## 4 Marine Experiments and Numerical Estimations of Doppler Shift Sustainability  
Marine experiments were conducted in collaboration with the Laboratory of acoustical tomography of Il'ichev Pacific Oceanological Institute FEB RAS in the July 2017 in the Peter the Great Bay in the Japanese (Eastern) Sea. The transmitting complex was located on the shore, and the transmitting antenna with the frequency band of 300-500 Hz was located on 1 m above the bottom and 150 m away from the sea shore. Preliminary, the estimations of vertical sound speed profile in the reception point were made and the depth-depended distribution of temperature was studied. Under conditions of summer hydrology (negative gradient of the sound speed profile) acoustical energy of the signal was focused in the near-bottom channel on the shelf zone with gradual slipping on the axis of deep underwater acoustic channel. That effect can be used for the conducting of long-haul underwater acoustic communication [19]. The signal was received on the ship at the distance of 25 km using a stationary hydrophone that was located near the sea bottom, when the total depth in reception point was around 100 m.  
Also, by emitting test M-sequence preamble with a length of 63 elements and convoluting by the matched filter on the receiver side, some estimations of underwater acoustic channel impulse responses were obtained. The format of M-sequences emitting was determined as phase-manipulated signal. During the sea trials formed wav-files with FM-OFDM-QPSK signals were sequentially emitted within 53 s from the transmitter in following order: starting preamble \(\to\) 10 symbols in the K1 mode \(\to\) 10 symbols in the K2 mode \(\to\) 10 symbols in the K4 mode \(\to\) 10 symbols in the K10 mode. Time diagram of the recorded signals are shown in Figure 6. In the received signals, the presence of strong impulse noises, resulted by external factors and noises of vessel equipment, can be noted. Average recorded values of the SNR were 20 dB and higher. Figure 5: BER of SNR performance acquired during the numerical simulation for channel responses \(H_{1}(\omega)\), \(H_{0.5}(\omega)\). For the recorded data amplitude clipping with saturation parameter \(\gamma=0.5\) was implemented, which helped to substantially decrease the resulting BER and the influence of strong impulse noises on the records, while decoding FM-OFDM-QPSK signals. To estimate a channel dynamic all three fragments went through symbol-by-symbol estimation of amplitude-frequency response of the channel in the bandwidth of 300-500 Hz by point FFT comparison of transmitted and acquired signals. The dynamic of amplitude-frequency response of the channel for the first three 53 s fragments of data transmission is presented in Figure 7.  
Based on performed estimation of amplitude-frequency response of the channel, it can be stated that during time of three packets transmission the transfer that is characteristic of the underwater acoustic channel is changing substantially on such a big distances. For that case, the time-variant frequency channel transfer function can be described by expression:  
\[\dot{H(\omega,t)}\approx A(t)+B(t)\times e^{-j\omega\times T} \tag{8}\]  
where \(A(t)\) and \(B(t)\)--amplitude functions of two rays arriving to the receiver with time lag T. Values of functions for this case belongs to range \(0.5\leq A(t),\ B(t)\leq 1\). According to the Figure 7, the interval of channel frequency coherence during the experiments was 70-80 Hz, which results beams path difference of \(T\approx 13\) ms. In Figure 8, the response of receiver matched filter on the M-sequence preamble is presented. The response represents an impulse response of underwater acoustic channel (with assumption that M-sequence autocorrelation function is ideal) in scale of several seconds. Specification of ray pattern in millisecond scale was acquired based on expression (8), and is also shown on Figure 8.  
Further frame synchronization FM-OFDM-QPSK signals were performed using beam with the maximum amplitude.