In a reconfigurable intelligent surface (RIS) assisted millimeter Wave (mmWave) communication system, the channel coefficient increases exponentially with the number of RIS elements which results in expensive pilot overhead. Most previous works have proposed some channel estimation algorithms for the estimation accuracy of cascaded channels, which have improved the estimation accuracy, but the pilot overhead is discouraging in the estimation process. To improve the channel estimation accuracy with reduced pilot overhead, we propose a two-stage channel estimation protocol by exploiting semi-passive elements and the coherent time difference of the channel, where the quasi-static channel between the base stations (BS) and RIS is estimated at the RIS, and the user (UE)-RIS time-varying channel is estimated at the BS. In the first stage, we formulate the BS-RIS channel estimation as a mathematical optimization problem by an iterative weighting method and then propose a gradient descent (GD)-based algorithm to solve it. In the second stage, we first transform the received the UE-RIS signal model into an equivalent parallel factor (PARAFAC) tensor model and estimate the UE-RIS channel by the least-squares (LS) algorithm. The simulation results show that the proposed method has better estimation accuracy than the LS, compression sensing (CS) and minimum mean square error (MMSE) methods with less pilot overhead, and the spectral efficiency is improved by at least 10.5% compared to the other three methods.
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