In this study a new approach to active-element pattern analysis, for large phased array antennas, was created using Floquet's theorem. The classic approach to finding active-element patterns uses a full array simulation that can become slow and produce patterns that are specific to certain elements in the array, though basically identical away from the array edge. Instead of producing specific active-element patterns an average active-element pattern could be created and then applied that to the array. The average active-element pattern can be used for every element in the array with a small margin of error. Using Floquet's theorem reduces any differences between elements in the array and gives the most accurate active-element pattern within a reasonable time constraint. Floquet average active-element patterns are computed by using an infinite array and a summation is done for the far-field radiation values of a finite array based on the number of elements using typical pattern multiplication techniques. Therefore, accuracy of the Floquet element approach is excellent for arrays on the size of hundreds to thousands of elements. An active-element pattern is determined by scanning the array and taking the far-field radiation value at each beam scan-angle. Each beam scan-angle value is a summation of the element radiation patterns in that specific direction. These beam scan-angle values are then reduced by the number of elements in the array to form a radiation pattern. This radiation pattern is the average active-element pattern. / Master of Science

Solving the key issue of sustainability of battery-powered sensors continues to attract significant research attention. The prevailing theme of this research is to address this concern using energy-efficient protocols based on a form of simple cooperative transmission (CT) called the opportunistic large arrays (OLAs), and intelligent exploitation of energy harvesting and hybrid energy storage systems (HESSs). The two key contributions of this research, namely, OLA with transmission threshold (OLA-T) and alternating OLA-T (A-OLA-T), offer an signal-to-noise ratio (SNR) advantage (i.e., benefits of diversity and array (power) gains) in a multi-path fading environment, thereby reducing transmit powers or extending range. Because these protocols do not address nodes individually, the network overhead remains constant for high density networks or nodes with mobility. During broadcasting across energy-constrained networks, while OLA-T saves energy by limiting node participation within a single broadcast, A-OLA-T optimizes over multiple broadcasts and drains the the nodes in an equitable fashion. Another important contribution of this research is the design and analysis of a novel routing metric called communications using HESS (CHESS), which extends the rechargeable battery (RB)-life by relaying exclusively with supercapacitor (SC) energy, and is asymptotically optimal with respect to the number of nodes in the network.