# A Survey on the Impact of Intelligent Surfaces in the Terahertz Communication Channel Models
## 3 THz Channel Modeling
### Deterministic Channel Model for THz Band  
Generally, the two deterministic models found in the literature are the ray-tracing (RT) and the finite-difference time domain (FDTD) models [95; 96; 97; 98]. These deterministic channel models are based on the theory of electromagnetic waves. However, their properties depend on the materials, propagation medium, and spatial positions of transmitter and receiver antennas. In this subsection, the RT is explored firstly and the FDTD secondly. Wireless communication channels are well-known to be subjected to the multipath phenomenon [99; 100]. This phenomenon occurs when the transmitted radio signal finds multiple paths between the transmitter and the receiver. However, its occurrence is connected to the propagation environment and the obstacles between the transmitter and receiver. Figure 4 shows from a pictorial perspective the main propagation phenomena. Figure 4: The ray-tracing method for deterministic channel modeling. As mentioned before, the RT technique analyzes the propagation of electromagnetic waves for each of these geometric paths. The absorption by water vapor molecules is one of the main factors that affect the propagation of waves in the THz band [101]. In addition to introducing thermal noise, absorption causes an attenuation of the signal sent to the receiver. As occurs in the most explored bands, also in the THz band, the propagation in free space must consider the propagation loss. Complete ray tracing models were developed for 0.06-10 THz [95] and 0.3 THz [96] frequency bands, respectively. According to [95], the THz channel band can be modeled as the superposition of line of sight (LoS), reflected, scattered, and diffracted waves attenuation related to many individual sub-bands. Furthermore, the propagation delay experienced by each wave is taken into account as per the path it traverses. The LoS channel transfer function can be represented by  
\[H_{\text{LoS}}(f)=H_{\text{Spr}}(f)H_{\text{Abs}}(f)e^{-\jmath\pi f\tau_{ \text{LoS}}}, \tag{2}\]  
where \(H_{\text{Spr}}(f)\) is a spreading loss function, \(H_{\text{Abs}}(f)\) is a molecular absorption loss function, \(\tau_{\text{LoS}}\) is the delay and \(f\) is the observed frequency. The channel transfer function of the reflected rays can be written according to  
\[H_{\text{Ref}}(f){=}\bigg{(}\frac{c}{4\pi f(r_{1}+r_{2})}\bigg{)}e^{-\jmath \pi f\tau_{\text{Ref}}-\frac{1}{2}k(f)(r_{1}+r_{2})}R(f), \tag{3}\]  
in which \(c\) is the speed of light, \(\tau_{\text{Ref}}\) is the time-of-arrival of the reflected ray, \(r_{1}\) is the distance between the transmitter and the reflector, \(r_{2}\) the distance between the reflector and the receiver, \(R(f)\) is the reflection coefficient, and \(k(f)\) is the absorption loss. The channel transfer function of the scattered ray propagation is  
\[H_{\text{Sca}}(f){=}\bigg{(}\frac{c}{4\pi f(s_{1}+s_{2})}\bigg{)}e^{-\jmath \pi f\tau_{\text{Sea}}-\frac{1}{2}k(f)(s_{1}+s_{2})}S(f), \tag{4}\]  
where \(\tau_{\text{Sea}}\) is the time-of-arrival of the scattered ray, \(s_{1}\) is the distance between the transmitter and the scattering point, \(s_{2}\) is the distance between the scattering point and the receiver, and \(S(f)\) is the scattering coefficient. Finally, the transfer function of the channel in the diffraction ray can be written as  
\[H_{\text{Diff}}(f){=}\bigg{(}\frac{c}{4\pi f(d_{1}+d_{2})}\bigg{)}e^{-\jmath \pi f\tau_{\text{Diff}}-\frac{1}{2}k(f)(d_{1}+d_{2})}L(f), \tag{5}\]  
in which \(\tau_{\text{Diff}}\) is the time of arrival of the diffracted ray, \(d_{1}\) is the distance between the transmitter and the diffracting point, \(d_{2}\) is the distance between the diffracting point and the receiver, and \(L(f)\) is the diffracting coefficient. Those different signal components are added to the receiver in the RT technique. Another way of characterizing THz waves is through [PERSON]'s equations [102].