# Estimate of Passive Time Reversal Communication Performance in Shallow Water
## 3 Experiment and Site  
The passive time reversal communication data used in this paper were acquired at two different sites having different sediment compositions (Figure 1a). The first experiment was conducted in May 2012 at a site located off the southeast coast of Korea (henceforth called'site 1'), at location \(35^{\circ}0.48^{\prime}\) N, \(129^{\circ}1.39^{\prime}\) E in waters 45 m in depth. This location was characterized by a sandy clay sediment having a mean grain size of 7 \(\phi\) (where \(\phi=-\log_{2}(d/d_{0})\), \(d\) is the grain diameter in millimeters, and \(d_{0}\) is a reference length of 1 mm). A detailed description of the experiment is provided in reference [23]. The second experiment was conducted off the east coast of Korea at the location \(37^{\circ}14.47^{\prime}\) N, \(129^{\circ}23.40^{\prime}\) E (henceforth called'site 2') in waters 60 m deep in April 2015. The sediment of site 2 was very fine sand having a mean grain size of 2.7 \(\phi\) based on a grab sample.  
The geometries of the two experiments were very similar except for the water depth (Figure 1b,c for sites 1 and 2, respectively). An omnidirectional transducer (NEPTUNE D-17, Neptune Sonar, East Yorkshire, UK) was deployed at depths of 32 m and 30 m at sites 1 and 2, respectively, from small fishing vessels. A uniformly spaced four-channel vertical receiving array (RESON TC-4014, Teledyne RESON, Frederikssund, Denmark), which covers a water column between 5 and 35 m in depth, was deployed from the side of the R/V Tamyang and another small fishing vessel at sites 1 and 2, respectively. The measurements were made at nominal source-receiver ranges of about 100, 500, and 1000 m for both sites. The sound speed profiles (SSP) during the measurements were measured by conductivity-temperature-depth (CTD) casts (AML, Sidney, BC, Canada), which are shown in Figure 1b,c. The SSP in site 2 has a more negative gradient when compared to that in site 1, and this causes the ray to refract downward to the bottom.  
The surficial sediment sound speeds for sites 1 and 2 were expected to be about 1478 and 1645 m/s based on the empirical relationship between the mean grain size and the sediment sound speed given in reference [24]. Therefore, \(c_{s}/c_{w}\ =\ 0.98\) (where \(c_{s}\) and \(c_{w}\) are the sound speeds at the surficial sediment and water above the bottom, respectively) for site 1, which corresponds to an acoustically slow bottom condition, whereas \(c_{s}/c_{w}\ =\ 1.12\) for site 2, which corresponds to a fast bottom condition. The properties of acoustic propagation in two different bottom conditions are very different from each other. The bottom loss is defined as \(-20 log_{10}|R|\), where \(R\) is the plane wave reflection coefficient for the seabed. The bottom loss was much larger for the slow bottom than the fast bottom. Most acoustic energy incident on the fast bottom at grazing angles smaller than the critical angle are reflected to the water medium, while most energy incident on the slow bottom at grazing angles near the angle of intromission are transmitted into the sediment. Therefore, communication channels in the fast bottom condition are much more reverberant than those in the slow bottom condition.  
The communication sequence consisted of a 20-ms-long linear frequency-modulated (LFM) pulse with a bandwidth of 13-17 kHz as a probe signal, followed by a pause lasting 0.5 s, followed by binary phase shift keying (BPSK) sequences lasting 3.5 s with a center frequency of 15 kHz. The symbol rate was 1000 symbols per second, and the signal bandwidth was 2 kHz. The pulse-shaping filter was a root raised cosine (RRC) filter with a roll-off factor of \(\beta~{}=~{}1\). Communication data packets were transmitted every 10 s and were repeated 15 times for each source-receiver range.