Computation over multiple access channel (CoMAC) scheme provides a promising solution to future large-scale wireless networks by utilizing the superposition property of the wireless channel to compute a class of functions with a summation structure (e.g., mean, norm, etc.). However, its implementation usually requires all nodes' channel state information (CSI) and its performance is limited by the channel condition of the worst node. In order to avoid massive CSI aggregation and improve the limited performance, we propose an automatic repeat request (ARQ)-aided CoMAC scheme in this paper. The transmitters and signaling procedures are designed to achieve the tradeoff between the achievable function rate and the transmission delay. The corresponding performance of the proposed ARQ-aided CoMAC scheme and the traditional ARQ-aided communication scheme are compared for both homogeneous networks and heterogeneous networks. By optimizing the ARQ level, we further maximize the achievable function rate of the proposed scheme. Asymptotic closed-form expressions are derived by resorting to the extreme value theory and point mass approximation. Monte Carlo simulations are given to illustrate and verify the performance of the proposed designs.

中文翻译：

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实现多路访问信道计算的最佳速率-延迟权衡


多址信道计算（CoMAC）方案通过利用无线信道的叠加特性来计算具有求和结构（例如均值、范数等）的一类函数，为未来大规模无线网络提供了一种有前途的解决方案。然而，其实现通常需要所有节点的信道状态信息（CSI），并且其性能受到最差节点的信道状况的限制。为了避免大规模CSI聚合并提高有限的性能，我们在本文中提出了一种自动重复请求（ARQ）辅助的CoMAC方案。发射机和信令程序被设计为实现可实现的功能速率和传输延迟之间的折衷。针对同质网络和异构网络，比较了所提出的 ARQ 辅助 CoMAC 方案和传统 ARQ 辅助通信方案的相应性能。通过优化 ARQ 级别，我们进一步最大化了所提出方案的可实现功能率。借助极值理论和点质量近似推导出渐近闭式表达式。蒙特卡罗模拟用于说明和验证所提出设计的性能。