This research is designed to develop and investigate newly defined problems: the Maximum Convex Sum (MCS), and its generalisation, the K-Maximum Convex Sum (K-MCS), in a two-dimensional (2D) array based on dynamic programming. The study centres on the concept of finding the most useful informative array portion as defined by different parameters involved in data, which is generically expressed in this thesis as the Maximum Sum Problem (MSP). This concept originates in the Maximum Sub-Array (MSA) problem, which relies on rectangular regions to find the informative array portion. From the above it follows that MSA and MCS belong to MSP. This research takes a new stand in using an alternative shape in the MSP context, which is the convex shape. Since 1977, there has been substantial research in the development of the Maximum Sub-Array (MSA) problem to find informative sub-array portions, running in the best possible time complexity. Conventionally the research norm has been to use the rectangular shape in the MSA framework without any investigation into an alternative shape for the MSP. Theoretically there are shapes that can improve the MSP outcome and their utility in applications; research has rarely discussed this. To advocate the use of a different shape in the MSP context requires rigorous investigation and also the creation of a platform to launch a new exploratory research area. This can then be developed further by considering the implications and practicality of the new approach. This thesis strives to open up a new research frontier based on using the convex shape in the MSP context. This research defines the new MCS problem in 2D; develops and evaluates algorithms that serve the MCS problem running in the best possible time complexity; incorporates techniques to advance the MCS algorithms; generalises the MCS problem to cover the K-Disjoint Maximum Convex Sums (K-DMCS) problem and the K-Overlapping Maximum Convex Sums (K-OMCS) problem; and eventually implements the MCS algorithmic framework using real data in an ecology application. Thus, this thesis provides a theoretical and practical framework that scientifically contributes to addressing some of the research gaps in the MSP and the new research path: the MCS problem. The MCS and K-MCS algorithmic models depart from using the rectangular shape as in MSA, and retain a time complexity that is within the best known time complexities of the MSA algorithms. Future in-depth studies on the Maximum Convex Sum (MCS) problem can advance the algorithms developed in this thesis and their time complexity.

Phased array antennas with small size and light weight are proposed to make signal transmitting more efficiently and accurately. These antennas have such advantages that they can realize beam scanning over a large range, accurately track and identify targets within the observation range. In beam scanning, the scan loss which is the difference between the scanned gain and broadside gain has a great impact on the performance of phased array antennas. This thesis aims to study how to reduce the scan loss while the beam is scanned over a wide range. One of the methods to reduce the scan loss is to widen the beam-width of the embedded radiation pattern. With the wide beam-width, the gain reduction due to beam scanning would be small. We propose a method to replace a conventional half-wavelength unit-cell in an array with a sub-array composed of 5 miniaturized elements with special phase/amplitude distribution. The size of the sub-array is finely tuned in this thesis to achieve the goal of wide beam-width without any grating lobe. Then, in order to further expand the beam-width, the ideal power divider is utilized to apply specific weight to the sub-array. The simulation result shows that the maximum scan loss for the considered case is 3.67dB over ±80° scan range with an voltage amplitude distribution of [0.234, 0.64, 0.26, 0.64, 0.234] (1) and a phase of 88° between the 5 sub-array elements, which can be realized by the ideal power divider. If the allowed gain reduction is relaxed to 5dB, the scan coverage can be extended to ±89°. / Fasstyrda antenner med eu liten storlek och låg vikt har förslegits för att göra signalöverföring effektivt och korrekt. Dessa antenner har stora fördelar i att de kan realisera stort område. De kan också följa och identifiera mål inom observationsområdet. Vid strålskanning är skanningsförlusten, som är skillnaden mellan den skannade förstärkningen och förstärkningen vid den breda sidan, följande har stor inverkan på prestandan hos fasstyrda antenner. Denna avhandling syftar till att studera hur man minskar skanningsförlusten när strålen skannar inom ett brett skanningsområde. En av metoderna för att minska skanningsförlusten är att bredda strålbredden i det inbyggda strålningsmönstret. Med en bred strålbredd blir förstärkningsminskningen på grund av strålskanning liten. Vi föreslår en metod för att ersätta en konventionell halvvågig enhetscell i en matris med en delmatris som består av 5 miniatyriserade element med speciell fas/amplitudfördelning. Storleken på delarrayen är finjusterad i denna avhandling för att uppnå målet med bred strålbredd utan någon gitterlob. För att ytterligare utöka strålbredden används sedan den ideala effektdelaren för att ge subarrayet en särskild vikt. Simuleringsresultatet visar att den maximala skanningsförlusten för det undersökta fallet är 3,67dB inom ±80° täckningsvinkel med amplitudfördelning av [0.234, 0.64, 0.26, 0.64, 0.234] (2) och fas av 88°, som kan realiseras av den idealiska effektdelaren. Om kravet på minskningen av förstårluing sänks till 5dB, kan täckningen breddas till ±89°.

In this dissertation, sparse processing of signals for directions-of-arrival (DoAs) estimation is addressed in the framework of Compressive Sensing (CS). In particular, DoAs estimation problem for different types of sources, systems, and applications are formulated in the CS paradigm. In addition, the fundamental conditions related to the ``Sparsity'' and ``Linearity'' are carefully exploited in order to apply confidently the CS-based methodologies. Moreover, innovative strategies for various systems and applications are developed, validated numerically, and analyzed extensively for different scenarios including signal to noise ratio (SNR), mutual coupling, and polarization loss. The more realistic data from electromagnetic (EM) simulators are often considered for various analysis to validate the potentialities of the proposed approaches. The performances of the proposed estimators are analyzed in terms of standard root-mean-square error (RMSE) with respect to different degrees-of-freedom (DoFs) of DoAs estimation problem including number of elements, number of signals, and signal properties. The outcomes reported in this thesis suggest that the proposed estimators are computationally efficient (i.e., appropriate for real time estimations), robust (i.e., appropriate for different heterogeneous scenarios), and versatile (i.e., easily adaptable for different systems).