# Chaotic Orthogonal Composite Sequence for 5G NR Time Service Signal Capture Algorithm
## 1 Introduction
[PERSON], [PERSON] et al. [21] proposed a wireless time synchronization scheme containing a 5G air interface, discussed related timing errors, and finally identified and resolved random errors unique to dense multipath fading environments. [PERSON], [PERSON] et al. [22] developed synchronizing three qubits to oscillate at the same frequency by applying an external field with a wavelength of 813.32 nm during 5G timing, significantly improving the stability of the timing system under various noise intensities. [PERSON], [PERSON] et al. [23] believed that in the 5G timing system, the radio link between base stations and user equipment (UE) would be affected by propagation delays, and they considered round-trip time (RTT) to be the only suitable method for achieving the most stringent time error budget requirements. [PERSON], [PERSON] et al. [24; 25] provided a detailed introduction to the physical layer of 5G NR, studied the performance of the 5G NR time synchronization process with imperfect channel state information (CSI), described the time synchronization process required for 5G NR, and evaluated the corresponding coverage probability and ergodic capacity under different scenarios of imperfect frequency offset correction and imperfect CSI. They ultimately concluded that the main challenge of the 5G NR system is time frequency synchronization under various newly defined frequency conditions. [PERSON] et al. [26] proposed achieving time synchronization in the 5G NR uplink by using block interleaved frequency division multiple reference signals (RS), effectively solving the aliasing effect caused by pseudo-paths in multipath channels when the channel transitions from the frequency domain to the time domain. In summary, the above researches are all based on the 3 GPP TS 38.331 standard protocol and study the part of the system information block (SIB9) in the existing 5G air interface system information that contains timing information. Most of them focus on reducing the impact of related noise on the 5G signal transmission path and do not involve the signal itself. The timing information in this 5G timing method is already specified in the 5G signal according to the 3 GPP TS 38.331 standard protocol, and it requires occupying a certain amount of 5G communication signal bandwidth. The 5G NR time service signal proposed in this paper is hidden in the 5G signal and transmitted through 5G base stations. This not only solves the disadvantage of traditional satellite timing signals being easily blocked but can also be applied to indoor scenarios where satellite signals cannot be received, providing time synchronization services for downstream devices [27; 28; 29]. Moreover, the 5G NR time service signal in this paper adopts a spread spectrum signal system, transmitting a weak power signal that appears to be \"submerged\" in the power of the 5G communication signal, sharing the 5G communication frequency band without occupying the 5G communication signal bandwidth. Capture technology, as a key part of spread spectrum signal reception technology, ensures that the receiver can correctly identify and decode the transmitted signal, which is crucial for maintaining the integrity and reliability of the communication link. The chaotic orthogonal combination spread spectrum sequence constructed in this paper has improved security over m-sequences [30], better autocorrelation than Walsh sequences [31], and the ability to effectively suppress the short-period characteristics that appear when the Tent-Map chaotic sequence [32; 33] takes special values. Using a parallel code phase search algorithm based on FFT, compared to traditional correlation capture algorithms, our approach greatly reduces the number of searches and capture time, improving the signal reception efficiency.