The next generation wireless network is expected to connect billions of nodes, which brings up the bottleneck on the communication speed for distributed data fusion. To overcome this challenge, computation over multiple access channel (CoMAC) was recently developed to compute the desired functions with a summation structure (e.g., mean, norm, etc.) by using the superposition property of wireless channels. This work aims to maximize the achievable function rate of reliable CoMAC in wireless networks. More specifically, considering channel fading and transceiver design, we derive the achievable function rate adopting the quantization and the nested lattice coding, which is determined by the number of nodes, the maximum value of messages and the quantization error threshold. Based on the derived result, the transceiver design is optimized to maximize the achievable function rate of the network. We first study a single cluster network without inter-cluster interference (ICI). Then, a multi-cluster network is further analyzed in which the clusters work in the same channel with ICI. In order to avoid the global channel state information (CSI) aggregation during the optimization, a low-complexity signaling procedure irrelevant with the number of nodes is proposed utilizing the channel reciprocity and the defined effective CSI.

中文翻译：

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MAC 上的计算：无线网络中可实现的函数速率最大化

下一代无线网络预计将连接数十亿个节点，这带来了分布式数据融合通信速度的瓶颈。为了克服这一挑战，最近开发了多接入信道计算 (CoMAC) 以通过使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）的所需函数。这项工作旨在最大限度地提高无线网络中可靠 CoMAC 的可实现功能率。更具体地说，考虑信道衰落和收发器设计，我们推导出采用量化和嵌套格编码的可实现函数率，其由节点数、消息的最大值和量化误差阈值决定。根据推导出的结果，收发器设计经过优化，以最大限度地提高网络可实现的功能率。我们首先研究没有集群间干扰（ICI）的单集群网络。然后，进一步分析多集群网络，其中集群与 ICI 工作在同一通道中。为了避免优化过程中全局信道状态信息(CSI)聚合，利用信道互易性和定义的有效CSI，提出了一种与节点数量无关的低复杂度信令过程。