## 3 The Proposed Detector for Uplink GF-NOMA Networks: FROMPUS
### Node C: Reverse-Select
However, when the continuous time slot's value changes to \(T=15\), the performances of all of the MUDs slightly improve, taking advantage of the slightly longer time slots. The last set of results in Figure 6(a),b shows the effects of increasing the overloading factor to more than 300, and increasing the number of active users to more than 30. In Figure 6(a), it can be seen that when the overloading factor is increased to 400% and the number of active users is fixed as 30, the performances of all of the MUDs deteriorates, with the proposed FROMPUS-based MUD still showing better performance than the other MUDs at higher SNR. It should be noted that most of the results presented in the literature are for overloading factors between 100% and 300%. Furthermore, as the number of active users increases to 40 from 20 with the overloading factor fixed at 200% (in comparison with Figure 3(b)), similar performance deteriorations are seen in all of the MUDs for the scenarios considered in this paper, while the proposed FROMPUS-based MUD still exhibits better performance than the other MUDs at higher SNR. Figure 6: _Cont._

Figure 6: Achievable BER versus SNR performance of the FROMPUS-based MUD in comparison with five other MUDs, overloading factor = 200%, \(\Im=20\): (**a**) \(T=5\); (**b**) \(T=10\); (**c**) \(T=15\). ## 5 Computational Complexity Analysis

This section presents the order of computational complexity cost for each of the MUDs, computer simulation results of which are documented in Section 4. The least expensive MUD in terms of computational complexity cost is the Comp Efficient OMP-based MUD, with a computational complexity cost of order \(O\left(UlogU\right)\). The OMP-based MUD has a complexity cost of \(O\left(N\Im^{2}\right)\). The complexity cost of the SOMP-based MUD is \(O\left(NU\Im^{2}\right)\). The Modified OMP-based MUD has a complexity cost of order \(O\left(\Im\left(NU+\Im^{2}N\right)\right)\), while the complexity cost of the Modified SP-based MUD is \(O\left(\Im\left(NU+\Im^{2}+\Im N\right)\right)\). The proposed FROMPUS-based MUD's complexity cost is higher than all of the other MUDs

Figure 7: Achievable BER versus SNR performance of the FROMPUS-based MUD in comparison with five other MUDs, \(T=5:\)(**a**) overloading factor = 400%, \(\Im=30\); (**b**) overloading factor = 200%, \(\Im=40\). except for the SOMP-based MUD, with its computational complexity cost estimated to be on about an order of \(O(\Im(5 NU+\Im(\Im+N+\Im N)))\). Given the advances in integrated circuit technology, the use of the FROMPUS-based MUD in uplink GF-NOMA networks will not be impeded by its computational complexity cost to a degree acceptable at the BS. Comparative complexity costs, along with some numerical results for all of the MUDs, are shown in Table 1.

## 6 Conclusions and Future Works

Different MUDs have been proposed in the literature, with some suffering from poor performance and some showing good performance but suffering from high computational complexity costs. This paper presents a new multiuser detector named Forward-Reverse OMP-Union-SP (FROMPUS)-based MUD. The proposed method shows good performance and also exhibits acceptable computational complexity cost in comparison with the other MUDs considered in this paper. For the detection procedure, FROMPUS exploits the idea of an initial support set, which serves as initial knowledge and is employed in the reconstruction of the active users' transmitted signals. This enhances the detection process of FROMPUS. Furthermore, FROMPUS takes advantage of the \"serial include\" technique of incorporating a potential candidate element in the support, as well as the reliability testing procedure in which the most prominent support set elements are selected from a pool of available elements. From the simulation results presented, it is evident that FROMPUS employs these features to enhance its performances: the FROMPUS-based MUD shows excellent performance in comparison with the other MUDs considered in this paper.