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.
The project has focused on the study of models of wireless communication networks and their informational limits. The objective was to characterize in a precise mathematical way the limits on the amount on information that can flow through a completely wireless network and how these limits can be achieved using architectures inspired by current techologies and simple network protocols. Most current wireless networks, like the cellular phone network, rely on a wired infrastructure (typically a fiber optics backbone) that can facilitate communication between users. When we make a phone call, we connect to the nearest base station that forwards data via a wired connection to the corresponding base station closest to the destination that makes the final transmission using radio waves. Instead, the type of wireless networks studied here are "flat" in the sense that they do not rely on any infrastructure, thus providing a working example of what can be ultimately be achieved by complete wireless transmission, see Figure 1. In our study, we succesfully applied tools from random graph theory, probability theory, electromagnetics and information theory to characterize the operational limits of wireless networks. One of the main results described in the relevant scientific literature has been the determination of a "scaling law" for large networks. It turns out that as networks grow larger in size, the amount of information that can flow through the network increases at a lower pace, so that the single user must inevitably perceive a decrease in connection quality. This effect can be explained by looking at Figure 2. Assume that the number of users in the network is n and the area of the network also to be n. Users are represented by black dots. Assume that each user generates an interference footprint represented by a small circular area around it. No other user within this area can transmit simultaneously otherwise the transmission is lost due to interference. The largest amount of information tranfer through the network can be measured by the number of simultaneous transmissions that can occur simultaneously and it is given by the number of disjoint circular discs that can fit on an ideal cut dividing the network into half. This number is much less than n, in fact it is given by the square root of n, as it is proportional to the side length of the network area. This argument was first noted non-rigorously by others in the literature. But it turns out that it can be made precise using electromagnetic theory and thus provides a fundamental physical limitation to our ability to communicate. Broad impacts of our project included the publication of a book on random networks for communcation that is currently used by a number of institutions in their graduate courses and the training of a young researchers who completed their PhD while sponsored by this project.
