# Dolphin Sounds-Inspired Covert Underwater Acoustic Communication and Micro-Modem
## 4 Bionic CUAC Scheme
### Algorithm Simulation and Realization  
This section introduces the specific process of algorithm implementation while referring to the literature [18] which is about covert UAC using dolphin sounds. In the modulation process, the data from the serial port is encoded first and each six bits are converted to decimal digits. The length of the time delay is calculated according to the time delay resolution. Delay difference is modulated between the interval of two signals according to the calculation. After assembling all click signals and time delay together, the synchronization head and the protection interval are added to the header of the signal. The process flow chart of bio-signal modulation is shown in Figure 8. The frame structure of the complete mimic bio-signal combined with whistle and clicks is shown in Figure 9.  
\(\tau_{dl}(i=1,2,3,\ldots,\)L) is the is the coding time, which refers to the time delay difference between two click signals. Each click signal time duration is represented by \(T_{cj}(j=0,1,2,\ldots,\)L). For each \(n\) bits of encoded information, the encoding time is divided into \((2^{n}-1)\) parts, and the time duration of each part is \(\Delta\tau\) that we set to 1 ms. Therefore, the time delay can be calculated as:  
\[\tau_{d}=\Delta\tau\cdot k\,\ k=0,1,\ldots,2^{n}-1. \tag{1}\]  
Here, \(k\) is the decimal information transformed by Gray code from a binary information source. For example, if each encoded element has seven bits of information, the encoding time would be divided into 127 parts. If the source information is 1010111, after Gray encoding there would be \(k=65\). Therefore, the time delay \(\tau_{d}\) would be 65 ms.  
Figure 7: Experimental prototype of the micro-modem; (**a**) Digital board of the micro-modem; (**b**) Modern hardware. As the width and encoding time of each click is variable, the communication data rate of the system can be calculated as:  
\[v=L\times n/\sum_{l=1}^{L}\left(T_{cl}+\tau_{dl}\right) \tag{2}\]  
At the receiver, side synchronization is achieved by the whistle. After synchronization, the protection interval and the first click signal are removed in order to reduce the time of operation as it does not carry any information and the length is known (\(l_{0}\)). The length of the signal in the first correlation operation is \(l_{1}+l_{t\max}\). The starting position is identified by correlation peaks of the last iteration. The signal length in the \(i\)-th correlation operation is \(l_{i}+l_{t\max}\). In this way, if there are \(\mathrm{L}+1\) clicks in a complete signal, the system needs to perform correlation \(\mathrm{L}\) times. Therefore, there is no need to perform correlation for the first click signal and ensure that the length of the signal results in the shortest first operation signal with no loss of information. The correlation peak position minus the length \(l_{i}\) is the corresponding time delay. We can obtain the transmitted data after converting the decimal data into binary data. Finally, the system will upload data to the host computer to be displayed through the serial port. The whole process flow chart is shown in Figure 10.  
The click signals we selected have excellent autocorrelation as shown in Figure 11. Different colors represent the correlation output between different click signals and the click signals group. Each peak reflects the autocorrelation of the click signals. Table 1 lists the normalized cross correlation and autocorrelation coefficients of each signal. Figure 8: Process flow chart of bio-signal modulation. Figure 9: Frame structure of the mimic bio-signal combined with whistle and clicks. From Table 2, we can ascertain that the correlation coefficients between the signals are less than 0.43. We obtained the bit error rate (BER) curve of the algorithm under white Gaussian noise by simulation.