# Achievable Rate of NOMA-Based Cooperative Spectrum-Sharing CRN over Nakagami-\(m\) Channels
## 5 Results and Discussion  
In this section, we present numerical results to validate the ergodic achievable rate analysis carried out in Section 3. We compare the derived analytical results with the simulation's results. Here, the outage probabilities of PR and SRs (given in [7]) are also incorporated in the results. Similarly to [7], we assume that \(\mathbb{E}\{|h_{p}|^{2}\}=\mathbb{E}\{|h_{s,k}|^{2}\}=0.1\) and \(\mathbb{E}\{|h_{s}|^{2}\}=\mathbb{E}\{|g_{p}|^{2}\}=\mathbb{E}\{|g_{s,k}|^{2 }\}=0.2\). The fading severity for all channels is set to \(m_{0}=m_{2}=m_{22}=2\). The simulation results are obtained by averaging over one million independent channel realizations. Figure 2 shows the ergodic achievable rate of the system (including PR and SRs) against various values of transmit SNR, where \(\rho_{p}=\rho_{s}\). We also plot the ergodic achievable rate of the PR and the ergodic achievable sum rate of SRs. Here, we assume that \(K=2\), \(\alpha_{1}=0.6\), \(\alpha_{2}=0.3\), and \(\alpha_{3}=0.1\), and the minimum rate requirements are set to \(R_{0}=R_{1}=R_{2}=0.5\) for this set of simulation. It is observed that the analytical ergodic achievable rate's results exactly match the simulation's results, thus validating the analytical analysis carried out in Section III. Moreover, it can be observed that the ergodic achievable rate increases with the increasing values of \(\rho_{p}\) and \(\rho_{s}\). Additionally, we see that the PR has a higher attainable rate than the SR, which is expected for CR as PR is the only licensed entity among all communicating nodes. Furthermore, for the values of \(\rho_{p}<10\) dB, it can be seen that the ergodic achievable rate is almost equivalent to zero. This is a result of the CRN's inability to satisfy the PR's minimum rate requirements for transmit power values below a certain threshold. If so, no CRN-based transmission will take place; instead, the PR will send its information directly to the destination without involving the SRs. We exclusively display the outcomes for the case where CRN is employed in Figure 2.  
By fixing the values of \(\rho_{p}\) and \(\rho_{s}\) to 20 dB in Figure 3, we offer findings for the system's ergodic attainable rate against different values of the Nakagami-\(m\) fading parameter for the same setup in Figure 2. We can see that the formulas hold for the non-integer values of \(m\), and the results show that the analytical and simulation findings are identical. Our analytical findings are equally valid in the case where \(m<1\), which is worst than the Rayleigh fading scenario. This graph depicts the range of our results and their applicability to all potential \(m\) values. Additionally, we can see that the achievable rate rises as the Nakagami-\(m\) parameter's value rises. Furthermore, we can see that the PR's achievable rate is roughly twice as high as the sum rate of all SRs overall, satisfying the PR rate's guaranteed conditions set forth by the CRN. On the same grounds in Figure 4, the ergodic achievable rates are plotted against different values of \(\alpha_{0}\) with \(K=2\) and \(R_{0}=R_{1}=R_{2}=0.5\). Here, we set \(\alpha_{1}=\left(\left(1-\alpha_{0}\right)/2\right)+0.025\) and \(\alpha_{2}=\left(\left(1-\alpha_{0}\right)/2\right)-0.025\). It can be seen that as the value of \(\alpha_{0}\) increases, the ergodic achievable sum rate of SRs decreases slightly because more power is allocated to the PR;  
Figure 3: Ergodic achievable rate performance versus Nakagami-m fading severity parameter. Figure 2: Ergodic achievable rate performance versus transmit SNR. hence, less power will be allocated to the SRs. Again, it can be observed that the derived analytical results are consistent with the simulation's results. Finally, we plot the ergodic achievable rates for different values of \(K\) (i.e., the number of SRs in the network) in Figure 5, where \(\rho_{p}=\rho_{s}=10\) dB, \(R_{0}=0.5\), and \(R_{1}\cdots R_{K}=0.05\). We set the value of \(\alpha_{0}\) to \(0.5\).