Prediction-and-Repair OMP for Channel Estimation in RIS-Assisted Slowly Time-Varying Sparse mmWave Channel

Abstract

Reconfigurable intelligent surfaces (RISs) are a promising technology for sixth-generation (6G) wireless networks. However, the independent mobility of multiple users and inaccurate prior information can cause the propagation of channel estimation errors in RIS-assisted slowly time-varying sparse cascaded channels. By exploiting the sparsity of the mmWave channel, the cascaded channel is represented in the angular domain with a time-invariant column support induced by the quasi-static RIS–base station (BS) link and a time-varying row support governed by the evolving user–RIS link, whose size changes under a path birth–death process. Based on this structure, we propose a prediction-and-repair Orthogonal Matching Pursuit (PR-OMP) estimator. Our algorithm predicts the current support from the previous block through a bounded candidate shift set and triggers a noise-floor-gated repair stage to correct inaccurate priors and to prevent error propagation in multi-block tracking. Residual-driven retention further adapts the support size to the time-varying path count without requiring it a priori. Simulation results demonstrate that the proposed PR-OMP algorithm achieves significant NMSE improvement with reduced pilot overhead and exhibits robust tracking performance under continuous multi-block channel estimation.