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.
