## 3 Analysis of the Time Fluctuation of Underwater Acoustic Communication Signals
### Analysis of the Time Distribution Characteristics of Noise Fields
There were 32 hydrophones in each array and the distance between the hydrophones was exactly 0.5 m, the horizontal communication distance was 3.5 km, the experimental sea state was approximately two levels, and the vertical distribution of the entire bandwidth SNR was counted. Figure 18 indicates the vertical fluctuation of the SNR of different arrays. Because the receiving array was limited by the size of the receiving ship, the relative horizontal distance between the arrays was not large and the gap between the SNR was small. During the underwater acoustic communication experiment, the auxiliary ship of the receiving ship was continuously working and displayed certain random fluctuations on the surface. As the receiving ship fluctuated up and down on the sea, the SNR of the surface array element was significantly lower than that of the underwater array element. With the increase in water depth, the variation range of the SNR gradually decreased and basically remained stable after 5 m underwater. Figure 19 demonstrates the statistical range of the space-time variation of the SNR of array 5 over 31.5 s. The black hexagon indicates the mean of the SNR within the changing range, which is in line with Figure 18. From the figure, it was relatively small and fluctuated dramatically, which matched the trend of the spatial and temporal distributions of the signal field and noise field of the single-frequency signal. However, the experimental signal was further processed to cope with the slight inconsistency of the fluctuation range. Signals with center frequencies of 9 kHz and 15 kHz and a length of 31.5 s were selected. The sampling frequency of the system was 50 kHz and the number of sample points was about 1,574,520. The processing results are shown in Figures 20 and 21. In these figures, the abscissa is the SNR and the ordinate is the depth, and the plots show the variation ranges of the SNR within the signal time of 31.5 s at different depths, with the blue point representing the mean value. With the increase in the processing bandwidth, the spatial-temporal variation range of the SNR was significantly reduced, and the SNR of the surface  
Figure 18: Signal-to-noise ratio of different arrays as a function of depth. array elements in the vertical direction was significantly lower than that in the water array elements, which verified the laws obtained using the theory and simulation experiments. Figure 22 shows the simulation experiments performed under the fixed coding method using the channel parameters in the ExDQ_1702 experiment and the bit error rate corresponding to different signal-to-noise ratios (SNRs) and mapping methods. It can be seen that as the SNR increased, the bit error rate decreased. When the SNR in the experiment is less than 10 dB, the system should avoid using the 16 QAM mapping method with a bit error rate higher than 0.01 and select other mapping methods according to the actual effective rate requirements. Figure 19: Signal-to-noise ratio fluctuation chart (fifth array). Figure 20: Signal-to-noise ratio vertical distribution (9 kHz): (**a**) bandwidth at 1 Hz, (**b**) bandwidth at 10 Hz, and (**c**) bandwidth at 500 Hz. Figure 21: Signal-to-noise ratio vertical distribution (15 kHz): (**a**) bandwidth at 1 Hz, (**b**) bandwidth at 10 Hz, and (**c**) bandwidth at 500 Hz.