## 4 Validation Through Sea Trials
### Processing and Analysis of the Second Group of Sea Trial Data  
Figure 12a displays the speed recorded during the second sea trial process by the BDS, while Figure 12b presents the results of the channel impulse response. It is evident that the channel exhibits significant multipath effects during the communication process, and the background noise interference is quite strong.  
Figure 11: **(a,c)** is despreading correlation peaks of symbols 32 and 33 by CCF-MSS, (**b,d**) is despreading correlation peaks of symbols 32 and 33 by FDE-MSS (first frame of first group).  
Figure 10: **(a)** is the CFO compensation estimated by CCF-MSS, (**b**) is the CFO compensation estimated by BDS output speed, (**c**) is the CFO compensation estimated by FDE-MSS (first group).  
Figure 9b,d presents the frame accuracy for the second group of trial processes. CCF-MSS maintains a zero bit error rate in each frame, whereas WDE-MSS demonstrates good decoding performance in the first two frames, corresponding to a time period of approximately 1 to 18 s. Based on the radial velocity data output from the BDS, the system is currently in an acceleration phase, with corresponding speeds ranging from approximately 0.3 to 0.7 m/s, and the corresponding acceleration is approximately 0.036 m/s\({}^{2}\). The performance of WDE-MSS deteriorates significantly after the third frame, and both CDE-MSS and FDE-MSS also exhibit bit errors. As seen in Figure 12a, there is a significant change in speed at the beginning of the third frame, with the maximum acceleration during the entire third frame reaching 1.065 m/s\({}^{2}\). The following section will analyze the decoding process of the third frame data from the second group of trials.  
Following the same analytical approach as previously discussed, we first analyze the CFO compensation results for the third frame data, as shown in Figure 13. At the beginning of the third frame, there is a significant change in CFO due to the high acceleration at that moment, and the CFO compensation results of CCF-MSS are largely consistent with the results calculated from the radial velocity output by the BDS, showing a similar trend of variation. However, the CFO values compensated by WDE-MSS exhibit significant discrepancies. Taking the despreading results of the third and fourth symbols in the third frame as an example, Figure 14 displays the correlation peaks for symbols 3 and 4 in the third frame, CCF-MSS shows a favorable despreading performance for symbols 1 and 2, with very sharp peaks, minimal interference, and correct decoding. During the despreading process of the second symbol, only two CFO searches were conducted, which was due to the accurate estimation of the CFO that met the preset threshold for the correlation cost factor ahead of time, leading to the termination of the search. This also reflects the efficiency of the CCF-MSS system. Figure 14b,d shows the despreading results for FDE-MSS, both of which are erroneous. According to the results of the second group of experiments, compared to FDE-MSS, CCF-MSS exhibits stronger resilience to acceleration and higher Doppler tolerance, allowing for correct decoding at an acceleration of 1.065 m/s\({}^{2}\).  
Figure 12: (**a**) is the speed of the second group processes recorded by BDS, (**b**) is the second group processes channel impulse response.