# A Survey on the Impact of Intelligent Surfaces in the Terahertz Communication Channel Models
## 4 IS-Aided THz Channels
As ISs can reduce the propagation loss with intelligent reflections in order to enhance the end-to-end system performance [28], channel modeling strategies for IS-aided communications systems are fundamental to provide detailed channel characteristics. In that context, [53; 114] evaluated the system performance when the LoS path from the transmitter to the receiver in a downlink THz indoor wireless communication is blocked. The system performance under the phenomenon of the receiver antenna beam misalignment was evaluated in terms of average SNR, ergodic capacity, and OP in [53]. The phase shift that each IS element must impose to steer the radiated beam towards the receiver in terms of the channel attenuation and its cumulative distribution function are presented in [114]. The study in [53] showed that receiver beam misalignment deteriorates the system performance, but increasing the IS size improves overall system performance. The authors in [114] showed the importance of considering the molecular absorption loss for IS-aided THz channel estimation and that there is a minimum transmitter power that can guarantee a high coverage probability. The system was modeled similarly to Figure 3 with the IS placed on the origin of \(x\)-\(y\) plane, the dimensions of the IS elements, denoted by \(d_{x}\) and \(d_{y}\), were in the range \([\lambda/10,\lambda/2]\)[115], and the transmitter and receiver located at distances \(d_{1}\) and \(d_{2}\) from the IS center, respectively. The arrival and departure angles of the signals from the transmitter and to the receiver in relation to the IS center, respectively, were then determined. Based on these assumptions, the resulting expression for the channel gain \(|h|\) at the receiver is given as [53; 114]  
\[|h|=\frac{m_{x}m_{y}\lambda|R|}{8d_{1}d_{2}\sqrt{\pi^{3}}}\sqrt{\tau(f,d_{1}+d _{2})}\sqrt{d_{x}d_{y}F_{1}F_{r}G_{t}G_{r}G_{\text{IS}}(\theta_{r},\phi_{r}+ \epsilon_{r})}, \tag{6}\]  
Figure 5: Example of communication with IS in THz band. in which \(|R|\), \(\tau(\cdot,\cdot)\), \(F_{t}\), \(F_{r}\), \(G_{t}\), \(G_{r}\), \(G_{\rm IS}(\cdot,\cdot)\), \(\theta_{r}\), \(\phi_{r}\), and \(e_{r}\) stand for the amplitude of the programmable reflection coefficient of each IS unit cell, transmittance of the absorbing atmospheric medium [116], transmitter normalized power radiation pattern, receiver normalized power radiation pattern, transmitter antenna gain, receiver antenna gain, an IS unit cell gain, receiver antenna bandwidth, angle of boresight direction, and receiver beam steering error angle, respectively. The IS unit cell gain \(G_{\rm IS}(\cdot,\cdot)\) is calculated as [53]  
\[G_{\rm IS}(\theta_{r},\phi_{r}+e_{r})=\frac{2\pi q_{r}}{\theta_{r}(q_{r}+1)}U \left(\frac{\theta_{r}}{2}-|\phi_{r}+e_{r}|\right)+\frac{2\pi}{(2\pi-\theta_{ r})(q_{r}+1)}U\left(|\phi_{r}+e_{r}|-\frac{\theta_{r}}{2}\right), \tag{7}\]  
in which \(U(\cdot)\), \(q_{r}=\frac{2\pi}{b_{r}(2\pi-\theta_{r})}\), and \(b_{r}\) represent the unit step function, forward-to-backward power ratio, and an antenna specific constant. Physically, it can be seen from the previous expressions that each IS unit cell impacts the channel gain at the receiver by means of their normalized received power ratio, aperture, phase shift, and reflection coefficient (see Appendix A in [114]). THz channels impairments are mainly represented by the transmittance of the absorbing atmospheric medium. Stochastically, the channel gain at the receiver is interpreted as the summation of the order of the IS size of products of channel coefficients between the transmitter and the IS and the IS and the receiver [28]. Mathematically,  
\[|h|=\sum_{i=1}^{N}h_{i}^{\rm Tx}g_{i}h_{i}^{\rm Rx}, \tag{8}\]  
in which \(N\), \(h_{i}^{\rm Tx}\), \(g_{i}\), \(h_{i}^{\rm Rx}\) are the number of IS elements, transmitter to IS channel coefficient, \(i\)-th IS element response, and IS to receiver channel coefficient.