While current cellular networks are based essentially on one-to-many and many-to-one single-hop subnets and cope with inter-cell interference by careful centralized resource planning, future wireless networks must consider heterogeneous environments characterized by user-deployed and user-operated infrastructure in which multiple flows and multiple hops will play an increasingly relevant role. Indeed, such networks are expected to open doors to trillions of dollars of e-commerce, while also providing vast amounts of easily accessible knowledge to the public. Developing a fundamental understanding of multihop multiflow wireless networks is therefore critically important at this time.
This exploratory project will seek to discover the fundamentals of such networks by obtaining their information theoretic capacity in an approximated sense. It is expected that scalable and extensible solutions are possible for such networks ranging from the seemingly simple ones involving two hops and two flows to apparently more complex ones involving multiple hops and more than two flows with arbitrary connectivity. In so demonstrating, multiple metrics will be employed. These metrics in the increasing order of accuracy in the high signal-to-noise ratio regime are (a) the fundamental limit on the available signaling (temporal/spectral/spatial) dimensions of the network, (b) the fundamental limit on the available signaling and signal-level dimensions, and (c) the capacity to within a (universal) constant number of bits independently of channel parameters.
Major outcome 1: The wireless networks of the future will be increasingly more user-deployed, self-configuring and adaptive. Dealing efficiently with network topology in order to maximize information transfer will be the key to success for future technologies. Towards that goal, we have been able to: - Characterize how network topology impacts the asymptotic behavior of the capacity of multi-hop wireless networks with two interfering information flows. - Develope new communication strategies that efficiently exploit network topology and multi-hop capability in order to deal with interference in two unicast wireless networks. Major outcome 2: The ever-growing demand for higher data rates places the conventional approaches to wireless network design under considerable stress. To meet this demand, future wireless networks are rapidly evolving towards high-density, user-deployed, and heterogeneous infrastructures. The combination of shared spectrum and the lack of centralized planning in such networks imply that nodes have to operate in the presence of significant interference. Towards that goal, we invented a new interference management scheme, named "aligned network diagonalization", which effectively utilizes cooperation among users in multi-hop wireless networks. The new scheme theoretically allows all source-destination pairs in a two-hop fully conneced network to asymptotically utilize the entire available spectrum. Major outcome 3: The modeling of background noise in point-to-point wireless channels as an additive Gaussian noise is well ?supported from both theoretical and practical viewpoints. However, as we move to "multihop multi?ow wireless ?networks" the validity/robustness of Gaussian models had remained unknown. We have ?established a general result that shows that the Gaussian noise is indeed the worst-case additive noise also in multihop multi?ow interference networks. While this is a result of its own interest in theoretical modeling of wireless ?networks, it can also be potentially utilized to study fundamental capacity limits of multihop multi?ow ?wireless networks by converting the problem into deterministic networks.
