## 2 System Model  
An ideal 5G micro-cell with a coverage radius of 200 m is shown in Figure 1. This micro-cell consists of a gNodeB which serves two users U\({}_{1}\) (near-user) and U\({}_{2}\) (far-user), via downlink PD-NOMA communication. The gNodeB and two users (U\({}_{1}\) and U\({}_{2}\)) are installed with single antennas. In the downlink PD-NOMA, the gNodeB is considered the controlling unit which allocates different powers to each serving user at the same time and frequency. The fuzzy inference system (FIS) based optimal PA strategy is used in the proposed methodology. To obtain user fairness, U\({}_{1}\) is given a minimum power and U\({}_{2}\) a maximum power, as demonstrated in Figure 1.  
At the gNodeB, random symbol bits for the ith user are generated, which is given by:  
\[r_{i}(t)=\sum_{l}b_{i}^{l}\delta(t-iT_{s}), \tag{1}\]  
where \(r_{i}(t)\) represents the randomly generated symbol bits and \(b_{i}^{l}\) is the \(ith\) user's \(1 th\) symbol. \(\delta\) and \(T_{s}\) represent the Dirac delta function and the sampling rates, respectively. For each user the absolute power factor is computed through FIS as shown in Section 3 and Appendix A. The output of the FIS system is normalized to obtain the actual power factors for each user and is given by:  
\[P_{i}=\frac{p_{i}^{{}^{\prime}}}{\sum_{i=1}^{2}p_{i}^{{}^{\prime}}}, \tag{2}\]  
where \(P_{i}\) and \(p_{i}^{{}^{\prime}}\) are the normalized and absolute power factors for \(ith\) user, respectively. The total normalized power for all users is constrained by:  
\[\sum_{i=1}^{2}P_{i}=1. \tag{3}\]  
Each user's signal is modulated with Binary Phase Shift Keying (BPSK) along distinct phase offsets and assigned with corresponding power factors via FIS at the gNodeB, and is given by:  
\[c_{i}(t)=\sqrt{P_{i}}r_{i}(t)=\sqrt{P_{i}}\sum_{l}b_{i}^{(l)}g(t-iT_{s}), \tag{4}\]  
where \(c_{i}(t)\) is the \(ith\) user's power multiplexed signal and \(g(t)\) stands for the transmitting pulse. The combined signal for both users is given by:  
\[x(t)=\sum_{i=1}^{2}\sqrt{P_{i}}c_{i}(t). \tag{5}\]  
The combined signal \(x(t)\) after passing through root raised cosine filter (RRCF) for pulse shaping is transmitted over a channel in the presence of additive white Gaussian noise (AWGN). Each user (U\({}_{i}\)) obtains the transmitted combined signal after it has been subjected to large-scale fading and is given by:  
\[Y_{i}(t)=\alpha_{i}x(t)+n_{i}(t), \tag{6}\]  
where \(Y_{i}(t)\) is the received combined signal at the \(ith\) receiver, \(\alpha_{i}\) is the channel gain and \(n_{i}(t)\) is the AWGN with zero mean and standard deviation \(\sigma\). The message signal is decoded by each receiver based on power levels. Signals with higher multiplexed power are decoded first, followed by those with lower power levels in descending order. The far-user (U\({}_{2}\)) will decode its signal immediately due to maximum power, whereas the near-user U\({}_{1}\) will conduct SIC to negate the influence of the U\({}_{2}\) signal and then decode its signal, which is provided by:  
\[\hat{x_{i}}(t)=Y_{i}(t)-x_{i^{\prime}}(t). \tag{7}\]  
Figure 1: SISO downlink PD-NOMA system (U\({}_{1}\) is near-user and U\({}_{2}\) is far-user).  
\(\hat{x}_{i}(t)\) is the decoded signal and \(x_{i^{\prime}}(t)\) is the SIC term. Here, \(i^{\prime}=2\) for near-user (U1) and \(i^{\prime}=1\) for far-user (U2). The proposed framework is represented in Figure 2, which illustrates a step-by-step block diagram of the proposed framework, where each user signal is given different phase shifts and assigned the associated power factors by employing an FIS-based system. All of the users' signals are superimposed, then sent over the channel after passing through a root-raised cosine filter (RRCF) for pulse shaping. At the receiving end, the incoming signal is processed once more by RRCF before being decoded using the SIC technique. The near-user U1 is used for cooperation to assist the far-user U2 using the D&F technique, which is further discussed in Section 3.2.