## 5 Simulation Results and Discussions
### Performance Evaluation  
Figure 3 presents the probability of failure \(P_{f}\) in detecting IFO in the AWGN channel. The theoretical analysis of the proposed scheme is obtained using (37) and the simulated results of the conventional schemes are plotted as benchmark. It is evident that the simulated curves match well with the theoretical curves in the case of the proposed method. More importantly, it can be seen that the probability of detection failure of the existing methods is significantly influenced by the presence of residual STO, while the performance of the proposed detection scheme is independent of \(\tau_{max}\). This robustness is obtained by using the temporal correlation from the received PSSS and SSSS sequences instead of differential correlation. Consequently, the influence of residual STO on the detection performance is eliminated in the process of performing (16). However, the performance  
Figure 2: Number of flops of the conventional and proposed joint detectors versus \(M\). degradation of the proposed detection scheme over the conventional methods is observed for low SNR values, which is the penalty for robustness to residual STO. This is attributed to the fact that squaring temporal correlation as described in (19) results in SNR loss. Because of its severe sensitivity to symbol timing errors, the benchmark methods do not work properly in the presence of residual STO especially as the SNR increases. Figures 4 and 5 show the overall probability of failure \(P_{o2}\) in jointly detecting IFO, SI, and sidelink ID in the various channel models characterized in Table 1. From the presented results, it can be seen that the detection accuracy of all detection schemes is affected by the amount of the frequency selectivity of the channel. This phenomenon is more pronounced for the conventional detection schemes, which is explained by the fact that the existing detection methods exploit the differential correlation under the assumption \(C_{l}(k)\approx C_{l}(k-1)\). This approximation proves to be valid for weakly frequency-selective channels as AWGN and EPA models, but is less appropriate for high frequency-selective channels as ETU and EDS. As reported in [34; 35], a typical SNR of LTE signal is around 5 dB in most cell areas and over 20 dB SNR is achieved in the cell center, while a low SNR of 0 dB or below can be observed near the cell edge. When there is frequency selectivity and residual STO, the performance of the proposed sequential method is still superior to that of the conventional method since the SSSS detection can be performed only after the PSSS being successfully identified. Specifically, the SNR regions of which the proposed scheme shows better performance are above 5 dB and 1 dB in the EPA and EDS channel models, respectively. Another interesting observation from Figure 5 is that a performance degradation in the proposed scheme occurs due to the high Doppler frequency especially in the ETU channel, however the impact of Doppler frequency on its detection performance is not critical. Since the frequency selectivity and STO are inevitable in D2D applications, it is concluded that the proposed detection scheme achieves good overall detection performance in a typical LTE SNR range with the complexity not higher than existing detection methods. Figure 3: Performance of the proposed and conventional detectors in the additive white Gaussian noise (AWGN): (**a**) \(\tau_{max}=0\) (**b**) \(\tau_{max}=10\). Figures 6 and 7 depict \(P_{o1}\) of the joint detection schemes using the extended CP and normal CP, respectively, when they have about the same computational complexity and \(\tau_{max}=20\) is set. Since the complexity of the proposed method is about half that of existing methods as shown in Figure 2, we average the proposed metric over two pairs of the synchronization signals in (25) so that the proposed IFO and SI detection scheme has approximately the same complexity as the conventional RCJD scheme when \(M=3\).