάνοντας υπόψη έναν περιορισμό της συνολικής εκπεμπόμενης ισχύoς. / In this diploma thesis, multiuser diversity and adaptive modulation in OFDMA systems is considered. Algorithms that take advantage of these gains are not specified by the WiMAX standard, and all WiMAX developer are free to develop their own innovative procedures. The idea is to develop algorithms for determining which users to schedule, how to allocate subcarriers to them, and how to determine the appropriate power levels for each user on each subcarrier. The downlink of a single-cell system is considered in the downlink transmission. The available resources to be distributed among the users of the OFDMA system comprise the subcarriers over which the signals of the users are transmitted and the available power that is allocated among subcarriers. Users estimate and feedback the channel state information (CSI) to a centralized base station, where subcarrier and power allocation are determined according to users’ CSI and the resource-allocation procedure. Once the subcarriers for each user have been determined, the base station must inform each user which subcarriers have been allocated to it. Typically, the resource allocation must be performed on the order of the channel coherence time, although it may be performed more frequently if a lot of users are competing for resources. In this diploma thesis, different resource allocation strategies for the downlink of an OFDMA system are compared. Each algorithm has a different objective. The resource allocation is usually formulated as a constrained optimization problem, to either (1) minimize the total transmit power with a constraint on the user data rate or (2) maximize the total data rate with a constraint on total transmit power. The proportional rate constraints (PRC) algorithm is to maximize the sum throughput, with the additional constraint that each user’s data rate is proportional to a set of predetermined system parameters. While the objective of the maximum sum rate (MSR) algorithm, is to maximize the sum rate of all users, given a total transmit power constraint.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-27Bitstream added on 2014-06-13T20:16:04Z : No. of bitstreams: 1 nunes_jb_me_sjrp.pdf: 1005590 bytes, checksum: 7da54a97a1f2ab452a315062071f2c4e (MD5) / Este trabalho trata do estudo da localização dos zeros dos polinômios gerados por uma determinada relação de recorrência de três termos. O objetivo principal é estudar limitantes, em termos dos coeficientes da relação de recorrência, para as regiões onde os zeros estão localizados. Os zeros são explorados atravé do problema de autovalor associado a uma matriz de Hessenberg. As aplicações são consideradas para polinômios de Szego fSng, alguns polinômios para- ortogonais ½Sn(z) + S¤n (z) 1 + Sn(0) ¾ e ½Sn(z) ¡ S¤n (z) 1 ¡ Sn+1(0) ¾, especialmente quando os coeficientes de reflexão são reais. Um outro caso especial considerado são os zeros do polinômio Pn(z) = n Xm=0 bmzm, onde os coeficientes bm; para m = 0; 1; : : : ; n, são complexos e diferentes de zeros. / In this work we studied the localization the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to study bounds, in terms of the coe±cients of the recurrence relation, for the regions where the zeros are located. The zeros are explored through an eigenvalue representation associated with a Hessenberg matrix. Applications are considered to Szeg}o polynomials fSng, some para-orthogonal polyno- mials ½Sn(z) + S¤n (z) 1 + Sn(0) ¾and ½Sn(z) ¡ S¤n (z) 1 ¡ Sn+1(0) ¾, especially when the re°ection coe±cients are real. As another special case, the zeros of the polynomial Pn(z) = n Xm=0 bmzm, where the non-zero complex coe±cients bm for m = 0; 1; : : : ; n, were considered.