A Generic Multi-dimensional Symbol Construction for Digital Over-the-Air Computation and Practical Aspects

Electrical Engineering and Systems Science > Signal Processing [Submitted on 16 Jun 2026] Title:A Generic Multi-dimensional Symbol Construction for Digital Over-the-Air Computation and Practical Aspects View PDFAbstract:In this paper, we propose a general-purpose multi-dimensional symbol construction for computing an arbitrary symmetric function with digital over-the-air computation (OAC) and discuss the practical aspects of coherent aggregation. For our first contribution, we discuss the categorical representation of a symmetric function. By using this representation and leveraging the sufficiency of the histogram to evaluate a symmetric function, i.e., inspired by type-based multiple access (TBMA), we introduce a general approach to design a single set of OAC symbols to compute any digital function. For our second contribution, we use a comprehensive platform based on low-cost nodes that maintain synchronization in time, frequency, phase, and amplitude via a trigger mechanism, enabling coherent OAC experiments without Global Positioning System (GPS) or cable-based synchronization. Using measurements from the platform, we characterize the phase and amplitude statistics of the composite channel to derive a realistic impairment model for coherent OAC. Through a comprehensive analysis, we demonstrate the effectiveness of the proposed scheme under impairments captured by the proposed model Current browse context: eess.SP References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.