Beamforming Design for Multi-Sector BD-RIS Assisted FL with AirComp

Federated learning (FL) is a promising approach that effectively and securely harnesses the vast amounts of data generated by the rapid proliferation of internet-connected devices. In FL, the transmission of model parameters over wireless channels plays a pivotal role in determining system performance. To optimize the wireless environment and boost communication efficiency, we present a novel FL beamforming design scheme that integrates multi-sector beyond diagonal reconfigurable intelligent surfaces (BD-RIS) with over-the-air computation (AirComp). The scheme leverages the waveform superposition property of wireless signals, using AirComp to rapidly aggregate the global model in FL. Additionally, the scheme utilizes BD- RIS to flexibly manip-ulate communication beams, improving user channel conditions and further reducing model aggregation errors. Specifically, we evaluate the impact of this design on FL systems and derive an upper limit on the gap between training loss and optimal loss. To minimize this gap, we formulate a joint optimization problem of BD- RIS passive beamforming and base station receive beamforming, and we propose an optimization algorithm based on successive convex approximation (SCA) and block coordinate descent (BCD) to solve it. Simulation results confirm that our de-sign significantly enhances user channel conditions and improves FL performance, with the benefits becoming more pronounced as the number of BD- RIS reflecting elements increases.