AI 中文总结
研究空中计算在实际部署中因依赖精确载波同步面临挑战的问题，提出基于KK接收的自相干、无合成器空中计算框架及信号域模型，减少控制开销、提高可扩展性，接近基带OAC理论性能极限，适用于毫米波和太赫兹系统。
AI 中文摘要
空中计算（OAC）通过利用多址信道的叠加特性，在无线网络中实现高效的函数聚合。然而，OAC的实际部署面临着对精确载波同步和相干接收的严重挑战，这在短距离和低复杂度系统中成本高昂且易受干扰。在这项工作中，我们提出了一种基于克拉默斯-克朗尼格（KK）接收的自相干、无合成器的空中计算框架。通过发送有偏的聚合波形，并在接收器处采用直接检测和KK相位重建，该方案在保留类似相干信号聚合的同时，消除了对显式载波恢复的需求。我们为KK接收下的多用户OAC开发了一个信号域系统模型，并提供了同步松弛分析，证明该架构从根本上消除了发射机和接收机之间的载波频率偏移（CFO）敏感性。通过将同步复杂性从严格的载波相位跟踪转移，并消除分布式相位对准要求，该框架降低了控制开销，提高了多用户聚合的可扩展性。详细的每符号均方误差（MSE）表征隔离了信道失配和KK重建噪声的影响，表明所提出的自相干架构在实际操作条件下接近基带OAC的理论性能极限。最后，我们证明该方法特别适用于毫米波和太赫兹系统，在这些系统中，振荡器相位不稳定性否则将成为可扩展相干OAC的一个基本瓶颈。
英文摘要
Over-the-air computation (OAC) enables efficient function aggregation in wireless networks by exploiting the superposition property of the multiple-access channel. However, practical deployment of OAC is severely challenged by the reliance on accurate carrier synchronization and coherent reception, which are costly and fragile, especially in short-range and low-complexity systems. In this work, we propose a \emph{self-coherent, synthesizer-free over-the-air computation framework} based on \emph{Kramers--Kronig (KK) reception}. By transmitting a biased aggregate waveform and employing direct detection followed by KK phase reconstruction at the receiver, the proposed scheme eliminates the need for explicit carrier recovery while preserving coherent-like signal aggregation. We develop a signal-domain system model for multi-user OAC under KK reception and provide a synchronization-relaxation analysis demonstrating that the proposed architecture fundamentally removes carrier-frequency offset (CFO) sensitivity between transmitters and receiver. By shifting synchronization complexity away from strict carrier-phase tracking and eliminating distributed phase alignment requirements, the framework reduces control overhead and improves scalability in multi-user aggregation. A detailed per-symbol mean-squared error (MSE) characterization isolates the impact of channel mismatch and KK reconstruction noise, showing that the proposed self-coherent architecture approaches the theoretical performance limits of baseband OAC under practical operating conditions. Finally, we demonstrate that the approach is particularly well suited for mmWave and sub-THz systems, where oscillator phase instability otherwise represents a fundamental bottleneck to scalable coherent OAC.
