Orientador: Eliana Xavier Linhares de Andrade / Banca: Alagacone Sri Ranga / Banca: Andre Piranhe da Silva / Resumo: 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 Szeg"o 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. / Abstract: 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. / Mestre

Submitted by DANIEL OLIVEIRA VERONESE null (veronese@icte.uftm.edu.br) on 2016-07-27T16:57:24Z No. of bitstreams: 1 Tese_Daniel.pdf: 842310 bytes, checksum: 2518e6833497ee87b3cf404db2fca49a (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-07-29T13:17:56Z (GMT) No. of bitstreams: 1 veronese_do_dr_sjrp.pdf: 842310 bytes, checksum: 2518e6833497ee87b3cf404db2fca49a (MD5) / Made available in DSpace on 2016-07-29T13:17:56Z (GMT). No. of bitstreams: 1 veronese_do_dr_sjrp.pdf: 842310 bytes, checksum: 2518e6833497ee87b3cf404db2fca49a (MD5) Previous issue date: 2016-07-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Dado um par de sequências reais, sendo uma delas sequência encadeada positiva, podemos considerar uma sequência de polinômios que satisfazem uma relação de recorrência de três termos, de tal modo que os zeros destes polinômios sejam simples e estejam sobre o círculo unitário. Neste trabalho mostramos que é possível obter, a partir dessa fórmula de recorrência, uma única medida não trivial no círculo unitário. Provamos também que a sequência de polinômios gerados por essa relação de recorrência é uma sequência de polinômios para-ortogonais associados à medida obtida. Além disso, obtemos limitantes para os zeros extremos de tais polinômios e fornecemos estimativas para o suporte da medida associada. / Given a pair of real sequences, where one of them is a positive chain sequence, we can associate a sequence of polynomials which satisfy a three term recurrence formula and such that the zeros of these polynomials are simple and lie on the unit circle. In this manuscript, we show that, starting from this three term recurrence formula, it is always possible to obtain a unique nontrivial measure on the unit circle. We also prove that the generated sequence of polynomials is a sequence of para-orthogonal polynomials associated with this measure. Furthermore, we obtain bounds for the extreme zeros of these polynomials and also provide estimates for the support of the associated measure.

La mise en œuvre de systèmes basés OFDMA nécessite une synchronisation de la fréquence très fine en raison de l'extrême sensibilité de l'OFDMA aux décalages en fréquence porteuse (CFO). La synchronisation en fréquence devient plus difficile dans les systèmes OFDMA en liaison montante. Nos objectifs comprennent l'étude et l'analyse des problèmes résultant de décalages de fréquence et la proposition de solutions pour lutter contre ces problèmes. Nous examinons d'abord les interférences résultant de décalages de fréquence porteuse présents dans l'oscillateur du terminal utilisateur. Nous démontrons que l'on doit prendre en compte le préfixe cyclique tout en analysant les interférences résultant du CFO. Ensuite, nous montrons qu'il existe une contradiction entre la diversité de fréquence de canal et la robustesse contre le CFO. Nous proposons un compromis sous la forme d'une taille de bloc de seuil, afin de permettre un bon compromis entre la diversité des canaux et de robustesse pour les CFO pour le cas où aucune connaissances du canal n'est disponible. Quand le canal est connu, nous proposons une allocation optimale par bloc grâce à laquelle la robustesse aux CFO et à la diversité de fréquence de canal peut être réalisée en utilisant une petite taille de bloc petit pour des CFO de petite valeur. Nous proposons également une valeur CFO critique, en dessous de laquelle l'allocation optimal par bloc est très performant.Ensuite, nous proposons des solutions pour deux problèmes importants rencontrés dans un système OFDMA en liaison montante.Premièrement, nous proposons une méthode efficace pour l'estimation conjointe des réponses impulsionnelles des canaux et fréquences porteuses basée sur l'approximation polynomiale.Notre méthode d'estimation conjointe est plus simple que les méthodes existantes, sans aucune dégradation de performance. Ensuite, nous proposons une méthode de compensation de CFO basée sur l'annulation des interférences successives (SIC). La méthode d'annulation proposée réduit la complexité de mise en oeuvre quand le nombre de porteuses est important. / One of the most prominent issues in the design and implementation of OFDMA based systems is the need for a very fine frequency synchronization due to the fact that OFDMA, like OFDM, is extremely sensitive to carrier frequency offsets (CFO). The task of frequency synchronization becomes more challenging in the uplink OFDMA-based systems where one OFDMA symbol is generated by the contribution of many different users. Our goals include the study and analysis of problems resulting from frequency mismatches provide solution to combat these problems. We first look at the interference resulting from CFOs, resulting from user terminal oscillator mismatch. We demonstrate that one must take into account the cyclic prefix while analyzing interference resulting from CFO. A new analytical expression of the ICI that takes into account the effect of CFO on the cyclic prefix is proposed. Then we focus our attention on analysis of the trade-off between channel frequency diversity and robustness against CFO and show that there exists a contradiction between the two. We propose a trade-off in the form of a Threshold blocksize, to allow a good compromise between the channel diversity and robustness for CFO for the case when no CSI is available. For system where CSI is available, we propose an optimal block carrier allocation scheme through which both robustness to CFO and channel frequency diversity can be achieved with small blocksize for small CFO. We also propose a Critical CFO value, above which the performance of the optimal block carrier allocation loses interest.Next we propose solutions for two important issues encountered in an uplink OFDMA system. First, we propose an efficient method for joint estimation of channel impulse responses and carrier frequency at the receiver based on polynomial approximation. Our proposed joint estimation method is simpler than the existing methods without any performance degradation. Next we propose a CFO compensation method based on successive interference cancellation. The proposed cancellation method reduces the implementation complexity faced in case of large DFT matrices.

ITC/USA 2009 Conference Proceedings / The Forty-Fifth Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2009 / Riviera Hotel & Convention Center, Las Vegas, Nevada / This paper provides an introduction to the Orthogonal Frequency Division Multiplexing (OFDM) scheme which has been proposed for future aeronautical telemetry applications. OFDM offers the potential for high data rates on radio channels with multipath such as aeronautical telemetry channels. This paper provides in introduction to OFDM and demonstrates how orthogonality is maintained over multipath channels by the introduction of a guard band and by the inclusion of a cyclic prefix. The simulation of OFDM in multipath is simulated and performance results are presented that show the degradation of this scheme on a multipath channel with and without the guard band and the cyclic prefix.

International Telemetering Conference Proceedings / October 25-28, 1993 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Two different types of tracking feeds are currently used in the majority of telemetry tracking antenna systems when autotrack operation is required. They are of the conical scanner or of the single channel monopulse family and they employ well known technologies. In broadband applications, these feeds all suffer from the same inherent degradation in efficiency caused by their inability to maintain a constant crossover loss value and by their failure to properly illuminate the reflector. In high dynamics situations they can also generate unwanted and sometimes detrimental modulation whenever on-axis tracking is not maintained. In addition, currently available versions of the conical scanner are not capable of high scan rates or of scan rate agility and they are ill-suited for use in tracking systems based on non-orthogonal axes positioners. This paper describes a new high efficiency tracking feed system based on proven conical scanner technology. Its design incorporates features such as variable crossover, steerable beam, high scan rates, scan rate agility as well as stable reference coordinate system. In addition to these features, this new feed is also capable of delivering, in all but one operational category, levels of performance superior to that achievable to date by any other implementation of the conical scanner or of the single channel monopulse technology.

International Telemetering Conference Proceedings / October 23-26, 2000 / Town & Country Hotel and Conference Center, San Diego, California / Three Quadrature Phase Shift Keying (QPSK) mapped COFDM systems demonstrating a continuum of complexity levels are simulated over an evolving three ray model of the multipath fading channel with parameters interpolated from actual channel sounding experiments. The first COFDM system uses coherent QPSK and convolutional coding with interleaving in frequency, channel equalization and soft decision decoding; the second uses convolutional coding with interleaving in frequency, Differential Phase Shift Keying (DPSK) and soft decision decoding; the third system uses a quaternary BCH code with DPSK mapping and Error and Erasure Decoding (EED). All three systems are shown to be able to provide reliable data communication during frequency selective fade events. Simulations demonstrate QPSK mapped COFDM with reasonable complexity performs well in a multipath frequency selective fading environment under parameters typically encountered in aeronautical telemetry.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this study, Ti6Al4V machining is modelled using finite element analysis of orthogonal machining. Orthogonal turning tests are conducted for the verification of FE models in terms of machining forces, temperatures, and chip geometry. Milling force predictions are made using the "unified" mechanics of cutting model which is applied to ball nose milling for this study. The model makes use of orthogonal cutting data, collected from the turning tests, to model milling forces. Model predictions are compared with test data from slot milling tests for verification. Finally a hybrid form of the "‘unified"’ model is presented in which orthogonal data, obtained from the FE simulations, is used to model ball nose milling operations. / AFRIKAANSE OPSOMMING: In hierdie studie word titaanmasjinering (Ti6Al4V) gemodelleer deur gebruik te maak van eindige element analise van ortogonale masjinering. Ortogonale draai toetse word uitgevoer om eindige element (FE) modelle te verifieer in terme van masjineringskragte, temperatuur en spaandergeometrie. Freeskragte word voorspel deur gebruik te maak van die "Unified Mechanics of Cutting" model wat toegepas word op ’n balneusfrees operasie in hierdie studie. Die model maak gebruik van ortogonale snydata, versamel gedurende snytoetse, om die freeskragte te modelleer. Die model word vervolgens vergelyk met die toetsdata afkomstig van die freestoetse vir verifikasie. Ten slotte word ’n hibriede weergawe van die model aangebied waarin ortogonale data verkry word van die FE simulasie om balneus freesoperasies te simuleer.

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2005. / Orthogonal Frequency Division Multiplexing (ODFM) has gained considerable attention the past couple of years. In our modern world the need for faster data transmission is never-ending. OFDM modulation provides us with a way of more densely packing modulated carriers in the frequency domain than other existing Frequency Multiplexing schemes, thus achieving higher data rates through communications channels. Software Defined Radio (SDR) creates a very good entry point for designing any communications system. SDR is an architecture that aims to minimise hardware components in electronic communications circuits by doing all possible processing in the software domain. Such systems have many advantages over existing hardware implementations and can be executed on various platforms and embedded systems, given that the appropriate analogue front ends are attached to the system.

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

In recent years, cellular systems based on orthogonal frequency division multiple access – time division duplex (OFDMA-TDD) have gained considerable popularity. Two of the major reasons for this are, on the one hand, that OFDMA enables the receiver to effectively cope with multipath propagation while keeping the complexity low. On the other hand, TDD offers efficient support for cell-specific uplink (UL)/downlink (DL) asymmetry demands by allowing each cell to independently set its UL/DL switching point (SP). However, cell-independent SP gives rise to crossed slots. In particular, crossed slots arise when neighbouring cells use the same slot in opposing link directions, resulting in base station (BS)-to-BS interference and mobile station (MS)-to-MS interference. BS-to-BS interference, in particular, can be quite detrimental due to the exposed location of BSs, which leads to high probability of line-of-sight (LOS) conditions. The aim of this thesis is to address the BS-to-BS interference problem in OFDMA-TDDcellular networks. A simulation-based approach is used to demonstrate the severity of BS-to-BS interference and a signal-to-interference-plus-noise ratio (SINR) equation for OFDMA is formulated to aid system performance analysis. The detrimental effects of crossed slot interference in OFDMA-TDD cellular networks are highlighted by comparing methods specifically targeting the crossed slots interference problem. In particular, the interference avoidance method fixed slot allocation (FSA) is compared against state of the art interference mitigation approaches, viz: random time slot opposing (RTSO) and zone division (ZD). The comparison is done based on Monte Carlo simulations and the main comparison metric is spectral efficiency calculated using the SINR equation formulated in this thesis. The simulation results demonstrate that when LOS conditions among BSs are present, both RTSO and ZD perform worse than FSA for all considered performance metrics. It is concluded from the results that current interference mitigation techniques do not offer an effective solution to the BS-to-BS interference problem. Hence, new interference avoidance methods, which unlike FSA, do not sacrifice the advantages of TDD are open research issues addressed in this thesis. The major contribution of this thesis is a novel cooperative resource balancing technique that offers a solution to the crossed slot problem. The novel concept, termed asymmetry balancing, is targeted towards next-generation cellular systems, envisaged to have ad hoc and multi-hop capabilities. Asymmetry balancing completely avoids crossed slots by keeping the TDD SPs synchronised among BSs. At the same time, the advantages of TDD are retained, which is enabled by introducing cooperation among the entities in the network. If a cell faces resource shortage in one link direction, while having free resources in the opposite link direction, the free resources can be used to support the overloaded link direction. In particular, traffic can be offloaded to near-by mobile stations at neighbouring cells that have available resources. To model the gains attained with asymmetry balancing, a mathematical framework is developed which is verified by Monte Carlo simulations. In addition, asymmetry balancing is compared against both ZD and FSA based on simulations and the results demonstrate the superior performance of asymmetry balancing. It can be concluded that the novel interference avoidance approach is a very promising candidate to.