## 5 Discussion  
In the simulation tests carried out, the differences between the pairs of cross-correlation coefficients, \(\{\tilde{c}_{IQ}^{h},\tilde{c}_{IQQI}^{h}\}\) and \(\{c_{IQ},c_{IQQI}\}\), were different depending on the channel tested. The highest distance measurement values (up to 0.22) were obtained for the BCH1 channel, where the transmitting and receiving transducers were suspended in the water. In case of the two other tested channels, namely, NOF1 and NCS1, the transmitting and receiving transducers were bottom-mounted. The distance measure \(d\) for NOF1 and NCS1 is less than 0.1. Another difference between the BCH1 and NCS1/NOF1 channels is the fact that in the case of BCH1 channel the ratio of the bandwidth (5 kHz) to the carrier frequency (35 kHz) is 1/7, while in the case of the NCS1 and NOF1 channels, this ratio is equal to 8 kHz/14 kHz = 4/7. Thus, the BCH1 channel is much more narrowband than the two other simulated UAC channels. Assuming that values of cross-correlation coefficients \(c_{IQ}\) and \(c_{IQQI}\) greater than 0.5 indicate that the channel is WSS, using both pairs of coefficients leads to the same Watermark channels classification results as being WSS. During the inland water experiment, the largest differences between the pairs of cross-correlation coefficients were obtained for the channel with the smallest range (340 m). In this case the distance measure \(d\) was up to 0.28. This channel is characterised by the strongest multipath propagation. In case of the longest range, namely, 1035 m, the distance measure between the coefficients was the lowest (up to 0.039). Both the coefficients \(c_{IQQI}^{h}\) and \(c_{IQQI}\) for the channel measured in bad atmospheric conditions over a distance of 550 m take values of less than 0.5. Thus, the channel was classified as non-WSS. Assessment of channel wide-sense stationarity based on the coefficients \(c_{IQ}\) and \(c_{IQQI}\), calculated directly from the complex envelope \(y(t)\) of the received signal, makes it possible to obtain the same classification result as using the coefficients \(\tilde{c}_{IQ}^{h}\) and \(\tilde{c}_{IQQI}^{h}\). At the same time, calculating \(c_{IQ}\) and \(c_{IQQI}\) requires fewer computational operations, due to the fact that the TVIR channel estimation step is omitted. Table 3 shows the sample calculation times and power consumption related to the estimation of the UAC channel TVIR by a fixed-point digital signal processor TMS320 VC5505 by Texas Instruments [22]. The size of the impulse response corresponds to the results of measurements obtained during the inland-water experiment at a distance of 1 km. For each impulse response, the size of the complex FFT and the corresponding calculation time and the amount of energy consumed by the processor were determined. The calculation time for each estimate is about 1.5-2 s. In the case of very short range systems, it is longer than the time at which the acoustic wave travels the path between the transmitter and receiver. It may be an undesirable, significant delay in the case of an adaptive UAC system. The signal processor needs 63.21 to 83.10 m) of energy to estimate the TVIR. If the calculation takes about 2 s, these values correspond to about 30-40 mW of power consumption. In case of the off-the-shelf acoustic modems, the power consumption on the receiving side usually does not exceed 1 W. Thus, every few dozen Watts of less power consumed might be a significant improvement of UAC system power efficiency.