  This paper integrates non-orthogonal 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 omni-directional coverage
extension. To capture the impact of non-ideal wireless channels on AirFL, a
closed-form expression for the optimality gap (a.k.a. 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 linear rate. To accelerate convergence while
satisfying quality-of-service requirements, a mixed-integer non-linear
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
non-convex subproblems iteratively. An alternating optimization algorithm is
then developed to find a suboptimal solution for the original MINLP problem.
Extensive simulation results show that i) the proposed framework can
efficiently support NOMA and AirFL users via concurrent uplink communications,
ii) our algorithms achieve faster convergence rate on IID and non-IID settings
compared to existing baselines, and iii) both the spectrum efficiency and
learning performance is significantly improved with the aid of the well-tuned
STAR-RIS.
