Doppler Shift and Channel Estimation for Intelligent Transparent Surface Assisted Communication Systems on High-Speed Railways

The emerging intelligent transparent surface (ITS), unlike the intelligent reflection surface (IRS), allows incident signals to penetrate it instead of being reflected, which enables the ITS to combat the severe signal penetration loss for high-speed railway (HSR) wireless communications. This paper thus investigates the channel estimation problem where the ITS is attached to the HSR carriage window. We first propose a new transmission scheme with two pilot blocks for each frame. Second, we formulate the channels as functions of physical parameters and thus transform the problem into a parameter recovery problem. Third, we develop a successive closed-form, maximum likelihood (ML) channel estimation algorithm. Specifically, each estimate is expressed as the sum of its perfectly known value and the estimation error. By leveraging the relationship between channels for the two pilot blocks, we eliminate the unknown parameters besides Doppler shifts, which can be thereby recovered. With the reconstructed Doppler-induced phase shifts, we acquire other channel parameters. Moreover, the Cramér-Rao lower bound (CRLB) for each parameter is derived as a performance benchmark. Finally, we provide numerical results to establish the effectiveness of our proposed estimators.