## 1 Introduction
Time reversal has emerged as a viable approach for overcoming signal dispersion for digital communication applications, for example, underwater acoustic communication [12] and ultra-wideband radio communication [13, 14, 15, 16]. In [17, 18], we develop a time reversal-based guided elastic wave communication scheme that utilizes steel pipes as transmission channels. The developed communication scheme was verified by preliminary experimental data collected from a steel pipe in a laboratory environment using acoustic wave excitation. The focus of this paper is to provide a comprehensive theoretical development of the proposed time reversal-based pulse position modulation (TR-PPM) method and conduct extensive experimental tests to examine the achievable bit error rate (BER) on steel pipe specimens with various configurations using lead zirconate titanate (PZT) wafer transducers. The contribution of the work described in this paper and our earlier papers [17, 18] focuses on the following two perspectives. First, we utilize the time reversal-based pulse position modulation (TR-PPM) method to achieve signal synchronization and symbol demodulation in order to compensate for severe channel dispersion and multi-modality in the elastic wave communication system design. In most communication systems, the receiver must know the exact starting time in order to demodulate the transmitted symbols correctly. The task for determining the starting time of symbols at the receiver from the distorted transmission signals is commonly called timing acquisition or synchronization. For high data rate communication using elastic waves, rapid and precise timing acquisition becomes very difficult for the PPM scheme, due to severe dispersion and the multi-modality of the underlying characteristics of elastic waves. This problem is somewhat similar to the ultra-wideband (UWB) communication systems, where a large number of resolvable paths in UWB channels may cause many possible starting times [19, 20, 21, 22]. In such cases, timing acquisition often requires complicated searching algorithms to estimate the start time for symbol demodulation. Hence, the hardware implementation is costly. The TR-PPM scheme we proposed in our earlier paper [17, 18] and this paper can be regarded as a channel-assisted timing algorithm, which does not require complicated channel estimation algorithms or circuits at the transmitter and the receiver. In our system, the physical channel is implicitly pre-equalized by the time reversed waveforms at the transmitter. By utilizing the intrinsic adaptive space-time focusing of time reversal, the proposed method needs only a small number of training preamble symbols performing in a pitch-catch mode to estimate the starting time of the symbols quickly, thus enabling subsequent symbol demodulation, despite the above-mentioned channel dispersion and multi-modality in elastic wave channels. Second, we conduct extensive test-bed studies in a laboratory environment to validate the feasibility of elastic wave data communication. The test bed includes PZT wafers, two different steel pipe specimens (_i.e._, a carbon steel pipe and a stainless steel pipe) and a National Instrument PXI acoustical measurement system that includes an arbitrary waveform generator and a digitizer. We note that data communication schemes using elastic waves have been reported for, for example, flood detection in oil rigs (see,e.g., [23, 24]), drill string telemetry [25] in the measurement while drilling (MWD) and logging while drilling (LWD) services in the oil and gas industry [26, 27] or Lamb wave communication (see e.g., [28]); systematic studies of high data rate communication schemes using elastic waves are lacking. We note that a pulse position modulation scheme using guided acoustic waves for flood detection was proposed in [23, 24]. However, the realized data rate was relatively low, because only a \(2\) kHz narrow frequency band (\(39\) kHz-\(41\) kHz) was used in order to overcome the problem of channel dispersion.