# Underwater Biomimetic Covert Acoustic Communications Mimicking Multiple Dolphin Whistles
## 4 Analysis of Experimental Results
### Computer Simulations and Ocean Experiments  
To demonstrate the communication performance of the proposed method, the whistles of Delphinus Delphis in Figure 1 were mimicked [28]. For comparing the data rates, the proposed method and the conventional methods of the CV-CFM of [12] and the TFSK of [13] were compared. Since the proposed and conventional methods utilized multiple overlapped whistles and a single whistle, respectively, the parameters of the proposed and conventional methods were different. For the proposed method, the number of total mimicked whistles was 116, where each of the 116 whistles was phase-modulated with a symbol bandwidth (\(f_{m}\)) of 300 Hz for CV-CFM. The \(\Delta f\) in Equation (2) and \(\Delta t\) in Equation (3) for TFSK were obtained to be 67 ms and 600 Hz, respectively. Given the whistle bandwidth of 7 kHz, 11 segments were set for the frequency shift modulation with three-bit modulations. \(M\) was set to be two to achieve the maximum transmission rate of one bit per time symbol. Since the performance of the proposed technique varies with the spreading code length, experiments were conducted with the spreading code lengths of two, three, and four. The parameters used for the simulation of the proposed method are shown in Table 1.  
For the conventional TFSK of [13], \(\Delta t\) was set to 11 ms and \(\Delta f\) was set to \(1/L_{w}\), where \(L_{w}\) was the average whistle length of 0.39 s with 2.5 Hz. Given the frequency range of \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline Carrier frequency & 16 kHz \\ Bandwidth & 7 kHz \\ \(f_{m}\) & 300 Hz \\ \(\Delta f\) & 600 Hz \\ \(\Delta t\) & 67 ms \\ The number of time, freq segments for TFSK & 11, 2 \\ Spreading code length & \(2,3,4\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameter for the proposed method. 7 kHz, the number of frequency bins (\(N\)) was set to 2730. Thus, for each whistle symbol, 11 bits for frequency and 1 bit for time delay were transmitted, resulting in a total of 12 bits per symbol. For the conventional CV-CFM, the symbol bandwidth was set to be 300 Hz. When the Delphinus Delphis whistle sounds were utilized for one minute and 10 s, the data rates for each technique are shown in Table 2.  
When the proposed method utilized \(L_{c}\) of two, three, and four, the transmission rates decreased by approximately 6.6%, 8.1%, and 9.9%, respectively, compared to the conventional methods [12]. The transmission rate of the proposed method was 15 times larger than that of [13]. The BER performances were compared in three different environments using an additive white Gaussian noise (AWGN) channel, modeled underwater channels, and real ocean experiments. Among the compared methods, the conventional method [13] was not adequate for normal communication due to its lower transmission rate. Therefore, the comparison between [12] and the proposed method was executed. The theoretically calculated BER in AWGN and the computer-simulated BER are displayed in Figure 7.  
In Figure 7, the dotted lines denote theoretically obtained BERs, while the solid lines represent BERs obtained by Monte Carlo simulations. The conventional method in [12] exhibits an error floor at a BER of \(10^{-2}\) due to inter-whistle interference. For the proposed method, however, the error floors occur at lower BERs of \(10^{-4}\), \(10^{-5}\), and \(10^{-6}\), when \(L_{c}\) was two, three, and four, respectively. If a target BER is set to be \(10^{-5}\), which is a typical BER, the optimal code length of the proposed method is three. Thus, the BER results of the AWGN simulation exhibit that the proposed scheme has the lowest BER with a better data rate. For the comparisons of the BER performance through the modeled underwater channel, the Bellhop tool generated the channel model at a point in