## 3 Communication Results by Experiments
### Results from Experiment II
Our hypothesis is that water suppresses certain guided wave modes in the pipe (such as flexural modes), due to the water damping effects [47]; thus, the adverse effect on time reversal focusing, due to a short inter-transducer distance, becomes less significant. Figure 7: Snapshots of waveforms obtained experimentally from TR-PPM data communications on a stainless steel pipe (not filled with water) at a data rate of \(10\) kbps. **(a)** Gaussian pilot signal of \(8\,\mu\)s; **(b)** received response after channel sounding; **(c)** time reversal transmission; **(d)** received time reversal focused waveform; **(e)** modulated time reversal PPM waveform; **(f)** received information carrying waveforms; and **(g)** zoomed-in plot of **(f)**. The red dashed lines indicate the starting positions of symbol frames. The transmitted bit stream in the time window of \(40\) ms and \(41\) ms is \([1\;1\;0\;1\;0\;0\;1\;1\;0\;1]\). Figure 8: Snapshots of the received information carrying waveforms in the time window of \(4.0\) ms - \(4.2\) ms obtained from a stainless steel pipe (not filled with water). The data rates are (**a**) \(10\) kbps; (**b**) \(20\) kbps; (**c**) \(50\) kbps; and (**d**) \(100\) kbps. Figure 9: Snapshots of waveforms obtained experimentally from TR-PPM data communications on a stainless steel pipe filled with water at a data rate of \(10\) kbps. (**a**) Gaussian pilot signal of \(8\mu s\); (**b**) received response after channel sounding; (**c**) time reversal transmission; (**d**) received time reversal focused waveform; (**e**) modulated time reversal PPM waveform; (**f**) received information carrying waveforms; and (**g**) zoomed-in plot of (**f**). The red dashed lines indicate the starting positions of symbol frames. The transmitted bit stream in the time window of \(40\) ms and \(41\) ms is \([1\;1\;1\;0\;1\;0\;0\;0\;1]\). As a result, we achieved a lower BER for TR-PPM communications on the pipe that was filled with water at the data rates of \(R=10,20,50,100\) kbps, compared to the scenario when the pipe was not filled with water. Next, Figure 10 depicts the snapshots of the received information carrying waveforms in the \(4.0\) ms - \(4.2\) ms time window under data rates of \(R=10,20,50,100\) kbps, respectively. The BER results are summarized in Table 3 and plotted in Figure 11.  
Furthermore, we also utilized time averaging (by a factor of \(10\)) to reduce noise level in the received responses for both scenarios (water filled and no water) on the stainless steel pipe specimen. The improvement due to time averaging is insignificant, as shown in the Table 4, where the BER results for the case of non-averaging and that of averaging at a \(100\) kbps data rate are summarized. The results are what we have expected, because Equation (29) reveals that the bit error rate depends on the noise power and the inter-symbol interference. Averaging will increase the signal-to-noise ratio by reducing the noise power, but has a limited effect on the side-band level that characterizes the inter-symbol interference. However, it is expected that time averaging would be effective in the environment when the noise level is relatively high.