The rapid growth of data hungry wireless applications has boosted the demand for wireless communication systems with improved reliability, wider coverage, and higher throughput. The main challenges facing the design of such systems are the limited resources, such as bandwidth, restricted transmission power, etc., and the impairments of the wireless channels, including fading effects, interference, and noise. Multiple-input multiple-output (MIMO) communication has been shown to be one of the most promising emerging wireless technologies that can efficiently enhance link reliability, improve system coverage, and boost the data transmission rate. Consequently, MIMO is now extensively adopted by many mainstream wireless industry standards, including 3GPP WCDMA/HSDPA, LTE, EVDO, WiFi, and WiMAX. By deploying multiple antennas at both transmitter and receiver sides, MIMO techniques license a new dimension (spatial dimension) that can be applied in various ways for combating the impairments of wireless networks. Furthermore, this new dimension has introduced a new concept known as Interference Alignment that can efficiently deal with the interference presentin the wireless communication networks. In particular, IA is highly attractive in terms of providing more degrees of freedom compared to techniques such as TDMA/FDMA. With this in mind, this thesis will focus on studying and developing advanced techniques and algorithms for reducing interference in cellular communication networks. The contributions of the thesis are as follows. Initially, a review is provided to reiterate some basic concepts of wireless communications and discuss the challenges faced by the techniques that deal with interference mitigation. Next, Chapter 3 presents a novel IA based cancellation scheme that is proposed for combating the interfering signals present in the compounded MIMO broadcast channels, where the users experience a multi-source transmission from several base stations. After defining the interference channel (IC) interference and X-channel interference, the partial transmit beamforming matrices of the closed-form downlink scheme alleviate the corresponding types of interference. Applying the proposed scheme allows one to treat the multi-cell network as a set of single-cell MIMO network, which leads to the simultaneous BER performance enhancement and data rate increase. Moreover, a generalization scheme is given to assign the appropriate antenna configuration for achieving maximum DoF. Furthermore, Chapter 4 demonstrates a comprehensive analysis on the number of DoF achievable by exploiting the transmit beamforming technique. Additionally, the proposed scheme is able to provide the maximum data rate under a certain antenna setting or compute a transmitter-receiver configuration in order to meet the required number of DoF. Chapter 5 considers a modified IA scheme for the compounded MIMO network when different classes of users communicate in the overlapped area. Due to various antenna settings of each receiver, the effect of spatial correlation on the achievable data rate is investigated. Moreover, an algorithm is derived for calculating the antenna configuration for different users classes. Then, the proposed scheme is extended for the case of Large-scale MIMO, which in turn provides sufficient insights into the impact of the deployment of a large number of antennas. Finally, Chapter 6 presents an alternative design of the IA scheme with no symbol extension for the cellular MIMO network. Subsequently, a modified eigenvalue-based scheme is proposed to enhance the overall system performance. Finally, the achievable data rate is calculated under different CSI acquisition scenarios. Chapter 7 concludes the thesis and provides a list of potential future work directions for further investigation.

This thesis concerns stressed spline structures. A spline is defined as `an initially straight member with identical second moment of area about any axis perpendicular to its centroidal axis, bent into a spatial curve'. An analytical proof is presented to show that the spline's torsional stiffness is of no importance in its analysis (provided construction details do not introduce any torsional moment). This paramount proof allows the formulation of a spline analysis that relies solely on three translational degrees of freedom (3DOF) per node. Applying this 3DOF analysis to unstrained curves and battened or hoop supported membranes is approximate since the bending stiffness would correspond to one direction only. A series of four test cases validates the proposed 3DOF analysis. The analysis is first applied to a laterally loaded spline ring, where solution convergence and the effect of unequal length segment modelling are investigated. Most significantly, this test case demonstrates that the spline ring has a greater out-of-plane stiffness than a pre-bent ring. This feature lies at the basis of spline stressed membranes - the spline has superior out-of-plane stiffness under the action of forces applied by the membrane. The second and third test cases -- buckling of elastica and of a shallow sinusoidal arch -- clearly demonstrate that the 3DOF analysis is much faster, more accurate, and produces results closer to the analytical values compared with a 6DOF analysis. The fourth test case proves the efficiency of the 3DOF analysis through investigating buckling behaviour and loads of four circular arches under radial loading. As the torsional stiffness does not enter the 3DOF analysis, the stiffness of a spline constructed of spliced segments is identical to that of a continuous spline. In order to demonstrate their feasibility, five medium span (161n-32m) Glass Fibre Reinforced Plastic (GFRP) and one large span (57nt) steel tensegrity stressed spline membranes are designed, form-found and analysed under realistic loading conditions. These design studies show firstly that the spline and membrane stresses occurring under loading are within acceptable material limits and secondly that buckling occurs at values much higher than those encountered in reality. This thesis has demonstrated that engineered stressed spline structures, for which the development of a 3DOF was essential, have great design potential.

abstract: Whilst linear mixed models offer a flexible approach to handle data with multiple sources of random variability, the related hypothesis testing for the fixed effects often encounters obstacles when the sample size is small and the underlying distribution for the test statistic is unknown. Consequently, five methods of denominator degrees of freedom approximations (residual, containment, between-within, Satterthwaite, Kenward-Roger) are developed to overcome this problem. This study aims to evaluate the performance of these five methods with a mixed model consisting of random intercept and random slope. Specifically, simulations are conducted to provide insights on the F-statistics, denominator degrees of freedom and p-values each method gives with respect to different settings of the sample structure, the fixed-effect slopes and the missing-data proportion. The simulation results show that the residual method performs the worst in terms of F-statistics and p-values. Also, Satterthwaite and Kenward-Roger methods tend to be more sensitive to the change of designs. The Kenward-Roger method performs the best in terms of F-statistics when the null hypothesis is true. / Dissertation/Thesis / Masters Thesis Statistics 2020

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The purpose of this dissertation is to find the channel capacity in optical fiber communication systems when incoherent detection is used with single (polarization filtering) and two-polarizations (no polarization filtering). Optical fiber systems employ photodetectors that convert optical intensity to electrical current. Bandpass vector fields may be represented by four orthogonal baseband components corresponding to two quadrature phases and two orthogonal polarizations. Intensity is proportional to the sum of the squares of these four components. In the case of a coherent receiver, a strong optical local oscillator (in phase and with same polarization as the signal) is added to the signal prior to the photodetector. This results in the removal of the quadrature phase and polarization components, and reduces to the one degree of freedom (DOF) case of signal plus local oscillator shot noise for which the Shannon channel capacity formula applies. Electrical noise following the photodetector may also be neglected if there is an optical amplifier before the photodetector in the receiver. The amplifier introduces amplified spontaneous emission noise containing both quadrature phase components and both polarizations (4 DOFs), but the 2 DOF case would result if a polarization filter were used. Although the 1 and 2 DOF cases are of less practical interest than the 4 DOF case, they provide useful benchmarks for comparing performance limits. We evaluate both spectral efficiency limits (bps/Hz) in the limit of high and low SNR for the 1,2 and 4 DOF cases and also find the power efficiency (minimum number of photons per bit) for each of these cases. It is shown that for high SNR the spectral efficiency is the same independent of the number of DOFs and that the half-Gaussian distribution is the optimum distribution. We are able to thus obtain a compact equation for spectral efficiency which behaves in a similar way to the Shannon capacity formula but with the SNR scaled by a constant. We also show that for low SNR the half-Gaussian distribution is not the optimum distribution as the slope of the mutual information changes with the square of SNR which would lead to the number of photons per bit becoming infinite in the limit of SNR going to zero. We use a modified half-Gaussian distribution which has a discrete component (an impulse function at the origin) and provide a simple proof that this distribution results in a mutual information that goes to zero linearly with SNR resulting in a minimum number of photons per bit. Furthermore, by increasing the magnitude of the discrete component at the origin, it is shown that the minimum number of photons per bit for the incoherent channel approaches that of the coherent channel. / Ph. D.

Doctor of Philosophy / Department of Electrical and Computer Engineering / Balasubramaniam Natarajan / Dale E. Schinstock / In this dissertation, two applications related to vision-based localization and mapping are considered: (1) improving navigation system based satellite location estimates by using on-board camera images, and (2) deriving position information from video stream and using it to aid an auto-pilot of an unmanned aerial vehicle (UAV). In the first part of this dissertation, a method for analyzing a minimization process called bundle adjustment (BA) used in stereo imagery based 3D terrain reconstruction to refine estimates of camera poses (positions and orientations) is presented. In particular, imagery obtained with pushbroom cameras is of interest. This work proposes a method to identify cases in which BA does not work as intended, i.e., the cases in which the pose estimates returned by the BA are not more accurate than estimates provided by a satellite navigation systems due to the existence of degrees of freedom (DOF) in BA. Use of inaccurate pose estimates causes warping and scaling effects in the reconstructed terrain and prevents the terrain from being used in scientific analysis. Main contributions of this part of work include: 1) formulation of a method for detecting DOF in the BA; and 2) identifying that two camera geometries commonly used to obtain stereo imagery have DOF. Also, this part presents results demonstrating that avoidance of the DOF can give significant accuracy gains in aerial imagery. The second part of this dissertation proposes a vision based system for UAV navigation. This is a monocular vision based simultaneous localization and mapping (SLAM) system, which measures the position and orientation of the camera and builds a map of the environment using a video-stream from a single camera. This is different from common SLAM solutions that use sensors that measure depth, like LIDAR, stereoscopic cameras or depth cameras. The SLAM solution was built by significantly modifying and extending a recent open-source SLAM solution that is fundamentally different from a traditional approach to solving SLAM problem. The modifications made are those needed to provide the position measurements necessary for the navigation solution on a UAV while simultaneously building the map, all while maintaining control of the UAV. The main contributions of this part include: 1) extension of the map building algorithm to enable it to be used realistically while controlling a UAV and simultaneously building the map; 2) improved performance of the SLAM algorithm for lower camera frame rates; and 3) the first known demonstration of a monocular SLAM algorithm successfully controlling a UAV while simultaneously building the map. This work demonstrates that a fully autonomous UAV that uses monocular vision for navigation is feasible, and can be effective in Global Positioning System denied environments.

Multiple-Input Multiple-Output (MIMO) systems are viewed as the last available supply for the ever-growing demand on higher data rates in modern wireless communication systems. Smart exploitation of the traditional wireless resources (time-slots or bandwidth under the same transmit power level) has reached its saturation point. By making better use of the free space between the radio links, based on the multipath radio wave propagation, MIMO systems have shown significant capacity improvement with the same traditional wireless resources. In this multi-disciplinary research, we are exploring the link between the electromagnetic propagation and the information theory. Unlike the majority of recent research work, we model the propagation channel matrix between the transmit/receive elements in a deterministic manner under the Maxwellian framework. Having included the environment properties and the characteristics of the radiating elements, the deterministic approach provides a realistic assessment of the MIMO system performance in specific scenarios. The problem addressed in this research is the evaluation of the multi-antenna systems degrees of freedom (DOF) by employing all the available electromagnetic diversity resources (spatial, pattern and polarization). Based on a developed well-defined power independent dimensionality (PID) metric, we start by investigating the information-bearing potential of the collocated multi-polarization MIMO system. We study the hexapole system (exploiting both electric and magnetic fields in conveying independent information) and compare it to the tripole systems (exploiting the vectorial polarization diversity of one field only). We present numerical results for 3 deterministic scenarios: a canonical free-space (near and far field exact solution), a canonical perfect electric conductor (PEC) corridor using rigorous modal analysis, and a lossy-wall corridor using image ray tracing (IRT). Next, we provide deterministic results for the more interesting sampling problem of the electromagnetic vector fields: given a specific MIMO array size, what is the optimum number of packed multi-polarization antennas (i.e. multi-polarization 1D, 2D or 3D sampling) that yields the largest PID for a given environment and what is the estimate of this PID? Using a canonical case of multi-polarized arrays inside a multipath-rich PEC corridor, we show that the spatial frequency spectrum of the electromagnetic field governs the optimum PID of the site-specific scenario. The problem is analogous to the DOF determination of an essentially time-limited-band-limited 1D scalar function using the framework of the prolate spheroidal wave functions. We also present simulation results for the same sampling problem in a lossy-wall indoor environment using IRT.

Multiple-Input Multiple-Output (MIMO) systems are viewed as the last available supply for the ever-growing demand on higher data rates in modern wireless communication systems. Smart exploitation of the traditional wireless resources (time-slots or bandwidth under the same transmit power level) has reached its saturation point. By making better use of the free space between the radio links, based on the multipath radio wave propagation, MIMO systems have shown significant capacity improvement with the same traditional wireless resources. In this multi-disciplinary research, we are exploring the link between the electromagnetic propagation and the information theory. Unlike the majority of recent research work, we model the propagation channel matrix between the transmit/receive elements in a deterministic manner under the Maxwellian framework. Having included the environment properties and the characteristics of the radiating elements, the deterministic approach provides a realistic assessment of the MIMO system performance in specific scenarios. The problem addressed in this research is the evaluation of the multi-antenna systems degrees of freedom (DOF) by employing all the available electromagnetic diversity resources (spatial, pattern and polarization). Based on a developed well-defined power independent dimensionality (PID) metric, we start by investigating the information-bearing potential of the collocated multi-polarization MIMO system. We study the hexapole system (exploiting both electric and magnetic fields in conveying independent information) and compare it to the tripole systems (exploiting the vectorial polarization diversity of one field only). We present numerical results for 3 deterministic scenarios: a canonical free-space (near and far field exact solution), a canonical perfect electric conductor (PEC) corridor using rigorous modal analysis, and a lossy-wall corridor using image ray tracing (IRT). Next, we provide deterministic results for the more interesting sampling problem of the electromagnetic vector fields: given a specific MIMO array size, what is the optimum number of packed multi-polarization antennas (i.e. multi-polarization 1D, 2D or 3D sampling) that yields the largest PID for a given environment and what is the estimate of this PID? Using a canonical case of multi-polarized arrays inside a multipath-rich PEC corridor, we show that the spatial frequency spectrum of the electromagnetic field governs the optimum PID of the site-specific scenario. The problem is analogous to the DOF determination of an essentially time-limited-band-limited 1D scalar function using the framework of the prolate spheroidal wave functions. We also present simulation results for the same sampling problem in a lossy-wall indoor environment using IRT.

In wireless channels and many other channels, interference is a central phenomenon. Mitigating interference is a key to improving system performance. To find the limit of the achievable rates for these channels in the presence of interference, the two-user Gaussian interference channel has been the subject of intensive study in network information theory. However, most current results have been obtained by assuming Gaussian input distributions. While optimal in single-user Gaussian channels, the issue with this assumption is that the Gaussian noise becomes the worst noise when the input distribution is also Gaussian. In this thesis, we propose a class of discrete constellations. We show that this class of constellations can automatically achieve the same sum rates as schemes that treat interference as noise or perform time sharing.

In wireless channels and many other channels, interference is a central phenomenon. Mitigating interference is a key to improving system performance. To find the limit of the achievable rates for these channels in the presence of interference, the two-user Gaussian interference channel has been the subject of intensive study in network information theory. However, most current results have been obtained by assuming Gaussian input distributions. While optimal in single-user Gaussian channels, the issue with this assumption is that the Gaussian noise becomes the worst noise when the input distribution is also Gaussian. In this thesis, we propose a class of discrete constellations. We show that this class of constellations can automatically achieve the same sum rates as schemes that treat interference as noise or perform time sharing.