## 2 System Model
### Channel Model  
Even though mmWave and THz bands share a few similarities, the THz channel presents several unique features that differentiate it from the mmWave channel. In the THz band, the very high scattering and diffraction losses tend to result in a much sparser channel  
Figure 2: Different precoder architectures for a mmWave/THz MIMO system based on phase shifters.  
in the angular domain with fewer multipath components (typically less than 10) [20]. Because of the referred phenomenon, the gap between the line of sight (LOS) and non-line of sight (NLOS) components tends to be very large, which often makes LOS-dominant with NLOS-assisted [28]. An additional aspect relies on the much larger bandwidth of THz signals which can suffer performance degradation due to the so-called beam split effect, where the transmission paths squint into different spatial directions depending on the subcarrier frequency [29]. In light of this, in this paper, we consider a clustered wideband geometric channel, which is commonly adopted both in mmWave [12] and THz literature [5; 6; 30; 31]. However, it should be noted that the hybrid precoding/combining approach proposed in this paper is independent of a specific MIMO channel. In this case, the frequency domain channel matrices can be characterized as:  
\[\begin{split}&\mathbf{H}_{k,u}=\gamma\Big{(}\alpha_{u}^{LOS} \mathbf{a}_{r}\Big{(}\phi_{u}^{r,LOS},\theta_{u}^{r,LOS}\Big{)}\mathbf{a}_{l} \Big{(}\phi_{u}^{t,LOS},\theta_{u}^{t,LOS}\Big{)}^{H}+\\ &+\sum\limits_{i=1}^{N_{cl}}\sum\limits_{l=1}^{N_{ray}}\alpha_{i, l,u}\mathbf{a}_{r}\Big{(}\phi_{i,l,u}^{r},\theta_{i,l,u}^{r}\Big{)}\mathbf{a}_{l} \Big{(}\phi_{i,l,u}^{t},\theta_{i,l,u}^{t}\Big{)}^{H}\Big{)}e^{-j2\pi\tau_{i,u }f_{i}},\end{split} \tag{7}\]  
where \(N_{cl}\) denotes the number of scattering clusters with each cluster \(i\), with a time delay of \(\tau_{i,u}\) and \(N_{ray}\) is the number of propagation paths per cluster. \(\alpha_{u}^{LOS}\) and \(\alpha_{i,l,u}\) are the complex gains of the LOS component and of the \(l\)th ray from cluster \(i\). Index \(u\) is the user (\(u=1,\ldots,N_{u}\)), \(f_{k}=f_{c}+\frac{B}{F}\Big{(}k-1-\frac{F-1}{2}\Big{)}\) (\(k=1,\ldots,F\)) is the \(k\)th subcarrier frequency, \(B\) is the bandwidth, \(f_{c}\) is the central frequency and \(\gamma\) is a normalizing factor \(\mathbb{E}\Big{[}\|\mathbf{H}_{k,u}\|_{F}^{2}\Big{]}=N_{tx}N_{rx}\). Vectors \(\mathbf{a}_{t}\Big{(}\phi_{i,l,u}^{t},\theta_{i,l,u}^{t}\Big{)}\) and \(\mathbf{a}_{r}\Big{(}\phi_{i,l,u}^{r},\theta_{i,l,u}^{r}\Big{)}\) represent the transmit and receive antenna array responses at the azimuth and elevation angles of \(\Big{(}\phi_{i,l,u}^{t},\theta_{i,l,u}^{t}\Big{)}\) and \(\Big{(}\phi_{i,l,u}^{r},\theta_{i,l,u}^{r}\Big{)}\), respectively. Vectors \(\mathbf{a}_{t}\Big{(}\phi_{u}^{t,LOS},\theta_{u}^{t,LOS}\Big{)}\) and \(\mathbf{a}_{r}\Big{(}\phi_{u}^{r,LOS},\theta_{u}^{r,LOS}\Big{)}\) have similar meanings but refer to the LOS path angles \(\Big{(}\phi_{u}^{t,LOS},\theta_{u}^{t,LOS}\Big{)}\) and \(\Big{(}\phi_{u}^{r,LOS},\theta_{u}^{r,LOS}\Big{)}\). By carefully selecting the parameters of the channel model it is possible to make it depict a mmWave or a THz channel. As represented in (7), this channel model includes both LOS and NLOS components. In the case of the NLOS components, we consider complex Gaussian distributed paths gains, as in [32]. Radio propagation measurements have shown that this type of cluster-based channel model can yield good agreements with real channel behavior at mmWave and subTHz frequencies [33].