# A Linear Strong Constraint Joint Solution Method Based on Angle Information Enhancement
## 3 A Synchronization and Fine Ranging Method Based on the 5G Signal  
### A Three-Stage Time-Frequency Synchronization Method Based on Group Peak Time Sequence Tracing  
When receiving 5G signals, the terminal gradually performs time-frequency synchronization, cell search, and obtains physical broadcast information of the cell based on the SSB. 5G NR introduces a global synchronization grid and a global synchronization channel number (GSCN), and the absolute frequency domain position of the SSB is placed on the global synchronization integer grid. The terminal searches at intervals of the global synchronization grid to obtain the absolute frequency domain position of the SSB. There are six configuration schemes for the time-domain transmission period of the SSB, including 5 ms, 10 ms, 20 ms, 40 ms, 80 ms, and 160 ms. In the actual downlink transmission process, due to the non-transparency of configuration information by users, the terminal assumes a cell search using the SSB with a transmission period of 20 ms after receiving the signal. When the user receives SSB information, they decode the PBCH to obtain the Master Information Block (MIB), perform blind detection using the MIB to obtain the System Information Block (SIB) information, and finally obtain the SSB transmission cycle through the SIB. Among them, the MIB provides various key physical layer parameters such as system frame number, bandwidth configuration, subcarrier spacing, and PDCCH configuration; the SIB provides detailed system and network information to ensure that terminals complete operations such as access, registration, and reselection. Accurate time-frequency synchronization is crucial for obtaining timely and accurate configuration and network information. The time-frequency synchronization algorithm is mainly divided into two types: PSS sequence cross-correlation detection and CP-based detection, aiming to obtain the time-frequency information of the PSS and the sector number \(N_{ID}^{(2)}\). The method based on the PSS sequence cross-correlation detection has good resistance to multipath and noise, and can accurately estimate timing information even in low signal-to-noise ratio situations. It can also  
effect is not significant. The reason for frequency offset is often due to the phenomenon of frequency asynchrony between the receiving and transmitting ends. Therefore, normalized frequency offset is often a decimal. This article uses a CP-based frequency offset estimation method to estimate and compensate for frequency offset. Afterwards, a method based on sliding PSS cross-correlation was used for fine timing synchronization, ultimately obtaining cell ID information, channel control information, and configuration information of various resources. In this section, coarse timing estimation is carried out through the group peak timing based on sliding window. Then, frequency offset cancellation is performed based on the CP. Finally, fine time-frequency information synchronization is achieved based on the PSS cross-correlation method. After time-frequency synchronization through the SSB, the SIB can be parsed to obtain relative time-frequency position information of the PRS. Tracking of the PRS is implemented to achieve high-precision distance measurement. 1.1 Group Peak Accumulation Timing Coarse Synchronization Algorithms for Multi-Window Joint Estimation  
Assuming that the expression of the time-domain baseband signal at the transmitting end is \(x[n]\) and the frequency-domain expression is \(X[k]\); The time-domain expression of the receiver is \(y[n]\), and its corresponding frequency-domain expression is \(Y[k]\). The CP of 5G NR serves as a guard interval and has the same data as the symbol tail, which can effectively perform timing synchronization. Assuming that the number of sampling points for the long CP in OFDM symbols is \(N_{CP}\), the number of sampling points for short CP is \(N_{cp}\), and the number of sampling points for each symbol is \(N_{FFT}\).