CAREER: Rethinking Dynamic Wireless Networks through the Lens of Riemannian Geometry

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The current revolution of wireless systems aims to support massive connectivity along with emerging applications, such as connected vehicles and extended reality, which simultaneously require high data rate and low latency. Dynamic network architectures, which include moving relays and flying drones, can support such requirements thanks to their adaptive nature. Maximizing data rate in such relay-assisted networks can be accomplished via 1) designing environment-aware and relay-based beamforming codebooks, 2) managing wireless interference that is caused by or towards relays, and 3) adaptive placement of relays. Unlike existing solutions for these problems, this project starts with a transformative modeling of the underlying data structures of wireless channels and network topologies over curved surfaces, known as Riemannian manifolds. The novel design of wireless networks through the lens of Riemannian manifolds leads to developing low-latency structure-aware (i.e., “gray-box”) machine learning (ML) models and low-complexity optimized solutions for these three problems. This project serves the national interest by promoting the progress of foundational science of wireless communications and networks along with providing the research community nationwide with fast ML models and efficient optimization tools, which will have far-reaching impact on addressing many challenges in wireless networks and alike. Furthermore, this project equips engineering students nationwide with new mathematical tools and hands-on educational platforms that uniquely integrate Riemannian geometry into wireless networks. Multiple undergraduate and graduate students, including underrepresented minorities, are mentored through this project. Finally, this project gravitates high-school students, including students with disabilities such as autism spectrum disorder, towards STEM through active engagement in interdisciplinary activities of non-Euclidean geometry, engineering, and neuroscience. This project aims to lay the foundations of utilizing Riemannian-geometric tools, particularly, geometric machine learning (G-ML) and conic geometric optimization (CGO), to advance the knowledge of designing dynamic networks with low latency, low complexity, and high data rate. Such goal is accomplished through synergistic integration of three components, which span multiple network layers (i.e., PHY, MAC, NET), as follows. First, environment-aware beamforming codebooks are developed using low-latency unsupervised G-ML models, thanks to representing the covariance matrices of spatially-correlated wireless channels over Riemannian manifolds. Second, wireless link scheduling and resource allocation mechanisms are developed using low-latency supervised G-ML models, which are based on jointly modeling the Riemannian-geometric and temporal structures of interference-aware network topologies over Riemannian manifolds. Finally, locations of relays are optimized for maximizing the network flow rate using low-complexity CGO, given the representation of relay-enhanced network topologies over Riemannian manifolds.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.