## 2 System Model  
### Transmitter and Receiver Model  
Let us consider a mmWave/THz hybrid MU-MIMO system, where an AP is equipped with \(N_{tx}\) antennas that transmit to \(N_{u}\) users simultaneously over \(F\) carriers. Each user is equipped with \(N_{tx}\) antennas that transmit to \(N_{u}\) users simultaneously. Each user is equipped with \(N_{rx}\) antennas over \(F\) carriers, such as the one described in Figure 1. \(N_{s}\) data streams are transmitted to each user and to each subcarrier, which can be represented as \(\mathbf{s}_{k}=\left[\mathbf{s}_{k,1}{}^{T}\dots\mathbf{s}_{k,N_{u}}{}^{T} \right]^{T}\), with \(\mathbf{s}_{k,u}\in\mathbb{C}^{N_{k}\times 1}\). Since a fully digital design would require a dedicated RF chain per antenna element, both the digital and analog processing blocks of the precoder and combiner are separated. By following this approach, it is possible to use reduced digital blocks with only a few radio frequency (RF) chains, which can be complemented by the analog blocks that are based on networks of phase-shifter and switches solely. It is assumed that \(N_{u}N_{s}\leq N_{RF}^{tx}\leq N_{tx}\) and \(N_{s}\leq N_{RF}^{rx}\leq N_{rx}\), where \(N_{RF}^{tx}\) and \(N_{RF}^{rx}\) are the number of RF chains at the AP and each user, respectively. The received signal model at user \(u\) and subcarrier \(k\) after the combiner can be written as:  
\[\mathbf{Y}_{k,u}=\sqrt{\rho_{u}}\mathbf{W}_{\text{BB}_{k,u}}^{H}\mathbf{W}_{ \text{RF}_{u}}^{H}\mathbf{H}_{k,u}\mathbf{F}_{\text{RF}}\mathbf{F}_{\text{BB} _{k}}\mathbf{s}_{k}+\mathbf{W}_{\text{BB}_{k,u}}^{H}\mathbf{W}_{\text{RF}}^{ H}\mathbf{n}_{k,u}, \tag{1}\]  
where \(\mathbf{H}_{k,u}\in\mathbb{C}^{N_{rx}\times N_{tx}}\) is the frequency domain channel matrix (assumed to be perfectly known at the transmitter and receiver) between the AP and the \(u\)th receiver at subcarrier \(k\). \(\mathbf{F}_{\text{RF}}\in\mathbb{C}^{N_{rx}\times N_{RF}^{rx}}\) and \(\mathbf{W}_{\text{RF}_{u}}\in\mathbb{C}^{N_{rx}\times N_{RF}^{rx}}\) represent the analog precoder and combiner, with \(u=1,\dots,N_{u},\rho_{u}\) denoting the average received power and vector \(\mathbf{n}_{k,u}\in\mathbb{C}^{N_{rx}\times 1}\) contain independent zero-mean circularly symmetric Gaussian noise samples with covariance \(\sigma_{n}^{2}\mathbf{I}_{N_{rx}}\). The digital baseband precoders are denoted by \(\mathbf{F}_{\text{BB}_{k}}\in\mathbb{C}^{N_{RF}^{rx}\times N_{u}N_{s}}\) and the combiners by \(\mathbf{W}_{\text{BB}_{k,u}}\in\mathbb{C}^{N_{RF}^{rx}\times N_{s}}\). In order to maintain the complexity of the implementation limited, the analog component is the same for all subcarriers, which means that \(\mathbf{F}_{\text{RF}}\) and \(\mathbf{W}_{\text{RF}}\) will be the same for all subcarriers. Considering the major issues related to spectral efficiency (SE), energy consumption and hardware implementation for THz pointed out in the introduction, in this study, we considered the architectures depicted in Figure 2[15; 28; 29; 30; 31]. The FC architecture is the closest to the performance of the digital architecture, but it is also the most power-consuming of the hybrid architectures. This is the main motivation for the development of partially connected architectures (AoSAs and DLoSAs) with the aim of trying to achieve similar performances to FC structures, but with lower energy consumption. The AoSAs architectures, especially the ones based on phase shifters, can be divided into two categories, namely, the ones based on single-phase shifters (SPS) and the ones based on double-phase shifters (DPS). Increasing the number of phase shifters connected to each antenna results in an improved performance but entails a higher energy consumption. On the other hand, DLoSAs represent a much more appealing solution due to the good compromise between performance and energy consumption (EC). However, the choice of the most suitable architecture depends on several aspects, which are related to the calculation of the \(\mathbf{F}_{\text{RF}}\) and \(\mathbf{F}_{\text{BB}}\) matrices.