###### Abstract
With this information at hand, the terminal can further exploit other important system information and complete its initial access to a serving cell. During the NR initial access procedure, the NR-PSS detection can be challenging due to the presence of substantial initial time and frequency offsets, which may result in performance degradation of the UE receiver [17; 18; 19]. To solve such a problem, a differential correlation strategy was devised to jointly detect the integer CFO (ICFO) and CIDS in the frequency domain [20; 21; 22; 23]. One approach presented in [20] is based on maximum likelihood (ML) detection, utilizing minimum mean-square-error (MMSE) reduced-rank approximation of the channel. Despite the ML approach offering optimal detection performance, its computational intensity makes it less suitable for practical implementations. Conversely, the joint synchronization of ICFO and NR-PSS presented in [21; 22] offers sub-optimal synchronization performance with moderate computational complexity as an alternative. In one paper [23], a reduced-complexity joint detection method for ICFO and NR-PSS was proposed using the cyclic-shifted property of NR-PSS. While this approach significantly reduces computational load, it does compromise performance to some extent. In 5G NR systems, the utilization of more affordable crystal oscillators in the UE may lead to considerable STO and CFO between the UE and the gNodeB. This misalignment introduces complexities in the process of performing the initial synchronization [13]. Moreover, utilizing beam-formed SS burst transmission with beam sweeping is essential for mitigating the increased channel propagation loss in the mmWave frequency band. However, due to beam sweeping, it may not be feasible to average NR-PSS synchronization over several time slots [9]. Since NR-SSS detection can only be carried out once the NR-PSS is completely recognized, the detection of NR-PSS becomes one of the utmost important and demanding tasks in the entire cell search procedure. As a result, developing a complexity-effective and still high-performance NR-PSS synchronization scheme becomes a crucial and difficult task in 5G NR communication systems. In this paper, we present a simplified formulation for NR-PSS synchronization in the 5G NR communication system. Using a cyclic-shifted feature of NR-PSS generated from m-sequence, we devise an effective ICFO and CIDS synchronization scheme without compromising detection performance. We theoretically derive the probability of detection failure of the proposed ICFO and CIDS synchronization scheme to assess its performance. Numerical examples indicate that the proposed ICFO and CIDS detection approach achieves comparable performance while significantly reducing complexity by over 90% compared to sub-optimal NR-PSS synchronization methods, regardless of the channel model. This makes it a promising candidate for the initial cell search in 5G NR communication systems. The remaining part of this paper is outlined as follows: In the next section, we introduce the signal model, SS, and cell search procedure in the 5G NR system. Section 3 presents our proposed joint ICFO and CIDS detection method, along with the theoretical performance analysis. Section 4 presents the experimental examples to verify the merits of the proposed NR-PSS synchronization scheme. Finally, in Section 5, we conclude with discussion.