Movable Antenna-Aided Federated Learning with Over-the-Air Aggregation: Joint Optimization of Positioning, Beamforming, and User Selection

Federated learning (FL) in wireless computing effectively utilizes communication bandwidth, yet it is vulnerable to errors during the analog aggregation process. While removing users with unfavorable channel conditions can mitigate these errors, it also reduces the available local training data for FL, which in turn hinders the convergence rate of the training process. To tackle this issue, we propose the use of movable antenna (MA) techniques to enhance the degrees of freedom within the channel space, ultimately boosting the convergence speed of FL training. Moreover, we develop a coordinated approach for uplink receiver beamforming, user selection, and MA positioning to optimize the convergence rate of wireless FL training in dynamic wireless environments. This stochastic optimization challenge is reformulated into a mixed-integer programming problem by utilizing the training loss upper bound. We then introduce a penalty dual decomposition (PDD) method to solve the mixed-integer mixed programming problem. Experimental results indicate that incorporating MA techniques significantly accelerates the training convergence of FL and greatly surpasses conventional methods.