# A Linear Strong Constraint Joint Solution Method Based on Angle Information Enhancement
## 5 Experimental Performance Verification  
### Time Frequency Synchronization Performance Verification  
To verify the time-frequency synchronization performance, the experimental parameters are shown in Table 1:  
Among them, the carrier frequency is 3.5 GHz, the subcarrier spacing is 30 kHz, the SSB uses Case B type, the number of resource blocks is 20, and the generated SSB time-frequency resources are shown in the figure below. On this basis, data are inserted into all symbols except for the symbol where the SSB is located. The resource allocation is shown in the following Figure 4, the SSB occupies 4 consecutive OFDM symbols in the time domain, and occupies 20 RBs (240 subcarriers) in the frequency domain. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Carrier Frequency & 3.5 GHz & Case types of SSB & B \\ Subcarrier Spacing & 30 kHz & Normalized & 0.25 \\ Fast Fourier & & frequency offset & 0.25 \\ Transform Point & 512 & Number of resource blocks & 20 \\ Number \(N_{\text{FFT}}\) & & & \\ Cyclic Prefix Mode & normal & Cell ID & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Time frequency synchronization parameter setting. Figure 4: SSB resource allocation diagram. (1) Timing coarse synchronization simulation and analysis  
Firstly, simulate and analyze the group peak accumulation timing coarse synchronization algorithm based on multi-window joint estimation. The subcarrier spacing of the SSB is 30 kHz, the CP type is conventional, and the number of Fourier transform points is 512. Therefore, only the CP of the first and fifteenth symbols are long CPs, corresponding to a length of 44 sampling points, while the CP of the remaining symbols are short CPs, corresponding to a length of 36 sampling points. If the propagation distance of wireless signals in the channel corresponds to a length of 500 samples. In this section, simulations were conducted for SNR = 5 dB, 15 dB, 25 dB, and 35 dB. The results are shown in the following Figure 5. When the signal-to-noise ratio is high, the accumulated group peaks are prominent, and the relative position relationship between each peak is obvious. As the received signal power decreases, although the peak can be identified, the peak to average ratio gradually decreases, and the relative position relationship between each peak gradually becomes blurred. The performance of the single group sliding window timing coarse synchronization method is simulated in Figure 2. Under low signal-to-noise ratio, this method cannot identify obvious peaks, and the relative relationship between group peaks is fuzzy, making it impossible to obtain timing synchronization information from them. From this, the algorithm proposed in this section has high robustness and still has coarse timing function under low SNR. Figure 5: Performance comparison of peak accumulation timing coarse synchronization algorithms for multi-window joint estimation under different SNR. In simulation, RMSE is used to evaluate the performance of the algorithm, which is defined as:  
\[RMSE=\sqrt{\frac{\sum_{p=1}^{P}\mid\hat{\pi}_{p}-\alpha_{true}\mid^{2}}{P}} \tag{67}\]  
Among them, \(\alpha_{true}\) represents the normalized true values of the CFO and STO, \(\hat{\pi}_{p}\) represents the estimated value of the \(p^{th}\) experiment, \(P\) represents the number of independent Monte Carlo experiments, and the results are calculated using \(P=500\). As shown in the above Figure 6, the synchronization performance of the CP-based timing coarse synchronization detection method deteriorates with the decrease in signal-to-noise ratio, and the traditional single window timing detection method is more sensitive to changes in signal-to-noise ratio. In low signal-to-noise ratio environments, traditional methods not only have inaccurate coarse synchronization, but also have a large degree of estimation dispersion, making it difficult to obtain accurate and stable synchronization performance.