# Distributed Interference-Aware Power Optimization for Multi-Task Over-the-Air Federated Learning
### Contributions  
This paper proposes an interference-aware distributed power control scheme tailored for parallel multi-task Air-FL scenarios. By leveraging the local CSI and IT constraints to enable each cell to autonomously manage its transmit power, our approach mitigates inter-cell interference and enhances overall system performance. Through rigorous analysis and extensive simulations, we demonstrate that our proposed scheme achieves near-optimal performance, which offers a practical and scalable solution for interference management in multi-cell Air-FL deployments. The primary contributions of this work are as follows:  
* **System modeling and centralized optimization**: We construct a multi-cell parallel Air-FL system model, detail the AirComp architecture between devices and APs, and establish the interference mechanisms under shared spectrum conditions. We analyze the impact of aggregation errors on the convergence of the optimality gap and formulate a power control optimization problem aimed at minimizing the total optimality gap across all cells. To characterize performance trade-offs, we employ the Pareto boundary theory and design a centralized power control algorithm to delineate the Pareto boundary. * **Distributed optimization via IT**: We propose a distributed optimization scheme based on IT, which decouples the globally coupled problem into locally solvable subproblems. Each cell independently adjusts its transmit power using local CSI. To address the non-convexity of the subproblems, we first transform them into convex \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Focuses** & **Contributions** & **Limitations** \\ \hline \multirow{3}{*}{[19]} & Achieved efficient downlink and & Constructed the Pareto boundary & Do not fully consider the \\  & uplink model aggregation in & to characterize performance & long-term effect of cumulative \\  & multi-cell Air-FL. & trade-offs among multiple tasks. & aggregation errors \\  & & & on convergence. \\ \hline \multirow{3}{*}{[20]} & Addressed inter-cell interference & Characterized Pareto-optimal & \multirow{3}{*}{Assumed low noise, neglected} \\  & in multi-cell using & gaps for inter-cell trade-offs and & higher-order errors, and \\  & simultaneously transmitting and & demonstrated mean squared & \\  & reflecting reconfigurable & error (MSE) reduction in & experimented only cover \\  & intelligent surface (STAR-RIS) & uplink/downlink & two-cell networks. \\  & assisted Air-FL. & via experiments. & \\ \hline \multirow{3}{*}{[21]} & Addressed data heterogeneity in & Derived the convergence bound & \multirow{3}{*}{AF with lower communication} \\  & hierarchical FL. & under inter-cluster interference & \\  & and data heterogeneity. & & overhead was not considered. \\ \hline \multirow{3}{*}{[22]} & Optimized the learning & Derived the impact of & \multirow{3}{*}{The impact of inter-cluster interference was not considered.} \\  & performance of two-tier Air-FL. & aggregation errors on & interference was not considered. \\  & convergence performance. & & \\ \hline \multirow{3}{*}{[23]} & Addressed the issues of low & Proposed a compressed & \multirow{3}{*}{Intra-group nodes require strict} \\  & communication efficiency and & sensing-based Air-FL framework & synchronization; \\  & weak privacy protection in & to achieve efficient and secure & \multirow{3}{*}{\
\begin{tabular}{} \end{tabular} } \\  & Air-FL spectrum sharing. & aggregation that is & \\  & Air-FL spectrum sharing. & noise-free/encryption-free. & \\ \hline \multirow{6}{*}{[24]} & \multirow{3}{*}{Optimized the joint edge & Proposed a theoretically & \multirow{3}{*}{
\begin{tabular}{} \end{tabular} } \\  & & guaranteed two-stage search & \\ \cline{1-1}  & aggregation and association & & \\ \cline{1-1}  & decision-making for Air-FL. & & \\ \cline{1-1} \cline{2-5}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of related work.