Reconfigurable intelligent surfaces (RISs) have been proposed recently as an enabling technology for tuning the wireless propagation channel between transceivers. To realize RISs advantages, however, accurate channel state information is required. In this paper, we consider a single-user RIS-aided system model and propose a two-stage high-resolution channel parameter estimation framework termed TRICE that exploits the low-rank nature of millimeter-wave MIMO channels. In both stages, we formulate the channel parameter estimation problem as a 2D direction-of-arrival estimation problem, for which several solution methods exist in the literature. Based on this formulation, we resort to a 2D DFT beamspace ESPRIT method to estimate the angular parameters of the involved communication channels. Our numerical results show that the proposed TRICE framework has a lower training overhead, as compared to benchmark methods, which makes it appealing in practical applications.

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In this work, we consider both channel estimation and reflection design problems in point-to-point reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) MIMO communication systems. First, we show that by exploiting the low-rank nature of mmWave MIMO channels, the received training signals can be written as a low-rank multiway tensor admitting a canonical polyadic (CP) decomposition. Utilizing such a structure, a tensor-based RIS channel estimation method (termed TenRICE) is proposed, wherein the tensor factor matrices are estimated using an alternating least squares method. Using TenRICE, the transmitter-to-RIS and the RIS-toreceiver channels are efficiently and separately estimated, up to a trivial scaling factor. After that, we formulate the beamforming and RIS reflection design as a spectral efficiency maximization problem. Due to its non-convexity, we propose a heuristic noniterative two-step method, where the RIS reflection vector is obtained in a closed form using a Frobenius-norm maximization (FroMax) strategy. Our numerical results show that TenRICE has a superior performance, compared to benchmark methods, approaching the Cramér-Rao lower bound with a low training overhead. Moreover, we show that FroMax achieves a comparable performance to benchmark methods with a lower complexity.