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In this paper, we investigate the uplink channel estimation problem in intelligent reflecting surface (IRS)-assisted broadband millimeter wave multi-input multi-output communication systems. Considering the channel sparsity in both the angle and delay domains, we decouple the channel estimation problem into several sub-problems, namely, sequential estimations of the angles at the user, the base station, and the IRS, alongside the propagation path delays. By exploiting the Vandermonde structure of both the array manifold and the phase difference among multiple subcarriers caused by delays, we propose a multi-stage atomic norm minimization-based (MS-ANM) channel estimation algorithm. In particular, we take full advantage of the sharing of angle information among all subcarriers in the broadband channel to enhance the estimation accuracy. To reduce the computational complexity, we further propose a multi-stage orthogonal matching pursuit-based (MS-OMP) algorithm. Simulation results show that the MS-ANM algorithm significantly outperforms the benchmark algorithms, and the MS-OMP algorithm strikes a good balance between performance and computational complexity. By fully exploring the channel's sparsity in the angle and delay domains along with the Vandermonde structure, both proposed algorithms remarkably reduce the training overhead and thus greatly improve the spectral efficiency over the benchmark algorithms.
Liu et al. (Tue,) studied this question.