# Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws

arXiv: https://arxiv.org/abs/1909.00329 · HTML: https://mlsanity.com/paper/1909.00329/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2019.

## Built on by (most cited first, 27 of 27)

- [Federated Learning over Wireless Device-to-Device Networks: Algorithms and Convergence Analysis](https://mlsanity.com/paper/2101.12704/) (2021)
- [Federated Learning: A Signal Processing Perspective](https://mlsanity.com/paper/2103.17150/) (2021)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Task-Oriented Over-the-Air Computation for Multi-Device Edge AI](https://mlsanity.com/paper/2211.01255/) (2022)
- [Federated Learning and Meta Learning: Approaches, Applications, and Directions](https://mlsanity.com/paper/2210.13111/) (2022)
- [Federated Learning over Wireless Networks: A Band-limited Coordinated Descent Approach](https://mlsanity.com/paper/2102.07972/) (2021)
- [Over-the-Air Computation Based on Balanced Number Systems for Federated Edge Learning](https://mlsanity.com/paper/2210.07012/) (2022)
- [Relay-Assisted Cooperative Federated Learning](https://mlsanity.com/paper/2107.09518/) (2021)
- [Collaborative Edge AI Inference over Cloud-RAN](https://mlsanity.com/paper/2404.06007/) (2024)
- [Over-the-Air Computation over Balanced Numerals](https://mlsanity.com/paper/2209.11004/) (2022)
- [Multiple Access in the Era of Distributed Computing and Edge Intelligence](https://mlsanity.com/paper/2403.07903/) (2024)
- [Over-the-Air Statistical Estimation](https://mlsanity.com/paper/2103.04014/) (2021)
- [Leveraging Channel Noise for Sampling and Privacy via Quantized Federated Langevin Monte Carlo](https://mlsanity.com/paper/2202.13932/) (2022)
- [Graph Neural Networks over the Air for Decentralized Tasks in Wireless Networks](https://mlsanity.com/paper/2302.08447/) (2023)
- [Over-the-Air Federated Learning with Retransmissions (Extended Version)](https://mlsanity.com/paper/2111.10267/) (2021)
- [Matching Pursuit Based Scheduling for Over-the-Air Federated Learning](https://mlsanity.com/paper/2206.06679/) (2022)
- [Rethinking Federated Learning Over the Air: The Blessing of Scaling Up](https://mlsanity.com/paper/2508.17697/) (2025)
- [Energy-Efficient Over-the-Air Federated Learning via Pinching Antenna Systems](https://mlsanity.com/paper/2602.14250/) (2026)
- [Adaptive Stochastic ADMM for Decentralized Reinforcement Learning in Edge Industrial IoT](https://mlsanity.com/paper/2107.00481/) (2021)
- [Private Federated Learning with Dynamic Power Control via Non-Coherent Over-the-Air Computation](https://mlsanity.com/paper/2308.02881/) (2023)
- [Joint Power Control and Data Size Selection for Over-the-Air Computation Aided Federated Learning](https://mlsanity.com/paper/2308.09072/) (2023)
- [Over-the-Air Computation Aided Federated Learning with the Aggregation of Normalized Gradient](https://mlsanity.com/paper/2308.09082/) (2023)
- [Waveform Design for Over-the-Air Computing](https://mlsanity.com/paper/2405.20877/) (2024)
- [Robust Regression with Ensembles Communicating over Noisy Channels](https://mlsanity.com/paper/2408.10942/) (2024)
- [Wireless Human-Machine Collaboration in Industry 5.0](https://mlsanity.com/paper/2410.14153/) (2024)
- [OptiVote: Non-Coherent FSO Over-the-Air Majority Vote for Communication-Efficient Distributed Federated Learning in Space Data Centers](https://mlsanity.com/paper/2512.24334/) (2025)
- [Logit-Aware MIMO AirComp for Distributed Mixture-of-Experts LLM Inference over Wireless Edge Networks](https://mlsanity.com/paper/2610.03741/) (2026)

## Abstract (arXiv)

For future Internet of Things (IoT)-based Big Data applications (e.g., smart cities/transportation), wireless data collection from ubiquitous massive smart sensors with limited spectrum bandwidth is very challenging. On the other hand, to interpret the meaning behind the collected data, it is also challenging for edge fusion centers running computing tasks over large data sets with limited computation capacity. To tackle these challenges, by exploiting the superposition property of a multiple-access channel and the functional decomposition properties, the recently proposed technique, over-the-air computation (AirComp), enables an effective joint data collection and computation from concurrent sensor transmissions. In this paper, we focus on a single-antenna AirComp system consisting of K sensors and one receiver (i.e., the fusion center). We consider an optimization problem to minimize the computation mean-squared error (MSE) of the K sensors' signals at the receiver by optimizing the transmitting-receiving (Tx-Rx) policy, under the peak power constraint of each sensor. Although the problem is not convex, we derive the computation-optimal policy in closed form. Also, we comprehensively investigate the ergodic performance of AirComp systems in terms of the average computation MSE and the average power consumption under Rayleigh fading channels with different Tx-Rx policies. For the computation-optimal policy, we prove that its average computation MSE has a decay rate of O(1/√K), and our numerical results illustrate that the policy also has a vanishing average power consumption with the increasing K, which jointly show the computation effectiveness and the energy efficiency of the policy with a large number of sensors.