Massive numbers of nodes will be connected in future wireless networks. This brings great difficulty to collect a large amount of data. Instead of collecting the data individually, computation over multi-access channels (CoMAC) provides an intelligent solution by computing a desired function over the air based on the signal-superposition property of wireless channels. To improve the spectrum efficiency in conventional CoMAC, we propose the use of non-orthogonal multiple access (NOMA) for functions in CoMAC. The desired functions are decomposed into several sub-functions, and multiple sub-functions are selected to be superposed over each resource block (RB). The corresponding achievable rate is derived based on sub-function superposition, which prevents a vanishing computation rate for large numbers of nodes. We further study the limiting case when the number of nodes goes to infinity. An exact expression of the rate is derived that provides a lower bound on the computation rate. Compared with existing CoMAC, the NOMA-based CoMAC not only achieves a higher computation rate but also provides an improved non-vanishing rate. Furthermore, the diversity order of the computation rate is derived, which shows that the system performance is dominated by the node with the worst channel gain among these sub-functions in each RB.

中文翻译：

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NOMA 增强的多接入信道计算

未来的无线网络中将连接大量节点。这给收集大量数据带来了很大的困难。多路访问信道计算 (CoMAC) 不是单独收集数据，而是基于无线信道的信号叠加特性，通过空中计算所需的函数来提供智能解决方案。为了提高传统 CoMAC 中的频谱效率，我们建议对 CoMAC 中的功能使用非正交多址 (NOMA)。需要的功能被分解成几个子功能，选择多个子功能叠加在每个资源块（RB）上。相应的可实现速率是基于子函数叠加得出的，这可以防止大量节点的计算速率消失。我们进一步研究了当节点数达到无穷大时的极限情况。推导出速率的精确表达式，提供计算速率的下限。与现有的 CoMAC 相比，基于 NOMA 的 CoMAC 不仅实现了更高的计算速率，而且还提供了改进的非消失率。进一步推导出计算速率的分集阶数，表明系统性能由每个RB中这些子函数中信道增益最差的节点主导。