## 3 The Proposed Detector for Uplink GF-NOMA Networks: FROMPUS
### Node C: Reverse-Select
The results are for a scenario in which the uplink GF-NOMA network is overloaded, similar to what can occur in any OMA-based network. In this instance, the MUDs that perform poorly are the OMP-based MUD, the Comp Efficient OMP-based MUD, and the SOMP-based MUD [11]. The worst performance is shown by the SOMP-based MUD, which is understandable, since it was originally designed to operate for signal recovery in an MMV model, rather than the SMV model considered in this paper. The proposed FROMPUS-based MUD shows the best performance out of all of the MUDs investigated in this paper, especially at higher SNR, while the Modified OMP-based MUD and the Modified SP-based MUD are the next best-performing MUDs, respectively. The results in Figure 3 illustrate the performances of all of the MUDs when the uplink GF-NOMA network is fully loaded. The performances of all of the MUDs follow the same trends when compared with the results presented in Figure 2. However, in Figure 4a,b, which shows the comparative performances of all of the MUDs when the network is overloaded with an overloading factor of 150%, it can be seen that the general performances of all of the MUDs are not as good as those presented in Figures 2 and 3. These results show that all of the MUDs find it difficult to recover the active users' transmitted signals in an overloading scenario. Under these conditions, it can be seen from Figure 4a that the proposed FROMPUS-based MUD still outperforms the Modified OMP-based MUD and the Modified SP-based MUD by 0.6 dB and 1.0 dB, respectively, and the other MUDs by 3.6 dB at a BER of \(10^{-2}\). In Figure 4b, the proposed FROMPUS-based MUD still outperforms the Modified OMP-based MUD and the Modified SP-based MUD by 0.7 dB and 1.6 dB, respectively, and the other MUDs by over 4.0 dB at a BER of \(10^{-2}\). The MUDs are assessed at a higher overloading factor of 300%, which is more aligned with massive connectivity in a typical uplink GF-NOMA network. The number of active users in the network is fixed at both \(\Im=20\) and \(\Im=30\), and the corresponding results are as shown in Figure 5a,b, respectively. With the other parameters fixed and the number of active users increased to \(\Im=30\), the performances of all of the MUDs deteriorate, with the Modified OMP-based MUD being affected significantly. The proposed FROMPUS-based MUD still shows exceptional performance at this stage, with a performance about 1.2 dB and 1.5 dB better than that of the Modified OMP-based MUD and that of the Modified SP-based MUD, respectively, and outperforms the other MUD by over 4.0 dB at a BER of \(10^{-2}\) in Figure 5a. The performance of the proposed FROMPUS-based MUD is better than that of the Modified SP-based MUD and the Modified OMP-based MUD, by about 1.0 dB and 2.0 dB, respectively, and is about 4.2 dB better than the other MUD at a BER of \(10^{-1}\). Figure 3: Achievable BER versus SNR performance of the FROMPUS-based MUD in comparison with five other MUDs: overloading factor = 100%, \(\Im=20\), and \(T=7\). Figure 2: Achievable BER versus SNR performance of the FROMPUS-based MUD in comparison with five other MUDs: overloading factor = 50%, \(\Im=20\), and \(T=7\). Figure 4: Achievable BER versus SNR performance of the FROMPUS-based MUD in comparison with five other MUDs, \(\Im=20\), and \(T=7\): (**a**) overloading factor = 150%; (**b**) overloading factor = 200%. The next set of results, shown in Figure 6a-c, are obtained when the MUDs are employed in the uplink GF-NOMA network for different values of the continuous time slots: \(T=5\), \(T=10\), and \(T=15\), respectively. The overloading factor is fixed at 200%,

Figure 5: Achievable BER versus SNR performance of the FROMPUS-based MUD in comparison with five other MUDs, overloading factor = 300%, \(T=7\): (**a**) \(\Im\) = 20; (**b**) \(\Im=30\). and the number of active users is fixed at \(\Im=20\). When the continuous time slot's value changes from \(T=5\) to \(T=10\), there is no obvious change in the performance of any of the MUDs.