# Best Relay Selection Strategy in Cooperative Spectrum Sharing Framework with Mobile-Based End User
## 3 Performance Analysis
On the other hand, this improvement would consume more power and would cost a bit more complexity to the system design where more relays are needed to be deployed. Appealingly, the simulation and analytical results are in perfect agreement, and the system performance might be improved by adding more relays inside the SU. The performance of the system model under different fading severity parameters of the channels between the SU relays \(R_{k}\) and SU destination \(D\) is shown in \[\gamma_{D}=max_{k=1,2,...,N}\{\gamma_{k}\} \tag{8}\]7 In particular, several values for \(m\) parameter of the complex Nakagami-\(m\) model were investigated where \(m<1\). It can be noticed that higher OPs occurred at small values of the \(m\) parameter. This is due to the impede of the direct propagation link. Specifically, more severe fading can be faced as \(m\) decreases and, therefore, a few indirect components would be recognised at the destination from the multipath. As a result, the case that assumes \(m=0.9\) (i.e., the less severe situation) performed better than the other cases because the transmitted signal would be less affected by the atmospheric conditions and the movement of the SU destination compared with the other cases. Moreover, it can be seen that as the maximum allowed interference power increases, the OP decreases and becomes less affected to inter-carrier interference at high vehicular speeds. The analytical and simulation results are identical for all cases. The PU location impact is investigated in \[\gamma_{D}=max_{k=1,2,...,N}\{\gamma_{k}\} \tag{8}\]8 The figure provides the OPs for different PU locations. The obtained results show that the PU location plays a crucial factor in the system performance. In particular, the OP decreases as the PU receiver departs from the SU and the interference threshold can be tolerated. This means that the OP becomes less sensitive to inter-carrier interference as the PU departs from the SU and, therefore, the case where the PU is located at (0.8, 0.8) is considered the best case among the others. Moreover, the numerical and simulation results are perfectly matched for all considered cases. \[\gamma_{D}=max_{k=1,2,...,N}\{\gamma_{k}\} \tag{8}\]9 OPs of CRN with mobile end user under different number of SU relays, (\(m=0.5\), \(speed=100\) Km/h). Finally, it is noteworthy to mention that all links connected with the mobile end user (i.e., SU \(D\)) are modelled using Nakagami-\(m\) distribution. Figure 5 shows a comparison of the OPs if the links connected with the mobile end user are modelled using Rayleigh distribution instead of Nakagami-\(m\) distribution. It can be seen that by modelling these links using the Rayleigh model, the OPs are the same under various speeds, which does not reflect the rapid changes in the actual environment for high vehicular speeds. It is doubtful to have the same OPs under different speeds of mobile end users and, hence, modelling these channels using Rayleigh distribution does not reflect the actual rapid changes of the environment. Therefore, the Nakagami-\(m\) fading model with \(m<1\) is considered superior compared with Rayleigh model and is considered the best fit model for such a scenario by obtaining different OPs under different speeds of the mobile end user. On the other hand, Figure 5 shows that, for the Nakagami-\(m\) model, as the mobile end user moved at high vehicular speeds, an increase in the OPs is observed and this is due to the increase in the rapid changes in the actual environment as the mobile end user speed increases. In addition, the system performance improved as the severity parameter \(m\) increased, which  
\[OP=P_{r}\Big{[}max_{k=1,2,...,N}(\gamma_{k})\leq 2^{2R_{0}}-1\Big{]} \tag{9}\]0 OPs of CRN with mobile end user under different PU locations, (\(m=0.5\), \(N=2\), \(speed=100\) Km/h). \[OP=P_{r}\Big{[}max_{k=1,2,...,N}(\gamma_{k})\leq 2^{2R_{0}}-1\Big{]} \tag{9}\]1 OPs of CRN with mobile end user under different severity parameters, (\(N=3\), \(speed=100\) Km/h). means a less severe environment.