## 4 Simulation Results
### Performance Evaluation
This observation can be explained by the fact that more hypotheses are required for ICFO detection than for CIDS detection, consequently resulting in a higher probability of detection failure. By employing a 127-length m-sequence with its near-zero autocorrelation feature, the probability of accurately detecting ICFO and CIDS under a non-zero CFO hypothesis increases in comparison to LTE-A systems [20; 21]. Figure 2: The probability of detection failure of the proposed NR-PSS synchronization schemes in AWGN and flat fading channels: (**a**) \(\eta=0\) (**b**) \(\eta=0.1\). Figure 5 offers a comparative analysis of the complexity and performance associated with the NR-PSS synchronization schemes versus \(M_{\rm p}\) and \(U\), respectively, when \(SNR=-5\) dB. When \(M_{\rm p}\) is fixed, it becomes apparent from Figure 5a that the proposed method significantly reduces computational complexity by 60.0% and 96.1% over the JDI-CID and AMMSE methods, respectively, demonstrating the tradeoff between detection capability and arithmetic operation. On the other hand, the SDICID method can be implemented with approximately 0.9 times the complexity on average compared to the proposed method. Figure 4: The probability of detection failure of the benchmark and proposed NR-PSS synchronization schemes versus SNR: (**a**) ICFO detection (**b**) CIDS detection. Figure 3: The probability of detection failure of the benchmark and proposed NR-PSS synchronization schemes versus SNR: (**a**) \(M_{\rm o}=1\) (**b**) \(M_{\rm o}=10\). NR-PSS detector, at the cost of detection performance. In Figure 5b, the detection probability denoted by \(\text{Prob}\{(\hat{v},\hat{w})=(\upsilon,w)\}\) is evaluated in the Vsd channel. As predicted, it is shown from Figure 5b that the performance of the NR-PSS detection methods undergoes degradation with an increase in \(U\). However, this decline in performance is relatively minor thanks to the adoption of the m-sequence. This phenomenon becomes apparent as \(M_{\upsilon}\) increases. For detection methods other than the AMMSE approach, achieving a target detection probability of 90% necessitates averaging over more NR-PSS symbols. Hence, employing the average estimate across multiple SSBs serves as a potential solution to enhance poor coverage areas, which will be further investigated in the following example. Figure 6 depicts \(P_{f}\) for the various NR-PSS synchronization schemes as a function of \(M_{\upsilon}\) at SNR values of \(-10\) and \(-5\) dB. To achieve the target detection probability of 90%, we denote the required number of averages as \(M_{a}\). When \(\text{SNR}=-5\) dB, it is evident from Figure 6a that the AMMSE and SDICID approaches use \(M_{a}=6\) and 17, respectively, while both JDICID and the proposed method require an average estimation of 11 NR-PSS symbols to achieve the target probability under the Vds channel condition. With this observation at hand, the arithmetic burden of the proposed method required to achieve the same target probability is reduced by 23.9%, 60.0%, and 93.0% compared with that of the SDICID, JDICID, and AMMSE approaches, respectively. More interestingly, the number of averaging symbols is substantially decreased in the case of the Vld channel, thanks to the time diversity effect across multiple SSBs. Compared to the results in Figure 6a, a larger \(M_{a}\) is required to obtain the target probability when \(\text{SNR}=-10\) dB, thereby leading to an increase in processing latency. On the other hand, the number of average estimations needed in the AMMSE method increases from \(M_{a}=1\) to 8 in the Vld channel, while the SDICID approach experiences a similar increase from \(M_{a}=5\) to 30. For both the JDICID and proposed methods, \(M_{a}\) increases from 3 to 18. In this case, the proposed method exhibits a 28.7%, 60.0%, and 91.4% reduction in complexity compared to the SDICID, JDICID, and AMMSE methods, respectively.