Efficient STAR-RIS Mode for Energy Minimization in WPT-FL Networks with NOMA

With the massive deployment of Internet of Things (IoT) devices in sixth-generation networks, several critical challenges have emerged, such as large communication overhead, coverage limitations, and limited battery lifespan due to high energy consumption. Federated learning (FL), wireless power transfer (WPT), multi-antenna access point (AP), and reconfigurable intelligent surfaces (RIS) can mitigate these challenges by reducing the need for large data transmissions, enabling sustainable energy harvesting, and optimizing the propagation environment. Compared to conventional RIS, simultaneously transmitting and reflecting (STAR)-RIS not only extends coverage from half-space to full-space but also improves energy saving through appropriate mode selection. Motivated by the need for sustainable, low-latency, and energy-efficient communication in large-scale IoT networks, this paper investigates the efficient STAR-RIS mode in the uplink and downlink phases of a WPT-FL multi-antenna AP network with non-orthogonal multiple access to minimize energy consumption, a joint optimization that remains largely unexplored in existing works on RIS or STAR-RIS. We formulate a non-convex energy minimization problem for different STAR-RIS modes, i.e., energy splitting (ES) and time switching (TS), in both uplink and downlink transmission phases, where STAR-RIS phase shift vectors, beamforming matrices, time and power for harvesting, uplink transmission, and downlink transmission, local processing time, and computation frequency for each user are jointly optimized. To tackle the non-convexity, the problem is decoupled into two subproblems: the first subproblem optimizes STAR-RIS phase shift vectors and beamforming matrices across all WPT-FL phases using block coordinate descent over either semi-definite programming or Rayleigh quotient problems, while the second one allocates time, power, and computation frequency via the one-dimensional search algorithms or the bisection algorithm. Simulation results demonstrate that TS STAR-RIS in both uplink and downlink transmissions achieves the lowest energy consumption, outperforming ES and conventional RIS schemes due to its flexible phase shift adaptation and lower interference levels.