Theoretical Foundations for Wireless Communication Networks

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AbstractIn lieu of a formal theory, designing wireless networks often relies on suboptimum rules that under-utilize the available resources. The objective of this research is to build on theoretical foundations of wireless networks by formulating generic optimization problems in a variety of settings. Questions about these problems are posed and answers are subsequently translated to fundamental properties. Among possible questions, this project focuses on the following ones: q1) How difficult are these optimization problems to solve? q2) What structural properties they possess? and q3)What solver(s) should be employed ? Answers to q1) determine whether optimal wireless networking is feasible; addressing q2) translates to architectural principles, e.g., optimal layered architectures; and responses to q3) lend themselves to working wireless network protocols.This project builds on a preliminary result which asserts that separating wireless networks into layers is optimal in the presence of random fading. The approach leverages this principle and related structural properties introduced by fading to develop a formal theory encompassing algorithmic, performance analysis and development issues including: i) dual decomposition stochastic optimization solvers; ii) physical layer innovations in cross-terminal optimization of interference; iii) convergence of on-line stochastic approximation solvers; iv) non-ergodic high-mobility wireless networks; and iv) cognitive radio networks. Successful completion of this research is of immediate interest to the 802.11 evolution of WLANs and the emerging initiatives in mobile ad hoc networks. The vision is ubiquitous incorporation of optimally designed protocols in future generation wireless networks and wireless sensor networks. In a broader sense, advances in the foundations of wireless networks will impact the class of stochastic transport networks which includes the power grid, the water distribution system and the transportation infrastructure.