Resultados espectrais relacionados com a estrutura dos grafos

Nesta tese são estabelecidas novas propriedades espectrais de grafos com estruturas específicas, como sejam os grafos separados em cliques e independentes e grafos duplamente separados em independentes, ou ainda grafos com conjuntos (κ,τ)-regulares. Alguns invariantes dos grafos separados em cliques e independentes são estudados, tendo como objectivo limitar o maior valor próprio do espectro Laplaciano sem sinal. A técnica do valor próprio é aplicada para obter alguns majorantes e minorantes do índice do espectro Laplaciano sem sinal dos grafos separados em cliques e independentes bem como sobre o índice dos grafos duplamente separados em independentes. São fornecidos alguns resultados computacionais de modo a obter uma melhor percepção da qualidade desses mesmos extremos. Estudamos igualmente os grafos com um conjunto (κ,τ)-regular que induz uma estrela complementar para um valor próprio não-principal $. Além disso, é mostrado que $=κ-τ. Usando uma abordagem baseada nos grafos estrela complementares construímos, em alguns casos, os respectivos grafos maximais. Uma caracterização dos grafos separados em cliques e independentes que envolve o índice e as entradas do vector principal é apresentada tal como um majorante do número da estabilidade dum grafo conexo.

Characterization of RSOA modulators in radio over fiber links

In this work physical and behavioral models for a bulk Reflective Semiconductor Optical Amplifier (RSOA) modulator in Radio over Fiber (RoF) links are proposed. The transmission performance of the RSOA modulator is predicted under broadband signal drive. At first, the simplified physical model for the RSOA modulator in RoF links is proposed, which is based on the rate equation and traveling-wave equations with several assumptions. The model is implemented with the Symbolically Defined Devices (SDD) in Advanced Design System (ADS) and validated with experimental results. Detailed analysis regarding optical gain, harmonic and intermodulation distortions, and transmission performance is performed. The distribution of the carrier and Amplified Spontaneous Emission (ASE) is also demonstrated. Behavioral modeling of the RSOA modulator is to enable us to investigate the nonlinear distortion of the RSOA modulator from another perspective in system level. The Amplitude-to-Amplitude Conversion (AM-AM) and Amplitude-to-Phase Conversion (AM-PM) distortions of the RSOA modulator are demonstrated based on an Artificial Neural Network (ANN) and a generalized polynomial model. Another behavioral model based on Xparameters was obtained from the physical model. Compensation of the nonlinearity of the RSOA modulator is carried out based on a memory polynomial model. The nonlinear distortion of the RSOA modulator is reduced successfully. The improvement of the 3rd order intermodulation distortion is up to 17 dB. The Error Vector Magnitude (EVM) is improved from 6.1% to 2.0%. In the last part of this work, the performance of Fibre Optic Networks for Distributed and Extendible Heterogeneous Radio Architectures and Service Provisioning (FUTON) systems, which is the four-channel virtual Multiple Input Multiple Output (MIMO), is predicted by using the developed physical model. Based on Subcarrier Multiplexing (SCM) techniques, four-channel signals with 100 MHz bandwidth per channel are generated and used to drive the RSOA modulator. The transmission performance of the RSOA modulator under the broadband multi channels is depicted with the figure of merit, EVM under di erent adrature Amplitude Modulation (QAM) level of 64 and 254 for various number of Orthogonal Frequency Division Multiplexing (OFDM) subcarriers of 64, 512, 1024 and 2048.