## 3 Communication Results by Experiments
### Results from Experiment II  
Next, we conducted experimental tests on a stainless steel pipe specimen of \(1.5\) meters in length, \(115\) mm in outside diameter and \(6\) mm in wall thickness. Our goals were to validate that our technique could be generalized to (1) pipes of different materials, dimensions and loading conditions; (2) sensors of different sizes and inter-sensor distances; and (3) different noise levels. Two PZT wafers (PSI-5A4E) were mounted on the surface of the pipe using cyanoacrylate adhesive, located \(0.69\) m apart. Each wafer was \(10\) mm long and \(10\) mm wide. The stainless steel pipe vertically stood on the floor, with the bottom end sealed with a rubber cap, which allows the pipe to hold water. Randomly generated bit streams at data rates of \(R=10,20,50,100\) kbps were sent through the pipe specimen using the TR-PPM method under two testing scenarios: the pipe was empty (without water) and the same pipe was filled with water. Furthermore, we also tested the communication results when the time averaging (\(10\) times) of received responses was employed when generating \(y(-t)\) for modulation. Similar to the experimental results on the carbon steel pipe, we observed a complex channel sounding response on the stainless steel pipe (see Figure 7(b)) and a strong time reversal focused peak (see Figure 7(d)). However, we also noticed a higher level of sidebands around the time reversal focused peak compared to what we observed in the carbon steel pipe specimen in Experiment I (see Figure 3(d)). This phenomena are caused by the relatively small ratio of the transmitter/receiver distance (\(D=0.69\) meter) to the pipe diameter (\(r=115\) mm), _i.e._, \(D/r=690/115=6\) for the stainless steel pipe setup, whereas the ratio is about \(D/r=1500/70=21\) for the configuration of the carbon steel pipe experiment in Experiment I. We note that elastic waves that propagate in pipes typically consist of longitudinal waves, torsional waves and flexural modes [45, 46]. After excitation, different wave modes would appear as the waves travel along the pipe and interrogate the pipe. Since only one PZT receiving sensor was used at a single position on the pipe, many wave modes that were excited by the transmitting PZT sensor could not  
Figure 6: **(a)** Obtained bit error rate _versus_ data rate at \(R=10,20,50,100\) kbps; **(b)** impact of noise reduction by time averaging. be captured, which, in turn, gave rise to a smaller focusing peak and larger sidebands after time reversal. We anticipate that using an array of PZT receivers could achieve a better time reversal focusing, because the use of a sensor array could capture more transmitted wave energy caused by various wave modes. Due to space limitation, the test results using sensor arrays will be reported elsewhere. Figure 7(g) depicts a zoomed-in plot of Figure 7(f) in the \(40\) ms - \(41\) ms time window, which includes the decoded \(10\)-bit stream as \([1\;1\;0\;1\;0\;0\;1\;1\;0\;1]\). Figure 8 depicts snapshots of the received information carrying waveforms in the \(4.0\) ms - \(4.2\) ms time window for the four different data rates. We repeated the same experimental procedure on the stainless steel pipe specimen by filling the pipe with water. When filling the pipe with water, a few drops of detergent liquid were added to the water to release bubbles at the pipe-water interface inside of the pipe. The bubbles were observed accumulating at the water surface and released to air instead. Figure 9 depicts the snapshots of waveforms obtained during the TR-PPM data communication schemes similar to what was presented in Figure 7 for the test scenario where no water is in the pipe specimen. Figure 9(d) and (g) show that the waveforms have less sidebands compared with Figure 7(d) and (g), which implies less interference caused by the sidebands of the time reversal focused response. The bit stream turns out to be more distinguishable when the pipe is filled with water.