In this dissertation a computationally efficient cognitive multiple-input multiple-output (MIMO) orthogonal frequency division duplexing (OFDM) detector is designed to decode perfect space-time coded signals which are able maximize the diversity and multiplexing properties of a rich fading MIMO channel. The adaptive nature of the cognitive detector allows a MIMO OFDM communication system to better meet to needs of future wireless communication networks which require both high reliability and low run-time complexity depending on the propagation environment. The cognitive detector in conjunction with perfect space-time coding is able to achieve up to a 2 dB bit-error rate (BER) improvement at low signal-to-noise ratio (SNR) while also achieving comparable runtime complexity in high SNR scenarios.

This thesis deals with two classes of space-time symmetries: emergent symmetries in the near-horizon region of rapidly rotating Kerr black holes and residual gauge symmetries. The main aim of the thesis is to investigate consequences and effects of these symmetries on black holes and gravitational radiation. The first class of symmetries is exploited to address questions of astrophysical relevance for force-free magnetospheres, thin accretion discs, and strong magnetic fields around Kerr black holes. We investigate how the dynamics of electromagnetic and matter fields is constrained by global conformal symmetries of the near-horizon geometry. In the context of force-free electrodynamics, we find exact solutions and classify them according to the highest weight representation of the isometry group. We introduce novel criteria to distinguish physical solutions and deduce bounds on conformal weights of electromagnetic fields. For thin accretion discs, within the Novikov-Thorne model, new properties arise in the high spin regime of the Kerr black hole. We find a novel self-similar solution and we explain the critical behaviour of the observables by symmetry arguments. Afterwards, we study an exact analytic solution to the Einstein-Maxwell theory. It describes a black hole immersed in a strong magnetic field and it shares the same near-horizon geometry of extreme Kerr black holes. We compute its total conserved mass by means of the covariant phase space formalism and study its thermodynamics. The second class of symmetries is considered in order to provide a new definition of gravitational multipole moments by means of Noether charges and by adopting the covariant phase space formalism. We show that such a definition in terms of Noether charges reproduces multipole moments in General Relativity. We propose to apply it to an arbitrary generally covariant metric theory of gravity. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Multiple-input multiple-output (MIMO) communication systems employ multiple antennas at the transmitter and the receiver. Multiple antennas provide capacity gain and/or robust performance over single antenna communications. Traditional automatic-repeat-request (ARQ) techniques developed for single-input single-output (SISO) communication systems have to be modified in order to be employed in MIMO communication systems. In this dissertation, we propose and analysis some ARQ techniques for MIMO communication systems. The basic retransmission protocols of ARQ, stop-and-wait (SW-ARQ), go-back-$N$ (GBN-ARQ), and selective repeat (SR-ARQ), designed for SISO communication systems are generalized for parallel multichannel communication systems. The generalized ARQ protocols seek to improve the channel utilization of multiple parallel channels with different transmission rates and different packet error rates. The generalized ARQ protocols are shown to improve the transmission delay as well. A type-I hybrid-ARQ error control is used to illustrate the throughput gain of employing ARQ error control into MIMO communication systems. With the channel information known at both the transmitter and the receiver, the MIMO channel is converted into a set of parallel independent subchannels. The performance of the type-I hybrid-ARQ error control is presented. Simulation results show the throughput gain of using an ARQ scheme in MIMO communication systems. When the channel state information is unknown to the transmitter, error control codes that span both space and time, so-called space-time coding, are explored in order to obtained spatial diversity. As a consequence, the coding scheme used for ARQ error control has to be designed in order to consider coding across both space and time. In this dissertation, we design a set of retransmission codes for a type-II hybrid-ARQ scheme employing the multidimensional space-time trellis code as the forward error control code. A concept of sup-optimal partitioning of the (super-)constellation is proposed. The hybrid-ARQ error control scheme, consisting of the optimal code for each transmission, outperforms the hybrid-ARQ error control scheme, consisting of the same code for all transmissions.

Aeronautical telemetry systems that transmit the same signal through multiple antennas from the flight vehicle suffer from severe link dropouts when the signals destructively interfere one with another at receiver. The underlying issue is a transmit array with element spacing far greater than the wavelength producing a transmit antenna pattern with significant and deep nulls. Recently, space-time coding techniques have been proven to resolve the issue for systems using linear modulations and shaped-offset quadrature shift keying (SOQPSK) modulation, a non-linear continuous phase modulation (CPM). This thesis examines application of space-time coding techniques to resolve the self-interference issue for another CPM modulation, the advanced range telemetry (ARTM) CPM. It is shown in this thesis among the two branches of space-time coding, space-time block coding (STBC) and space-time trellis coding (STTC), only the latter offers a solution for a full rate, low complexity, no hardware modification implementation. Various candidate STTCs are identified via simulation using the pair-wise error probability as a performance metric. One STTC is identified with trivial implementation costs and an error performance that is a function of code length.

<p> This thesis investigates the application of multiple model estimation algorithms to the problem of channel equalization for digital data transmission and channel tracking for space-time block coded systems with non-Gaussian additive noise. Recently, a network of Kalman filters (NKF) has been reported for the equalization of digital communication channels based on the approximation of the a posteriori probability density function of a sequence of delayed symbols by a weighted Gaussian sum. A serious drawback of this approach is that the number of Gaussian terms in the sum increases exponentially through iterations. In this thesis, firstly, we have shown that the NKF-based equalizer can be further improved by considering the interactions between the parallel filters in an efficient way. To this end, we take resort to the Interacting Multiple Model (IMM) estimator widely used in the area of multiple target tracking. The IMM is a very effective approach when the system exhibits discrete uncertainties in the dynamic or measurement model as well as continuous uncertainties in state values. A computationally feasible implementation based on a weighted sum of Gaussian approximation of the density functions of the data signals is introduced. Next, we present an adaptive multiple model blind equalization algorithm based on the IMM estimator to estimate the channel and the transmitted sequence corrupted by intersymbol interference and noise. It is shown through simulations that the proposed IMM-based equalizer offers substantially improved performance relative to the blind equalizer based on a (static or non-interacting) network of extended Kalman filters. It obviates the exponential growth of the state complexity caused by increasing channel memory length. The proposed approaches avoid the exponential growth of the number of terms used in the weighted Gaussian sum approximation of the plant noise making it practical for real-time processing.</p> <p> Finally, we consider the problem of channel estimation and tracking for space-time block coded systems contaminated by additive non-Gaussian noise. In many practical wireless channels in which space-time block coding techniques may be applied, the ambient noise is likely to have an impulsive component that gives rise to larger tail probabilities than is predicted by the Gaussian model. Although Kalman filters are often used in practice to track the channel variation, they are notoriously sensitive to heavy-tailed outliers and model mismatches resulting from the presence of impulsive noise. Non-Gaussian noise environments require the modification of standard filters to perform acceptably. Based on the coding/decoding technique, we propose a robust IMM algorithm approach in estimating time-selective fading channels when the measurements are perturbed by the presence of impulsive noise. The impulsive noise is modeled by a two terms Gaussian mixture distribution. Simulations demonstrate that the proposed method yields substantially improved performance compared to the conventional Kalman filter algorithm using the clipping or localization approaches to handle impulses in the observation. It is also shown that IMM-based approach performs robustly even when the prior information about the impulsive noise is not known exactly.</p> / Thesis / Master of Applied Science (MASc)

First demonstrated by Isaac Newton in his prism experiment, angular dispersion (AD) is a prevalent effect in optics where each wavelength in a pulsed field propagates at a different angle. Angular dispersion occurs after a collimated pulse traverses a diffractive or dispersive device and, as a result, helps modify the group velocity of a pulse in free space and introduces group-velocity dispersion into the freely propagating wave packet. These are essential ingredients in group-velocity matching and dispersion cancellation in various optical settings. With 300 years of development, it was only recently that a new class of angular dispersion materialized as non-differentiable AD. This non-differentiable AD has also been studied under the moniker space-time wave packets (STWP) and has shown to be propagation-invariant and possess arbitrary group velocity. In this dissertation, I will study (1) the underpinning theory of how non-differentiable AD allows for an optical field to break the pre-conceived notions of group velocity, group velocity dispersion (GVD), and pulse front tilt for on-axis propagation through analytical and experimental demonstrations. From these developments, I will (2) apply these concepts of non-differentiable AD to dispersive materials. I will validate these analytical predictions through experiments showing that propagation-invariant wave packets can also be supported in normal and anomalous media. Moreover, I will prove, through the use of non-differentiable AD, that the dispersive properties of a material can be overwritten to produce arbitrary group velocity and GVD characteristics. With this new information on propagation-invariant fields in dispersive materials, I will (3) exhibit new classes of optical fields that were previously theorized but never synthesized in dispersive materials, such as the X- to O- transition in anomalous GVD materials, which will be connected to the de-Broglie-Mackinnon wave packet and particle wave packets. To address the propagation invariance of non-differentiable AD, I will (4) demonstrate the STWP propagation throughout a kilometer in a turbulent environment and develop a new Rayleigh length for the STWP. Finally, I will (5) establish the consequences of discretization on the non-differentiable AD and produce a new form of the Talbot effect in which the temporal and spatial degrees of freedom are interlocked along with independent spatial and temporal Talbot effects in free space.

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In geostatistical analysis, we are faced with the formidable challenge of specifying a valid spatio-temporal covariance function, either directly or through the construction of processes. This task is di cult as these functions should yield positive de nite covariance matrices. In recent years, we have seen a ourishing of methods and theories on constructing spatiotemporal covariance functions satisfying the positive de niteness requirement. The current state-of-the-art when modeling environmental processes are those that embed the associated physical laws of the system. The class of Lagrangian spatio-temporal covariance functions ful lls this requirement. Moreover, this class possesses the allure that they turn already established purely spatial covariance functions into spatio-temporal covariance functions by a direct application of the concept of Lagrangian reference frame. In the three main chapters that comprise this dissertation, several developments are proposed and new features are provided to this special class. First, the application of the Lagrangian reference frame on transported purely spatial random elds with second-order nonstationarity is explored, an appropriate estimation methodology is proposed, and the consequences of model misspeci cation is tackled. Furthermore, the new Lagrangian models and the new estimation technique are used to analyze particulate matter concentrations over Saudi Arabia. Second, a multivariate version of the Lagrangian framework is established, catering to both secondorder stationary and nonstationary spatio-temporal random elds. The capabilities of the Lagrangian spatio-temporal cross-covariance functions are demonstrated on a bivariate reanalysis climate model output dataset previously analyzed using purely spatial covariance functions. Lastly, the class of Lagrangian spatio-temporal cross-covariance functions with multiple transport behaviors is presented, its properties are explored, and its use is demonstrated on a bivariate pollutant dataset of particulate matter in Saudi Arabia. Moreover, the importance of accounting for multiple transport behaviors is discussed and validated via numerical experiments. Together, these three extensions to the Lagrangian framework makes it a more viable geostatistical approach in modeling realistic transport scenarios.