Two-level structured Bayesian sparse recovery for cascaded uplink channel estimation in RIS-assisted mmWave MIMO systems

Abstract

Accurate and efficient channel estimation remains a major challenge in reconfigurable intelligent surface (RIS)-assisted multi-user millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems, especially under limited pilot resources and low signal-to-noise ratio (SNR) conditions. This paper proposes two novel structured channel estimation algorithms for RIS-assisted multi-user mmWave MIMO systems: Maximum A Posteriori Two-Level Structured Orthogonal Matching Pursuit (MAP-TLSOMP) and Two-Level Structured Refinement Orthogonal Matching Pursuit (TL-SR-OMP). Unlike prior work, our approach explicitly models both hierarchical sparsity and inter-user common support, providing robust, scalable recovery even under severe pilot and SNR constraints. 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 simulations show both algorithms yield significant normalized mean squared error (NMSE) and average spectral efficiency (ASE) gains over existing methods (such as Orthogonal Matching Pursuit (OMP), Simultaneous OMP (SOMP), Double-Structured OMP (DS-OMP) and Bayesian Fast Variational Block Sparse Bayesian Learning (Bayesian-FVBSBL)), with TL-SR-OMP uniquely offering a practical trade-off between accuracy and complexity ideal for large-scale deployments. Furthermore, both methods yield notable improvements in 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.