Two-Stage Deep-Learning-Aided Compressed Sensing for Channel Estimation in STAR–RIS-Assisted mmWave Systems

Channel estimation in simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted millimeter-wave (mmWave) systems faces significant challenges due to numerous cascaded channels and passive STAR-RIS elements. While least squares (LS) methods incur high pilot overhead and compressed sensing (CS) approaches require impractical prior sparsity knowledge, we propose a two-stage deep learning-aided CS (TSDL-CS) framework exploiting the double-structured sparsity of STAR-RIS mmWave channels. The first stage detects the common channel support structure shared across all users, while the second stage refines user-specific features on a reduced sub-matrix. Both stages incorporate specialized attention mechanisms and are followed by a small-scale LS refinement to accurately estimate channels with significantly reduced pilot overhead. To maintain performance in dynamic environments, we introduce hierarchical online adaptive learning enabling real-time updates via lightweight fine-tuning, retraining, and transfer learning. We validate our approach using both statistical channel models and realistic ray-tracing simulations via NVIDIA Sionna across urban, indoor, and suburban scenarios with hardware impairments. Simulation results demonstrate that TSDL-CS significantly outperforms conventional and deep learning baselines, achieving reliable performance with NMSE below -7 dB while reducing the required pilot overhead by 75% compared to conventional LS.