## 4 Experimental Data Analysis and Processing  
Because the proposed receiving and processing method is based on some assumptions, it is necessary to carry out experiments in a real marine environment to verify the effectiveness of the scheme. Because of this, a mobile UWA spread spectrum communication trial was conducted in Weihai, China in May of 2021. In the experiment, the length of one data packet is 7.15 s. It includes a 0.2 s linear frequency modulation synchronization signal, 0.2 s protection interval, 6.35 s data frame, and 0.4 s protection interval at the end of the data. The frequency bandwidth is 2 kHz (2-4 kHz). The carrier center frequency is 3 kHz. The sampling rate is 18 kHz, and each spreading symbol carries 3 bits of data. ([PERSON] has confirmed in [41] that using an MSS symbol to carry 3 bits of data is the best compromise between communication rate and system hardware complexity. If more bits are carried, the complexity of this method will exceed that of the spread spectrum \(M\)-ary PSK algorithm.) The chip length is 127 for each symbol. The duration of each symbol is 63.5 ms, with 300 bits of data per packet, and a total of 40 packets of data are transmitted. The trial scenario is shown in Figure 12; the receiving end (point R in Figure 12) is fixed, the transmitting ship (point T in Figure 12) moves with the ocean current at a speed of 0-3 m/s, and the distance is 3.7-4.0 km. In order to reflect the BER performance of the proposed method, channel coding is not used. The measurement of coherence time is of great significance for the design of the UWA communication system. For the UWA channel which changes slowly (the coherence time is tens of seconds or even more), the length of the data frame can be increased to improve the effectiveness of the system without frequent use of a detection signal and protection interval. For the time-varied channel (the coherence time is hundreds of milliseconds or even less), the symbol-by-symbol data processing method we proposed is a better choice. In Figures 13 and 14, we find that the channel structure changes fast, resulting in a short channel coherence time. Within 0.667 s, the temporal coherence decreases below 0.707, so the coherence time of the UWA channel is about 0.667 s. In the experiment, the duration of one data frame is 7.15 s, which is far longer than the coherence time. It is inappropriate to treat the whole data frame as affected by a constant Doppler factor. However, the one symbol length is only 0.0635 s. Therefore, within a symbol duration, we consider that the channel is time invariant (including the multipath structure and the Doppler factor). Utilizing symbol-by-symbol Doppler estimation and synchronization, we can decode correctly. The experimental results prove this. Figure 12: Schematic diagram of trial scenario. The receiving end (point R) is fixed, the transmitting ship (point T) moves with the ocean current at a speed of 0–3 m/s, and the distance is 3.7–4.0 km. Figure 13: Time-varying channel impulse response. The time-varying channel impulse response is shown in Figure 13. We do not perform Doppler compensation processing at the receiving end. It can be seen that the moving speed is relatively consistent in one direction. The time delay is about 10 ms, and the energy of the main path is intense, which is in line with the assumptions of the channel modeling. The transducer is placed 8 m undersea, and the hydrophone is about 10 m underwater. The sound speed profile diagram is shown in Figure 15. Due to the downward bending sound line, the communication distance cannot be too far. We process the collected 40 packets of data and compare the proposed method with the sliding correlation method in a conventional incoherent MSS system. Moreover, the average Doppler compensation is added to the MSS method using the sliding correlation. In Figure 16, the green blocks show the BER performance of the proposed method. Our method does not need the Doppler compensation technique.