## 4 Experimental Data Analysis and Processing
The blue blocks display the BER of the MSS method using the sliding correlation, and there is no Doppler compensation processing in the receiver. We abbreviate this method as \"sliding correlation without compensation\". The purple blocks exhibit the BER of the MSS method with the sliding correlation. The difference is, before de-spreading, we perform Doppler coarse  
Figure 14: Temporal coherence of UWA channel. Figure 15: Sound speed profile diagram. estimation and compensation for this method. We abbreviate it as \"sliding correlation with compensation\". We try to explore whether the absence of the Doppler compensation affects the performance of the proposed method. As shown in Figure 16, the proposed method has 33 packets of data decoded correctly, five packets with the BER of 1e\(-\)3, and two packets with the BER about 1-2%. The optimized method obviously outperforms the two sliding correlation methods without the help of the Doppler compensation technique. The BER performance of the sliding correlation method with Doppler compensation is slightly better than that without Doppler compensation. In most cases, Doppler compensation before sliding correlation despreading improves the system performance. However, when the local instantaneous mutation of the Doppler factor is serious, the Doppler compensation affects the overall decoding effect of the signal. It is explained in the next diagram. Taking the 14 th packet data with error in the proposed method as an example, in Figure 17, there is one error bit in the 94 th symbol and two in the 100 th symbol. The difference between the Doppler factor estimation of the 94 th and 100 th symbols and their previous symbols are 0.003 and 0.005, respectively. Because the Doppler estimation range of the proposed method is not set that large, it causes bit error. In fact, the error can be corrected by expanding the search range. For this sudden change of velocity in variable-speed motion, the BER of the sliding correlation despreading method without and with Doppler compensations is 2% and 1.67%, respectively, which are both higher than that of the proposed method. The number of error bits of the sliding correlation method without Doppler compensation is six. Using Doppler compensation in the sliding correlation method, there are five error bits. For the ninth packet, we can see more abrupt changes in Doppler occurring for this packet in Figure 18. By using the proposed optimization scheme, this method is well adapted to this mutation and complete error-free decoding. However, the BER of the two conventional methods is 3.33% and 5%, respectively. Without using Doppler compensation, the sliding correlation method obtains ten error bits. While using Doppler compensation, there are 15 error bits, which is even worse. When the underwater acoustic channel changes slowly, the Doppler compensation based on an average Doppler factor generally has a positive impact on the sliding correlation method. However, when the Doppler varies within the duration of one signal frame, this Doppler compensation method is counterproductive because the Doppler compensation based on an average Doppler factor often causes a more serious Doppler effect in some parts of the whole signal frame. In Figure 18, the Doppler varies more violently in the 6 th and 79 th  
Figure 16: BER performance of three methods. compensation, and there are five error bits in the 6 th and 79 th symbols using the sliding correlation method with Doppler compensation, while there is only one error bit in the 79 th symbol without Doppler compensation. Moreover, we can find that the sliding correlation method has no good solution for the case where the Doppler change exceeds 1e\(-\)3. As shown in the figure, the wrong symbols are behind the sudden change of the Doppler. In other words, although Doppler compensation plays a role in the mutation position, it intensifies the Doppler effect of subsequent symbols, thus affecting the normal decoding. The BER of 40 data packets in the proposed method is 0.0917%.