CAREER: The Transmission Capacity of Hierarchical Wireless Networks

在过去的十年中，无线网络经历了从原始的电路交换链路到多用户分组交换网络的显著演变，合作程度和复杂性不断提高。在接下来的十年里，它们进一步发展的一个主要障碍是缺乏关于具有相互依赖的链路的网络的描述性理论，最明显的是自组织网络和网状网络。这个问题已经被证明是一项艰巨的任务，原因是(I)由于节点相互作用而导致的容量区域的维度，以及(Ii)吞吐量、延迟、能源效率和连通性的相互竞争的限制。如果不考虑已经取得的重大进展，缺乏明确的结果已经阻碍了自组网、网状网和传感器网络的系统设计，从而阻碍了它们的开发和商业化。这项研究涉及发展一种用于自组织网络的描述性容量理论，该理论应该能够：(1)准确地描述物理参数和先进无线电技术的影响，(2)准确地计算网络中发送器和接收器之间的空间相互作用，以及(3)提供对较低“层”的有用抽象。这是使用一种基于随机几何(受信息论的激励)的新方法来实现的，我们将其称为传输能力。这项研究的关键理论里程碑是：(I)在随机几何、随机矩阵理论和信息论在自组织和分层无线网络中的应用方面做出了重大贡献；(Ii)可以用来表征任何可想到的技术或方案对自组织网络容量的影响的有用理论；以及(Iii)将影响未来无线网络标准设计原则的具体结果的推导。

In the past decade, wireless networks have undergone a remarkable evolution from primitive circuit-switched links to multiuser packet-switched networks with increasing levels of cooperation and sophistication. In the coming decade, a primary impediment to their further evolution is the lack of a descriptive theory for networks with interdependent links, most notably ad hoc and mesh networks. This problem has proven to be a daunting task due to (i) the dimensionality of the capacity region due to the node interactions, and (ii) the competing constraints of throughput, delay, energy efficiency, and connectivity. Without discounting the significant progress that has been made, the lack of crisp results has handicapped the system design of ad hoc, mesh, and sensor networks, and therefore impeded their development and commercialization. This research involves the development of a descriptive capacity theory for ad hoc networks that should be capable of the following: (1) Accurate characterization of the effects from physical parameters and advanced radio technologies, (2) accurately accounting of the spatial interactions between the transmitters and receivers in the network, and (3) providing a useful abstraction of the lower "layers". This is accomplished using a novel approach based on stochastic geometry (motivated by information theory) that we term the transmission capacity. The key theoretical milestones for this research are (i) substantial contributions in the application of stochastic geometry, random matrix theory, and information theory to ad hoc and hierarchical wireless networks, (ii) a useful theory that can be used to characterize the effect of any conceivable technology or scheme on ad hoc network capacity, and (iii) the derivation of specific results that will impact design principles of future wireless networking standards.