Deep Unfolding for SIM-Assisted Multiband MU-MISO Downlink Systems

To improve the efficiency of scarce radio-frequency (RF) resources in next-generation wireless systems, an intelligent transceiver architecture based on stacked intelligent metasurfaces (SIM) has recently emerged, where multiple programmable metasurface layers are cascaded and each layer comprises passive meta-atoms that perform beamforming directly in the wave domain. In parallel, inter-band carrier aggregation enables multi-band transmission with high spectral efficiency. Their integration in multi-band multiuser downlink transmission is challenging because a single SIM phase configuration must remain effective across all subcarriers, while user scheduling and power allocation vary across scheduling intervals. To address these challenges, we propose an alternating-optimization framework that decomposes the joint design into a power-constrained precoder update and a SIM phase update. For the SIM phase subproblem, we develop a physically consistent multi-band deep-unfolding network (MBDU-Net) that unrolls projected-gradient phase updates into a compact trainable architecture. Each stage computes an analytic gradient from the cascaded SIM channel model and learns lightweight parameters, including per-stage step sizes and band-aware scaling, enabling fast convergence. Numerical results for multi-band multiuser downlink scenarios demonstrate reliable convergence and consistent sum-rate gains on unseen channel realizations.