abstract: Modern software and hardware systems are composed of a large number of components. Often different components of a system interact with each other in unforeseen and undesired ways to cause failures. Covering arrays are a useful mathematical tool for testing all possible t-way interactions among the components of a system. The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements on both of these questions using tools from the probabilistic method and randomized algorithms. First, a series of improvements is developed on the previously known upper bounds on covering array numbers. An estimate for the discrete Stein-Lovász-Johnson bound is derived and the Stein- Lovász -Johnson bound is improved upon using an alteration strategy. Then group actions on the set of symbols are explored to establish two asymptotic upper bounds on covering array numbers that are tighter than any of the presently known bounds. Second, an algorithmic paradigm, called the two-stage framework, is introduced for covering array construction. A number of concrete algorithms from this framework are analyzed, and it is shown that they outperform current methods in the range of parameter values that are of practical relevance. In some cases, a reduction in the number of tests by more than 50% is achieved. Third, the Lovász local lemma is applied on covering perfect hash families to obtain an upper bound on covering array numbers that is tightest of all known bounds. This bound leads to a Moser-Tardos type algorithm that employs linear algebraic computation over finite fields to construct covering arrays. In some cases, this algorithm outperforms currently used methods by more than an 80% margin. Finally, partial covering arrays are introduced to investigate a few practically relevant relaxations of the covering requirement. Using probabilistic methods, bounds are obtained on partial covering arrays that are significantly smaller than for covering arrays. Also, randomized algorithms are provided that construct such arrays in expected polynomial time. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2016

An active, broadband antenna module amenable for use in low cost phased arrays is proposed. The module consists of a Vivaldi antenna integrated with a frequency conversion integrated circuit. A method of orthogonally mounting endfire antennas onto an array motherboard is developed using castellated vias. A castellated active isolated Vivaldi antenna package is designed, fabricated, and measured. An 8x1 phased array of castellated, active Vivaldi antenna packages is designed and assembled. Each element has approximately one octave of bandwidth centered in X-band, and each is mounted onto a coplanar waveguide motherboard. Radiation patterns of the array are measured at several frequencies and scan angles.

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Adaptive array antennas use has been limited to non-commercial applications due to their high cost and hardware complexity. The implementation cost of adaptive array antennas can be kept to a minimum by using cost effective antennas, reducing the number of elements in the array and implementing efficient beamforming techniques. This thesis presents techniques for the design of adaptive array antennas which will enable their cost effective implementation in wireless communication systems. The techniques are investigated from three perspectives, namely, reconfigurable antenna design, wide scan array design and single-port beamforming technique. A novel single-feed polarisation reconfigurable antenna design is proposed in the first stage of this study. Different polarisation states, namely, linear polarisation (LP), left-hand circular polarisation (LHCP) and right-hand circular polarisation (RHCP), are achieved by perturbing the shape of the main radiating structure of the antenna. The proposed antenna exhibits good axial ratio (< 3 dB at 2.4 GHz) and has high radiation efficiency in both polarisation modes (91.5 % - LHCP and 86.9 % - RHCP). With a compact single feeding structure, the antenna is suitable for implementation in wireless communication devices. The second stage of the study presents the design procedure of wide scan adaptive array antennas with reduced number of elements. Adaptive array antennas with limited number of elements have limited scanning range, reduced angular scanning resolution and high sidelobe levels. To date, design synthesis of adaptive array antennas has been targeted on arrays with a large number of elements. This thesis presents a comprehensive analysis of adaptive array antennas with less than 10 elements. Different array configurations are analysed and various array design parameters such as number of elements, separation between elements and orientation of the elements are analysed in terms of their 3 dB scan range. The proposed array, the 3-faceted array, achieves a scanning range up to ±70°, which is higher than ±56° obtained from the Uniform Linear Array. The faceted arrays are then evaluated in the context of adaptive beamforming properties. It was shown that the 3-faceted array is suitable for adaptive array applications in wireless communication systems as it achieves the highest directivity compared to other faceted structures. The 3-faceted array is then synthesised for low sidelobe level. Phase correction together with amplitude tapering technique is applied to the 3-faceted array. The use of conventional and tuneable windowing techniques on the 3- faceted array is also analysed. The final stage of the study investigates beamforming techniques for the adaptive array antenna. In the first part, beamforming algorithms using different performance criteria, which include maximum signal-to noise-ratio (SINR), minimum (mean-square Error) MSE and power minimisation, are evaluated. In the second part, single-port beamforming techniques are explored. In previous single-port beamforming methods, the spatial information of the signals is not fully recovered and this limits the use of conventional adaptive beamforming algorithms. In this thesis, a novel signal estimation technique using pseudo-inverse function for single-port beamforming is proposed. The proposed polarisation reconfigurable antenna, the 3-faceted array antenna and the single-port beamforming technique achieve the required performance, which suggests the potential of adaptive array antennas to be deployed commercially, especially in wireless communication industry.

ITC/USA 2005 Conference Proceedings / The Forty-First Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2005 / Riviera Hotel & Convention Center, Las Vegas, Nevada / Multiple discrete antennas distributed around the circumference of a large missile and driven by one transmitter are sometimes used to radiate telemetry omnidirectionally. But driving discrete antennas separated by several wavelengths around the missile body with a single transmitter can result in an antenna pattern with deep nulls in the roll plane. Varying the relative signal phase or amplitude among the signals driving the antennas as well as the polarization of the antennas can be used to change the nulls in an attempt to decrease the null depth. In this paper the effects of phase, amplitude, and polarization on the roll-plane pattern are examined and measurement data presented.

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