# Measurement and Modeling of Narrowband Channels for Ultrasonic Underwater Communications
## 3 Ultrasonic Measurements for UAC
### Measurement Results  
The set of measured channel configurations is described in Table 1, including the sounding signal frequency (SF), the transducers' depth (TD), the transducers' separation (TS) or link distance and the average sea depth (ASD). A segment of the captured signal on reception on Channel A6-128 is shown in Figure 3 as an example where the signal level fluctuation due to fading is evident. From this type of signal, several parameters of the channel behavior can be extracted (prior to do that, the stationarity of the channels has been confirmed by comparing the CDF of successive measurements in the same scenario). Figure 3: Segment of the received signal in Channel A6-128. Figure 2: Measurements setup: (**a**) block diagram of the measurement equipment; (**b**) picture of the receiver part at the laboratory. * _Channel attenuation_. This parameter is an estimation, using short time averaging, of the instantaneous attenuation (the inverse of the channel gain) measured from the registered data (not to be confused with path loss). The change in the channel gain produced by the fading is evaluated from the measurements. The range of values observed in the channel attenuation is shown in Table 2 for each group of measurements: _i.e._, channels with the A code (TS = 50 m), B code (TS = 100 m) and C code (TS = 200 m). * _Coherence time / Doppler spread_: The small time scale variation of the underwater environment produces a variant shift of the received signal frequency due to the Doppler effect. A way of quantizing the variation of the channel is through the Doppler spread, defined as the rms (root mean square) bandwidth [13] of the received signal spectrum when a pure tone is transmitted (the so-called Doppler spectrum). An alternative parameter is the coherence time, which is inversely proportional to the Doppler spread. It measures the period over which the channel can be considered time invariant. Different criteria are considered in the literature to determine the inverse proportionality constant between both parameters. The one selected here yields the relation coherence time = 0.2/Doppler spread [13]. In Figure 4, the Doppler spectra measured in Channels A6-32, A6-64 and A6-128 are shown. The values obtained for the coherence time and Doppler spread for each channel are listed in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Channel Code** & **SF (kHz)** & **TD (m)** & **TS (m)** & **ASD (m)** \\ \hline A6-32 & 32 & 6 & 50 & 16 \\ A6-64 & 64 & 6 & 50 & 16 \\ A6-128 & 128 & 6 & 50 & 16 \\ B6-32 & 32 & 6 & 100 & 20 \\ B6-64 & 64 & 6 & 100 & 20 \\ B6-128 & 128 & 6 & 100 & 20 \\ C3-64 & 64 & 3 & 200 & 25 \\ C9-32 & 32 & 9 & 200 & 25 \\ C9-64 & 64 & 9 & 200 & 25 \\ C9-128 & 128 & 9 & 200 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of measured channel characteristics. SF: Sounding signal frequency, TD: Transducers’ depth; TS: Transducers’ separation; ASD: Average sea depth. Figure 4: Normalized Doppler spectrum in Channels A6-32, A6-64 and A6-128. * Fading statistics: Fading has been characterized by measuring the fluctuations on the channel power gain, \(\alpha^{2}\), from the fluctuations of the received signal envelope (see Figure 3). The samples of the channel gain \(\alpha\) are assumed random, stationary and ergodic. The amount of fading (AoF) is defined as the dispersion in the distribution of \(\alpha^{2}\), _i.e._, the variance divided by the mean square [15]. A normalization of \(\alpha^{2}\) is carried out before data processing, so that \(E[\alpha^{2}]=1\) and, hence, AoF can be directly related to the variance. The collected channel gain samples are afterwards processed to obtain the cumulative distribution function (CDF) of the channel power gain.