The emerging concept of Over-the-Air (OtA) computation has shown great potential for achieving resource-efficient data aggregation across large wireless networks. However, current research in this area has been limited to the standard many-to-one topology, where multiple nodes transmit data to a single receiver. In this study, we address the problem of applying OtA computation to scenarios with multiple receivers, and propose a novel communication design that exploits joint precoding and decoding over multiple time slots. To determine the optimal precoding and decoding vectors, we formulate an optimization problem that aims to minimize the mean squared error of the desired computations while satisfying the unbiasedness condition and power constraints. Our proposed multi-slot design is shown to be effective in saving communication resources (e.g., time slots) and achieving smaller estimation errors compared to the baseline approach of separating different receivers over time.

翻译：新兴的空中计算（OtA）概念在实现大规模无线网络资源高效数据聚合方面展现出巨大潜力。然而，当前该领域的研究仍局限于标准的“多对一”拓扑结构，即多个节点向单一接收器传输数据。本研究针对空中计算在多接收器场景中的应用问题，提出了一种利用多时隙联合预编码与解码的新型通信设计方案。为确定最优预编码与解码向量，我们构建了一个优化问题，旨在满足无偏性条件与功率约束的同时，最小化目标计算的均方误差。与将不同接收器按时间分隔的基线方法相比，所提出的多时隙设计能有效节省通信资源（如时隙），并实现更小的估计误差。