# On the Feasibility of Distributed Phase Synchronization for Coherent Signal Superposition

arXiv: https://arxiv.org/abs/2506.22252 · HTML: https://mlsanity.com/paper/2506.22252/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2025.

## Built on by (most cited first, 3 of 3)

- [Learned Digital Over-the-Air Computing for Federated Edge Learning](https://mlsanity.com/paper/2509.16577/) (2025)
- [Learned Digital Codes for Over-the-Air Computation in Federated Edge Learning](https://mlsanity.com/paper/2512.19777/) (2025)
- [Hybrid Channel Estimation with Quantized Phase Feedback for Over-the-Air Computation](https://mlsanity.com/paper/2601.16054/) (2026)

## Abstract (arXiv)

In this study, we analyze the feasibility of distributed phase synchronization for coherent signal superposition, a fundamental enabler for paradigms such as coherent over-the-air computation (OAC), distributed beamforming, and interference alignment, under mobility and hardware impairments. With the focus on coherent OAC, we introduce phase-coded pilots (PCPs), a strategy where the radios communicate with each other to eliminate the round-trip phase change in the uplink (UL) and downlink (DL) to align the phase of the received symbol at a desired angle. In this study, considering a carrier frequency offset (CFO)-resilient multi-user procedure, we derive the statistics of the phase deviations to assess how fast the phase coherency degrades. Our results show that residual CFO is a major factor determining the duration of phase coherency, in addition to the non-negligible effects of mobility and the number of nodes in the network. We also provide a proof-of-concept demonstration for coherent signal superposition by using off-the-shelf radios to demonstrate the feasibility of PCPs in practice.