## 5 Simulation Results
To estimate the objective function and constraints, it is also necessary to evaluate 8 equations and one additional equation for obtaining the fitness function in (18). Second, for each particle, we require to calculate two random numbers and evaluate 8 equations for the velocity update and position update since we have four variables. Third, we limit the position of the particle and find the local and best positions by computing six equations. Then, for each particle \(n\), we need to execute around 35 equations. Since the algorithm repeats the process for a total of \(It_{\text{max}}\) iterations, the total number of equations to be evaluated is \(35\times S\times It_{\text{max}}\), which can be mathematically expressed as the computational complexity of \(\mathcal{O}\left(S\times It_{\text{max}}\right)\). In the case of the exhaustive search method, the complexity depends on the range of the variables which is based on numerical precision. Let us define \(\zeta\) as the steps used for the power variables, then the total possible values for the variable \(p_{1}\) are \(\mathrm{Y}_{p_{1}}=\left\lfloor\left(P_{T}^{\text{max}}-p_{1\,\text{min}}+ \zeta\right)/_{\zeta}\right\rfloor\), where the same procedure is applied to the other variables to obtain \(\mathrm{Y}_{p_{2}}\), \(\mathrm{Y}_{p_{3}}\) and \(\mathrm{Y}_{p_{r}}\). Then, for the ES method, we need to evaluate the objective function and constraints a total number of \(\mathrm{Y}_{p_{1}}\times\mathrm{Y}_{p_{2}}\times\mathrm{Y}_{p_{3}}\times \mathrm{Y}_{p_{r}}\) times. We can observe that the proposed PSO-based scheme permits a huge reduction in the computational complexity compared with the exhaustive search. For instance, in the case of \(\phi_{1}=\phi_{2}=1(\text{bits/s/Hz})\) and \(\zeta=-18\,\text{dBm}\) with a step of \(\zeta=1\), the computational time of ES is around 72,4492 (s), which increases exponentially by reducing the value of \(\zeta\), i.e., with more numerical precision. By contrast, the PSO-based algorithm achieves a computational time of 18.92 (ms) with a number of particles equal to 20 and 90 iterations as we can see in Table 2.  
Figure 4 shows a comparison of SEE performance between our proposal using NOMA and the conventional OMA scheme in accordance with the SEE objective function versus the minimum data rate at the secondary users when the minimum energy harvested by the EH user is \(\zeta=-15\,\text{dBm}\), when the maximum available transmission power at the transmitter and the relay is \(P_{T}=P_{R}=30\,\text{dBm}\). From Figure 4, we can see that the NOMA scheme significantly outperforms the traditional OMA. This is because, under NOMA, the location of both users is exploited to simultaneously transmit to User 1 and User 2, in which the power allocated for the distant user is higher, compared to the power allocated for the closer user. This strategy is complemented with SIC in which the closer user first decodes the message of the distant user, where the SINR is high since it has the higher power, and it then subtracts that contribution to easily decode its own message (the message for the closer user). For the distant user, the interference from the message of the closer user is low, since the power allocated to this message is not high. On the other hand, the OMA scheme does not use SIC and the transmitter needs different periods of time to send each message to each intended user. Then, the transmission under the NOMA scheme is completed in two phases, as shown in Figure 1, while the transmission under OMA is completed in three phases. Therefore, because NOMA uses the resources more efficiently, it achieves better performance than the OMA scheme. Moreover, we can see that the result obtained by our proposed PSO-based method achieves performance very close to that obtained by the exhaustive search method, but with lower complexity.