# The Long-Range Biomimetic Covert Communication Method Mimicking Large Whale
## 2 Modeling Whistles of the Right Humpback Whale  
Whales communicate with each other using whistles. For the long-range biomimicking communication method, we selected the RHW as a mimicking model. The RHW is about 15 m long and makes sounds from tens to hundreds of hertz. Figure 1 shows the spectrogram of the whistles of the RHW. Figure 1 shows three frequency contours of the whale whistle starting at 150 Hz. In Figure 1a,d, the frequency of the whistle is 150 Hz until halfway through the whistle. Then it increases to 250-300 Hz. In Figure 1b,e, the whistle frequency increases linearly from 150 Hz to 300 Hz. The whistles in Figure 1c,f also start at 150 Hz but end at 200 Hz. As shown in Figure 1, whales generate various whistles, but we can see that there is a specific habit when whales make whistle sounds. The frequency values of the whistle are limited according to their habits [27; 28; 29; 30]. For example, if the RHW starts the whistle at 150 Hz,  
Figure 1: Spectrogram of whistles of the RHW: (**a**), (**d**) Pattern 1; (**b**), (**e**) Pattern 2; (**c**), (**f**) Pattern 3.  
we can infer that whales are used to generating sounds under 300 Hz halfway through the whistle. In this paper, we propose a biom mimicking communication method using the whistle-generating habit of whales. One of the simple examples of the proposed method is shown in Figure 1d,e. The whistles in Figure 1d,e start at 150 Hz. Then, at 0.55 s of whistle time, bit 0 is modulated when the frequency value of the whistle is 150 Hz (red box). If the frequency value of the whistle is 200 Hz, it indicates bit 1 (white box). Likewise, if the whistle-generating habit of the RHW is modeled, we can transmit binary information according to the modeling results. As shown in Figure 1, pre-recorded whistles are already contaminated with noise, and communication performance cannot be guaranteed when the pre-recorded whistle is utilized directly. Therefore, in this paper, a whale whistle is modeled. The whistle-generating habit of the whale is that the subsequent frequency values are restricted by the frequency value of the previous time [27; 28; 29; 30]. This habit is suitable for Markov chain (MC)-based modeling, and some studies have analyzed the time-dependent frequency change of whistles using MC [31; 32; 33; 34; 35; 36; 37]. However, applying conventional modeling methods directly to the proposed methods is difficult due to the degradation of BER performance. The time-frequency orthogonality between symbols must be maintained for the low BER. However, conventional modeling methods do not consider this orthogonality. Therefore, the time-dependent frequency change of the whistles is modeled in a time-frequency unit that satisfies the orthogonality. The proposed method represents information bits using the frequency change with time. The symbol can be distinguished when the time and frequency change is greater than twice the reciprocal of the symbol duration, such as linear frequency modulation (LFM). For the modeling, the frequency values of a whistle over time were extracted by short-time Fourier transform (STFT). When the time window length of STFT is \(\Delta T\), the minimum frequency unit that guarantees the orthogonality between two different LFMs is \(2/\Delta T\). Thus, the frequency resolution of STFT \(\Delta F\) is \(2/\Delta T\). As a result of STFT, the whistle is represented in the 2D domain with \(K\)-length of the time sample and \(L\)-length of the frequency sample. Figure 2a shows the \((L\times K)\) size of the 2D whistle. In Figure 2, \(T_{w}\) is the time length of the whistle. We can obtain one frequency value for each \(K\) column from the 2D whistle, and the time-dependent frequency change is obtained as \(\text{F}=[f_{1},\ldots,f_{k},\ldots,f_{k}]\). If we obtain the F matrix from \(N\) whistles, the probability distribution of the frequency change over time can be obtained using Markov-chain modeling.