Over-the-Air Multitask Federated Learning via Cost-Effective Hybrid Beamforming

Over-the-air computation (AirComp) has recently emerged as a pivotal technique for communication-efficient federated learning (FL) in resource-constrained wireless networks. Though AirComp leverages the superposition property of multiple access channels for computation, it inherently limits its ability to manage inter-task interference in multi-task computing. In this paper, we propose a cost-effective hybrid beamforming scheme at the receiver to enable simultaneous multi-task FL, where analog and digital beamforming are respectively designed for statistical long-term inter-task interference elimination and instantaneous cooperative interference management. Specifically, inspiring by the favorable propagation and channel hardening properties of large-scale antenna arrays, we first propose an analog beamforming method for statistical interference elimination. Analytical results reveal that the interference power decays at an order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal{O}\left(1/N_{r}\right)$</tex-math></inline-formula> with respect to the number of analog phase shifters, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N_{r}$</tex-math></inline-formula>, even under imperfect channel estimation, and remains unaffected by the quantization precision of the phase shifters. Furthermore, focusing on FL convergence performance, we formulate a joint optimization of transmit power and digital combiner to balance the tradeoff between multiple FL tasks. To address coupled variables, we derive the optimal digital combiner in closed form, facilitating the problem transformation into a pure power optimization. Given its nonconvex form, successive convex approximation (SCA) is adopted with a convergence guarantee to a stationary solution. Numerical results demonstrate the effectiveness of the proposed hybrid beamforming method and show that the performance upper bound of ideal learning without errors can be achieved by increasing the number of low-precision analog phase shifters.