STAR-RIS Assisted Over-the-Air Vertical Federated Learning in Multi-Cell Wireless Networks

Vertical federated learning (FL) is a critical enabler for distributed artificial intelligence services in the emerging 6G era, as it allows for secure and efficient collaboration of machine learning among a wide range of Internet of Things devices. However, current studies of wireless FL typically consider a single task in a single-cell wireless network, ignoring the impact of inter-cell interference on learning performance. In this study, we investigate a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted over-the-air computation based vertical FL system in multi-cell networks, in which a STAR-RIS is positioned at the cell edge to assist in the execution of various FL tasks across multiple cells. We establish the convergence of the proposed system and present the Pareto boundary of the optimality gaps to depict the trade-off between different cells. Based on the analysis, we jointly design the transmit and receive beamforming, as well as the STAR-RIS transmission and reflection coefficient matrices, with the goal of minimizing the aggregate of the gaps of all cells. To address the non-convex resource allocation problem, we employ a successive convex approximation based algorithm. Numerical experiments demonstrate that compared with conventional approaches, the proposed STAR-RIS assisted vertical FL model and the co-operative resource allocation algorithm achieve much lower mean-squared error for both uplink and downlink transmission in multi-cell wireless networks, resulting in improved learning performance for vertical FL.