# Hybrid Channel Estimation with Quantized Phase Feedback for Over-the-Air Computation

arXiv: https://arxiv.org/abs/2601.16054 · HTML: https://mlsanity.com/paper/2601.16054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 7 of 7)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Over-the-Air Aggregation for Federated Learning: Waveform Superposition and Prototype Validation](https://mlsanity.com/paper/2110.14285/) (2021)
- [On the Feasibility of Distributed Phase Synchronization for Coherent Signal Superposition](https://mlsanity.com/paper/2506.22252/) (2025)
- [Massive Synchrony in Distributed Antenna Systems](https://mlsanity.com/paper/2401.11730/) (2024)
- [Correctly Modeling TX and RX Chain in (Distributed) Massive MIMO -- New Fundamental Insights on Coherency](https://mlsanity.com/paper/2206.14752/) (2022)

## Abstract (arXiv)

To reduce the signaling overhead of over-the-air computation, a hybrid channel estimation scheme is proposed, where reciprocity-based and feedback-based channel estimation are combined. In particular, the impact of quantized phase-feedback is studied while the amplitude is assumed estimated exactly. The scheme enables selecting the estimation precision of amplitude and phase separately, depending on the importance of each. Two variants of the scheme are proposed: As shown through simulations and theory, the second variant with reciprocity-based estimation of the channel phase, and optimal quantization of phase feedback, can outperform the first variant estimating the phase by feedback only.