# Improving Passive Time Reversal Underwater Acoustic Communications Using Subarray Processing
## 5 Lake Experiment
### Experiment Setup  
The DJK15 experiment was conducted in Danjiangkou River, Henan Province, China, in January 2015. The water depth was 45-50 m. The source is deployed at 20 m below the surface. The receiver array was deployed at depths between 18-20 m. It consists of two subarrays, each with four  
Figure 4: Channel impulse responses (CIR) snapshots in simulation.  
Figure 5: Output signal-to-noise (SNR) varies with input SNR.  
hydrophones uniformly spaced at 0.25 m. Two subarrays are soft connected. The top hydrophones (1,2,3,4) belong to the first subarray, and the bottom hydrophones (5,6,7,8) belong to the second subarray. The data were transmitted from the source using QPSK modulation with a carrier frequency of 6 kHz and a bandwidth of 4 kHz. The structured signal was transmitted as shown in Figure 6. The transmitted signal structure was a 0.1 s linear frequency modulated signal and 0.1 s guard period followed by the data.  
The distance between transmitter and receiver was 7.4 km. The data rate is 8 kbits/s with QPSK modulation for a symbol rate of 4 k-symbols/s. Each packet was 2.8 s, including 10,366 QPSK symbols, of which 500 symbols were training sequences. Ten packets were transmitted during that experiment. In total, the transmitted signal contained 10,366 \(\times\) 10 \(\times\) 2 = 20,7320 information bits. The sound speed profile was plotted at a function of depth, as shown in Figure 7.  
The detail parameters of the communication system used in the lake experiment are shown in Table 1. The recursive least squares (RLS) algorithm is used for the adaptive MC-DFE. The order of feedforward and feedback filter were 50 and 50, respectively. The other parameters in the DFE and DPLL are the same as the simulation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Description** & **Values** \\ \hline \(T_{c}\) & Symbol duration & 0.25 ms \\ \(M\) & Total sensor numbers & 8 \\ \(K\) & Oversampling rate & 2 \\ \(N_{p}\) & The training symbol length & 500 \\ \(N_{f}\) & Feedforward filter order & 50 \\ \(N_{b}\) & Backward filter order & 50 \\ \(K_{1}\) & Proportional tracking constants in PLL & 0.005 \\ \(K_{2}\) & Intergral tracking constants in PLL & 0.005 \\ \(\lambda\) & RLS forgetting factor in DFE & 0.999 \\ \hline \hline \end{tabular}
\end{table}
Table 1: System parameters.  
Figure 6: Transmitted signal structure.  
Figure 7: Sound speed profile in DJK15 lake experiment.  
The received SNRs of hydrophones (1,2,3,4) and hydrophones (5,6,7,8) was about 7 dB and 2 dB, respectively. The second subarray was rotated by the water current, and hence, it may not point to the transmitter. This is the reason that the received SNR of the second subarray is lower than the first subarray. The second subarray was rotated by the water current, and hence, it may not point to the transmitter. This is the reason that the received SNR of the second subarray is lower than the first subarray.  
Figure 8: Examples of CIRs estimated using the least mean squares (LMS) algorithm from the DJK15 data: The 20 ms delay spread in the channel amounted to ISI spanning about L = 80 symbols.  
one. The DJK15 channels varied slowly with time. Examples of CIRs for the transmissions from the source to the top and bottom receivers are shown in Figure 8. There were approximately 20 ms of delay spread in the channel, which amounted to ISI spanning about L = 80 symbols. Examples of CIRs are shown as a function of geotime in Figure 8a-h for the transmissions from the source to receivers 1-8. The top receiver is sensor one. For this receiver, the multipath structures remain relatively stable over a 5 s duration. Figure 9 plots the \(q\) functions for different subarrays using the measured CIRs from the DJK15 experiment. The top panel in each figure shows a snapshot of the normalized \(q\) function.