Secure Energy-Efficient Uplink Transmission in Movable-Element RIS-aided Systems with Movable Antennas and Artificial Noise

Abstract

Secure energy efficiency (SEE) has emerged as a key performance metric for next-generation wireless networks, where energy sustainability and information security must be jointly guaranteed. This paper investigates secure uplink transmission in a full-duplex (FD) base station (BS) system equipped with movable antennas (MAs) and assisted by a movable-element reconfigurable intelligent surface (ME-RIS) in the presence of multiple cooperative passive eavesdroppers. The objective is to maximize SEE by jointly optimizing the users'transmit powers, BS receive postcoders, artificial noise (AN) transmit power and beamforming, RIS phase shifts, and the two-dimensional positions of both the BS antennas and RIS elements. The resulting optimization problem is highly nonconvex due to the fractional SEE objective, coupled secrecy-rate expressions, residual self-interference (SI), unit-modulus RIS phase-shift constraints, movable-position constraints, inter-element spacing requirements, and the nonlinear dependence of the channels on the movable antenna and RIS-element positions. To address these challenges, we propose a hybrid gradient-based meta-learning (H-GML) framework. In the proposed method, the BS receive postcoders and AN direction are updated using closed-form solutions derived from generalized Rayleigh quotient formulations, while the remaining coupled variables are updated by neural meta-optimizers that learn gradient-based update directions directly from the SEE optimization objective without requiring offline labeled training data. Simulation results show that the proposed H-GML design achieves better performance than the AO benchmark and significantly outperforms fixed-geometry, random RIS, no-AN, and no-Eve-knowledge baselines.