## 4 Simulation and Experimental Results  
The start and end frequencies of the LFM synchronization signal were \(f_{0}=7.5\) kHz and \(f_{1}=12.5\) kHz, respectively, and its duration was \(T_{\text{Sync}}=25.6\) ms. Therefore, according to (8), the ratio of the bias delay to the Doppler was \(\rho=-0.064\) s. The duration of the quadrature phase shift keying (QPSK) symbol was \(T_{\text{Sym}}=0.2\) ms and the passband and baseband sample intervals were \(T_{\text{PB}}=0.0125\) ms and \(T_{\text{BB}}=0.1\) ms, respectively. For example, with a Doppler scaler \(\gamma=0.001\), the delay bias after the correlation was \(\Delta=\rho\gamma=0.064\) ms, which caused a symbol phase rotation of \(115.2^{\circ}\), and therefore the adaption of the equalizer was necessary if the bias was uncompensated. In the packet, there were \(N_{\text{Frm}}=14\) frames whose individual duration was \(T_{\text{Frm}}=0.4928\) s, and the total number of the LFM signals was \(N_{\text{Frm}}+1=15\), which was equal to the sizes for both the input and output of the DNN model. Table 1 outlines the hyper-parameters of the DNN model. The model was trained in the simulation data generated in accordance with Figure 1, with a constant wind speed of 15 m/s. The number of training samples was 100,000, with the epochs being 50. The training was completed in 56 s on a laptop computer with an Intel i7-8750 CPU at a 2.2 GHz clock frequency. The bias was estimated by the trained DNN model and eliminated in the delay estimation. The unbiased positions of the LFMs were interpolated by the cubic spline function to obtain the timing offset for the whole packet. For comparison, the unbiased positions were interpolated by the linear function in the simulations. The additional positions used include biased positions directly given by the correlation and perfect positions. The number of the validation samples was 2000 for each wind speed condition, and the wind speed in the test varied from 5 to 25 m/s. The root-mean-square errors (RMSEs) of the timing offsets for the whole packet were compared in the simulations, as shown in Figure 4. It should be noted that we first investigated the performance of the DNN models trained at different wind speeds to select the appropriate DNN model, and the results are shown in Figure 4 for comparison. It can be concluded that the model trained at a specific wind speed can cope with all test scenarios at lower wind speeds and some test scenarios at higher wind speeds within a certain range, since the spectral component of high wind speed can cover the spectral component of low wind speed. However, for extremely high wind speeds, the sample distribution space is wider, and more training samples are needed to avoid overfitting. Based on the above factors, in the following analysis, the network model trained at a wind speed of 15 m/s was adopted to process the test data. We then focused on the performance comparison of the pairwise combination of the three LFM position estimation methods and the two interpolation methods. The biased LFM synchronization performed the worst for both interpolation methods, and because of the bias causing RMSE degradation, spline interpolation did not improve the performance as compared to linear interpolation. After the bias was eliminated through  
Figure 3: The timing offset compensation in the baseband. the DNN model, it performed nearly the same as the perfect LFM synchronizations under the condition of either interpolation method, and specifically, spline interpolation could obtain a half-RMSE of linear interpolation. For the proposed scheme of the DNN model and spline interpolation, the RSME was nearly 0.01 ms in various wind speeds, which means a phase rotation error of 18\({}^{\circ}\). The RMSE floor was mainly caused by the high-frequency components of the surface motion and the limited repetition frequency of the LFMs. Increasing the LFMs for the same packet duration suppressed the RMSE but sacrificed the transmission bandwidth.