## 4 Results
### Underwater Experiment  
The inland water channel measurements were conducted on the 4 th and 5 th of May 2017, in the Wdzydze Lake on the northern edge of the Bory Tucholskie forest complex (53\({}^{\circ}\)58\({}^{\prime}\)31\({}^{\prime\prime}\) N 17\({}^{\circ}\)54\({}^{\prime}\)19\({}^{\prime\prime}\) E). The bottom of the lake falls steeply into the depths of the water. In the shore zone, it is lined with gravel-stony material, and in the deeper parts, covered with a layer of mud. Wdzydze Lake is in many respects very similar to the Baltic Sea. A significant part of the lake area is more than 40 m deep, and the deepest area is more than 70 m deep. The shape of the bottom of the Wdzydze lake is more diverse than the bottom of the Baltic Sea; thus, the propagation conditions are even more difficult than those in the sea. The weather was windy and it was raining on the 4 th May, when the measurements were performed at a distance of 550 m. The next day, during the measurements at distances of 340 m and 1035 m, the weather was windless; it was not raining and the water surface was calm. Each probe signal was generated using a computer with MATLAB software. Conversion from digital to analogue signal was performed using a digital-to-analogue converter from an NI USB-6363 device. Next, the signal was amplified and transmitted to water by an underwater telephone HTL-10 [20]. The transmission stand was placed on board the boat. The same equipment was used in the receiving stand, but was configured differently. The boat was not anchored, but drifted very slowly. Therefore, the Doppler effect had an effect on the transmitted signal, but to a much lesser extent than strong multipath propagation. The receiving equipment was placed in a measuring container whose position was fixed. The transmission transducer was sunk to a depth of 10 m, regardless of the water depth of about 20-30 m. The receiving transducer was sunk to a depth of 4 m at a constant water depth of 7 m; thus, even a slight rippling of the water had an effect on the stationarity of the received signal. A more detailed description of the experimental set-up can be found in [21]. Figure 3 shows the absolute values of exemplary impulse responses for each of measured channels. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Channel**} & **m-Sequence** & \multirow{2}{*}{**Bandwidth**} & **Probe Sequence** & \multirow{2}{*}{\(\bar{c}_{IQ}^{h}\)} & \multirow{2}{*}{\(c_{IQ}\)} & \multirow{2}{*}{\(\bar{c}_{IQQI}^{h}\)} & \multirow{2}{*}{\(c_{IQQI}\)} & \multirow{2}{*}{\(d\)} \\  & **Order** & & & & & & & \\ \hline NOF1 & 8 & 8 kHz & 32 ms & 0.7469 & 0.6590 & 0.6790 & 0.7126 & 0.0941 \\ NOF1 & 10 & 8 kHz & 128 ms & 0.7414 & 0.6374 & 0.6936 & 0.6748 & 0.1057 \\ NCS1 & 8 & 8 kHz & 32 ms & 0.6349 & 0.6114 & 0.6248 & 0.6374 & 0.0267 \\ NCS1 & 10 & 8 kHz & 128 ms & 0.5617 & 0.5302 & 0.5842 & 0.5385 & 0.0555 \\ BCH1 & 8 & 5 kHz & 51 ms & 0.9165 & 0.7868 & 0.8611 & 0.7988 & 0.1439 \\ BCH1 & 10 & 5 kHz & 205 ms & 0.8747 & 0.6916 & 0.8307 & 0.7099 & 0.2194 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of simulation tests. During the experiment, the PRBS probe signal was transmitted, based on m-sequences of order 8 and 10, repeated 500 times, and occupied frequency bands of 5 kHz, 8 kHz, and 10 kHz. The carrier frequency and the sampling frequency were equal to 30 and 200 kHz, respectively. Due to different propagation conditions and different transmission powers of the measuring system, the received signal to noise ratio (SNR) was different for each of the three measured channels. At a distance of 340 m, the SNR was in the range of 10 to 13 dB; at a distance of 550 m it was in the range of 13 to 18 dB; and at a distance of 1035 m the SNR was in the range of 32 to 35 dB. On the basis of the received signals, similar to the simulation experiment, after performing a matched filtration, the impulse response estimates were determined. Next, the coefficients \(\hat{a}_{IQ}^{h}\), \(\hat{c}_{IQQI}^{h}\), were calculated.