## 3 Network Model of the mmWave MIMO NR-Relay Node (RN) Cooperative System
### D&F NR-RN Implementation  
In this subsection, a NR-D&F protocol employing 5G communication ToolBox of MATLAB(tm) is presented. NR-D&F RN was implemented, where Frequency Division Duplexing (FDD-5G), multiple antennas, and out-band operation-that is, the two links (backhaul and access links) have different frequencies-are considered, which the Backhaul Link and Access Link work in FR1 and FR2, respectively. The implemented NR-D&F strategy estimates the channel or has the channel knowledge to perform received signal processing, depending on whether this functionality is activated, as can be seen in Figure 5.  
From Figure 5, in the first-phase of the NR-D&F protocol, the IQ is captured with the Receiver block. After the acquisition of the data symbols, any significant frequency derivation must be estimated and eliminated, and the time offset must be performed, without which many errors would be propagated. After the steps described previously, the New Radio CP-OFDM is demodulated through the NR CP-OFDM Demodulate block, which is helped by a configuration structure, taking into account the sample rate of the received signal. In this regard, subcarrier spacing, cyclic prefix, the number of cell id, and the number of resource blocks are determined in the NR Basic Structure block. The first task after the received signal demodulation is to determine the channel, in which it should be noticed that the NR-D&F RN can be obtained two types of the channel by mean of two blocks (NR Perfect Channel Estimation and LS NR Channel Estimation blocks). In this context, the usage channel will depend on the selected point in switch 1. Thus, when point 1 is chosen the NR-D&F RN have knowledge of the channel, which in our case is the channel \(\mathbf{H}^{1}\) (CDL-D). However, when point 2 is selected the NR-D&F protocol performs a channel estimation through the LS NR Channel Estimation block, which is realized in two steps: first, the frequency responses for the subcarriers of the pilot symbols are determined, based on the Least Square (LS) estimator. On the other hand, from the first step, the frequency responses of the subcarriers of the data symbols can be derived by interpolation methods employing the adjacent pilot symbols. Finally, the demodulated received signal (\(\mathbf{Y}_{\text{DF}}^{1}\)) and the estimated channel matrix (\(\hat{\mathbf{H}}^{1}\)) are processed through Algorithm 1 for the Decode-and-Encode of each subframe. Furthermore, for the proper functioning of Algorithm 1, the NR-PDSCH, Decode NR-DLSCH and encode NR-DLSCH configure blocks are token as input, which provide the parameter to decoding and encoding the PDSCH and DLSCH channels. This algorithm executes the decode and encode of the physical, control, and data channels, as well as determining other reference signals. It can be observed in Algorithm 1 that, in order to maximize the equalization Signal-to-Noise Ratio (SNR), the Mean Maximum Error square (MMSE) equalizer is employed. Besides, in the proposed algorithm, the sub-indices \((\cdot)^{\mathbf{d}}\) and \((\cdot)^{\mathbf{c}}\) in the functions describe the processes of decoding and encoding, as well as the sub-indices \((\cdot)^{\mathbf{b}}\) and \((\cdot)^{\mathbf{s}}\) in the outputs of the functions represent data bits and data symbols, respectively. The **NR-P\({}^{\mathbf{c}}\)** function, mapping each symbol, DMRS and PTRS signal in the resource grid, and the \(\hat{\mathbf{x}}\) subframe to the output of the function, is obtained. Finally, concatenating each subframe is performed by mean of the \(\mathbf{Cat}(\cdot)\) function, from which all frames to re-transmitting are saved. \(\hat{\mathbf{X}}\), the resultant signal to the output of Algorithm 1, is  
Figure 5: Decode-and-Forward (D&F) mmWave NR-RN processing blocks. is to increase the output signal level and isolate it from the mixer load variations. The electrical specifications of the different RF subsystems are shown in Table 1.  
For the first stage of the NR-EU (FR2-Rx), a mmWave receiver chain was designed and implemented.