AI 中文总结
研究用于EML操作的可重复使用双输入AirComp门，避免特定节点非线性门设计。给定显式EML树，推导AWGN等实现，表征树的多项指标，通过示例给出误差条件，数字接口传播相关误差。
AI 中文摘要
无线计算（AirComp）利用多址叠加来计算分布式数据的函数，而无需单独解码所有终端消息。我们研究了一种用于指数减对数（EML）操作\(\eml(u,v)=\exp(u)-\log(v)\)，\(v>0\)的可重复使用的双输入AirComp门。这样，规定的实允许EML树的所有内部节点都重用一种门类型，避免了特定节点的非线性门设计。给定一个显式EML树，其中间对数参数在给定紧凑域上保持正值，我们在峰值功率约束下推导了加性高斯白噪声（AWGN）和相干平坦衰落实现。然后，我们对完整树的门评估次数、依赖深度、评估延迟、节点可行性、确定性误差传播、正性保持和高概率AWGN误差界进行了表征。一个四终端两跳示例给出了明确的正性和端到端误差条件，并且数字接口在整个树中传播量化和门误差。
英文摘要
Over-the-air computation (AirComp) exploits multiple-access superposition to compute functions of distributed data without separately decoding all terminal messages. We study a reusable two-input AirComp gate for the exp-minus-log (EML) operation $\eml(u,v)=\exp(u)-\log(v)$, $v>0$. Thus, all internal nodes of a prescribed real-admissible EML tree reuse one gate type, avoiding node-specific nonlinear gate designs. Given an explicit EML tree whose intermediate logarithm arguments remain positive on a given compact domain, we derive additive white Gaussian noise (AWGN) and coherent flat fading implementations under peak-power constraints. We then characterize the number of gate evaluations, the dependency depth, evaluation latency, node-wise feasibility, deterministic error propagation, positivity preservation, and a high-probability AWGN error bound for the complete tree. A four-terminal two-hop example gives explicit positivity and end-to-end error conditions, and a digital interface propagates quantization and gate errors across the tree.
