Theoretical Foundations for Wireless Communication Networks

摘要无线网络的设计通常依赖于未充分利用可用资源的次优规则，而不是正式的理论。这项研究的目的是建立在无线网络的理论基础上，通过在不同的设置下制定通用的优化问题。提出了关于这些问题的问题，并随后将答案转化为基本性质。在可能的问题中，本项目侧重于以下几个问题：Q1)这些优化问题解决起来有多难？Q2)它们具有哪些结构特性？和Q3)应该使用什么解算器(S)？Q1)的答案确定最佳无线联网是否可行；寻址Q2)转化为架构原则，例如最佳分层架构；以及对Q3)的响应适合工作的无线网络协议。该项目建立在一个初步结果的基础上，该初步结果断言在存在随机衰落的情况下将无线网络分成层是最优的。该方法利用这一原理和衰落引入的相关结构特性来开发包括算法、性能分析和开发问题的形式化理论，包括：i)双重分解随机优化求解器；ii)干扰跨终端优化中的物理层创新；iii)在线随机近似求解器的收敛；iv)非遍历高移动性无线网络；以及iv)认知无线电网络。这项研究的成功完成对无线局域网802.11的演进和移动自组织网络中的新兴倡议具有直接的意义。其愿景是在下一代无线网络和无线传感器网络中无处不在地结合优化设计的协议。在更广泛的意义上，无线网络基础的进步将影响包括电网、供水系统和交通基础设施在内的一类随机传输网络。

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.