## 4 Results
### Underwater Experiment
Simultaneously, the complex envelope \(y(t)\) of each of received signals was divided into segments of duration corresponding to the duration of a single PRBS sequence, and the coefficients \(c_{IQ}\) and \(c_{IQQI}\) were determined. Next, the values of the distance measure \(d\) according to Equation (10) were calculated. The results of analysis of the transmitted PRBS signals and estimated TVIRs are shown in Table 2. As seen in Figure 3 there is a small Doppler shift observed in the impulse responses measured at distances of 340 and 550 m. The impulse responses were resampled to remove the influence of the Doppler effect. The cross correlation coefficients were calculated for both cases: before and after resampling. The values of the coefficients and the distance measure calculated after resampling the TVIR are written in brackets. It is clearly seen that a small Doppler shift due to the drifting of the boat with the transmitting stand does not significantly affect the obtained results. The values of cross-correlation coefficients \(\{\hat{c}_{IQ}^{h},\hat{c}_{IQQI}^{h}\}\), and \(\{c_{IQ},c_{IQQI}\}\) are also presented in Figure 4.  
As the measurement system range increases, the difference between the cross-correlation coefficients \(\{\hat{c}_{IQ}^{h},\hat{c}_{IQQI}^{h}\}\) and \(\{c_{IQ},c_{IQQI}\}\) decreases. At a range of 340 m, the distance measure \(d\) is up to 0.28, while for a distance of 1035 m it does not exceed the value of 0.04. At the same time the highest correlation coefficient results were obtained for the channel at a distance of 1035 m. This channel turned out to be the strongest wide-sense stationary. The lowest coefficient results were obtained for the 550 m channel, in which transmission was carried out in bad weather conditions. The \(c_{IQQI}\) values below 0.5 do not allow it to be classified as WSS. Figure 4: Results of inland water experiment; correlation coefficients calculated on the basis of: time-varying impulse response (*) and pseudo-random binary sequence probe signal (o). Figure 3: The module of exemplary time-varying impulse responses of the inland water channel. In order to estimate the impact of SNR (which was different during measurements at different distances) on the results obtained, additional simulation tests were performed using the signals measured at a distance of 1035 m (SNR was the largest in this case). Additive Gaussian noise of a different level was added to the signal, and then the correlation coefficients were calculated. The results are shown in Figure 5. It is clearly seen that if the SNR is equal or greater than 10 dB, the effect of additive noise on the calculation results is negligible. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Distance** & **m-Seq.** & **B** & **Probe Seq.** & \(\hat{c}_{IQ}^{h}\) & \(\hat{c}_{IQ}^{h}\) & \(\hat{c}_{IQQI}^{h}\) & \(\hat{c}_{IQQI}\) & \(\hat{d}\) \\
**[m]** & **Order** & **[kHz]** & **Duration [ms]** & \(\hat{c}_{IQ}^{h}\) & \(\hat{c}_{IQ}\) & \(\hat{c}_{IQQI}^{h}\) & \(\hat{c}_{IQQI}\) & \(\hat{d}\) \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 2: Results of inland-water experimental tests  
Figure 5: Correlation coefficients calculated on the basis of a signal received at a distance of 1035 m, disturbed by simulated AWGN; the dashed line represents the coefficient value obtained in the measurements.