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.
While current wireless networks are based essentially on one-to-many and many-to-one single-hop sub-networks (e.g., 2/3/4 G cells, or WiFi hot-spots) and cope with inter-cell interference by careful centralized resource planning, future networks will be based on a multitude of access technologies, frequency bands, and cell sizes, possibly self-organized and user-deployed, for costs and flexibility reasons. Because of the lack of wired infrastructure (most of the USA still gets its Internet access to slow DSL lines), or in order to exploit a much denser spatial reuse, multiple flows and multiple hops will play a more and more relevant role. Therefore, laying down a fundamental understanding of multihop multiflow wireless networks is critically important at this time. Solving the capacity of multihop multiflow wireless networks in the strict Shannon-theoretic sense is arguably the yet unachieved holy grail of network information theory. In this project we have discovered some fundamentals features of such networks and have characterized their capacity in an approximated sense in a number of important special cases. We demonstrated that scalable and extensible solutions are indeed possible for the problem of approximating the capacity of wireless networks ranging from seemingly simple networks involving two hops and two flows to apparently more complex ones involving multiple hops and more than two flows with arbitrary connectivity. The outcomes of this short and highly focused project serve both as a starting point for a broader and more cmprehensive theoretical investigation, which we are carrying out in a larger follow-up project currently under execution, and as a clear theoretical basis to inspire design guidelines of actual systems of future generation, laying down the technology understanding that will be able to address the pressing ``spectrum crunch'' problem that is currently looming over the wireless industry and, as a side effect, over the whole infrmation society and Internet economy, given the fact that wireless has become by far the most favorite medium to access the Internet cloud by the users worldwide.
