CIF: Small: Mathematical Tools for Unifying and Simplifying the Analysis and Optimization of Wireless Networks

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The advent of Internet-of-Things (IoT) devices that are connected through wireless networks will dramatically transform the way people and machines interact with their world, enabling many new applications ranging from environmental sensing and disaster relief to smart grids, intelligent transportation, and mobile healthcare. Given the limited wireless spectrum, any wireless communication technique should optimally utilize the limited radio resources. Network operators should be able to quantify the performance of the emerging adaptable wireless networks under realistic assumptions of propagation environments prior to deployment. However, the design space for such exploration is huge and an exhaustive exploration of this space via experimental studies and/or simulation approaches is typically impractical, time-consuming and/or expensive. This project attacks this challenge by developing novel analytical tools that are both simple in form and easy to evaluate, yet yield accurate performance predictions in relevant operational regimes. These tools will yield deep insights into the dependence of various design parameters on system performance. This knowledge, in turn, will guide wireless system engineers and network operators in their designs and efficiently perform system trade-off studies at a fraction of computer simulations run-time and costs, especially at early design stages. The educational and outreach activities will substantially improve the wireless research and education infrastructure at a historically black university and produce a skilled workforce in a rapidly growing field. Today, it is extremely challenging to accurately characterizing the wireless link layer performances of advanced transceivers that capture the non-linearity of the propagation medium, multi-path fading and co-channel interference. The principal difficulty stems from finding analytically tractable expressions (preferably in closed-form) for the density function of various arithmetic combinations (e.g., partial sums, ratios, products, powers) of random variables drawn from generalized fading distributions. Moreover, limitations of the state-of-the-art exact analytical tools impede efficient computations of some important new wireless performance measures such as the higher-order statistics of channel capacity and symbol error probabilities in generalized fading channel models. This project seeks to address these challenges by focusing on three specific research tasks: (1) develop new classes of asymptotic performance bounds/approximations for accurately predicting wireless networks perturbed by multi-path fading and interference in generalized stochastic fading environments; (2) develop closed-form exponential-type approximations for powers of the conditional error probabilities of digital modulations as well as alternative integral representations for the Nuttall-Q, Marcum-Q and incomplete Gamma functions that will facilitate the statistical averaging task of random variables in their arguments; and (3) build upon the mathematical tools developed in tasks (1) and (2) in unifying and simplifying the analysis and optimization of emerging wireless systems. This project's framework is expected to yield computationally stable and efficient solutions to numerous wireless performance analyses problems that heretofore had resisted solutions in simple forms, facilitate investigation and development of cross-layer design rules for next-generation adaptable wireless networks as well as bridge some knowledge gaps in wireless communication theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.