To meet the increasing demands for high data rates and large capacity, next generation wireless communication systems require transceivers equipped with a large number of antennas. Massive multiple-input multiple-output (MIMO) with metasurface antennas has emerged as a promising solution. In this paper, we investigate the channel estimation problem for the emerging reconfigurable intelligent metasurface antenna (RIMSA) array systems. Specifically, we develop a two-stage refinement (TSR) channel estimation method based on the compressed sensing (CS) principle. In the first stage, we exploit the antenna structure of RIMSA to receive pilots by setting identical phase response vectors across all RIMSAs. In this manner, the coherence of the measurement matrix under the CS framework is reduced and the channel estimation performance is improved. However, this special design introduces channel direction-of-arrival (DoA) estimation ambiguity and yields an ambiguous candidate DoA set. In the second stage, we optimize the phase responses of the metamaterial elements to resolve the ambiguity and accurately estimate the DoAs and channel coefficients. Overall, the estimation accuracy is improved in the first stage at the cost of ambiguity, and this ambiguity is eliminated in the second stage. We illustrate the performance advantages of the TSR method by presenting the numerical results and comparing it with the existing methods.

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