## 5 Simulation Results
Nonetheless, the proposed approximation on the outage probability of the  
Figure 4: Numerical and simulated outage probability results versus SNR per information bit \(E_{b}/N_{0}\) at the destination of the CC-HIR-RS-CPS (\(\rho_{r}=0.5\) for all relays) and CC-HIR-RS-OPS schemes for different number of relays, direct communication, and one relay communication applying conventional DF strategy for \(R=0.5\) bit/s/Hz. CC-SIR-RS-CPS scheme given in (30) is very close to the simulation results. This finding confirms that the proposed analytical approximation of the outage probability is accurate enough and validates the adequacy of using the Monte Carlo method to calculate the integral in (29). In addition, Figure 5 reveals that the outage performance of the CC-SIR-RS-FLPS is better than that of the CC-SIR-RS-CPS for the whole range of SNR, which confirms the benefit of the fuzzy logic-based power-splitting approach. The outage performance behavior of the CC-SIR-RS scheme is similar to that of the CC-HIR-RS scheme with regard to increasing the number of relays and compared to the outage performance of the one relay communication with conventional DF strategy and that of the direct link communication. In addition, Figure 6 illustrates that the performance of the coded cooperative scheme with SIR deploying the proposed RGL model is better than that using the GL, SN, and SS models. The experiment is carried out for one relay \((R_{1})\), constant PSR \(\rho=0.5\), and threshold information rate \(R=0.5\) bit\(/\mathrm{s}/\mathrm{Hz}\). The figure shows that the performance of the coded cooperative scheme with SIR improves by approximately 1.7 dB, 1.4 dB, and 0.6 dB when using the RGL model compared to that using the SN, GL, and SS models, respectively, at the outage probability of \(10^{-2}\). This finding reveals that applying the RGL model is adequate for modelling the soft estimated symbols at the output of the relay soft encoder the SIR strategy, when the source-relay and relay-destination links experience Rayleigh fading. For the purpose of comparison between HIR and SIR strategies, Figure 7 illustrates the simulated outage probabilities of the CC-HIR-RS-OPS and CC-HIR-RS-FLPS schemes, which shows that the outage performance of the CC-SIR-RS-FLPS is slightly better than that of the CC-HIR-RS-OPS, whereas the outage performance comparison between the CC-HIR-RS-CPS and CC-SIR-RS-CPS schemes could be simply interpreted from Figures 4 and 5. It is worth noting that the simulations are carried out considering the SNR costs per information bit due to the CRC code applied by the HIR strategy to verify the error-free decoding of the received message from the source. In other words, the code rate at the relays with HIR strategy is \(R_{R}=K/(N_{R}+N_{CRC})\), where \(N_{CRC}\) is the number of additional check bits due to the CRC code and is equal to 16 in this work. Figure 5: Numerical and simulated outage probability results versus SNR per information bit \(E_{b}/N_{0}\) at the destination of the CC-SIR-RS-CPS scheme (\(\rho_{r}=0.5\) for all relays) and simulated outage results of the CC-HIR-RS-FLPS scheme for different number of relays, direct communication, and one relay communication applying conventional DF strategy for \(R=0.5\) bit\(/\mathrm{s}/\mathrm{Hz}\). In addition, Figure 8 shows the outage probability of the CC-HIR-RS-CPS and CC-SIR-RS-CPS schemes when applying different PSRs in the interval \([0.1,0.9]\). The performance of the CC-HIR-RS-OPS and CC-SIR-RS-FLPS schemes are also depicted through constant lines displaying the outage probabilities for a given relay number. The simulations are carried out for relay selection schemes with two and four relays, \(E_{b}/N_{0}=10\) dB, and threshold information rate \(R=0.5\,\mathrm{bit/s/Hz}\). The figure shows that the PSRs that attain the best outage performance for the CC-HIR-RS-CPS and CC-SIR-RS-CPS schemes are approximately 0.45 and 0.5, respectively.