## 1 Introduction  
Shallow underwater acoustic communication channels are characterised by disadvantageous transmission properties. Reflections from the sea-bottom and the water's surface cause multipathpropagation, which goes hand-in-hand with the refraction phenomenon, caused by a significant change in sound velocity as a function of depth [1]. The movement of the UAC system's transmitter and receiver causes a Doppler effect, resulting in the time-domain scaling of a broadband communication signal. Moreover, UAC channel propagation conditions can change over time [2]. Depending on the phenomena under consideration, the variability of the transmission properties can be in the order of several months (i.e., seasons), several days and hours (i.e., tides, times of day), minutes (i.e., internal waves), a few seconds (i.e., surface waves), or milliseconds. The transmission properties of a shallow UAC channel can be fully described by its time-varying impulse response, measured commonly by a correlation method, and modelled as a tapped delay line \(h(t,\tau)\)[3]. A single realisation of \(h(t,\tau)\) is defined in a window of observation time \(t\) and delay \(\tau\). The impulse response \(h(t,\tau)\) can be treated as a two-dimensional stationary random process that fulfils the WSSUS assumption. Then, it is possible to calculate the 2-dimensional scattering function \(S(\tau,\
u)=\int_{\Delta t}\int_{\Delta f}R_{h}(\Delta t,\Delta f)e^{-\jmath \pi(\
u\Delta t-\tau\Delta f)d\Delta t\Delta f}\), where \(R_{h}(\Delta\tau,\Delta f)\) is the space-time-frequency correlation function of the channel, obtained on the basis of \(h(t,\tau)\). It is the basis for calculation of the transition parameters; namely, multipath delay spread \(\tau_{M}\), Doppler spread \(\
u_{M}\), coherence time \(T_{C}\), and coherence bandwidth \(B_{C}\)[4]. As it is shown in [5], UAC channels are hardly ever WSSUS, and thus the transmission parameters can be determined only in a restricted period of time, and in a limited frequency range. Determining the time interval wherein the second-order statistics of impulse response are independent of time is important for the performance of communication systems working in nonstationary conditions. Only within this time interval is it possible to calculate transmission parameters \(\{\tau_{M},T_{C},\
u_{M},B_{C}\}\). Moreover, within this time interval, the signal received by the UAC system receiver represents a WSS process, and its power spectrum can be defined via a Fourier transform, according to the Wiener-Khinchin Theorem. This is especially important for signal detection performed in the frequency domain, as is the case with communication systems using the Orthogonal Frequency-Division Multiplexing (OFDM), and the Frequency Hopping Spread Spectrum (FHSS) techniques [4; 6; 7]. Studies on the validity of the WSS assumption are relatively rare. Several authors have proposed methods designed to test the similarity of the spectral properties of a time-series [8; 9]. The relationship between the radiocommunication signal bandwidth and the wireless channel stationarity is described in [10]. The stationarity of a UAC channel was studied in [11]. The authors described the influence of the wind-driven surface wave variability on fluctuations of the channel Power Spectral Density (PSD). A trend-stationary channel model was proposed in [12] for underwater communication system. In [13], the stationarity of PSD is analysed to verify if the UAC channel can be considered to be a WSS process. Most of these methods are based on spectral analysis. In [14], a novel time-domain method for verifying the WSS feature of UAC channels is described. Statistical properties of the real and imaginary parts of the impulse response, measured using the correlation method, are exploited to test the WSS assumption fulfilment. In [6] a similar method is proposed to assess whether the channel is WSS/non-WSS on the basis of the complex envelope of a received probe signal. However, the method was tested only in simulation conditions.