Over-the-air computation (OAC) enables low-latency aggregation over multiple-access channels (MACs) by exploiting the superposition property of the wireless medium to compute functions efficiently in distributed networks. A critical but often overlooked challenge is that electromagnetic interference in practical radio channels frequently exhibits heavy-tailed behavior, causing strong impulsive noise that severely degrades computation performance. This work studies digital OAC with QAM-based signaling under heavy-tailed interference modeled by a Cauchy distribution (lacking a finite second moment). We seek QAM-like constellations that minimize the mean-squared error (MSE) of sum aggregation subject to an average-power constraint. The problem is formulated as a constrained optimization, whose solution yields unique optimality conditions. Numerical results confirm the effectiveness of the proposed design. Notably, the framework extends naturally to nomographic functions, broader constellation families, and alternative noise models.

翻译：空中计算（OAC）利用无线介质的叠加特性，可在多址信道（MAC）上实现低延迟聚合，从而在分布式网络中高效计算函数。一个关键但常被忽视的挑战是，实际无线信道中的电磁干扰常呈现重尾特性，产生强烈的脉冲噪声，严重降低计算性能。本文研究基于QAM调制的数字OAC在服从柯西分布（缺乏有限二阶矩）的重尾干扰下的性能。我们寻求在平均功率约束下最小化和聚合均方误差（MSE）的类QAM星座。该问题被表述为一个约束优化问题，其解导出了唯一的最优性条件。数值结果验证了所提设计的有效性。值得注意的是，该框架可自然扩展到诺模图函数、更广泛的星座族以及替代噪声模型。