Super-Resolution Channel Estimation for RIS-Aided Multi-User mmWave Systems: Dictionary Adaptation and Error Modeling

To achieve effective channel estimation for reconfigurable intelligent surface (RIS)-aided multi-user (MU) millimeter wave (mmWave) systems, existing methods commonly exploit the shared RIS-base station (BS) channel characteristic; however, doing so inevitably decomposes estimation of cascaded channels into multiple stages, causing error propagation. To this end, this paper proposes a novel two-stage error-aware super-resolution channel estimation method that leverages the ambiguity and correlation arising from the shared channel, featuring performance enhancement, pilot overhead reduction, and a unique error-aware compensation mechanism. Specifically, in Stage I, the method estimates the common ambiguous RIS-BS channel by exploiting the MU diversity gain. In Stage II, the measurement matrix is constructed using the Stage I estimates, which enables joint space-time measurements and is perturbed by the estimation errors propagated from Stage I. Owing to these two distinctive characteristics, Stage II can use a significantly reduced number of pilots to not only estimate the ambiguous user-RIS channels of all users but, importantly, explicitly and adaptively estimate and then compensate for the shared errors propagated from Stage I via MU diversity gain, thereby effectively addressing error propagation and enhancing overall estimation performance. Accordingly, the MU super-resolution cascaded channel estimation is formulated into two types of tractable nonconvex optimizations, namely nonlinear approximations and joint sparse recovery and dictionary adaptation problems. Grid search-based and majorization-minimization-based solution procedures are developed to efficiently address these two types, respectively. Theoretical analysis of the proposed method is provided, and simulation results are presented to validate its effectiveness, further confirming the performance gains achieved by the unique error-aware compensation mechanism.