## 3 Optimal Power Allocation (PA), Cooperative Relaying and Channel Models in PD-NOMA
### Cooperative Relaying and Channel Models in PD-NOMA  
In cooperative relaying communication, the strong node is used as a relay to assist the weak node in the system. A strong node has better channel conditions than a weak node. In the proposed model, the strong and weak nodes are U\({}_{1}\) and U\({}_{2}\), respectively, as shown in Figure 8. The weak node faces critical signal losses due to multiple issues such as greater distance separation, foliage depth, and low signal-to-noise ratio. Although PD-NOMA assigns higher power to far users' signals to ensure user fairness, it is further needed to assist them from strong nodes as well, which provide indirect line-of-sight (LOS) paths between the gNodeB and the far-users (U\({}_{2}\) here). In Figure 8, U\({}_{2}\) being located at a maximum distance and foliage depth faces signal degradation and results in intense path losses. To address this issue that occurs in ordinary PD-NOMA, the proposed model incorporates cooperative relaying into the existing system by treating U\({}_{1}\) as a relay that uses the decode and forward (D&F) method to assist U\({}_{2}\). Specifically, during the time slot (\(t_{1}\)), both users U\({}_{1}\) and U\({}_{2}\) receives the combined signal. The U\({}_{1}\) first decodes the U\({}_{2}\) signal using basic NOMA principles and performs SIC on the U\({}_{2}\) signal to retrieve its signal. The U\({}_{2}\) signal is regenerated from the previously decoded \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**S.no** & **d** & **SNR** & **d\({}_{f}\)** & **Power Level** \\ \hline  
& H \\ \hline \end{tabular}
\end{table} 
Table 1: Human Intuition based FIS system for Optimal PA in PD-NOMA. signal at U1 and forwarded to the U2 receiver at time slot (\(t_{2}\)). Cooperation in the system can be implemented at the expense of increased bandwidth consumption. Now U2 has two signals: a degraded signal from the gNodeB with higher path losses and a D&F signal from node U1. The maximum ratio combining (MRC) technique is then used by the U2 receiver to decode its signal. We used three types of channel models: NYUSIM, Rician, and Rayleigh channels, to study the behavior of the proposed model. The NYUSIM [43] channel model, which was created specifically for 5G wireless communication protocols and covers a frequency range of 500 MHz to 100 GHz. The path loss (PL) calculated for each user signal by passing it through the NYUSIM channel model is given by:  
\[\text{PL}(f_{c},d)[\text{dB}]=\text{FSPL}(f_{c},1\text{ m})[\text{dB}]+10n\text{log}_{10}(d/d_{0})+\text{AT}[\text{dB}]+X_{ \sigma}. \tag{10}\]  
\(f_{c}\) is the carrier frequency in gigahertz and \(d\) is the 3D distance between each user and the gNodeB. \(d_{o}\) is the reference distance of 1 m, \(n\) denotes the path loss exponent, and AT denotes the attenuation effect from the surrounding environment. \(X_{\sigma}\) represents a Gaussian random variable with zero mean and a variance of 2.52. The free space path loss (FSPL) in Equation (10) is given by:  
\[\text{FSPL}(f_{c},1\text{ m})[\text{dB}] =20\text{log}_{10}(\frac{4\pi\times f_{c}\times 10^{9}}{c}) \tag{11}\] \[=32.4[\text{dB}]+20\text{log}_{10}(f_{c}),\]  
where, \(c\) denotes speed of light. The 3-D distance separation is given by:  
\[d=\sqrt{d_{2D}^{2}+(h_{t}-h_{r})^{2}}, \tag{12}\]  
where \(d_{2D}\) denotes the 2-D distance separation for each user from the gNodeB, \(h_{t}\) and \(h_{r}\) are the gNodeB and each user heights, respectively. The environment attenuation is given by:  
\[\text{AT}[\text{dB}]=\beta[\text{dB}/\text{m}]\times d[\text{m}]. \tag{13}\]  
Here, \(\beta\) represents the factor of attenuation from the surrounding environment and \(d[\text{m}]\) is the 3D distance separation. The proposed model is also simulated in the Rician and Rayleigh fading channels. In the Rician fading channel, the SUI-3 (Stanford University Interm channel model 3) parameters are used in the simulation.