# Adaptive Modulation Tracking for High-Precision Time-Delay Estimation in Multipath HF Channels
## 5 Discussion  
This study proposes the Modulation Signal-based Adaptive Time-delay Estimation (MATE) algorithm. MATE achieves significant improvements in time-delay estimation accuracy within complex HF channels by decoupling carrier and modulation signals, as well as integrating PLL and DLL techniques. Simulation results based on the Patterson channel model demonstrate that MATE achieves an average time-delay estimation error of approximately 0.01 ms with a standard deviation of approximately 0.01 ms. Compared to the traditional GCC method, MATE represents a 94.12% reduction in mean error and a 96.43% reduction in standard deviation. This performance enhancement is attributed to MATE's effective utilization of the autocorrelation properties of 8 PSK signals, enabling compensation for carrier frequency offsets and suppression of multipath interference. Crucially, compared to existing approaches, MATE eliminates the dependency on pseudo-random sequences and is directly applicable to non-spreading modulation schemes such as 8 PSK. This overcomes a key limitation of conventional methods, which often rely on specific signal formats, and demonstrates superior resilience against frequency-shift perturbations, robustness under multipath conditions, and enhanced algorithmic generalizability. Validation using actual measurement data from the Xi'an-Urumqi HF link confirmed the algorithm's robustness in real-world ionospheric environments. Notably, when the energy of multipath components varied dynamically, the GCC algorithm exhibited significant estimation bias due to its reliance on single-path correlation peak detection. In contrast, MATE's tracking loop, incorporating real-time phase locking, maintained estimation stability, with its delay estimation fluctuation (\(\sigma=0.001\) ms) being substantially lower than that of GCC (\(\sigma=0.049\) ms). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Computational Complexity** & **Running Time of Measured** \\  & & **Data (s)** \\ \hline MATE & \(O(NlogN)+(K-1)O(N)\) & 80.22 \\ GCC & \(KO(NlogN)\) & 189.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of algorithm complexity. However, this study has certain limitations. Primarily, the current algorithm is designed for narrowband HF channels (bandwidth \(\leq\) 10 kHz), and its applicability to broadband scenarios requires further investigation. Furthermore, although MATE outperforms traditional methods in multipath environments, its resolution capability in dense multipath scenarios remains constrained by the signal's autocorrelation properties, potentially leading to estimation ambiguities. Future research will explore extending MATE's applicability to higher-order modulation schemes such as QAM to enhance cross-scenario adaptability, investigate the integration of sparse reconstruction techniques (e.g., Orthogonal Matching Pursuit algorithm) to improve resolution in dense multipath environments, examine fusion with deep learning methodologies to leverage neural networks for robust feature learning and noise modeling, and address broadband challenges through extended HF channel models and corresponding algorithmic adaptations. The findings of this study provide crucial technical support for HF applications such as over-the-horizon positioning and ionospheric sounding. MATE offers a high-precision, robust, and relatively low-complexity solution to the time-delay estimation problem in complex HF channels. More importantly, the enhanced precision and robustness of MATE in estimating signal time-of-arrival directly translate to improved accuracy and reliability for a wide range of sensor systems that rely on HF signal propagation for timing, positioning, or environmental sensing. This includes distributed HF sensor networks for remote monitoring and HF-based remote sensing platforms, where precise TOA detection is fundamental to data integrity and system performance. Conceptualization, H.W. ; Methodology, Q.J. ; Software, Q.J. ; Validation, Q.J. ; Resources, H.W. ; Supervision, H.W.