Browsing by Subject "Probabilistic Model"
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Item A Probabilistic Model of Spectrum Occupancy, User Activity, and System Throughput for OFDMA based Cognitive Radio Systems(2013-05-07) Rahimian, NarimanWith advances in communications technologies, there is a constant need for higher data rates. One possible solution to overcome this need is to allocate additional bandwidth. However, due to spectrum scarcity this is no longer feasible. In addition, the results of spectrum measurement campaigns discovered the fact that the available spectrum is under-utilized. One of the most significant solutions to solve the under- utilization of radio-frequency (RF) spectrum is the cognitive radio (CR) concept. A valid mathematical model that can be applied for most practical scenarios and also captures the random fluctuations of the spectrum is necessary. This model provides a significant insight and also a better quantitative understanding of such systems and this is the topic of this dissertation. Compact mathematical formulations that describe the realistic spectrum usage would improve the recent theoretical work to a large extent. The data generated for such models, provide a mean for a more realistic evaluation of the performance of CR systems. However, measurement based models require a large amount of data and are subject to measurement errors. They are also likely to be subject to the measurement time, location, and methodology. In the first part of this dissertation, we introduce cognitive radio networks and their role on solving the problem of under-utilized spectrum. In the second part of this dissertation, we target the random variable which accounts for the fraction of available subcarriers for the secondary users in an OFDMA based CR system. The time and location dependency of the traffic is taken into account by a non-homogenous Poisson Point Process (PPP). In the third part, we propose a comprehensive statistical model for user activity, spectrum occupancy, and system throughput in the presence of mutual interference in an OFDMA-based CR network which accounts for the sensing procedure of spectrum sensor, spectrum demand-model and spatial density of primary users, system objective for user satisfaction which is to support as many users as possible, and environment-dependent conditions such as propagation path loss, shadowing, and channel fading. In the last part of this dissertation, unlike the second and the third parts that the modeling is theoretical and based on limiting assumptions, the spectrum usage modeling is based on real data collected from an extensive measurement.Item Comparative Deterministic and Probabilistic Modeling in Geotechnics: Applications to Stabilization of Organic Soils, Determination of Unknown Foundations for Bridge Scour, and One-Dimensional Diffusion Processes(2013-08-08) Yousefpour, NeginThis study presents different aspects on the use of deterministic methods including Artificial Neural Networks (ANNs), and linear and nonlinear regression, as well as probabilistic methods including Bayesian inference and Monte Carlo methods to develop reliable solutions for challenging problems in geotechnics. This study addresses the theoretical and computational advantages and limitations of these methods in application to: 1) prediction of the stiffness and strength of stabilized organic soils, 2) determination of unknown foundations for bridges vulnerable to scour, and 3) uncertainty quantification for one-dimensional diffusion processes. ANNs were successfully implemented in this study to develop nonlinear models for the mechanical properties of stabilized organic soils. ANN models were able to learn from the training examples and then generalize the trend to make predictions for the stiffness and strength of stabilized organic soils. A stepwise parameter selection and a sensitivity analysis method were implemented to identify the most relevant factors for the prediction of the stiffness and strength. Also, the variations of the stiffness and strength with respect to each factor were investigated. A deterministic and a probabilistic approach were proposed to evaluate the characteristics of unknown foundations of bridges subjected to scour. The proposed methods were successfully implemented and validated by collecting data for bridges in the Bryan District. ANN models were developed and trained using the database of bridges to predict the foundation type and embedment depth. The probabilistic Bayesian approach generated probability distributions for the foundation and soil characteristics and was able to capture the uncertainty in the predictions. The parametric and numerical uncertainties in the one-dimensional diffusion process were evaluated under varying observation conditions. The inverse problem was solved using Bayesian inference formulated by both the analytical and numerical solutions of the ordinary differential equation of diffusion. The numerical uncertainty was evaluated by comparing the mean and standard deviation of the posterior realizations of the process corresponding to the analytical and numerical solutions of the forward problem. It was shown that higher correlation in the structure of the observations increased both parametric and numerical uncertainties, whereas increasing the number of data dramatically decreased the uncertainties in the diffusion process.