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

2026-07-20

AI Summary

This work addresses the poor robustness and high cost of conventional over-the-air computation (AirComp) in millimeter-wave and sub-terahertz bands, where stringent carrier synchronization is undermined by oscillator phase instability. To circumvent the need for high-precision frequency synthesizers, the authors propose a self-coherent AirComp framework that transmits offset-aggregated signals and leverages a Kramers–Kronig (KK) receiver for direct detection and implicit phase reconstruction, thereby eliminating explicit carrier recovery. By introducing the KK reception mechanism into multi-user AirComp for the first time, the approach fundamentally removes sensitivity to carrier frequency offsets and obviates distributed phase alignment, drastically reducing synchronization overhead and enhancing scalability. Theoretical analysis and simulations demonstrate that the proposed architecture approaches the performance limits of baseband AirComp under practical conditions, with mean-square error evaluations confirming its effectiveness in suppressing channel mismatch and KK reconstruction noise—making it particularly suitable for efficient function aggregation in sub-terahertz systems.

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.

Problem

• Over-the-air computation
• carrier synchronization
• coherent reception
• phase instability
• sub-THz

Innovation

• self-coherent
• Kramers–Kronig reception
• over-the-air computation
• carrier synchronization
• sub-THz