# Performance Analysis of Two-Hop mmWave Relay Nodes over the 5G NR Uplink Signal
## 2 System Model and Basic Assumptions
### Uplink mmWave MIMO D&F Implementation  
In this subsection, we present the mmWave D&F strategy without and with channel knowledge. Our scheme to develop uplink mmWave MIMO D&F relay nodes uses an uplink 5G NR signal standardized by 3 GPP. From the implementation point of view, the protocols have been developed using the 5G communication ToolBox of MatlabTM software. Figure 5: Amplify-and-forward (A&F) uplink mmWave MIMO new radio relay node processing blocks. Additionally, Frequency Division Duplexing (FDD-5G), single and multiple antennas, and out-band operation (access link in mmWave band and backhaul link in sub-6 GHz band) have been considered. As mentioned previously, two D&F strategies are proposed and implemented in this paper, the first of which has the channel knowledge to perform receiving signal decoding and the second of which takes into account the Least Square (LS) channel estimator; therefore, this functionality depends on whether it is activated or not, as can be observed in Figure 6.  
In Figure 6, the uplink mmWave MIMO new radio decode-and-forward (D&F) relay node processing blocks with and without channel knowledge are presented. From the figure, firstly, IQ signals are captured using the RF mmWave receive chains (\(\mathbf{M}_{\text{RR}}\)), in which the number of receivers antennas is the same to the number of RF mmWave receive (FR2-Rx). After the acquisition of the transmitted data, any significant frequency derivation must be estimated and eliminated, without which many errors would propagate in the uplink received signal. This process is performed correlating the received uplink waveform with the uplink DM-RS. Thus, the adjusted uplink NR received signal is demodulated through the uplink NR CP-OFDM demodulated block. To achieve the signal demodulation, an uplink NR basic structure was used, which supports the sample rate, subcarrier spacing, the number of the Cell Identity (Cell ID), Cyclic Prefix (CP), and the number of Resource Blocks (RBs) of the uplink received waveform. After the steps described above, the algorithm should be determined to obtain the channel matrix, as can be seen in Figure 6. Considering the selected functionality in the relaying protocol, switch 1 will select position 1 (uplink NR perfect channel estimation). In the case of switch point 2, the D&F strategy determines the channel matrix in two stages: (a) the frequency responses for the subcarrier of the pilot symbols are obtained based on the least square algorithm and (b) the frequency responses of the subcarriers of the data symbols can be derived by interpolation methods using the adjacent pilot symbols, as has been employed in [17; 18]. The LS estimator is used to  
Figure 6: Decode-and-forward (D&F) uplink mmWave MIMO new radio relay node processing blocks. equalize the channel frequency responses at pilot locations sent from different sources at all receiver antennas and can be written as  
\[\hat{\mathbf{H}}_{\text{P}}^{1}=\mathbf{X}_{\text{P}}^{1}\mathbf{Y}_{\text{DF} ^{2}}, \tag{10}\]  
where \(\mathbf{Y}_{\text{DF}_{\text{P}}}^{1}=\mathbf{H}_{\text{P}}^{1}\mathbf{X}_{ \text{P}}+\mathbf{N}_{\text{DF}_{\text{P}}^{1}}^{1}\), which is achieved due to the resource blocks in LTE and 5G are allocated over M layers, T subcarriers, and L time slots. Therefore, the matrix \(\mathbf{Y}_{\text{DF}}^{1}\) is comprised of both data symbols and pilot symbols. Algorithm 1 executes the decoding and encoding of the physical, control, and data channels. In this context, the uplink 5G NR communication system, the Physical Uplink Shared Channel (PUSCH) is used to provide physical layer signaling to support Medium Access Control (MAC) layer operation. From Algorithm 1, it can be observed that the required inputs are the following: the estimated channel (\(\hat{\mathbf{H}}^{1}\)), the uplink demodulated received signal (\(\mathbf{Y}_{\text{DF}}^{1}\)), the NR-PUSCH, decode NR-ULSCH, and encode NR-ULSCH configure blocks, which provide the parameters to decode and encode the PUSCH and UL-SCH channels.