# Federated Edge Learning with Misaligned Over-The-Air Computation

arXiv: https://arxiv.org/abs/2102.13604 · HTML: https://mlsanity.com/paper/2102.13604/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 26 Feb 2021.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [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)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Machine Learning in the Air](https://mlsanity.com/paper/1904.12385/) (2019)
- [Communicate to Learn at the Edge](https://mlsanity.com/paper/2009.13269/) (2020)
- [Energy-Aware Analog Aggregation for Federated Learning with Redundant Data](https://mlsanity.com/paper/1911.00188/) (2019)
- [Collaborative Machine Learning at the Wireless Edge with Blind Transmitters](https://mlsanity.com/paper/1907.03909/) (2019)

## Built on by (most cited first, 30 of 30)

- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [Dynamic Scheduling for Over-the-Air Federated Edge Learning with Energy Constraints](https://mlsanity.com/paper/2106.00490/) (2021)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Machine Learning for Large-Scale Optimization in 6G Wireless Networks](https://mlsanity.com/paper/2301.03377/) (2023)
- [Federated Learning and Meta Learning: Approaches, Applications, and Directions](https://mlsanity.com/paper/2210.13111/) (2022)
- [A Survey on Integrated Sensing, Communication, and Computation](https://mlsanity.com/paper/2408.08074/) (2024)
- [Training Machine Learning models at the Edge: A Survey](https://mlsanity.com/paper/2403.02619/) (2024)
- [Over-the-Air Federated Edge Learning with Hierarchical Clustering](https://mlsanity.com/paper/2207.09232/) (2022)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Fast Federated Edge Learning with Overlapped Communication and Computation and Channel-Aware Fair Client Scheduling](https://mlsanity.com/paper/2109.06710/) (2021)
- [AttentionCode: Ultra-Reliable Feedback Codes for Short-Packet Communications](https://mlsanity.com/paper/2205.14955/) (2022)
- [Blind Federated Learning via Over-the-Air q-QAM](https://mlsanity.com/paper/2311.04253/) (2023)
- [Over-the-Air Split Machine Learning in Wireless MIMO Networks](https://mlsanity.com/paper/2210.04742/) (2022)
- [Semantic Communications with Discrete-time Analog Transmission: A PAPR Perspective](https://mlsanity.com/paper/2208.08342/) (2022)
- [Point Cloud Compression with Implicit Neural Representations: A Unified Framework](https://mlsanity.com/paper/2405.11493/) (2024)
- [Communication and Energy Efficient Wireless Federated Learning with Intrinsic Privacy](https://mlsanity.com/paper/2304.07460/) (2023)
- [Private Collaborative Edge Inference via Over-the-Air Computation](https://mlsanity.com/paper/2407.21151/) (2024)
- [Adaptive Federated Learning Over the Air](https://mlsanity.com/paper/2403.06528/) (2024)
- [Age-Based Device Selection and Transmit Power Optimization in Over-the-Air Federated Learning](https://mlsanity.com/paper/2501.01828/) (2025)
- [Over-the-Air Federated Learning: Rethinking Edge AI Through Signal Processing](https://mlsanity.com/paper/2512.03719/) (2025)
- [DEEP-IoT: Downlink-Enhanced Efficient-Power Internet of Things](https://mlsanity.com/paper/2403.00321/) (2024)
- [Digital Over-the-Air Federated Learning in Multi-Antenna Systems](https://mlsanity.com/paper/2302.14648/) (2023)
- [Accelerating Wireless Federated Learning via Nesterov's Momentum and Distributed Principle Component Analysis](https://mlsanity.com/paper/2303.17885/) (2023)
- [Semi-Asynchronous Federated Edge Learning Mechanism via Over-the-air Computation](https://mlsanity.com/paper/2305.04066/) (2023)
- [Over-the-Air Computation in OFDM Systems with Imperfect Channel State Information](https://mlsanity.com/paper/2307.05357/) (2023)
- [Rich-ARQ: From 1-bit Acknowledgment to Rich Neural Coded Feedback](https://mlsanity.com/paper/2602.07886/) (2026)
- [MD-AirComp+: Adaptive Quantization for Blind Massive Digital Over-the-Air Computation](https://mlsanity.com/paper/2602.18332/) (2026)
- [Out-of-Air Computation: Enabling Structured Function Extraction from Wireless Superposition](https://mlsanity.com/paper/2604.04312/) (2026)
- [AI Tool Discovery at Scale: All You Need is DNS](https://mlsanity.com/paper/2607.18242/) (2026)
- [Logit-Aware MIMO AirComp for Distributed Mixture-of-Experts LLM Inference over Wireless Edge Networks](https://mlsanity.com/paper/2610.03741/) (2026)

## Abstract (arXiv)

Over-the-air computation (OAC) is a promising technique to realize fast model aggregation in the uplink of federated edge learning. OAC, however, hinges on accurate channel-gain precoding and strict synchronization among the edge devices, which are challenging in practice. As such, how to design the maximum likelihood (ML) estimator in the presence of residual channel-gain mismatch and asynchronies is an open problem. To fill this gap, this paper formulates the problem of misaligned OAC for federated edge learning and puts forth a whitened matched filtering and sampling scheme to obtain oversampled, but independent, samples from the misaligned and overlapped signals. Given the whitened samples, a sum-product ML estimator and an aligned-sample estimator are devised to estimate the arithmetic sum of the transmitted symbols. In particular, the computational complexity of our sum-product ML estimator is linear in the packet length and hence is significantly lower than the conventional ML estimator. Extensive simulations on the test accuracy versus the average received energy per symbol to noise power spectral density ratio (EsN0) yield two main results: 1) In the low EsN0 regime, the aligned-sample estimator can achieve superior test accuracy provided that the phase misalignment is non-severe. In contrast, the ML estimator does not work well due to the error propagation and noise enhancement in the estimation process. 2) In the high EsN0 regime, the ML estimator attains the optimal learning performance regardless of the severity of phase misalignment. On the other hand, the aligned-sample estimator suffers from a test-accuracy loss caused by phase misalignment.