# Performance Analysis of Two-Hop mmWave Relay Nodes over the 5G NR Uplink Signal
## 2 System Model and Basic Assumptions  
In this section, we will describe both the relay node architecture and its implementation. First of all, the signal model of the proposed relays in this article will be explained. A&F and D&F relay nodes deal with different signal models. Additionally, the advantages and the main differences between both schemes will be highlighted. Then, the implementation of a link-level co-operative simulator using Matlab(tm) and Simulink(tm) software will be explained. Figure 1 shows a two-hop uplink mmWave MIMO NR-RN system model in a wireless network. The architecture consists of one source node (NR-UE), an intermediate node (NR-RN protocol), and a destination node (gNodeB) working in a Half Duplex (HD). From Figure 1, it can be seen that the NR-UE node includes two blocks: the baseband signal processing block and an array of transmitter chains in the 5G FR2 (26 GHz) band (FR2-Tx). In this architecture, an essential node is the new radio relay node, which comprises an array of receiver chains in mmWave (FR2-Rx), where its function is to convert the 5G FR2 frequency band to baseband. Furthermore, the baseband signal processing block involves two blocks, receiver and transmitter baseband signal processing, which are described, respectively, through \(\mathbf{R}_{\mathrm{BBR}}\) and \(\mathbf{R}_{\mathrm{BBT}}\) matrices. Finally, the third block in the NR-RN strategy contains an array of FR1-Tx to up-convert the baseband signal to the 5G FR1 (3.5 GHz) frequency band, which, in our link-level co-operative simulator, was implemented by means of Universal Software Radio Peripheral (USRP). On the other hand, the gNodeB includes two blocks: the baseband processing block (\(\mathbf{T}_{\mathrm{BB}}\)) and an array of RF Chains (FR1  
Figure 1: Uplink mmWave MIMO New Radio (NR)-relay node architecture. Rx) to down-convert the 3.5 GHz to the baseband frequency band. It should be noted that, in this paper, the direct link between the source and destination, is not studied because it is considered to operate in different band frequencies. We consider an uplink mmWave co-operative Single-User (SU)-MIMO system employing precoding in the UE, RN strategy, and gNodeB. In this sense, to enable the precoding technique, we assumed that the NR-UE and RN protocols have full channel side information knowledge. In this context, the precoding process in the NR-UE can be described by the product between the mmWave RF transmitter, \(\mathbf{M}_{\text{ST}}\in\mathbb{C}^{\text{NR}_{\text{T}}\times\text{NR}_{\text {T}}^{\text{S}}}\), and the baseband precoding matrix, \(\mathbf{G}_{\text{BB}}\in\mathbb{C}^{\text{NR}_{\text{T}}^{\text{S}}\times \text{NR}_{\text{s}}}\). We assume that at the NR-UE, the number of transmitter antennas is \(\text{N}_{\text{T}}^{\text{S}}\), the number of data symbols is \(\text{N}_{\text{s}}\), and the number of FR2 transmitters (FR2-Tx) is the same as the transmitter antennas. Therefore, the transmitted signal from the user equipment can be given by  
\[\mathbf{X}=\mathbf{M}_{\text{ST}}\mathbf{G}_{\text{BB}}\mathbf{S}, \tag{1}\]  
where \(\mathbf{S}\in\mathbb{C}^{\text{N}_{\text{s}}\times\text{T}}\) data symbols with T is the number of used subcarriers for the transmission, and power normalization is satisfied such that \(||\mathbf{M}_{\text{ST}}\mathbf{G}_{\text{BB}}||_{\text{F}}^{2}=\text{TN}_{ \text{T}}^{\text{S}}\). Figure 2 displays the 3 GPP 5G NR uplink system model used to represent the NR-UE in this paper. The input data symbols (\(\text{N}_{\text{s}}\)) are fed into the UL-SCH and PUSCH coding block and over the resultant PUSCH is applied the modulation scheme (in this paper 64-QAM and 256-QAM have been implemented) and the precoding stages. Then, these complex-valued modulation symbols are mapped onto one or multiple transmission layers on the antenna ports.