CAREER: Random Networks for Wireless Communication

由于需要了解下一代大规模无线系统的基本特性，该项目为其分析和设计引入了新的范例，这些范例位于统计物理和网络信息理论的前沿。利用来自随机图和渗流理论的最先进的工具，以及开发新的方法，目标是为大规模通信系统的新理论奠定基础。在无线网络中，没有静态链路的先验概念，只有可以以任意复杂的方式共享介质的节点的空间配置。为此，引入了一种新的网络链路动态定义。这取决于干扰和信息率的概念。利用节点配置的几何特性，然后考虑了一系列基本问题，从可实现的吞吐量到能效、容错和分布式网络编码。研究工作得到了教育努力的补充，通过课程开发培养新的工程师，计划在研究生水平引入一门关于随机网络的新课程，并撰写一本致力于通信的随机网络的书。预期的结果包括新的数学理论的基础，该理论将导致对大规模无线设备网络的当前理解和预测行为的基本进步。无论是在引入新的数学方法方面，还是在它们对其他科学领域的适用性方面，这些结果预计也将产生远远超出无线通信网络领域的影响。

Motivated by the need to understand the basic properties of next generation large-scale wireless systems, this project introduces new paradigms for their analysis and design that lie at the frontier of statistical physics and network information theory. Leveraging state of the art tools from random graphs and percolation theory, as well as developing new methods, the objective is to set the foundations for a new theory of large-scale communication systems. In wireless networks there is no a priori notion of static links, but only spatial configurations of nodes that can share the medium in arbitrarily complex ways. Hence, a new dynamic definition of network link is introduced. This depends on the notion of interference and of information rate. Exploiting geometric properties of node configurations, a series of fundamental problems that range from achievable throughput to energy efficiency, fault tolerance, and distributed network coding are then considered.The research effort is complemented by an educational effort to train new engineers through curriculum development, plans to introduce a new course on random networks to be taught at the graduate level, and through the writing of a book devoted to random networks for communication.Expected results include the foundations of a new mathematical theory that will lead to basic advancements in both the current understanding and the predicted behavior of large-scale networks of wireless devices. Results are also expected to have implications well beyond the field of wireless communication networks, both in terms of the introduction of new mathematical methods, and of their applicability to other fields of science.