# A Method for Underwater Wireless Data Transmission in a Hydroacoustic Channel under NLOS Conditions
## 5 Results  
### Propagation Conditions  
In order to determine the propagation conditions for individual measurement points, using the transmitted preamble, the impulse responses were estimated using the correlation method as described in [23]. The module form of the impulse response estimates at individual measurement points is shown in Figure 6. The presented estimates were normalized with respect to the maximum value, separately for each measurement point. It is clearly visible that, as the set of receiving hydrophones is moved in the created corridor, LOS conditions are present at the first measuring point, and NLOS conditions prevail in the subsequent points. It can be determined on the basis of the appearance time of the peak of the estimation of impulse response, i.e., only in the first measurement point the signal arriving directly has the highest power. Based on the determined estimates of the channel impulse responses, in accordance with the recommendations of ITU-R P.1407-7 [24], the average number of replicas at each measurement point was determined. The results are shown in Figure 7. The results show that as the receiver set is moved deeper into the corridor, the average number of replicas increases significantly, even above 100 at the last measurement point. This clearly demonstrates the conditions of strong multipath signal propagation. Figure 6: Modules of estimates of impulse responses at measurement points. Figure 7: Average number of replicas at measurement points. Using the power profile of the received signals as a function of delay \(\tau\) (PDP--power delay profile), it is possible to determine the total power \(P_{m}\) of all signal replicas registered at individual measurement points [24]:  
\[P_{m}=\sum_{i=1}^{N}p(\tau_{i}), \tag{11}\]  
where \(p(\tau_{i})\) is power of \(i\)-th replica, \(N\)--amount of replicas. This allows the average delay of received replicas to be calculated according to the dependency [24]:  
\[\overline{\tau}=\frac{\sum_{i=1}^{N}\tau_{i}p(\tau_{i})}{P_{m}}. \tag{12}\]  
On this basis, the root mean square delay spread was determined according to the equation [24]:  
\[\tau_{rms}=\sqrt{\frac{\sum_{i=1}^{N}\tau_{i}^{2}p(\tau_{i})}{P_{m}}-\overline {\tau}^{2}}. \tag{13}\]  
The obtained results are shown in Figure 8.  
The \(\tau_{rms}\) delay spread increases significantly from approx. 1 ms at the first measurement points to almost 1.8 ms at 4 th measurement point. In the following measurement points, this increase is much smaller. The power relations between the recorded signals at individual measuring points were determined. Changes in the power of received signals at individual measurement points are shown in Figure 9, where \(P_{max}\) is the maximal measured power from all measurement points and \(P_{p}\) is the measured power in \(p\)-th point. As expected, the signal power decreases by up to 30 dB as moving down the corridor. Figure 8: Root mean square delay spread \(\tau_{rms}\) at measurement points. Figure 9: Change of signal power at measurement points. The distributions of replicas amplitudes at individual measurement points were determined. For this purpose, normalized amplitude histograms were created and compared with the Weibull, Rayleigh and Nakagami distributions. An example of the comparison of the obtained histogram from 12 impulse response measurements with the adopted distributions for the measurement point No. 5 is shown in Figure 7.0  
In order to assess the adequacy of the considered distributions to describe the statistical properties of the replica amplitudes, the so-called non-dimensional error index (NDEI) defined as the ratio of the root mean squared error to the standard deviation of the histogram:  
Figure 7.1  
where: \(h_{i}\)--the histogram value of the normalized replica amplitudes for \(i\)-th measurement, \(\hat{p}\)--probability density estimator, \(\overline{h}\)--mean value of the histogram, \(N\)--number of intervals in the histogram.