CIF: Small: A Space Dimension Approach for Wireless Netowrk Information Theory

该项目考虑了无线网络中通信的物理限制，以及如何通过通信协议以有效的方式实现这些限制。具体而言，它的目的是使用基于物理的创新方法来确定网络容量的基本限制，而不是假设随机传播信道模型。该项目的重点是表征无线网络可以提供的空间分集的数量，这被证明是确定其容量的核心问题之一。空间多样性是根据传播场的维数来量化的，传播场是通过网络承载信息的。因此，该项目将信息论、连续向量空间的泛函分析、电磁理论和网络联系起来，旨在为无线网络开发信息论。该项目考虑了无线网络的不同几何配置，并确定了相应的空间自由度的数量。然后，它考虑了窄带和宽带频率传输的影响。结果是在缩放法，以及容量的法律是不是渐近的网络中的节点数。

This project considers the physical limits of communication in a wireless network and how these limits can be achieved by communication protocols in an effective way. Specifically, it aims at determining the fundamental limits of the capacity of the network using an innovative approach based on physics, rather than postulating random propagation channel models. The project focuses on the characterization of the amount of spatial diversity that a wireless networks can provide, which is shown to be one of the central issues to determine its capacity. The spatial diversity is quantified in terms of the dimensionality of the propagating field, which is what carries the information through the network. Hence, drawing connections between information theory, functional analysis of continuous vector spaces, electromagnetic theory, and networks, the project aims at developing an information theory for wireless networks. The project considers different geometric configurations of wireless network, and determines their corresponding number of spatial degrees of freedom. It then considers both the effects of narrow-band and wide-band frequency transmission. Results are in terms of scaling laws, as well as capacity laws that are not asymptotic in the number of nodes in the network.