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

当前的无线系统革命旨在支持大规模连接以及新兴应用，例如联网汽车和扩展现实，这些应用同时需要高数据速率和低延迟。动态网络架构，包括移动中继和飞行无人机，由于其自适应特性，可以支持这些要求。在这种中继辅助网络中，最大限度地提高数据速率可以通过以下方式实现：1)设计环境感知和基于中继的波束形成码本，2)管理由中继引起或朝向中继的无线干扰，以及3)自适应中继的放置。与这些问题的现有解决方案不同，该项目首先对曲面（即黎曼流形）上的无线信道和网络拓扑的底层数据结构进行转换建模。通过黎曼流形透镜的无线网络的新设计导致开发低延迟结构感知（即“灰盒”）机器学习（ML）模型和针对这三个问题的低复杂性优化解决方案。该项目通过促进无线通信和网络基础科学的进步，为全国研究界提供快速的机器学习模型和高效的优化工具，为解决无线网络等领域的许多挑战提供深远的影响，从而服务于国家利益。此外，该项目为全国的工程专业学生提供了新的数学工具和实践教育平台，将黎曼几何独特地集成到无线网络中。多个本科生和研究生，包括代表性不足的少数民族，通过这个项目的指导。最后，该项目通过积极参与非欧几里得几何、工程和神经科学的跨学科活动，吸引高中生，包括自闭症谱系障碍等残疾学生向STEM学习。本项目旨在为利用黎曼几何工具，特别是几何机器学习（G-ML）和二次几何优化（CGO）奠定基础，以提高设计低延迟，低复杂性和高数据速率的动态网络的知识。这一目标是通过三个组件的协同集成来实现的，这三个组件跨越多个网络层（即PHY， MAC， NET），如下所示。首先，使用低延迟无监督G-ML模型开发环境感知波束形成码本，这要归功于在黎曼流形上表示空间相关无线信道的协方差矩阵。其次，利用低延迟监督G-ML模型开发了无线链路调度和资源分配机制，该模型基于黎曼流形上干扰感知网络拓扑的黎曼几何和时间结构的联合建模。最后，考虑到黎曼流形上中继增强网络拓扑的表示，利用低复杂度CGO优化了中继的位置，以最大限度地提高网络流量。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.