# Communication Rate Increase in Drill Strings of Oil and Gas Wells Using Multiple Actuators
## 4 Experimental Results on Communication and Data Detection
### One Actuator Transmitting One Data Stream  
In this section, we consider the experiments where Tx 1 in Figure 1a transmitted fifty OFDM symbols in a row over the bandwidth of 2-6 kHz, repeated five times in order to have multiple trials. With the same transmit power per actuator throughout the entire paper and in all of the experiments, the measured bit error rates (BERs)--that is, bit error probabilities--for various receiving sensors at different positions identified in Figure 1b are presented in Figure 4. For each sensor at each position, five BERs and their average are provided, as obtained from five trials. It was observed that quite often the BERs of the strain sensor receiver were smaller than the BERs of the accelerometer receivers.  
Figure 4: Bit error rates of various receiving sensors at different positions, with one actuator transmitting one data stream. The receivers were a strain sensor and a triaxial accelerometer with \(x\), \(y\), and \(z\) channels. The piecewise linear graphs represent the average BERs of each sensor versus the sensor position.  
Figure 3: Magnitudes of impulse responses of the channels measured by the receiving sensors in Figure 1b.  
The signal-to-noise ratio (SNR) for each BER data point of Figure 4 and their average over five trials are provided in Figure 5. The SNRs reported throughout this paper were obtained by calculating the ratio of the power of pilot sub-carriers to the power of null sub-carriers [7]. In most cases, the SNRs of the strain sensor receiver were observed to be smaller than SNRs of the accelerometer receivers. This can be attributed to the sensitivity of the particular strain sensor used in the experiments, which produced weaker signals compared to the accelerometer signals, as discussed in the previous section.  
The smaller BERs of the strain sensor receiver, while having smaller SNRs, can be related to the relatively flat strain channel frequency response in Figure 2. This makes equalization and data detection simpler and more accurate, compared to the non-flat and frequency-selective behavior of the acceleration channels' frequency responses in Figure 2.  
To better understand the data presented in Figures 4 and 5, their measurement results averaged over five different receiver positions are listed in Table 1. It was observed that the BER of the strain sensor receiver was smaller than the BERs of the accelerometer receivers. This can be attributed to the relatively flat strain channel frequency response in Figure 2, which rendered equalization and data detection more accurate than the frequency-selective and non-flat acceleration channels' frequency responses in Figure 2. The smaller SNR of the strain sensor receiver can be related to the sensitivity of the specific strain sensor used in the experiments, which produced weaker signals than the accelerometer signals, as mentioned in Section 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Receiving Sensor** & **BER** & **SNR (dB)** \\ \hline Strain & \(2.7\times 10^{-04}\) & 2.4 \\ X-Acceleration & \(2.2\times 10^{-03}\) & 5.2 \\ Y-Acceleration & \(1.1\times 10^{-03}\) & 6.5 \\ Z-Acceleration & \(3.5\times 10^{-03}\) & 5.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Average BERs and SNRs of various receiving sensors, with one actuator transmitting one data stream.  
Figure 5: Signal-to-noise ratios of various receiving sensors at different positions, with one actuator transmitting one data stream. The receivers were a strain sensor and a triaxial accelerometer with \(x\), \(y\), and \(z\) channels. The piecewise linear graphs represent the average SNRs of each sensor versus the sensor position.