## 3 Network Model of the mmWave MIMO NR-Relay Node (RN) Cooperative System
### D&F NR-RN Implementation
Its block diagram, shown in Figure 7, has the same structure as transmitter chain and uses the same components, except that the power amplifier (PA) is replaced by a low noise amplifier (LNA). Specifically, the LNA from Hitttite HMC519 LC4 [28] was employed. The noise figure of this amplifier directly limits the sensitivity of the receiver. The electrical specifications of the low noise amplifier are shown in Table 1. As mentioned above, the platform was designed with connectorized off-the-shelf components, allowing for easy characterization and integration into the transceiver (Rx-Tx) mmWave radio platform. The cost of the mmWave transmitter and receiver chains is, approximately, 11,000s. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Gali\({}_{84}\)** & **HMC292 ALC3B** & **HMC499 LC4** & **HMC944 APM5E** & **HMC519 LC4** \\ \hline Frequency Range (GHz) & 0–6 & 14–30 & 24–28 & 20–28 & 18–28 \\ G\({}_{\text{lin}}\) (dB) & 19.2 & -9 & 16 & 16 & 14.4 \\ Local Oscillator Frequency (GHz) & - & 25 & - & - & - \\ Input Return Loss (dB) & 18 & 13.2 & 8 & 12 & 15 \\ Output Return Loss (dB) & 8.9 & 12.5 & 12 & 22 & 20 \\ OIP3 (dBm) & 38 & 20 & 34 & 36 & 23 \\ P\({}_{\text{1 dB,out}}\) (dBm) & 21.2 & 9 & 23 & 27 & 11 \\ P\({}_{\text{sat,out}}\) (dBm) & 22.1 & 13 & 23.5 & 28 & 14 \\ Noise Figure (dB) & 4.4 & 10 & 5 & 4 & 3.5 \\ GS\({}_{\text{sat}}\) (dB) & 3.5 & 2.2 & 4 & 5 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the elements of mmWave transmitter and receiver chains. Figure 6: Subsystems of the mmWave transmitter chain (FR2-Tx). Figure 7: Subsystems of the mmWave receiver chain (FR2-Rx). To support flexible development, we have designed our RF transmitter and receiver chains to allow easy integration with USRP radio software. This allows easy manipulation of the mmWs signals using our SDR platform developed for the implementation of Relay Nodos in the Research Group [29; 30]. Simulink(tm) software of Mathworks was used to simulate the RF transmitter and receiver chains. This simulation software uses a power series model or polynomial model for nonlinear circuit modeling without memory. This model is widely used in the literature and is given by [31; 32],  
\[\mathrm{V}_{0}(t)=\sum_{k=0}^{\mathrm{K}}\mathrm{C}_{2k+1}[\mathrm{V}_{\mathrm{ in}}(t)]^{(2k+1)}, \tag{14}\]  
where K is nonlinear order, \(\mathrm{V}_{0}(t)\) is the output signal, \(\mathrm{V}_{\mathrm{in}}(t)\) is the input signal, and \(\mathrm{C}_{2k+1}\) is the \((2k+1)\) the real polynomial coefficient. According to the Simulink(tm) manual [33], the order of the nonlinearity will depend on the nonlinear parameters available for the different RF subsystems of the transmitting and receiving chain. In general, for all RF subsystems, we have: (a) the output third-order intercept point (OIP3), (b) the output power at 1 dB compression (\(\mathrm{P}_{\mathrm{1 dB,out}}\)), (c) the output power saturation (\(\mathrm{P}_{\mathrm{sat,out}}\)), and (d) the gain compression at saturation (\(\mathrm{GC}_{\mathrm{sat}}\)). Under these conditions, we will have a nonlinearity of order K = 7 and Equation (14) translates to:  
\[