## 4 Conclusions and Discussions  
In this paper, we present the theoretical background and experimental studies of the time reversal-based timing acquisition and pulse position modulation method for pulsed wideband elastic wave communication on steel pipes. In this method, the focusing properties of time reversal are used to exploit the strong dispersion and multi-modality of elastic channels to enable accurate timing acquisition and symbol demodulation. As a result, a single finger receiver combined with a single sliding correlation detector suffices for the system to rapidly obtain the starting time. Once the timing offset between the  
\begin{table}
\begin{tabular}{l c c c} \hline  & **BER** & **No Averaging** & **Averaging 10 Times** \\ \hline Without & mean & \(0.190\) & \(0.181\) \\ Water & std & \(0.027\) & \(0.015\) \\ \hline With & mean & \(0.129\) & \(0.095\) \\ Water & std & \(0.015\) & \(0.012\) \\ \hline \end{tabular}
\end{table}
Table 4: Impact of Noise Reduction by Time Averaging at \(100\) kbps.  
Figure 11: Obtained bit error rate _versus_ data rates of \(R=10,20,50,100\) kbps for stainless steel pipe specimen.  
transmitting sensor and the receiving sensor is obtained, modulated symbols are transmitted, received and demodulated to recover the original information symbol. Therefore, complicated channel estimation algorithms are not necessary, due to time reversal, and the computational efficiency is improved. From a hardware perspective, sophisticated circuit implementation is not required.  
We conducted experimental studies on steel pipe specimens using piezoelectric PZT sensors in a laboratory environment. The experimental results demonstrate that the proposed TR-PPM scheme achieves robust communications at data rates of \(10\) kbps and \(20\) kbps on steel pipe specimens in spite of the severe channel dispersion and multi-modality of the elastic channels. To achieve higher data rates, more complicated processing techniques, such as adaptive equalization or error control coding should be used in conjunction with the time reversal approach. In addition, we note that the system has been tested over a rather small distance (a maximum of \(1.5\) meter), due to limitation of the specimen's dimension. The estimated attenuation factor is about \(26\ \mathrm{dB/m}\), as described in Section 3.3. In general, as they are propagating, guided waves may experience attenuation or reduction in amplitude. This scenario occurs mainly in two situations or a combination of both [48]: _i.e._, material absorption of wave energy due to viscoelastic materials in the medium [49] and energy leakage into a different medium at the boundaries [50]. The efficacy of the proposed TR-PPM over distances that are an order of magnitude greater than the ones tested in our experiments is influenced by the attenuation factor, which, in turn, depends on the excitation frequency, the material property, the type of generated wave modes, _etc._ Although not tested in a more realistic environment on sub-sea structures or pipelines, the proposed scheme is expected to perform well over a longer distance in a larger scale, for example, a \(50\) meter range if a \(60\ \mathrm{dB}\) signal-to-noise ratio (SNR) loss is allowed, due to wave attenuation, based on the observed \(26\ \mathrm{dB/m}\) attenuation factor.  
[PERSON] was supported in part by the National Science Foundation under grant no. CMMI-1126008 and a subcontract from Carnegie Mellon University funded by the National Science Foundation under grant no. CNS-0930868. [PERSON] was supported by Westinghouse Electric Company. The authors would like to thank Professors [PERSON], [PERSON] and [PERSON] for the discussions and comments on the experiments.  
The authors declare no conflict of interest.