## 2 System Model and Basic Assumptions  
### Model Description  
In this section, the two-hop mmWave MIMO NR RN cooperative architecture, shown in Figure 1, will be presented and described. It comprises a gNodeB, a NR-RN and a NR-User Equipment (NR-UE) working in a Half-Duplex (HD). a) The gNodeB includes two blocks: the baseband signal processing block and array of RF amplifiers chains to up-convert the signal to 5G FR1 (<6 GHz) frequency band (FR1-Tx). In our architecture, these signal processing and up-conversion stages were implemented using Universal Software Radio Peripheral (USRP). b) The other important block of the system is the NR-RN. Its function is to convert the 5G FR1 (<6 GHz) frequency band (Backhaul Link -FR1-) to mmWave bands (Access Link -FR2-). It comprises an array of receiver chains in 5G FR1 band (FR1-Rx), emulated by USRPs, a baseband signal processing block for the implementation of the signal processing algorithms associated with the implemented relaying strategies ( \(\mathbf{R}_{\text{BBT}}\) and \(\mathbf{R}_{\text{BBR}}\) matrices, in Sections 2.2 and 2.3), and a mmWave conversion stage (FR2-Tx) and c) finally, the third block, NR-UE, which consists of an array of mmWave receiver chains (FR2-Rx), which receives the signal from the FR2-Tx chains through the access link, and down-convert it for further processing in the baseband block (\(\mathbf{G}_{\text{BB}}\)). The direct link between the gNodeB and the UE is not studied because it is considered to operate in different band frequencies.  
We assume that at the gNodeB, the number of transmit antennas is \(\text{N}_{\text{T}}^{\text{S}}\), the number of data symbols is \(\text{N}_{\text{s}}\), and the number of FR1 transmitters (FR1-Tx) is equal to \(\text{N}_{\text{T}}^{\text{S}}\). From Figure 1, the RN is equipped \(\text{N}_{\text{R}}^{\text{R}}\) receive antenna in which corresponding with the number of FR1 receiver (FR1-Rx), and RF mm-Wave chains (FR2-Tx) and number of the transmitter antennas, both equal to \(\text{N}_{\text{T}}^{\text{R}}\). In addition, in the destination, the number of FR2 receiver (FR2-Rx) depends to the number of receiver antennas \(\text{N}_{\text{R}}^{\text{D}}\).  
We consider downlink cooperative SU-MIMO system using precoding in the gNodeB, RN, and UE. To enable precoding, we assume that the gNodeB and RN has full channel side information knowledge. In fact, the precoding process in the source can be represented by the product between the RF transmitter, \(\mathbf{M}_{\text{ST}}\in\mathbb{C}^{\text{N}_{\text{T}}^{\text{S}}\times \text{N}_{\text{s}}^{\text{S}}}\), and the baseband precoding matrix, \(\mathbf{T}_{\text{BB}}\in\mathbb{C}^{\text{N}_{\text{T}}^{\text{S}}\times \text{N}_{\text{s}}}\). The source transmits \(\mathbf{S}\in\mathbb{C}^{\text{N}_{\text{s}}\times\text{T}}\) data symbols, where T is the number of used subcarrier for the transmission. Therefore, the transmitted signal from the source can be expressed by  
\[\mathbf{X}=\mathbf{M}_{\text{ST}}\mathbf{T}_{\text{BB}}\mathbf{S}, \tag{1}\]  
Figure 1: MIMO Millimeter-Wave (mmWave) downlink New Radio (NR)-Relay Node (RN) structure.  
where power normalization is satisfied such that \(||\mathbf{M}_{\text{T}}^{\text{S}}\mathbf{T}_{\text{BB}}||_{\text{F}}^{2}=\text{ TN}_{\text{T}}^{\text{S}}\). The transmitted signal (1) from gNodeB is implemented through the gNodeB structure explained in Figure 2, where the data symbols (\(\text{N}_{\text{s}}\)) are coded through the DL-SCH and PDSCH Coding block. After that, over PDSCH is performed the modulation (depend on the implemented M-QAM constellation) and the precoding stage. Then, reference signals are mapped and CP-OFDM modulation is performed. Finally, it is inserted a portion of SS Burst and the baseband signal is upconverted to the FR1 band by \(\mathbf{M}_{\text{ST}}\). It should be noticed that the generated and configuration of the signal and channels in the gNodeB fulfill the 5G NR standardization of the 3 GPP, which is one of the main novelty of our proposal.