When Phase Doesn't Matter: Self-Coherent Over-the-Air Computation at Sub-THz

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.