# Long-Range Acoustic Communication Using Differential Chirp Spread Spectrum
## 5 Experiment  
### Lake Trial  
We conducted a lake trial using a proven signal through simulation. The experiment was conducted in May 2020, in South Korea. The experiment was conducted slightly differently on different dates. The experimental configurations are shown in Table 3. The transmitter used Neptune D/17/BB, and the receiver used Reson TC-4032 [29,30]. The communication method was single-input single-output (SISO) communication. There were two bases in the center of the lake that fixed the transmitter and receiver, and one unfixed barge. The distance between the bases was fixed at about 180 m. There was continuous travel by wind or by engine power. In the experimental configuration, the distance between the transceiver was fixed at about 180 m in Experiments 1 and 3, and the barge moved unfixed between 100 m and 300 m in the 2 nd experiment. The depth of the lake was about 50 m, and the receiver was always fixed at a depth of about 25 m. The depth of the transmitter was varied: 20 m on the 1 st, 10 m on the 2 nd and 5 m on the 3 rd experiment. To analyze the signals, an understanding of the channel environment is essential. We analyzed the channel characteristics of each channel at which the signal was transmitted in order to determine whether there was a change in performance according to the channel impulse response (CIR). The channel  
Figure 4: Results of the simulation: (**a**) performance according to the signal-to-noise ratio (SNR) and (**b**) performance according to Doppler. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Sampling frequency & 192,000 Hz & LFM interval & 1 s \\ Carrier frequency & 16,000 Hz & Guard interval & 1 s \\ Data rate & 100 bps & Number of bits & 336 bits \\ Bandwidth & 2000 Hz & Preamble & 511 bits \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters for the lake experiment from May, 2020.  
measured the LFM pings with a length of 0.128 ms by repeatedly transmitting 200 times. A measured CIR is expressed as  
\[s_{Rx}(t)=h(t)\otimes s_{Tx}(t), \tag{10}\]  
where \(s_{Rx}\) is the received signal; \(s_{Tx}\) is the transmitted signal; and \(h\) is the CIR. In Equation (10), \(h\) is cut to the length of the ping and is expressed again in matrix \(\mathbf{H}\), which is expressed as  
\[\mathbf{H}=h(q,n), \tag{11}\]  
where \(q\) is the time delay and n is a time instant. We can calculate the delay in Doppler spread function by \(\mathbf{H}\). The FFT of \(\mathbf{H}\) gives a spreading function, as expressed by Equation (12),  
\[\mathbf{S}(q,k)=F(\mathbf{H}) \tag{12}\]  
and summation of the delay axis provides an estimate of the Doppler spectrum \(P_{\wp}\):  
\[P_{\wp}=\sum_{q=0}^{N-1}\bigl{|}\mathbf{S}(q,k)\bigr{|}^{2}. \tag{13}\]  
The characteristics of each experiment are expressed in Figures 5-7. Figures 5a, 6a and 7a represent the CIR of each experiment; Figures 5b, 6b and 7b represents the delay-Doppler spread spectrum of each experiment; Figures 5c, 6c and 7c is the power delay profile; and Figures 5d, 6d and 7d is the Doppler power spectrum. Figure 5: The lake-measured channel in the 1 st experiment: (**a**) CIR; (**b**) delay-Doppler spread spectrum; (**c**) power delay profile; (**d**) Doppler power spectrum. The 1 st experiment had a number of multipaths, and a slight tilt was seen in the CIR. The channel was not constant, and a slight tilt was seen, so there was some time variance. The delay-Doppler spread spectrum showed that it moved to \(-0.49\) knot with a Doppler frequency of about \(-2.7\) Hz. In the 2 nd experiment, the receiver was fixed in the same position, but the transmitter was placed in a barge. So, the 2 nd had 2 multipaths and a big tilt was seen in the CIR. The delay-Doppler spread spectrum showed that it moved to 2.18 knots with a Doppler frequency of about 12 Hz. In the 3 rd experiment, the location was the same as in the 1 st experiment, but there was a difference in multipath, depending on the depth of the water.