## 2 Technical Background of D&F Co-Operative 5G System Model
Therefore, considering the prior assumptions and a single-user (SU) downlink, the transmitted 5G downlink waveform from the source can be expressed as  
\[\mathbf{X}=\mathbf{M}_{\text{ST}}\mathbf{T}_{\text{BB}}\mathbf{S}, \tag{1}\]  
where power normalization is satisfied by \(||\mathbf{M}_{\text{ST}}\mathbf{T}_{\text{BB}}||_{\text{F}}^{2}=\text{TN}_{ \text{T}}^{\text{S}}\). At the D&F node, N\({}_{\text{R}}^{\text{R}}\) and N\({}_{\text{T}}^{\text{R}}\), respectively, are receiver and transmitter antennas. Considering the proposed D&F node in Figure 1, the received signal processing is performed in two stages. First of all, the transmitted signal from gnodeB is received and decoded by the D&F protocol. After that, the detected data symbols are encoded and forwarded to the destination. It is worth highlighting that the proposed D&F is equivalent to a layer 2 LTE  
Figure 1: system model for 5G DL transmission via D&F co-operative architecture. relaying technology, taking into account the 3 GPP standardization and new release [17]. Therefore, the received signal matrix at the relay node can be written as  
\[\mathbf{Y}_{\rm DF}^{1}=\mathbf{H}^{1}\mathbf{X}+\mathbf{N}_{\rm DF}^{1}=\mathbf{ H}^{1}\mathbf{M}_{\rm ST}\mathbf{T}_{\rm BB}\mathbf{S}+\mathbf{N}_{\rm DF}^{1}. \tag{2}\]  
Here, \(\mathbf{H}^{1}\in\mathbb{C}^{\rm N_{R}^{R}\times N_{\rm T}^{S}}\) and \(\mathbf{N}_{\rm DF}^{1}\in\mathbb{C}^{\rm N_{R}^{R}\times T}\) are the outdoor sub-6 GHz channel matrix between the FR1-Tx chains of the gnodeB and D&F node, and the additive white Gaussian noise (AWGN) matrix with zero mean and variance \(\sigma_{\rm N_{\rm DF}}^{2}\) at each antenna of D&F strategy, respectively. Furthermore, the \(\mathbf{N}_{\rm R}^{R}\times\mathbf{N}_{\rm R}^{R}\) analog receiver \(\mathbf{M}_{\rm RR}\) matrix at the D&F node is composed of \(\mathbf{N}_{\rm R}^{R}\) FR1-Rx chains. Hence, the signal \(\mathbf{Y}_{\rm DF}^{1}\) at the D&F protocol in Figure 1 after analog receiver matrix is  
\[\hat{\mathbf{Y}}_{\rm DF}^{1}=\mathbf{M}_{\rm RR}^{\rm H}\mathbf{H}^{1} \mathbf{X}+\mathbf{M}_{\rm RR}^{\rm H}\mathbf{N}_{\rm DF}^{1}=\mathbf{M}_{\rm RR }^{\rm H}\mathbf{H}^{1}\mathbf{M}_{\rm ST}\mathbf{T}_{\rm BB}\mathbf{S}+ \mathbf{M}_{\rm RR}^{\rm H}\mathbf{N}_{\rm DF}^{1}=\hat{\mathbf{H}}^{1} \mathbf{X}+\hat{\mathbf{N}}_{\rm DF}^{1} \tag{3}\]  
where \(\hat{\mathbf{Y}}_{\rm DF}^{1}=\mathbf{M}_{\rm RR}^{\rm H}\mathbf{Y}_{\rm DF}^ {1}\). \(\hat{\mathbf{N}}_{\rm DF}^{1}=\mathbf{M}_{\rm RR}^{\rm H}\mathbf{N}_{\rm DF}^{1}\), and \(\hat{\mathbf{H}}^{1}=\mathbf{M}_{\rm RR}^{\rm H}\mathbf{H}^{1}\) are, respectively, the estimated noise and channel matrices between the gnodeB and D&F protocol. As shown in Figure 1, the decoding and encoding stages in the D&F protocol are performed through \(\mathbf{R}_{\rm BBH}\in\mathbb{C}^{\rm N_{r}\times N_{\rm R}^{R}}\) and \(\mathbf{R}_{\rm BBT}\in\mathbb{C}^{\rm N_{r}^{R}\times N_{\rm r}}\) matrices, respectively. In this sense, once we have estimated the data symbols matrix (\(\mathbf{\hat{S}}\)) and consequently with D&F access architecture system, the transmitted signal by the D&F node can be defined as  
\[\hat{\mathbf{X}}=\mathbf{M}_{\rm RT}\mathbf{R}_{\rm BBH}\mathbf{\hat{S}}, \tag{4}\]  
where \(\mathbf{M}_{\rm RT}\in\mathbb{C}^{\rm N_{T}^{R}\times N_{\rm T}^{R}}\) denotes the IF\(\rightarrow\)RF converter matrix in the relay node implemented by the RF transmitter chains of an USRP platform. In addition, \(\mathbf{R}_{\rm BBT}\in\mathbb{C}^{\rm N_{r}^{R}\times N_{\rm r}}\) is the digital baseband precoder matrix in the transmitter side of the D&F node.