Deep Unfolding for Joint Antenna Selection, Phase Shift Design, and Power Allocation in SIM-Assisted MU-MISO Systems

Abstract

Stacked intelligent metasurfaces (SIMs) have emerged as a promising paradigm for wave-domain signal processing in next-generation wireless networks. In this paper, we investigate the joint optimization of antenna selection, SIM phase-shift design, and power allocation in SIM-assisted multiuser multiple-input single-output (MU-MISO) systems to maximize the achievable downlink sum rate. To handle the resulting mixed discrete-continuous constraints, we introduce differentiable reparameterizations and derive analytical gradients for the three coupled variable blocks under the cascaded multilayer propagation model. Building on these physics-aware gradient directions, we propose a model-driven unrolled full-gradient optimization (UFGO) network that unfolds the analytical joint-gradient update process into a trainable architecture with a fixed number of unfolded layers. Each unfolded layer performs learnable block-specific updates guided by the physics-aware analytical gradients and employs differentiable reparameterizations to preserve variable feasibility, thereby enabling efficient online inference while retaining the interpretability of model-based optimization. Simulation results show that UFGO achieves sum-rate performance comparable to the high-iteration FGJO benchmark while requiring substantially lower runtime than the high-iteration AO and FGJO methods. Comparisons with the corresponding variants without antenna selection further demonstrate the performance benefit of adaptive antenna selection. Additional evaluations under electromagnetic propagation model mismatch, imperfect channel state information (CSI), and frequency-selective fading demonstrate the performance resilience of UFGO under practical model and channel uncertainties, supporting its applicability to latency-sensitive SIM configuration.