# Over-the-Air Computation Systems: Optimal Design with Sum-Power Constraint

arXiv: https://arxiv.org/abs/2005.09139 · HTML: https://mlsanity.com/paper/2005.09139/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2020.

## Built on by (most cited first, 8 of 8)

- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [A Survey on Integrated Sensing, Communication, and Computation](https://mlsanity.com/paper/2408.08074/) (2024)
- [Over-the-Air Computation Based on Balanced Number Systems for Federated Edge Learning](https://mlsanity.com/paper/2210.07012/) (2022)
- [User Scheduling for Federated Learning Through Over-the-Air Computation](https://mlsanity.com/paper/2108.02891/) (2021)
- [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)
- [Over-the-Air Federated Learning with Retransmissions (Extended Version)](https://mlsanity.com/paper/2111.10267/) (2021)
- [Digital Over-the-Air Federated Learning in Multi-Antenna Systems](https://mlsanity.com/paper/2302.14648/) (2023)

## Abstract (arXiv)

Over-the-air computation (AirComp), which leverages the superposition property of wireless multiple-access channel (MAC) and the mathematical tool of function representation, has been considered as a promising technique for effective collection and computation of massive sensor data in wireless Big Data applications. In most of the existing work on AirComp, optimal system-parameter design is commonly considered under the peak-power constraint of each sensor. In this paper, we propose an optimal transmitter-receiver (Tx-Rx) parameter design problem to minimize the computation mean-squared error (MSE) of an AirComp system under the sum-power constraint of the sensors. We solve the non-convex problem and obtain a closed-form solution. Also, we investigate another problem that minimizes the sum power of the sensors under the constraint of computation MSE. Our results show that in both of the problems, the sensors with poor and good channel conditions should use less power than the ones with moderate channel conditions.