# Adaptive Modulation Tracking for High-Precision Time-Delay Estimation in Multipath HF Channels
## 4 Simulation Results and Experimental Verification
### Verification of Actual Measurement Data  
The measured data are collected from the HF communication link from Xi'an, Shaanxi Province to Urumqi, Xinjiang Province, and the transmitted signal is modulated by 8 PSK with 196 code elements as one transmission cycle, the data length is 86 cycles, the center frequency is 12.36 MHz, the signal bandwidth is 9.6 kHz, and the sampling rate at the receiving is set to 120 MHz. The measured scenario covers the typical ionospheric propagation characteristics, and it has the characteristics of multipath effects and a slowly time-varying channel.  
In order to verify the actual performance of the MATE algorithm, it is analyzed in comparison with the GCC algorithm. The correctness of the algorithm is verified by analyzing the outputs of different branches, considering the real delay agnostic to the real test environment.  
Figure 11 shows the comparison of the delay estimation results of the two algorithms. The data show that the fluctuation amplitude of the delay estimation curve of the MATE algorithm (\(\sigma\) = 0.001 ms) is significantly lower than that of the GCC algorithm (\(\sigma\) = 0.049 ms), which reflects a stronger resistance to channel time-varying capability. In particular, the GCC algorithm shows significant estimation bias after the 75 th cycle,  
Figure 10: Time-delay estimation error results.  
Figure 9: Time-delay estimation results.  
which is due to the attenuation of the first arriving path gain as a result of the dynamic changes in the HF channel, whereas the GCC relies on the single-path correlation peak detection, which is susceptible to the change in the intensity of the multipath components.  
Figure 12 compares the distribution of correlation peaks corresponding to the acquisition frequency of the HF data in the 1 st and 78 th cycles, and it can be seen that the correlation peak energy of the first reach path in the 78 th cycle decreases by about 50% compared with that in the 1 st cycle, confirming the degradation of the first reach path gain due to channel fading, which is directly correlated to the fluctuation in the estimation of the GCC algorithm in this time period.  
Studies [28; 29] have shown that when the algorithm successfully locks the signal, the Prompt branch energy should be about twice as much as the Early and Late branches, and the in-phase component (I-path) is dominant, while the quadrature component (Q-path) tends to be close to zero. Figure 13 shows that the in-phase integral value of the Prompt branch of the MATE algorithm is stable at about 0.05, and the quadrature value is close to 0. In Figure 14, the energy of the Prompt branch is about twice that of the Early/Late branch, which verifies the effectiveness of the tracking loop and the accuracy of the phase estimation.  
Figure 11: Time-delay estimation results.  
Figure 12: Corresponding values for acquisition frequency.  
Figure 15 shows the key parameters of the tracking loop: the modulated signal number phase error (DLL output) is stable within \(\pm\)0.06 code slice, and the carrier phase error (PLL output) and carrier frequency error (FLL output) are close to 0, which indicates that the loop successfully achieves carrier stripping and phase locking. The MATE delay estimation values in Figure 15d show a narrow band distribution around the mean value of 9.93 ms, which further verifies the high-accuracy characteristics of the algorithm in real channels.  
Figure 14: Comparison of Prompt–Early/Late Energy.  
Figure 13: Comparison of in-phase and quadrature energy.