  In wireless systems aided by reconfigurable intelligent surfaces (RISs),
channel state information plays a pivotal role in achieving the performance
gain of RISs. Mobility renders accurate channel estimation (CE) more
challenging due to the Doppler effect. In this letter, we propose two practical
wideband CE schemes incorporating Doppler shift adjustment (DSA) for multi-path
and single-path propagation environments, respectively, for RIS-assisted
communication with passive reflecting elements. For the multi-path scenario,
ordinary CE is first executed assuming quasi-static channels, followed by DSA
realized via joint RIS reflection pattern selection and transformations between
frequency and time domains. The proposed CE necessitates only one more symbol
incurring negligible extra overhead compared with the number of symbols
required for the original CE. For the single-path case which is especially
applicable to millimeter-wave and terahertz systems, a novel low-complexity CE
method is devised capitalizing on the form of the array factors at the RIS.
Simulation results demonstrate that the proposed algorithms yield high CE
accuracy and achievable rate with low complexity, and outperform representative
benchmark schemes.
