## 4 Performance Evaluations
### Lake Experiment  
In order to further verify the performance of the proposed turbo equalizer, a lake experiment was carried out in Dongjiang Lake on 6 July 2023, and the experimental scene layout is shown in Figure 8. The underwater communication distance is 6 km, the transmitting transducer and the receiving hydrophone are at a water depth of 30 m, the two platforms move relative to each other, and the parameters of the SC signal transmitted in the experiment are consistent with the simulation. To compare and analyze the proposed turbo equalizer, the communication experimental data were processed accordingly, and three experimental scenarios were simulated in which the correlation peaks could be accurately identified, the correlation peaks could not be identified, and with the presence of multiple correlation peaks. The corresponding times of these three scenarios correspond to 11:54:45, 11:56:25, and 11:58:05, respectively. Three sets of typical experiments are selected for detailed comparison and analysis, and the cross-correlation results between the communication waveform and the LFM signal are  
Figure 7: Comparison of equalizer performance under different conditions. shown in Figure 9. The experiments are processed by two methods: the conventional TEQ based on timescale estimation and the proposed DAM-TEQ. For the three sets of experiments, the constellation diagram obtained by the two equalizer processing methods is shown in Figure 10. In the first set of experiments, the precise position of the synchronization signal before and after the signal frame can be obtained by the method of cross-correlation and maximum search, and the received signal can be accurately processed by using the traditional Doppler estimation compensation method and turbo equalization, and the results show no BER. At the same time, the constellation diagram conforms to the characteristics of the BPSK-modulated signal, as shown in (a), (b) in Figure 10. However, in the second and third sets of experiments, due to the influence of complex time-varying channels such as multipath effects, the  
Figure 8: Experimental setup. Figure 9: Correlation output between the communication signal and the LFM. phenomenon of weak correlation peaks or multiple correlation peaks appeared, and the accurate correlation peak position could not be obtained, resulting in the failure of the conventional method to work on an accurate timescale. Doppler compensation cannot be used to estimate the signal frame duration accurately. The processing results show a high BER, and the constellation diagram distribution is chaotic, as shown in (c), (d), (e), and (f) in Figure 10. In this method, the decoding performance cannot be improved after multiple iterations of turbo equalization, which means that turbo equalization fails. Correspondingly, the DAM-TEQ can adaptively update the resampling branch through the coefficient detection method, realize a Doppler estimation and compensation, and obtain a better BER performance for the three sets of experiments. It can be seen from the constellation diagram of the three sets of experiments that there is a slight error in the Doppler rough estimation of the first stage of the proposed equalizer, which causes the constellation diagram to rotate slightly, but it is still within an acceptable range, which can be corrected by parallel turbo equalization. At the same time, the compensated signal can be decoded by multiple iterations of the turbo equalizer to achieve error-free information transmission. The results of each group of experiments were compared and presented by BER (no iteration), as shown in groups 1, 3, and 5 in Table 3. In addition, the table also records the number of branch updates and iterations with a BER of 0 after using the DAM-TEQ.