Two-Stage Sparse Recovery for Off-Grid Cascaded Channel Estimation in RIS-Assisted mmWave Systems

Accurate cascaded channel estimation is crucial for unlocking the full potential of reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) systems. While compressive sensing reduces pilot overhead, conventional estimators suffer from severe performance degradation due to off-grid leakage induced by the continuous nature of spatial angles. To address this issue, we propose a two-stage channel estimation framework that divides the estimation process into two sequential phases, namely support selection and amplitude recovery. Based on this framework, we design an algorithm termed TS-PO. In the first stage, a preconditioned linear Bregman iteration (PLBI) mechanism is employed to identify the true channel support. Subsequently, the second stage utilizes a localized orthogonal matching pursuit (OMP) refinement to accurately recover the physical channel gains. Simulation results demonstrate the effectiveness of the proposed TS-PO in suppressing off-grid energy leakage. Specifically, it effectively mitigates the estimation error floor, achieves high reconstruction accuracy under stringent pilot overhead constraints, and exhibits strong robustness in dense multipath environments.