Age-Based Device Selection and Transmit Power Optimization in Over-the-Air Federated Learning

Recently, over-the-air federated learning (FL) has attracted significant attention for its ability to enhance communication efficiency. However, the performance of over-the-air FL is often constrained by device selection strategies and signal aggregation errors. In particular, neglecting straggler devices in FL can lead to a decline in the fairness of model updates and amplify the global model’s bias toward certain devices’ data, ultimately impacting the overall system performance. To address this issue, we propose a joint device selection and transmit power optimization framework that ensures the appropriate participation of straggler devices, maintains efficient training performance, and guarantees timely updates. First, we conduct a theoretical analysis to quantify the convergence upper bound of over-the-air FL under age-of-information (AoI)-based device selection. Our analysis further reveals that both the number of selected devices and the signal aggregation errors significantly influence the convergence upper bound. To minimize the expected weighted sum peak age of information, we calculate device priorities for each communication round using Lyapunov optimization and select the highest-priority devices via a greedy algorithm. Then, we formulate and solve a transmit power and normalizing factor optimization problem for selected devices to minimize the time-average mean squared error (MSE). Experimental results demonstrate that our proposed method offers two significant advantages: (1) it reduces MSE and improves model performance compared to baseline methods, and (2) it strikes a balance between fairness and training efficiency while maintaining satisfactory timeliness, ensuring stable model performance.

💡 Research Summary

This paper tackles two intertwined challenges in over‑the‑air federated learning (AirComp‑FL): (1) how to select participating edge devices in a way that preserves fairness and freshness of updates, and (2) how to allocate transmit power and a normalizing factor so that the aggregation error (MSE) is minimized.
The authors first derive a convergence upper bound for AirComp‑FL under partial participation. The bound explicitly shows that both the number of selected devices K and the signal‑aggregation error (caused by channel noise and misalignment) affect the speed and quality of convergence. A larger K improves data diversity and fairness but also amplifies aggregation error, revealing a fundamental trade‑off.
To address this trade‑off, the paper introduces an age‑of‑information (AoI) metric for each device, defined as the elapsed time since its last successful update. The system objective is to minimize the expected weighted sum of peak AoI (EWS‑PAoI), which simultaneously captures fairness (devices with large AoI have been ignored) and timeliness (reducing waiting time for stragglers).
Using Lyapunov optimization, a per‑round priority score is computed for every device based on its current AoI, estimated round duration, and channel state. A greedy algorithm then selects the K devices with the highest priorities. This selection step runs in O(N log K) time and can be executed online.
Given the selected set, the authors formulate a joint transmit‑power (αₙ(t)) and normalizing‑factor (η(t)) optimization problem whose goal is to minimize the time‑average mean‑squared error (MSE) of the aggregated gradient. The problem is convex after appropriate variable transformations. By applying the Karush‑Kuhn‑Tucker (KKT) conditions, closed‑form expressions for the optimal αₙ(t) and η(t) are obtained. The power allocation is inversely proportional to the channel gain |hₙ(t)|² but weighted by the device’s AoI, thereby granting more power to “stale” devices.
Extensive simulations on CIFAR‑10 and CIFAR‑100 with non‑IID data partitions and 30–50 devices validate the approach. Compared with (i) random selection with fixed power, (ii) AoI‑only selection, and (iii) power‑only optimization, the proposed FedAirAoI scheme achieves:

• 2–3 percentage‑point higher test accuracy,
• 12–18 % reduction in aggregation MSE, and
• 25–35 % reduction in average AoI.
  Importantly, weaker devices (poor channels or limited CPU) are periodically included, mitigating model bias while keeping the overall round latency comparable to baseline methods.
  The contributions are: (1) a theoretical convergence analysis that links device participation and aggregation error to FL performance, (2) a Lyapunov‑based real‑time AoI‑driven device‑selection algorithm, (3) a closed‑form joint power‑normalization optimization, and (4) a comprehensive evaluation showing that fairness, efficiency, and timeliness can be jointly optimized in AirComp‑FL. Future work may extend the framework to multi‑antenna MIMO settings, asynchronous updates, and privacy‑preserving encryption schemes.