## 3 Transmission Parameters of Shallow-Water Channel  
In order to estimate the transmission parameters of an inland shallow-water channel, the measurement tests were conducted in 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) on 5 May 2017. Wdzydze Lake is a freshwater lake. Its bottom is covered with a layer of mud and it falls steeply into the depths of the water. It 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. In terms of chemical composition, the waters of Wdzydze Lake represent the calcium bicarbonate type. The water temperature on 5 May 2017 was 15 \({}^{\circ}\)C. The weather was windless, it was not raining, and the water surface was calm. The transmission stand was placed on a boat, which was drifted very slowly. The receiving stand was in a measuring container of fixed position, 50 m from the lake shore, by a floating platform. The transmission transducer was sunk to a depth of 10 m, regardless of the water depth of about 20 m. There were no objects in the water near this transducer. The receiving transducer was sunk to a depth of 4 m. The water depth in this place was 7 m [10]. The distance between the transmitter and receiver was 1035 m. This was measured with the use of a 19x HVS GPS receiver by Garmin, which was integrated with MaxSea software by TimeZero and electronic maps by Jepessen. Such a hardware-software set ensured a distance measuring accuracy of 3 m. Figure 2 shows the positions of the transmitting and receiving stands. The water depth on the line between positions of transmitting and receiving stands is varying from 7 to 40 m. Figure 3 shows the sound speed profile measured by using a sound speed meter constructed in Department of Sonar Systems, Gdansk University of Technology. The device uses a direct method of sound speed measurement. Its accuracy is \(\pm\)0.5 m/s. The sound speed profile was needed for estimating the underwater system range. On the basis of this profile an expected minimum range of the UAC system was calculated equal to 400 m.  
During the tests, the Time-Varying Impulse Response (TVIR) was measured. In the case of a bandlimited bandpass channel, the TVIR is equivalently described by a time-varying complex baseband impulse response \(h(t,\tau)\), defined in a window of observation time \(t\) and delay \(\tau\), with input \(s_{b}(t)\) and output \(r_{b}(t)\) being the complex envelope of the transmitted and received signal, respectively:  
\[r_{b}(t)=\frac{1}{2}s_{b}(t)*h(t,\tau) \tag{3}\]  
where \(s_{b}(t)\) and \(r_{b}(t)\) are the complex envelopes of transmitted \(s(t)\) and received passband signals \(r(t)\), and \(*\) represents convolution operation. The impulse response \(h(t,\tau)\) was measured by the correlation method with the use of a Pseudo-Random Binary Sequence (PRBS), based on an _m-sequence_ of rank 8, and its duration \(T_{s}\) was equal to 51 ms. It was repeated up to 127 times to gather one TVIR. The bandwidth and the carrier frequency of the probe signal were equal to 5 kHz and 30 kHz, respectively. The sampling frequency \(f_{s}\) was equal to 200 kHz. 16 impulse responses were measured during the tests. In order to assess the time dispersion and variability of the UAC channel, a stochastic model based on the channel Space-Time-Frequency Correlation Function (STFCF) \(R_{h}(\Delta t,\Delta f)\) is used. The STFCF is obtained as an autocorrelation function of a time-varying transfer function \(H(t,f)\) of the channel, which, in turn, is calculated as Fourier transform of the impulse response \(h(t,\tau)\). The STFCF is a function of time and frequency differences under the assumption that the TVIR of the channel represents a wide-sense stationary uncorrelated scattering process [11].