# RIS-Assisted High-Speed Communications with Time-Varying Distance-Dependent Rician Channels
###### Abstract
Besides, [PERSON] et al. [10] revealed that with the RIS, the SE and the Doppler effect can be respectively maximized and minimized simultaneously. The authors of [11] investigated the impact of hardware impairments (HWI) on the performance of Doppler mitigation by the RIS in HSC. Interestingly, they showed that the HWI enlarges the delay spread of the HSC, but not the ability to mitigate Doppler effects. Moreover, the authors of [12] showed that due to the HWI, a multiple RIS system suffers from a wider delay spread as well as significant degradation of the SE. However, the channel models considered in [10; 11; 12] did not take into account the non-light-of-sight (NLoS), i.e., the Rayleigh component. Besides, it is noteworthy that [7; 8; 9; 10; 11; 12] did not consider distance-dependent Rician factors, which is not practical in HSC systems. This is because the distances of the direct and the cascaded links vary dramatically considering the mobility of the transceiver [6; 13]; it is more practical to include the distance-dependent Rician factor in the channel model for HSC systems. In particular, when the transceivers are far away from one another, the NLoS part dominates the channel, but the light-of-sight (LoS) channel leads when they are close. [PERSON] et al. [14] proposed a continuous time-varying channel model for a satellite communication system with the RIS. This model, however, did not consider the NLoS part. Based on the model in [14], [PERSON] et al. [15] revealed that the Doppler shift (DS) cannot be removed if the direct link exists in an RIS-assisted communication system. However, if the direct link is blocked, the DS can be mitigated totally. [PERSON] [16] showed that the Doppler effect would disappear if there were enough RISs deployed around the scattering environment, but the proposed model is too simple since the author assumed every RIS in the system only contains one reflective element, which cannot beamform the incident signal in reality. Therefore, we consider more practical channel modeling for the RIS-assisted HSC system in this paper. A geometry-based stochastic model (GBSM) has been applied for modeling the RIS-assisted communication system recently [17; 18]. Its computational complexity, however, precludes subsequent research. Similarly, some models are so simple that they cannot reflect the characteristics of the HSC system with RIS [10; 14; 15; 16]. Given this background, in this paper, we first propose a time-varying model for the RIS-aided HSC system containing the NLoS part, the DS term, and the distance-dependent Rician factors. We replace the empirical constants with distance-dependent linear expressions to define the dynamic Rician factors and then analyze the SE and outage probability of the proposed system. Table 1 compares and contrasts our contributions to state-of-the-art RIS-assisted HSC studies. In particular, Refs. [10; 11; 14; 15] did not consider the NLoS part, the DS term, or the distance-dependent Rician factor; [PERSON]. [12; 16; 19] ignored the DS term and the distance-dependent Rician factor. Besides, although [PERSON]. [7; 8] considered the NLoS part and the DS term, they used fixed Rician factors, which are impractical. Moreover, in [17; 18], the authors used the GBSM method to model the channel. However, they also ignored the dynamic Rician factors, and the modeling complexities are very high. The major contributions of this paper are as follows: \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Consider the** & **Consider the** & **Consider the Distance-** & **Modeling** \\  & **NLoS Part?** & **DS Term?** & **Dependent Rician Factor?** & **Complexity** \\ \hline
[10; 11; 14; 15] & No & No & No & Low \\
[12; 16; 19] & Yes & No & No & Low \\
[7] & Yes & Yes & No & Moderate \\
[8] & Yes & Yes & No & High \\
[17; 18] & Yes & Yes & No & High \\ Ours & Yes & Yes & Yes & Low \\ \hline \hline \end{tabular}
\end{table} 
Table 1: State-of-the-art time-varying RIS-assisted HSC models. * We propose a time-varying channel model for RIS-assisted HSC systems.