## 4 Results
### Experiments
The received SNR is approximately 10.08 dB. In total, we received 88 frame signals in this trial. Figure 14 shows that the overall carrier Doppler frequency shift is within 3 Hz, and the receiving ship drifts to the transmitter during the lake trial. The frame BER results are plotted in Figure 15, where Figure 15a is the comparison result after one turbo iteration and Figure 15b is the result after four turbo iterations. For convenience, we place the frames without symbol error on the level of BER = \(10^{-4}\). It is obvious that the proposed VSTD-TEQ substantially outperforms the conventional SDA-TEQ and VSD-TEQ. After four turbo iterations, the number of frames involving the symbol error of the proposed VSTD-TEQ decreases rapidly, while the SDA-TEQ still retains abundant frames with detection errors. Figure 11: The experimental set-up of lake trial. Figure 14: Estimated carrier Doppler frequency shift of 1500 m received frames (the red asterisk is the mean carrier Doppler frequency shift of one frame). Figure 12: Example of received signals of the 1500 m lake trial. Figure 13: Estimated CIRs of the 1500 m lake trial over a period of time. Figure 15: Frame BER comparisons of the 1500 m lake trial. The results of BER range comparisons are shown in Figure 16, and the BER values of 1500 m received frames are divided into several intervals. In Figure 16a, 79.55% and 87.50% of the received frames achieve zero symbol errors for the VSD-TEQ and VSTD-TEQ, respectively, after one turbo iteration. In Figure 16b, after four turbo iterations, 95.45% and 98.86% of the received frames achieve zero symbol errors for the VSD-TEQ and VSTD-TEQ, respectively. On the contrary, there are only 71.60% frames that reach BER = 0 with SDA-TEQ after four turbo iterations. Moreover, there are 6.82% frames that remain at BER \(>10^{-1}\) gradation. Apparently, the comparison results above strongly express the BER performance superiority of the proposed VSTD-TEQ over the SDA-TEQ. The overall performance comparison is presented in Figure 17. In the first iteration, the MSE between the VSD-TEQ and VSTD-TEQ is almost no different. The reason for this is the absence of _a prior_ information about the detection symbols. With four turbo iterations, the MSE difference attains about 5 dB between the VSTD-TEQ and the SDA-TEQ. The contribution of the fractionally spaced structure SISO equalizer is more than the bidirectional combination. In Figure 17b, the total BER of the 1500 m lake trial is decreased from \(1.50\times 10^{-2}\), with the SDA-TEQ, to \(2.22\times 10^{-5}\), with the VSTD-TEQ. The bidirectional combination sped up the convergence rate of the turbo iterations: the iterative time of convergence is only three iterations for the VSTD-TEQ, while the VSD-TEQ needs more than seven iterations. Compared with the simulation results above, the performance of the lake trial results deteriorated significantly. The reason for this is that the field channel is much more complicated corresponding to the simulations, and the compar  
Figure 16: BER range comparisons of the 1500 m lake trial. Figure 17: Performance comparisons of the 1500 m lake trial. even more striking when observing Figures 8 and 13. The topography of the experimental site is confined and curved, so that the acoustic reflection phenomenon may occur more frequently. The summer climate is always a troublesome problem for UWA communications as it makes the acoustic propagation path difficult to predict and time-varying [46; 47]. Another reason is the motion of the ship caused by waggle and water flow; thus, some propagation paths do not endure for a frame. The unstable paths may appear or disappear unexpectedly. All these facts contribute to the troublesome field channel. On the contrary, the channels generated by Bellhop have a relatively stable structure, and the simulations reflect a wide range of scenarios instead of the special experimental site.