# Resource-Element Energy Difference for Noncoherent Over-the-Air Federated Learning

arXiv: https://arxiv.org/abs/2605.07263 · HTML: https://mlsanity.com/paper/2605.07263/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 23 of 23)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [Over-The-Air Federated Learning: Status Quo, Open Challenges, and Future Directions](https://mlsanity.com/paper/2307.00974/) (2023)
- [Random Orthogonalization for Federated Learning in Massive MIMO Systems](https://mlsanity.com/paper/2201.12490/) (2022)
- [Over-the-Air Computation for 6G: Foundations, Technologies, and Applications](https://mlsanity.com/paper/2210.10524/) (2022)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Distributed Learning over a Wireless Network with Non-coherent Majority Vote Computation](https://mlsanity.com/paper/2209.04692/) (2022)
- [Non-Coherent Over-the-Air Decentralized Gradient Descent](https://mlsanity.com/paper/2211.10777/) (2022)
- [Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow](https://mlsanity.com/paper/1811.04644/) (2018)
- [Blind Federated Learning via Over-the-Air q-QAM](https://mlsanity.com/paper/2311.04253/) (2023)
- [Waveforms for Computing Over the Air](https://mlsanity.com/paper/2405.17007/) (2024)
- [Over-the-Air Federated Learning via Weighted Aggregation](https://mlsanity.com/paper/2409.07822/) (2024)
- [Adaptive Federated Learning Over the Air](https://mlsanity.com/paper/2403.06528/) (2024)
- [NCAirFL: CSI-Free Over-the-Air Federated Learning Based on Non-Coherent Detection](https://mlsanity.com/paper/2411.13000/) (2024)

## Abstract (arXiv)

Over-the-air federated learning (OTA-FL) reduces uplink latency by aggregating client updates directly over the wireless multiple-access channel. Coherent analog aggregation realizes this idea by aligning the phases and amplitudes of simultaneously transmitted waveforms, which typically requires synchronization, instantaneous channel-state information (CSI), phase compensation, and power control. Noncoherent energy detection removes the need for phase-coherent combining, but a single energy measurement is nonnegative and, therefore, cannot represent signed model updates. This paper introduces resource-element energy difference (REED), a noncoherent physical-layer primitive for continuous signed aggregation. REED maps the positive and negative parts of each real-valued update to transmit energies on paired orthogonal resource elements and estimates the signed sum by subtracting the corresponding received energies. The construction uses slow-timescale calibration of average channel powers, but does not require instantaneous transmitter- or receiver-side CSI or channel inversion. For independent Rayleigh fading, we derive exact first- and second-moment expressions for single-shot REED and for a chip-diverse extension that spreads each coordinate over multiple independently faded paired chips. The resulting variance laws separate fading-induced self-noise, signal-noise interaction, and receiver-noise fluctuation, giving an explicit diversity-resource tradeoff. More->The rest of abstract is in the paper.