## 2 Technical Background of D&F Co-Operative 5G System Model  
The section presents the system model for 5G DL transmission via the proposed D&F co-operative architecture, as shown in Figure 1. The application scenario main of the proposed D&F access architecture is for sub-6 GHz indoor coverage. In this sense, D&F co-operative 5G network can communicate with both gnodeB and UE through backhaul and access links, respectively, as can be seen in Figure 1. The proposed D&F downlink co-operative 5G communication network comprises one gnodeB, an intermediate decode-and-forward relay node, and a destination (UE), which operates in a half-duplex (HD) mode. The gnodeB architecture is composed of two blocks mainly. Firstly, the baseband signal processing block is described by the \(\mathbf{T}_{\mathrm{BB}}\) matrix. This block considers a digital baseband recoder to configure the physical, control, and data channels, as well as the reference signals, taking into account the \(\mathrm{N}_{\mathrm{s}}\) transmitted signals and modulation scheme. After that, the configured output signal from the digital baseband precoder is modulated by the 5G CP-OFDM modulator block, obtaining the downlink 5G waveform. The second block in the gnodeB considers RF transmit chains (FR1-Tx) to up-convert and amplify the baseband signal to a 5G frequency band, which in this work is 3.5 GHz. From the point of hardware, the interface has been developed through the SDR platform and power amplifier (PA), as will be explained later on. In the proposed 5G co-operative network, D&F node introduces numerous advantages for effective 5G indoor coverage, where deployed as an intermediate node between outdoor source and indoor destination. D&F protocol comprises an array of receiver chains in sub-6 GHz (FR1-Rx) frequency band, for which the main function is to convert the FR1 band to baseband frequency band. The RF receiver stage (\(\mathbf{M}_{\text{RR}}\)) in the D&F is implemented through the receiver RF chains in the SDR platform. In addition, it comprises two baseband signal processing algorithms associated with the receiver (\(\mathbf{R}_{\text{BBR}}\)) and the transmit (\(\mathbf{R}_{\text{BBT}}\)) stages. Finally, the RF transmit (FR1-Tx) stage (\(\mathbf{M}_{\text{RT}}\)) in the D&F node up-converts the retransmitted baseband 5G signal to the FR1 (3.5 GHz) frequency band by means of the USRP platform. Then, in destination (UE) are inverted the operations performed by the source to estimate the received 5G signal through the D&F, which is achieved by the RF receiver chains (FR1-Rx) (it is implemented by means of USRP and described mathematically by \(\mathbf{M}_{\text{DR}}\) matrix). Furthermore, the baseband matrix \(\mathbf{G}_{\text{BB}}\) demodulates and decodes the 5G signal and NR channels, respectively. Consider the 5G DL transmission over a co-operative wireless transmission channel, based on a D&F relay network system model, as shown in Figure 1, where a gnodeB has N\({}_{\text{T}}^{\text{S}}\), respectively, transmit antennas, power amplifiers, and RF chains. At the source, N\({}_{\text{s}}\) is number of data symbols (M-QAM modulation scheme), therefore, the modulated data symbols matrix is given by \(\mathbf{S}\in\mathbb{C}^{\text{N}_{\text{s}}\times\text{T}}\), where T is the number of used subcarriers for the transmission (depending on bandwidth and subcarrier spacing). The \(\mathbf{T}_{\text{BB}}\in\mathbb{C}^{\text{N}_{\text{s}}^{\text{S}}\times \text{N}_{\text{s}}}\) baseband precoding matrix is used for modeling the control, data, physical, and reference signals as standardized by the 3 GPP [10; 11], as well as modulating the waveform of the 5G downlink. The gnodeB hosts N\({}_{\text{T}}^{\text{S}}\) RF transmitter (FR1-Tx) and is described by \(\mathbf{M}_{\text{ST}}\)\(\in\mathbb{C}^{\text{N}_{\text{T}}^{\text{S}}\times\text{N}_{\text{T}}^{\text{S}}}\) matrix.