# Communication Rate Increase in Drill Strings of Oil and Gas Wells Using Multiple Actuators
## 4 Experimental Results on Communication and Data Detection
### Two Actuators Simultaneously Transmitting Two Data Streams  
Here we consider the experiments where Tx 1 and Tx 2 in Figure 1a both transmitted two different sets of data simultaneously and with the same power over the same bandwidth of 2 to 6 kHz. More specifically, each actuator transmitted fifty OFDM symbols in a row, repeated five times in order to have multiple trials. This simultaneous transmission of two data streams doubled the transmission rate, without any bandwidth increase. To separate and demodulate the two data streams at the receive side, two receiving sensors were used in this paper: the strain sensor and the triaxial accelerometer. Since the latter had the three \(x\), \(y\), and \(z\) acceleration channels, there were six possible receiver configurations using two channels: strain and \(x\)-acceleration, strain and \(y\)-acceleration, strain and \(z\)-acceleration, \(x\)-acceleration and \(z\)-acceleration, and \(y\)-acceleration and \(z\)-acceleration. Details of the data separation and detection method are discussed in the Appendix A. Measured BERs and SNRs for these six receivers at different positions identified in Figure 1b are presented in Figures 6-11, respectively. For each receiver at each position, five BERs, five SNRs, and their averages for each of the first and the second data streams are provided, as obtained from five trials. To compare performance of these six 2 \(\times\) 2 systems with two transmitting actuators and a two-channel receiver, the best performance of the one actuator system of the previous subsection was considered as a benchmark. According to Figure 4, the lowest average BERs were below \(10^{-3}\) for the system with the strain receiver, for average SNRs less than 4 dB at various receiver positions. Based on Figure 7 and compared to this benchmark, the two-actuator system using the strain and the \(y\)-acceleration receivers offered the best performance among the six two-actuator systems. This is because in all the receiver positions its average BERs were less than \(10^{-3}\), with average SNRs close to or less than 4 dB. The second-best two-actuator system appeared to be the one which utilized the strain and the \(x\)-acceleration receivers, whose BERs and SNRs are shown in Figure 6.  
Figure 6: BERs (**top**) and SNRs (**bottom**) at different receiver positions, with two actuators transmitting two data streams simultaneously. The receivers were a strain sensor and the \(x\)-channel of a triaxial accelerometer. The piecewise linear graphs represent average BERs and SNRs for each of the two data streams versus the receiver position. Note that average BERs of the two-actuator systems that did not use the strain sensor receiver were all greater than \(10^{-3}\) at all positions, for average SNRs ranging from 1.5 to 9 dB (see Figures 9-11). As discussed in the previous section, this can be related to the relatively flat strain channel frequency response, which made equalization and data detection simpler and more accurate compared to the non-flat and frequency-selective behavior of the acceleration channels. To better comprehend the data presented in Figures 6-11, their measurement results averaged over five different receiver positions and over two data streams are provided in Table 2. It was observed that when the strain sensor was one of the receivers, the BER tended to be smaller. This held true even for strain and \(z\)-acceleration in Table 2, if the abnormally high BERs in Figure 8 for this receiver pair at 40 cm were not included in the average, which updated the BER and SNR for this receiver pair in Table 2 to 2.6 \(\times\)\(10^{-4}\) and 3.4 dB, respectively. Overall, these smaller BERs can be attributed to the relatively flat strain channel frequency response, which made data recovery and equalization simpler and more effective, compared to the acceleration channels which were non-flat and more frequency selective.