| The focus of this thesis is the development and use of decomposition methods for the joint optimization of the physical (rate and power control), data link (MAC/scheduling), network (routing), and application layers of wireless networks. Our models provide theoretical performance upper bounds that can be used to derive design principles for various applications such as energy-efficient wireless sensor networks and high-throughput wireless ad hoc networks.;We introduce the Generalized Cross-Layer Optimization Problem : a constrained utility maximization model that enables the analysis of arbitrary network topologies (e.g. ad hoc networks, cellular networks, and mesh networks) under various requirements and constraints. We show that this problem unifies various special-case formulations and can be reduced to well-known problems like throughput maximization, network lifetime maximization, and uniform capacity maximization.;Using decomposition methods, we demonstrate how the Generalized Cross-Layer Optimization Problem can be divided into two independent sub-problems: The Upper Layer Problem, corresponding to the application and network layers, and the Lower Layer Problem, corresponding to the data link and physical layers. By solving both problems interactively, we prove that we can obtain a global optimal solution to the Generalized Cross-Layer Optimization Problem. We observe that most of the mathematical complexity of cross-layer optimization for wireless networks is contained within the Lower Layer Problem. We thus develop additional decomposition techniques tailored at efficiently solving the Lower Layer Problem.;We also examine the complexity and scalability issues of cross-layer optimization in wireless networks. The decomposition methods we present permit calculation of exact upper-bound solutions for the performance of ad hoc networks with up to 30 nodes and mesh networks with up to 40 nodes---a marked improvement in scalability over that of previous similar studies. We look in varying degrees of detail at the tradeoffs among characteristics such as capacity, fairness, coverage area, and power control.;This thesis concludes by presenting Geometric Decomposition, a novel decomposition method for the data link layer (scheduling). Using Geometric Decomposition, we show that it is possible to leverage the geometric properties of a network to divide it into different regions while still obtaining tight upper-bound estimates for the original Generalized Cross-Layer Optimization Problem. |
