## 4 Marine Experiments and Numerical Estimations of Doppler Shift Sustainability
According to the test responses of underwater acoustic channel preliminary overlapping of weaker delayed copies of the FM-OFDM signals on the main symbol was detected. Such a situation created relatively \"soft\" conditions for OFDM symbols reception. In that case, conditions of numerical experiments (described in the Part 2) surpassed sea trials conditions in terms of level of difficulty of channel impulse response, which caused higher values of BER in numerical experiments. Results of decoding of FM-OFDM-QPSK signals that were received during in-situ experiments are presented in the Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline
**FM-OFDM-QPSK Mode** & **BER1** & **BER2** & **BER3** & **Bitrate (bps)** \\ \hline K1 & 0.1093 & 0.138 & 0.1343 & 167 \\ K2 & 0.05618 & 0.0749 & 0.06991 & 83 \\ K4 & 0.01247 & 0.0698 & 0.04489 & 42 \\ K10 & 161 bits without errors & 0.031 & 0 & 17 \\ \hline \end{tabular}
\end{table} 
Table 3: Results of decoding of FM-OFDM-QPSK signals, recorded during sea trials on the distance of 25 km. Figure 6: Time diagrams of the recorded signals on the 25 km distance. Figure 8: Responses of the matched filter on the M-sequences with length of 63 symbols. Figure 7: Dynamic of amplitude-frequency response of underwater acoustic channel for all three iterations of FM-OFDM-QPSK symbols transmission. To estimate the correspondence between performance data acquired during additional numerical simulation and values that were obtained during following sea trials two channel responses were chosen because they were similar to the ones obtained during real underwater acoustic channel amplitude-frequency response estimation on the distances up to 25 km. Analytically, these responses each consisted of two beams with 13 ms difference in time of arrival can be presented as:  
\[H_{a}(\omega)=1+0.7\times e^{-j\omega\cdot 13\times 10^{-3}}\]  
\[H_{b}(\omega)=0.7+1\times e^{-j\omega\cdot 13\times 10^{-3}}\]  
The system of FM-OFDM frame synchronization (SYNC) was tuned in two variants: for the work relying on the first beam and beam with the maximum magnitude. The BER results under signal convolution in the K1, K2, K3, and K10 mode with the responses \(H_{a}(\omega)\) and \(H_{b}(\omega)\) and SNR = 15 dB and different synchronization type is shown in the Table 4.  
Simulation results with different synchronization types shows the necessity in precise frame synchronization of demodulated OFDM-QPSK symbols on beam with the maximum amplitude. Obtained during sea trials results have good accordance with results of numerical modeling in the Table 3. However, numerical models have no consideration of strong impulse noises on the receiving signal, and as a result, BER obtained in sea trials are higher. To increase believability of the reception of transmitting data it is possible to use full complex transfer characteristic of the channel for correction of OFDM symbols group by first estimating symbol with periodical repetition of the channel estimation. In conducted sea experiments, the Doppler shift was not observed in proper values due to low signal reflections from sea surface and the immobility of transmitter and receiver. So, the sea trials were supplemented by additional numerical modeling. Received signals were demodulated with artificially added strong frequency shifts for the estimation of FM-OFDM Doppler shift resilience. Additional estimations of BER for different modes were made during modeling. As mentioned before, the frequency shift of FM-OFDM signal causes an appearance of steady component in the real part of OFDM signal on the FM demodulator output, which has minimal influence on further OFDM demodulation using FFT. Serious deviations of carrier frequency (up to 10%), as it shown on Figure 9, lead to small changes in BER values for received signals in modes K1, K2, K4. Mode K10 did not shown any additional errors.