# A Survey on the Impact of Intelligent Surfaces in the Terahertz Communication Channel Models
## 2 IS in Wireless Communication
### IS Operation  
Each IS surface element is considered the same size, i.e., they share the \(\Delta x\) width and \(\Delta y\) height. Also, they contain \(N\) PIN diodes assembled on dielectric substrates that connect the reflective element to the ground when the via hole is electrically charged. The IS element impedance is an association of all layers impedance [75].  
As the IS controller applies a bias voltage to the feeding lines, the IS element is energized across the via hole, and the PIN diodes change their states between \"on\" and \"off\" accordingly. The point in incorporating PIN diodes is to adjust the IS element frequency response dynamically [72]. Figure 2 shows the equivalent circuit for the IS element and both PIN diode states. For a horizontally polarized incident wave, the ground bars around the IS element central patch act as inductors horizontally [68]. With the PIN diode insertion on the IS element, its reverse bias or forward equivalent circuits can be applied to estimate the transmission coefficient and 3 dB cut-off angular frequency of the IS element.  
The combination of the \(N\) PIN diode states leads to distinct phase shifts for each IS element. As the signal arrives at the IS element, two other signals are formed: the transmissive and reflective signals. There are \(2^{N}\) possible phase shifts within the angle of \(2\pi\) rad [88]. Say, a signal arrives at the IS \(k\)-th element within the direction \(\xi_{\rm A}(k)=(\theta_{\rm A}(k),\phi_{\rm A}(k))\), the corresponding reflected or transmitted signal is redirected by a phase shift \(\psi(k)\), obtained from the combination of the IS \(k\)-th element PIN diode states, such that the departure direction is \(\xi_{\rm D}(k)=(\theta_{\rm D}(k),\phi_{\rm D}(k))\). The IS element phase shift determines the transmissive and reflective signal directions concurrently. Figure 3 illustrates the angles of arrival and departure for a signal reaching an IS \(k\)-th element. The phase shift imposed by every IS element accounts for the IS surface phase shift. If there are \(m\) IS elements, the phase shifts of the IS surface can be written as the vector \(\phi_{\rm IS}=[\phi_{\rm D}(1),\ldots,\phi_{\rm D}(m)]\).  
Figure 3: Angles of arrival and departure for a signal reaching the IS \(k\)-th element.  
Figure 2: IS element and PIN diode state equivalent circuits.  
The influence of the IS \(k\)-th element over the upcoming signal was experimentally obtained as a function of the arrival direction, departure direction, and the phase shift as [88]  
\[g_{k}(\xi_{\rm A}(k),\ \xi_{\rm D}(k),\psi(k))=\sqrt{G_{k}K_{\rm A}(k)K_{\rm D}(k) \Delta x\Delta y|\gamma_{k}|^{2}}e^{-j\psi(k)}, \tag{1}\]  
in which \(G_{k}\) is the antenna gain of the IS \(k\)-th element, \(\gamma_{k}\) is the power ratio of the departure signal to the arrival signal, and \(K_{\rm A}(k)\) and \(K_{\rm D}(k)\) are the normalized power radiation pattern of the arrival signal and departure signal, respectively. This influence is a complex number that forces a gain and phase shift to the departure signal.