Browsing by Subject "Space-time"
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Item New advances in symbol timing synchronization of single-carrier, multi-carrier and space-time multiple-antenna systems(Texas A&M University, 2005-11-01) Wu, Yik ChungIn this dissertation, the problem of symbol timing synchronization for the following three different communication systems is studied: 1) conventional single-carrier transmissions with single antenna in both transmitter and receiver; 2) single-carrier transmissions with multiple antennas at both transmitter and receiver; and 3) orthogonal frequency division multiplexing (OFDM) based IEEE 802.11a wireless local area networks (WLANs). For conventional single-carrier, single-antenna systems, a general feedforward symbol-timing estimation framework is developed based on the conditional maximum likelihood principle. The proposed algorithm is applied to linear modulations and two commonly used continuous phase modulations: MSK and GMSK. The performance of the proposed estimator is analyzed analytically and via simulations. Moreover, using the newly developed general estimation framework, all the previously proposed digital blind feedforward symbol timing estimators employing second-order statistics are cast into a unified framework. The finite sample mean-square error expression for this class of estimators is established and the best estimators are determined. Simulation results are presented to corroborate the analytical results. Moving on to single-carrier, multiple-antenna systems, we present two algorithms. The first algorithm is based on a heuristic argument and it improves the optimum sample selection algorithm by Naguib et al. so that accurate timing estimates can be obtained even if the oversampling ratio is small. The performance of the proposed algorithm is analyzed both analytically and via simulations. The second algorithm is based on the maximum likelihood principle. The data aided (DA) and non-data aided (NDA) ML symbol timing estimators and their cor- responding CCRB and MCRB in MIMO correlated ??at-fading channels are derived. It is shown that the improved algorithm developed based on the heuristic argument is just a special case of the DA ML estimator. Simulation results under different operating conditions are given to assess and compare the performances of the DA and NDA ML estimators with respect to their corresponding CCRBs and MCRBs. In the last part of this dissertation, the ML timing synchronizer for IEEE 802.11a WLANs on frequency-selective fading channels is developed. The proposed algorithm is compared with four of the most representative timing synchronization algorithms, one specically designed for IEEE 802.11a WLANs and three other algorithms designed for general OFDM frame synchronization.Item Space-time discontinuous Petrov-Galerkin finite elements for transient fluid mechanics(2016-05) Ellis, Truman Everett; Demkowicz, Leszek; Moser, Robert D; Hughes, Thomas J.R; Dawson, Clint N; Bui, TanInitial mesh design for computational fluid dynamics can be a time-consuming and expensive process. The stability properties and nonlinear convergence of most numerical methods rely on a minimum level of mesh resolution. This means that unless the initial computational mesh is fine enough, convergence can not be guaranteed. Any meshes below this minimum resolution level are termed to be in the ``pre-asymptotic regime.'' This condition implies that meshes need to in some way anticipate the solution before it is known. On top of the minimum requirement that the surface meshes must adequately represent the geometry of the problem under consideration, resolution requirements on the volume mesh make the CFD practitioner's job significantly more time consuming. In contrast to most other numerical methods, the discontinuous Petrov-Galerkin finite element method retains exceptional stability on extremely coarse meshes. DPG is also inherently very adaptive. It is possible to compute the residual error without knowledge of the exact solution, which can be used to robustly drive adaptivity. This results in a very automated technology, as the user can initialize a computation on the coarsest mesh which adequately represents the geometry then step back and let the program solve and adapt iteratively until it resolves the solution features. A common complaint of minimum residual methods by computational fluid dynamics practitioners is that they are not locally conservative. In this thesis, this concern is addressed by developing a locally conservative DPG formulation by augmenting the system with Lagrange multipliers. The resulting DPG formulation is then proved to be robust and shown to produce superior numerical results over standard DPG on a selection of test problems. Adaptive convergence to steady incompressible and compressible Navier-Stokes solutions was explored in Jesse Chan's and Nathan Roberts' dissertations. Space-time offers a natural extension to transient problems as it preserves the stability and adaptivity properties of DPG in the time dimension. Space-time also offers more extensive parallelization capability than problems treated with traditional time stepping as it allows multigrid concurrently in both space and time. A proof of concept space-time DPG formulation is developed for transient convection-diffusion. The robust test norms derived for steady convection-diffusion are extended to the space-time case and proofs of robustness are provided. Numerical results verify the robust behavior and near $L^2$ optimality of the resulting solutions. The space-time formulation for convection-diffusion is then extended to transient incompressible and compressible Navier-Stokes by analogy. Several numerical experiments are performed, but a mathematical analysis is not attempted for these nonlinear problems. Several side topics are explored such as a study of the compressible Navier-Stokes equations under various variable transformations and the development of consistent test norms through the concept of physical entropy.