Non-coherent over-the-air (NCOTA) computation enables low-latency and bandwidth-efficient decentralized optimization by exploiting the average energy superposition property of wireless channels. It has recently been proposed as a powerful tool for executing consensus-based optimization algorithms in fully decentralized systems. A key advantage of NCOTA is that it enables unbiased consensus estimation without channel state information at either transmitters or receivers, requires no transmission scheduling, and scales efficiently to dense network deployments. However, NCOTA is inherently susceptible to external interference, which can bias the consensus estimate and deteriorate the convergence of the underlying decentralized optimization algorithm. In this paper, we propose a novel interference-robust (IR-)NCOTA scheme. The core idea is to apply a coordinated random rotation of the frame of reference across all nodes, and transmit a pseudo-random pilot signal, allowing to transform external interference into a circularly symmetric distribution with zero mean relative to the rotated frame. This ensures that the consensus estimates remain unbiased, preserving the convergence guarantees of the underlying optimization algorithm. Through numerical results on a classification task, it is demonstrated that IR-NCOTA exhibits superior performance over the baseline NCOTA algorithm in the presence of external interference.

翻译：非相干空中计算通过利用无线信道的平均能量叠加特性，实现了低延迟和带宽高效的去中心化优化。该技术最近被提出作为在全去中心化系统中执行基于共识的优化算法的有力工具。NCOTA的关键优势在于：它能够在收发端均无需信道状态信息的条件下实现无偏共识估计，无需传输调度，并能高效扩展至密集网络部署。然而，NCOTA本质上易受外部干扰影响，这可能导致共识估计产生偏差，并恶化底层去中心化优化算法的收敛性。本文提出了一种新颖的抗干扰NCOTA方案。其核心思想是在所有节点间协调实施参考系的随机旋转，并发送伪随机导频信号，从而将外部干扰转化为相对于旋转后参考系具有零均值的圆对称分布。这确保了共识估计保持无偏性，维护了底层优化算法的收敛性保证。通过在分类任务上的数值结果证明，在存在外部干扰的情况下，IR-NCOTA相较于基线NCOTA算法表现出更优越的性能。