The abstract boundary construction of Scott and Szekeres has proven a practical classification scheme for boundary points of pseudo-Riemannian manifolds. It has also proved its utility in problems associated with the re-embedding of exact solutions containing directional singularities in space-time. Moreover it provides a model for singularities in space-time - essential singularities. However the literature has been devoid of abstract boundary results which have results of direct physical applicability.¶ This thesis presents several theorems on the existence of essential singularities in space-time and on how the abstract boundary allows definition of optimal em- beddings for depicting space-time. Firstly, a review of other boundary constructions for space-time is made with particular emphasis on the deficiencies they possess for describing singularities. The abstract boundary construction is then pedagogically defined and an overview of previous research provided.¶ We prove that strongly causal, maximally extended space-times possess essential singularities if and only if they possess incomplete causal geodesics. This result creates a link between the Hawking-Penrose incompleteness theorems and the existence of essential singularities. Using this result again together with the work of Beem on the stability of geodesic incompleteness it is possible to prove the stability of existence for essential singularities.¶ Invariant topological contact properties of abstract boundary points are presented for the first time and used to define partial cross sections, which are an generalization of the notion of embedding for boundary points. Partial cross sections are then used to define a model for an optimal embedding of space-time.¶ Finally we end with a presentation of the current research into the relationship between curvature singularities and the abstract boundary. This work proposes that the abstract boundary may provide the correct framework to prove curvature singularity theorems for General Relativity. This exciting development would culminate over 30 years of research into the physical conditions required for curvature singularities in space-time.

In many command and control situations the understanding of dynamic events is crucial. With today’s development of hard- and software architecture, we have the possibility to visualize data in two-dimensional (2D) and three-dimensional (3D) images. The aim of this thesis is therefore to investigate different approaches to visualizing dynamic events. The visualization techniques investigated include 2D animation and time representations as markings on a 2D map. In 3D the visualization technique investigated is the “space time-cube” A further aim is to study whether the Cue Probability Learning (CPL) paradigm can be used to evaluate visualizations. By mapping time onto a spatial dimension, in the 2D visualization as lines with different densities and in 3D as height over the map, a simultaneous visualization of space and time is possible. The findings are that this mapping of time onto space is beneficial to users as compared with animations, but the two mapping techniques are not interchangeable. If a task requires judgments of metric spatial properties, a 2D visualization is more beneficial; however, if the task only requires judgments of more qualitative aspects, a 3D visualization is more beneficial. When we look at a 3D visualization, we utilize different sources of depth information. These sources are always present and each defines either a 3D scene or a projection surface. By using these different sources of depth information wisely, a visualization can be created that efficiently shows relevant information to a user while requiring a minimal amount of specialized hardware. Finally, the CPL paradigm seems to be a worthwhile option as an experimental paradigm in visualization experiments. One of the advantages of CPL is that novice users can be trained to be task experts in a controlled and time-efficient way.

A new version of the Deforming-Spatial-Domain/Stabilized Space--Time (DSD/SST) formulation of incompressible flows has been introduced recently to have additional subgrid-scale representation features. This is the space--time version of the residual-based variational multiscale (VMS) method. The new version is called DSD/SST-VMST (i.e. the version with the VMS turbulence model) and also Space--Time VMS (ST-VMS). The thesis starts with a brief overview of the ST-VMS method. It continues with a comprehensive set of test computations with 3D airfoil geometries at high Reynolds numbers and comparison with experimental data. The thesis shows that the test computations signal a promising future for the ST-VMS method.

A new version of the Deforming-Spatial-Domain/Stabilized Space--Time (DSD/SST) formulation of incompressible flows has been introduced recently to have additional subgrid-scale representation features. This is the space--time version of the residual-based variational multiscale (VMS) method. The new version is called DSD/SST-VMST (i.e. the version with the VMS turbulence model) and also Space--Time VMS (ST-VMS). The thesis starts with a brief overview of the ST-VMS method. It continues with a comprehensive set of test computations with 3D airfoil geometries at high Reynolds numbers and comparison with experimental data. The thesis shows that the test computations signal a promising future for the ST-VMS method.

In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We then turn our attention to the problem of embedding any given <i>n</i>-dimensional spacetime within an (<i>n</i>+1)-dimensional manifold, paying special attention to how any structure from the extra dimension modifies the standard <i>n</i>-dimensional Einstein equations. Using results derived from this investigation and the formalism derived for test particles and gyroscopes, we systematically introduce three specific higher-dimensional models and classify their properties; including the Space-Time-Matter and two types of braneworld models. The remainder of the thesis concentrates on specific higher-dimensional cosmological models drawn from the above mentioned scenarios; including an analysis of the embedding of Friedmann-Lemaitre-Robertson-Walker submanifolds in 5-dimensional Minkowski and topological Schwarzschild spaces, and an investigation of the dynamics of a <i>d</i>-brane that takes the form of a thin shell encircling a (<i>d</i>+2)-dimensional topological black hole in anti-deSitter space. The latter is derived from a finite-dimensional action principle, which allows us to consider the canonical quantization of the model and the solutions of the resulting Wheeler-DeWitt equation.

The general objective of this proposed research is to design and develop signal acquisition and tracking algorithms for multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) systems for fixed wireless access applications. The algorithms are specifically targeted for systems that work in time division multiple access and frequency division multiple access frame modes. In our research, we first develop a comprehensive system model for a MIMO-OFDM system under the influence of the radio frequency (RF) oscillator frequency offset, sampling frequency (SF) offset, RF oscillator phase noise, frequency selective channel impairments and finally the additive white Gaussian noise. We then develop the acquisition and tracking algorithms to estimate and track all these parameters. The acquisition and tracking algorithms are assisted by a preamble consisting of one or more training sequences and pilot symbol matrices. Along with the signal acquisition and tracking algorithms, we also consider design of the MIMO-OFDM preamble and pilot signals that enable the suggested algorithms to work efficiently. Signal acquisition as defined in our research consists of time and RF synchronization, SF offset estimation and correction, phase noise estimation and correction and finally channel estimation. Signal tracking consists of RF, SF, phase noise and channel tracking. Time synchronization, RF oscillator frequency offset, SF oscillator frequency offset, phase noise and channel estimation and tracking are all research topics by themselves. A large number of studies have addressed these issues, but usually individually and for single-input single-output (SISO) OFDM systems. In the proposed research we present a complete suite of signal acquisition and tracking algorithms for MIMO-OFDM systems along with Cramr-Rao bounds for the SISO-OFDM case. In addition, we also derive the Maximum Likelihood (ML) estimates of the parameters for the SISO-OFDM case. Our proposed research is unique from the existing literature in that it presents a complete receiver implementation for MIMO-OFDM systems and accounts for the cumulative effects of all possible acquisition and tracking errors on the bit error rate (BER) performance. The suggested algorithms and the pilot/training schemes may be applied to any MIMO OFDM system and are independent of the space-time coding techniques that are employed.

Technological progress in the field of wireless communications over the past few years has only been matched by the increasing demand for sophisticated services at lower costs. A significant breakthrough was achieved in the design of efficient wireless communication systems with the advent of the diversity concept. Spatial diversity exploits the availability of multiple spatial paths between the transmitter and receiver by placing antenna arrays at either end. In addition to improving the reliability of communication by creating redundant copies of the transmitted information at the receiver, wireless transceivers with multiple antennas exploit the spatial degrees of freedom to multiplex multiple streams of data and achieve significant gains in spectral efficiencies. In this thesis, we design spatial diversity techniques for slow-fading wireless channels. There are two parts to this thesis: In Part I we propose spatial diversity techniques for point-to-point single-user wireless systems, while in Part II we propose multiuser cooperative diversity techniques for multiuser wireless communication systems. In the first part, we propose a set of new wireless communication techniques for multiple-input, multiple-output (MIMO) channels over Rayleigh slow-fading wireless channels. We introduce MIMO transceivers that achieve high data rates and low error rates using a class of MIMO systems known as layered space-time (ST) architectures, which use low complexity, suboptimal decoders such as successive cancellation (SC) decoders. We propose a set of improved layered space-time architectures and show that it is possible to achieve near-optimal error performance over MIMO channels while requiring just SC decoding at the receiver. We show that these architectures achieve high rate and diversity gains. We also show that some of the proposed layered space-time architectures could find applications in multiple-access communications as low-complexity solutions for achieving near-optimum performance. In the second part of this thesis, we propose novel techniques for cooperative communication between terminals in multiuser wireless communication systems. Cooperative communication is a concept where neighboring terminals share their antennas and signal processing resources to create a virtual transmit array . In addition to transmitting their own information, users in a cooperative communication system listen to transmission from other users and relay this information to the destination, thus creating multiple paths between transmitter and receiver. This form of diversity, known as cooperative diversity, helps improve the overall reliability of all the users in a network. We start with a simple three node multiple-access system where two users are communicating with a common destination. We propose new high-rate cooperation strategies which achieve the full diversity gain offered by the cooperative channel for this simple system. We propose a new framework to address the tradeoff between cooperation and independent transmission over a multiple access channel and determine the conditions under which each idea is better than the other. Finally, we propose a high rate cooperation protocol which achieves the maximum diversity over a multiple access system with an arbitrary number of users and achieves high rates which scale favorably as the number of users increases.

The code division multiple access (CDMA) system implemented by the direct-sequence (DS) spread spectrum (SS) technique is one of the most promising multiplexing technologies for wireless communications services. The SS communication adopts a technique of using much wider bandwidth necessary to transmit the information over the channel. In the DS-CDMA system, due to the inherent structure interference, referred to as the multiple access interference (MAI), the system performance might degrade. Next, for DS-CDMA systems over frequency-selective fading channels, the effect of inter symbol interference (ISI) will exist, such that a multiuser RAKE receiver has to be employed to combat the ISI as well as MAI. Since, in practical wireless communication environment, there may have several communication systems operated in the same area at the same time. In this thesis, we consider the environment of DS-CDMA systems, where the asynchronous narrow band interference (NBI) due to other systems is joined suddenly to the CDMA system. In general, when a system works in a stable state with adaptive detectors, a suddenly joined NBI signal will cause the system performance to be crash down. Under such circumstance, the existing conventional adaptive RAKE detectors may not be able to track well for the rapidly sudden changing NBI associated with the problems of ISI and MAI. It is known that the adaptive filtering algorithms, based on the sliding window linear constrained recursive least squares (SW LC-RLS), is very attractive to a violent changing environment. The main concern of this thesis is to propose a novel sliding window constant modulus RLS (SW CM-RLS) algorithm, based on the Min/max criterion, to deal with the NBI for DS-CDMA system over multipath channels. For simplicity and having less system complexity the generalized side-lobe canceller (GSC) structure is employed, and is referred to as the SW CM-GSC-RLS algorithm. The aim of the SW CM-GSC-RLS algorithm is used to alleviate the effect of NBI. It has the advantages of having faster convergence property and tracking ability, and can be applied to the environment in which the NBI is suddenly joined to the system under the effect of channel mismatch to achieve desired performance. At the end of this thesis, we extend the idea of the proposed algorithm to the space-time DS-CDMA RAKE receiver, in which the adaptive beamformer with temporal domain DS-CDMA receiver is employed. Via computer simulation results, we show that our new proposed schemes outperform the conventional CM GSC-RLS algorithm as well as the GSC-RLS algorithm (the so-called LCMV approach), in terms of mean square error of estimating channel impulse response, output signal to interference plus noise ratio and bit-error-rate.

Space-Time Adaptive Processing (STAP) is an effective method in Ground Moving Target Indicator (GMTI) operation of airborne radars. Clutter suppression is the key to successful MTI operation. Airborne radars are different than the ground based ones in regard to clutter due to the displacement of the platform during operation. When STAP methods are to be investigated, one needs to have accurate signal models while evaluating performance. In this thesis, a comprehensive received signal model is developed first for an airborne antenna array. The impacts of the aircraft motion and irregularities in it, aircraft displacement during reception, intrinsic clutter motion and radar parameters have been accounted in the model and incorporated into a simulator environment. To verify the correctness of the signal simulator, the classical DPCA approach and optimum STAP methods are inspected.

This thesis presents a comparison between two transmit diversity schemes, namely space-time coding and time-switched transmit diversity (TSTD) over block-fading and time-varying multi-input single-output (MISO) channels with different channel parameters. The schemes are concatenated with outer channel codes in order to achieve spatio-temporal diversity. The analytical results are derived for the error performances of the systems and the simulation results as well as outage probabilities are provided. Besides, the details of the pilot-symbol-aided modulation (PSAM) technique are investigated and the error performances of the systems are analyzed when the channel state information is estimated with PSAM. It is demonstrated using the analytical and simulation results that TSTD have a comparable error performance with the space-time coding techniques and it even outperforms the space-time codes for some channel parameters. Our results indicate that TSTD can be suggested as an alternative to space-time codes in some time-varying channels especially due to the implementation simplicity.