When Phase Doesn't Matter: Self-Coherent Over-the-Air Computation at Sub-THz
2026-07-20 • Information Theory
Information Theory
AI summaryⓘ
The authors address challenges in wireless data aggregation caused by the need for precise carrier synchronization, which is difficult and expensive, especially in short-range or simple devices. They propose a new method using Kramers--Kronig reception that transmits a biased signal and reconstructs the phase without needing explicit carrier recovery. This approach reduces synchronization demands and improves scalability in multi-user systems by removing sensitivity to carrier frequency offsets. Their analysis shows this method achieves near-optimal performance and is especially useful for high-frequency systems like mmWave and sub-THz where phase instability is a major problem.
Over-the-air computationKramers--Kronig receptionCarrier synchronizationCarrier frequency offsetPhase reconstructionMulti-user aggregationmmWavesub-THz communicationMean-squared errorCoherent reception
Authors
Sherif Ghozzy, Mohamed Seif, H. Vincent Poor, Kaushik Sengupta
Abstract
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.