STAR-RIS Integrated Nonorthogonal Multiple Access and Over-the-Air Federated Learning: Framework, Analysis, and Optimization

Abstract

This article integrates nonorthogonal multiple access (NOMA) and over-the-air federated learning (AirFL) into a unified framework using one simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). The STAR-RIS plays an important role in adjusting the decoding order of hybrid users for efficient interference mitigation and omnidirectional coverage extension. To capture the impact of nonideal wireless channels on AirFL, a closed-form expression for the optimality gap (also known as the convergence upper bound) between the actual loss and the optimal loss is derived. This analysis reveals that the learning performance is significantly affected by the active and passive beamforming schemes, as well as wireless noise. Furthermore, when the learning rate diminishes as the training proceeds, the optimality gap is explicitly shown to converge with a linear rate. To accelerate convergence while satisfying quality-of-service requirements, a mixed-integer nonlinear programming (MINLP) problem is formulated by jointly designing the transmit power at users and the configuration mode of STAR-RIS. Next, a trust-region-based successive convex approximation method and a penalty-based semidefinite relaxation approach are proposed to handle the decoupled nonconvex subproblems iteratively. An alternating optimization algorithm is then developed to find a suboptimal solution for the original MINLP problem. Extensive simulation results show that: 1) the proposed framework can efficiently support NOMA and AirFL users via concurrent uplink communications; 2) our algorithms achieve a faster convergence rate on independent and identically distributed (IID) and non-IID settings compared to the existing baselines; and 3) both the spectrum efficiency and learning performance are significantly improved with the aid of the well-tuned STAR-RIS.