# Improving Passive Time Reversal Underwater Acoustic Communications Using Subarray Processing
## 5 Lake Experiment
### Results  
The performance metric is the uncoded BER and the output SNR. The proposed TR-DFE uses two subarrays with sensors (1,2,3,4) and (5,6,7,8). Table 2 illustrates the BER results of 10 packets using different receiver algorithms. The conventional TR-DFE achieved BERs between \(1\times 10^{-2}\) and \(1\times\leavevmode\
obreak\ 10^{-1}\), while the proposed TR-MC-DFE achieved BERs between \(3\times 10^{-4}\) and \(1\times 10^{-2}\). Compared with the conventional TR-DFE, the average BER of TR-MC-DFE was reduced by an order of magnitude. The OMP and IPNLMS sparse channel estimation algorithms further improved the BER performance as shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Packet Nos. **} & \multicolumn{3}{c}{**TR-DFE**} & \multicolumn{3}{c}{**TR-MC-DFE**} \\ \cline{2-7}  & **LS** & **OMP** & **IPNLMS** & **LS** & **OMP** & **IPNLMS** \\ \hline
1 & 0.054 & 0.0206 & 0.0135 & 0.0043 & 0.0007 & 0.0003 \\
2 & 0.074 & 0.0194 & 0.0256 & 0.0085 & 0.0016 & 0.0025 \\
3 & 0.064 & 0.0169 & 0.0  
The output SNR and MSE of 10 packets for the DJK15 experiment with different receiver algorithms are shown in Figure 10. The conventional TR-DFE achieved output SNRs between 4 dB and 8 dB, while the proposed TR-MC-DFE achieved output SNRs between 7 dB and 11 dB. The output SNR improvements obtained from subarray processing were about 3 dB, with the same for three channel estimation algorithms. For comparison, the output SNR performance of the MC-DFE was also plotted in Figure 10. The output SNR of MC-DFE was very close to that of the TR-MC-DFE except for packet 3, which failed to decode successfully. However, the computational complexity of the 8-channel DFE is much higher than TR-DFE and TR-MC-DFE, when the above parameters are selected. To illustrate the improvement of the proposed TR-MC-DFE over the conventional TR-DFE, we chose the first packet among 10 packets to present the scatter plot of equalized QPSK signals using the IPNLMS channel estimation algorithm shown in Figure 11, which includes the following: (a) conventional TR-DFE; (b) TR-MC-DFE; and (c) MC-DFE. The output SNRs are 7.8 dB, 11 dB, and 10.6 dB, with the corresponding bit error rates of \(1.35\times 10^{-2}\), \(3.0\times 10^{-4}\), and \(1.0\times 10^{-3}\), respectively. Using the conventional TR-DFE with IPNLMS, the average uncoded BER and output SNR for 10 packets are \(2.1\times 10^{-2}\) and 7.3 dB, while using the proposed TR-MC-DFE with IPNLMS, the average  
Figure 11: Scatter plot of the equalized first packet signal: (**a**) the conventional TR-DFE, (**b**) the proposed TR-MC-DFE (\(P=2\)) and (**c**) MC-DFE. Figure 10: Performance for 10 packets using different methods. Results of the conventional TR-DFE are represented by solid lines. Results of the proposed method are represented by dot-dashed lines: (**a**) output SNR performance and (**b**) Mean squared error (MSE) performance. uncoded BER and output SNR for 10 packets are \(1.5\times 10^{-3}\) and 10.3 dB. The average output SNR improvement is 3 dB, whereas the maximum output SNR improvement is 3.5 dB among 10 packets. Figure 12a,b show the output SNRs using hydrophones (1,2,3,4) and hydrophones (5,6,7,8) with LS, OMP, IPLNLMS and MC-DFE, respectively. The TR-DFE receiver using second hydrophones fails to demodulate because of the low SNRs shown in Figure 12b. Comparing Figures 10a and 12a, the hydrophones (5,6,7,8) have no contribution to the output SNR improvement of the conventional TR-DFE. However, the hydrophones (5,6,7,8) still have contribution to output SNR improvement of the proposed TR-MC-DFE shown in Figure 10.  
For fixed-length arrays, TR-MC-DFE with different subarray lengths (number of subarrays) have different performance and computational complexity. A trade-off needs to be made between computational complexity and receiver performance. Meanwhile, a minimum subarray length is required to obtain a acceptable Q function (ISI).