# A Survey on the Impact of Intelligent Surfaces in the Terahertz Communication Channel Models
## 4 IS-Aided THz Channels
The application of holographic ISs in the THz mMIMO systems is proposed in [52], where the channel is modeled considering the IS-aided THz mMIMO system over a frequency-selective fading channel. Based on the Fourier transform, the authors introduce an angular domain beamforming framework and obtain closed-form expressions for the beamforming design in two specific cases. In order to reduce the uplink pilot-overhead, a compressed sensing-based channel estimation algorithm is proposed, where the sparsity of the THz MIMO channel is exploited in both the angular domain and the delay domain. They consider the system operating in time division duplex (TDD) mode and consequently assume channel reciprocity between uplink and downlink. This work shows the effectiveness of the holographic IS on THz MIMO channels supporting THz mMIMO systems. In [50], the small-scale amplitude fading of THz signals is modeled with the help of previous measurement data by using the fluctuating two-ray (FTR) distributions [126]. FTR fading model can fit the signal amplitude fading of THz communication in the IS-aided channel modeling. A swarm intelligence algorithm obtains the phase shifts under discrete phase-shift constraints. Essential performance metrics were obtained based on real THz signal measurements, essential performance metrics were obtained, including the OP and ergodic capacity. The authors derived expressions of OP for a IS-aided THz communications system. They obtained an expression for ideal radio frequency chains for the ergodic capacity. A THz IS can establish favorable wireless channel responses by controlling the multipath and the diversity of the wireless propagation environment through its elements. By exploiting unmanned aerial vehicle (UAV), real-time adjustments can effectively mitigate the multipath and Doppler effects caused by the movement. The authors in [54] jointly optimized the UAVs trajectory, the continuous phase shift of IS, power control, and the allocation of THz sub-bands. They determined the UAV trajectory and IS phase-shift by closed-form expressions using a successive convex approximation (SCA) algorithm [127]. The mobility of devices challenges the THz link reliability and THz network performance. By directing beams toward the receiver to enable THz communication links, ISs can solve those issues and ensure mobile THz communication. Thus, the feasibility of mobile THz wireless communication systems of the THz links has been one of the pressing as well as challenging research targets. Considering satellite networks, Ref. [128] showed that the integration of IS and low Earth orbit satellites can create a sophisticated architecture to operate at 350 GHz that can improve the SNR with the increasing of IS elements. In [128], the authors concluded that the error rate performance is proportional to the number of IS elements and satellites in the form of \(P_{e}\propto N^{2M}\), where \(P_{e}\), \(N\), and \(M\) are the bit error rate, number of IS elements, and the number of satellites, respectively. Table 2 compares the related articles and explores some aspects of the THz communication channels. The topics cover channel modeling characteristics at THz band, including performance evaluation models, system setup for performing channel design objectives, and channel optimization techniques. \begin{table}
\begin{tabular}{c c c c c} \hline
**Reference** & **Performance Evaluation** & **System Model** & **Design Objective** & **Optimization Techniques** \\ \hline \multirow{4}{*}{[29]} & & & Maximize signal reflection & \\  & & & and restore LoS link & \\  & & & between the transmitter & \\  & & & and receiver blocked & \\  & & & by obstacles & \\ \hline \multirow{2}{*}{[30]} & Adaptively selecting & & & Spectral efficiency with \\  & step size & & & phase shift adjust & \\ \hline \multirow{2}{*}{[31]} & & & Expression that & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\