Two-Level Structured Bayesian Sparse Recovery for Cascaded Uplink Channel Estimation in RIS-Assisted mmWave MIMO Systems

Accurate and efficient channel estimation remains a major challenge in reconfigurable intelligent surface (RIS)-assisted multi-user millimeter-wave (mmWave) MIMO systems, especially under limited pilot resources and low signal-to-noise ratio (SNR) conditions. This paper proposes two advanced algorithms, MAP-TLSOMP and TL-SR-OMP, that jointly exploit the hierarchical sparsity and inter-user common support structures inherent in the cascaded BS–RIS–user channels. The MAP-TLSOMP algorithm integrates Bayesian inference with subspace projections to enhance estimation fidelity, while TL-SR-OMP adopts a lightweight consensus-based refinement strategy to reduce computational complexity. Extensive simulation results reveal that both algorithms significantly outperform conventional techniques such as OMP, SOMP, and DS-OMP in terms of normalized mean squared error (NMSE), particularly in pilot-constrained regimes. TL-SR-OMP offers near-MAP performance while reducing complexity, rendering it an attractive choice for real-time, large-scale deployments. Furthermore, both methods yield notable improvements in average spectral efficiency (ASE) and exhibit robust scalability with increasing user densities. While the evaluation assumes ideal RIS configurations and static channels, the proposed framework offers a promising basis for future enhancements involving dynamic RIS control, mobility, and hardware impairments. Overall, this study contributes an efficient and scalable channel estimation paradigm tailored for next-generation RIS-enabled wireless systems.