CAREER: The Transmission Capacity of Hierarchical Wireless Networks

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In the past decade, wireless networks have undergone a remarkable evolution from primitive circuit-switched links to multiuser packet-switched networks with increasing levels of cooperation and sophistication. In the coming decade, a primary impediment to their further evolution is the lack of a descriptive theory for networks with interdependent links, most notably ad hoc and mesh networks. This problem has proven to be a daunting task due to (i) the dimensionality of the capacity region due to the node interactions, and (ii) the competing constraints of throughput, delay, energy efficiency, and connectivity. Without discounting the significant progress that has been made, the lack of crisp results has handicapped the system design of ad hoc, mesh, and sensor networks, and therefore impeded their development and commercialization. This research involves the development of a descriptive capacity theory for ad hoc networks that should be capable of the following: (1) Accurate characterization of the effects from physical parameters and advanced radio technologies, (2) accurately accounting of the spatial interactions between the transmitters and receivers in the network, and (3) providing a useful abstraction of the lower "layers". This is accomplished using a novel approach based on stochastic geometry (motivated by information theory) that we term the transmission capacity. The key theoretical milestones for this research are (i) substantial contributions in the application of stochastic geometry, random matrix theory, and information theory to ad hoc and hierarchical wireless networks, (ii) a useful theory that can be used to characterize the effect of any conceivable technology or scheme on ad hoc network capacity, and (iii) the derivation of specific results that will impact design principles of future wireless networking standards.