Wireless devices and applications have been an unavoidable part of human lives in the past decade. In the past few years, the global mobile data traffic has grown considerably and is expected to grow even faster in future. Given the fact that the number of wireless nodes has significantly increased, the contention and interference on the license-free industrial, scientific, and medical band has become severer than ever. Cognitive radio nodes were introduced in the past decade to mitigate the issues related to spectrum scarcity. In this dissertation, we focus on the interference and performance analysis of networks coexisting with cognitive radio networks and address the design and analysis of spectrum allocation and routing for cognitive radio networks. Spectrum allocation enables nodes to construct a link on a common channel at the same time so they can start communicating with each other. We introduce a new approach for the modeling and analysis of interference and spectrum allocation schemes for cognitive radio networks with arbitrarily-shaped network regions. First, for the first time in the literature, we propose a simple and efficient approach that can derive the distribution of the distance between an arbitrary interior/exterior reference point and a random point within an arbitrary convex/concave irregular polygon. This tool is essential in analyzing important distance-related performance metrics in wireless communication networks. Second, considering the importance of interference analysis in cognitive radio networks and its important role in designing spectrum allocation schemes, we model and analyze a heterogeneous cellular network consisting of several cognitive femto cells and a coexisting multi-cell network. Besides the cumulative interference, important distance-related performance metrics have been investigated, such as the signal-to-interference ratio and outage probability. Finally, the spectrum allocation and routing problems in cognitive radio networks have been discussed. Considering a wireless cognitive radio network coexisting with a cellular network with irregular polygon-shaped cells, we have used the tools developed in this dissertation and proposed a joint spectrum allocation and routing scheme. / Graduate

Made available in DSpace on 2015-03-26T13:45:34Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1893968 bytes, checksum: ce37a1814e775a74aa222b17583fdc19 (MD5) Previous issue date: 2012-02-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation aims to study two topics related to modern topology and geometry. The first of these themes is dedicated to the study of packaging and record covering spheres in the hyperbolic plane, in which we treat the study results due to Bavard (1996) [3]. The second issue that was addressed refers to the study of edges pairing for irregular polygons. In this part we try to expose an example, created during our studies, for a pairing that generates a tiling of the hyperbolic plane by an irregular polygon. Also use the techniques developed by Mercio Botelho Faria, Catarina Mendes de Jesus and Panteleón D. R. Sanchez in [14] to obtain matching of edges of regular polygons through surgeries in surfaces associated with trivalent graphs. / Esta dissertação tem como objetivo o estudo de dois temas ligados a topologia e a geometria moderna. O primeiro destes temas é dedicado ao estudo de empacotamento e coberturas de discos do plano hiperbólico, no qual tratamos de estudar resultados devidos a Bavard (1996) [3]. Já o segundo tema que foi abordado se refere ao estudo de emparelhamento de arestas para polígonos irregulares. Nesta parte tratamos de expor um exemplo, criado durante nossos estudos, para um emparelhamento que gera um ladrilhamento do plano hiperbólico por um polígono irregular. Além disso utilizamos as técnicas desenvolvidas por Mercio Botelho Faria, Catarina Mendes de Jesus e Panteleón D. R. Sanchez em [14] para obtermos emparelhamentos de arestas de polígonos regulares por meio de cirurgias em superfícies associadas a grafos trivalentes.