## 4 Results and Discussion
### Data Communication Reliability along the MDPE Pipe  
The previous section evaluated the impact of the soil on acoustic signal attenuation using the pipe wall as a waveguide and provided a better understanding of its attenuation along the pipeline. This section determines the reliability of data communication over longer distances. Data communication reliability, in this context, is assessed using the bit error ratio (BER), which is defined as the probability of incorrectly decoding a previously  
Figure 11: (**a**) Numerical prediction of acoustic attenuation along infinitely long buried MDPE pipe and (**b**) buried MDPE pipe of 6 m length. transmitted digital information signal at a digital communication receiver [19; 32]. Using on-off keying (OOK) digital modulation, for example, BER along the pipe can be expressed as  
\[BER=\frac{1}{2}erfc\Big{(}\sqrt{\
icefrac{{1}{2}SNR}{{R}}}\Big{)} \tag{6}\]  
where \(SNR\) is the signal-to-noise ratio of the digital information signal and \(rfc(x)\) is the complementary error function (\(erfc(0)=1\)). Due to the acoustic signal attenuation along the pipe, SNR will reduce at increasing distances along the pipe. Thus, Equation (6) is used to examine data communication reliability along the exposed and buried MDPE pipes and predict the maximum distances at which reliable digital communication can be achieved. Using the acoustic-based digital communication system described in [29], the relative amplitude between a signal pre-amplifier and the input threshold of a phase-locked loop (PLL) signal decoder at the digital communication receiver can be expressed as  
\[SNR=20\log_{10}\frac{V_{out}}{V_{in}} \tag{7}\]  
where \(SNR\) (dB) is the signal-to-noise ratio between the signal pre-amplifier output and the PLL input threshold, \(V_{out}\) (V) is the signal pre-amplifier output voltage and \(V_{in}\) (V) is the PLL input threshold. The maximum output voltage of the signal pre-amplifier was 4 V while the PLL input threshold was 0.2 V [29]. Using Equation (7), the maximum SNR between \(V_{out}\) and \(V_{in}\) was calculated as 26 dB (which can be considered as the initial SNR for Equation (6)). Using this information as well as the numerically predicted and experimentally measured acoustic attenuation along the exposed and buried MDPE pipes, the maximum ranges at which reliable digital communication can be achieved are shown in Figure 12.  
Figure 12: Acoustic data communication reliability along (**a**) exposed and (**b**) buried MDPE pipes. From Figure 12, the maximum distances at which data communication is theoretically possible along the exposed MDPE pipe vary depending on the acoustic attenuation prediction along the pipe. To predict the maximum distance, a BER of 0.01 (or 1%), as suggested by [33], was used as the minimum threshold below which data communication can be safely assumed to be reliable. Figure 12a highlights that the maximum acoustic data communication distance (18 m) determined agrees for both the numerically and experimentally predicted acoustic attenuations which were close to each other. In contrast, the results in Figure 12b demonstrated the differences using both the measured and predicted acoustic attenuation with distances of 5 m and 11 m, respectively. This indicates the importance of accurately predicting the signal attenuation. Nevertheless, acoustic data communication at distances of up to 11 m is theoretically possible along a buried MDPE with pipe wall discontinuities at each end.