# Digital Over-the-Air Federated Learning in Multi-Antenna Systems

arXiv: https://arxiv.org/abs/2302.14648 · HTML: https://mlsanity.com/paper/2302.14648/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 72 references that are in the map.
- First posted on arXiv 4 Feb 2023.

## Builds on (most cited first, 30 of 35)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Federated Learning for Internet of Things: A Comprehensive Survey](https://mlsanity.com/paper/2104.07914/) (2021)
- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [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)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [Federated Dropout -- A Simple Approach for Enabling Federated Learning on Resource Constrained Devices](https://mlsanity.com/paper/2109.15258/) (2021)
- [Federated Learning over Wireless Device-to-Device Networks: Algorithms and Convergence Analysis](https://mlsanity.com/paper/2101.12704/) (2021)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Federated Learning via Intelligent Reflecting Surface](https://mlsanity.com/paper/2011.05051/) (2020)
- [Federated Edge Learning with Misaligned Over-The-Air Computation](https://mlsanity.com/paper/2102.13604/) (2021)
- [Learning Rate Optimization for Federated Learning Exploiting Over-the-air Computation](https://mlsanity.com/paper/2102.02946/) (2021)
- [Joint Device Selection and Power Control for Wireless Federated Learning](https://mlsanity.com/paper/2205.09306/) (2022)
- [Adaptive Federated Learning With Gradient Compression in Uplink NOMA](https://mlsanity.com/paper/2003.01344/) (2020)
- [Parallel Successive Learning for Dynamic Distributed Model Training over Heterogeneous Wireless Networks](https://mlsanity.com/paper/2202.02947/) (2022)
- [Fast Convergence Algorithm for Analog Federated Learning](https://mlsanity.com/paper/2011.06658/) (2020)
- [Interference Management for Over-the-Air Federated Learning in Multi-Cell Wireless Networks](https://mlsanity.com/paper/2206.02398/) (2022)
- [Random Orthogonalization for Federated Learning in Massive MIMO Systems](https://mlsanity.com/paper/2201.12490/) (2022)
- [Over-the-Air Computation with DFT-spread OFDM for Federated Edge Learning](https://mlsanity.com/paper/2112.13439/) (2021)
- [Over-the-Air Computation Systems: Optimal Design with Sum-Power Constraint](https://mlsanity.com/paper/2005.09139/) (2020)
- [STAR-RIS Integrated Non-Orthogonal Multiple Access and Over-the-Air Federated Learning: Framework, Analysis, and Optimization](https://mlsanity.com/paper/2106.08592/) (2021)
- [Over-the-Air Federated Multi-Task Learning Over MIMO Multiple Access Channels](https://mlsanity.com/paper/2112.13603/) (2021)
- [A Machine Learning Approach for Task and Resource Allocation in Mobile Edge Computing Based Networks](https://mlsanity.com/paper/2007.10102/) (2020)
- [User Scheduling for Federated Learning Through Over-the-Air Computation](https://mlsanity.com/paper/2108.02891/) (2021)
- [Balancing Rates and Variance via Adaptive Batch-Size for Stochastic Optimization Problems](https://mlsanity.com/paper/2007.01219/) (2020)
- [Cluster-Based Cooperative Digital Over-the-Air Aggregation for Wireless Federated Edge Learning](https://mlsanity.com/paper/2008.00994/) (2020)
- [Broadband Digital Over-the-Air Computation for Asynchronous Federated Edge Learning](https://mlsanity.com/paper/2111.10508/) (2021)
- [Energy and Spectrum Efficient Federated Learning via High-Precision Over-the-Air Computation](https://mlsanity.com/paper/2208.07237/) (2022)

## Built on by (most cited first, 1 of 1)

- [Out-of-Air Computation: Enabling Structured Function Extraction from Wireless Superposition](https://mlsanity.com/paper/2604.04312/) (2026)

## Abstract (arXiv)

In this paper, the performance optimization of federated learning (FL), when deployed over a realistic wireless multiple-input multiple-output (MIMO) communication system with digital modulation and over-the-air computation (AirComp) is studied. In particular, a MIMO system is considered in which edge devices transmit their local FL models (trained using their locally collected data) to a parameter server (PS) using beamforming to maximize the number of devices scheduled for transmission. The PS, acting as a central controller, generates a global FL model using the received local FL models and broadcasts it back to all devices. Due to the limited bandwidth in a wireless network, AirComp is adopted to enable efficient wireless data aggregation. However, fading of wireless channels can produce aggregate distortions in an AirComp-based FL scheme. To tackle this challenge, we propose a modified federated averaging (FedAvg) algorithm that combines digital modulation with AirComp to mitigate wireless fading while ensuring the communication efficiency. This is achieved by a joint transmit and receive beamforming design, which is formulated as an optimization problem to dynamically adjust the beamforming matrices based on current FL model parameters so as to minimize the transmitting error and ensure the FL performance. To achieve this goal, we first analytically characterize how the beamforming matrices affect the performance of the FedAvg in different iterations. Based on this relationship, an artificial neural network (ANN) is used to estimate the local FL models of all devices and adjust the beamforming matrices at the PS for future model transmission. The algorithmic advantages and improved performance of the proposed methodologies are demonstrated through extensive numerical experiments.