# Underwater Biomimetic Covert Acoustic Communications Mimicking Multiple Dolphin Whistles
## 2 Modulation  
Most dolphins live in groups and generate multiple whistles to communicate with each other. As a result, multiple group whistles are often observed simultaneously [15; 16; 17; 18; 19; 20; 21; 22; 23]. To enhance the covertness of underwater biomimetic covert communication, mimicking dolphin group sounds is needed rather than mimicking conventional single whistle sounds. In this paper, the proposed underwater biomimetic covert communication method mimics the multiple whistles by combining the TFSK with the CV-CFM methods to increase the covertness and the data transmission rate while preserving the BER performance. The conventional TFSK modulation technique involves extracting frequency contours from the original dolphin whistle, generating signals with the same frequency contour, and then shifting the whistles in the time-frequency domain to convey bits. On the other hand, the CV-CFM technique maps the bits using the divided phase-modulated symbols from the whistle frequency contour. Due to the characteristics of underwater acoustic communications, the frequency changes between symbols in a single whistle are larger than the coherent bandwidth, and non-coherent modulation such as DPSK needs to be used [24]. However, both the original TFSK and CV-CFM techniques were designed to mimic the sounds of a single dolphin. Consequently, the combination of these two methods directly leads to interference between multiple whistles, resulting in reduced detection performance due to the signal interference at the receiver. To address this limitation, this section presents a technique for combining TFSK and CV-CFM to increase the transmission rate while considering interference mitigation. For the interference at the overlapped whistles, the proposed method detects the interference locations of the whistles and mitigates interference to improve detection performance at the receiver. The dolphin group sound in Figure 1 is an example of multiple dolphin whistles. To mimic the multiple dolphin whistles, the proposed method employs a two-step approach. First, the individual whistle signals are modulated by the TFSK technique to allocate a portion of the transmission bits. Then, the CV-CFM is applied to allocate the remaining transmission bits. Since the bits are simultaneously allocated to TFSK and CV-CFM, this approach increases the data transmission rate compared to either of the two transmission methods. The block diagram of the proposed method is shown in Figure 2.  
In this paper, the proposed method mimics \(L\)-multiple biomimetic whistles to generate multiple whistles. For mimicking multiple dolphin whistles, the TFSK modulation technique is first applied to each whistle signal, followed by the CV-CFM modulation. Assume that the frequency change function over time for the \(l\)-th (\(1\leq l\leq L\)) whistle is denoted as \(f_{l}(t)\)[12], and the modeling of the \(l\)-th individual whistle is expressed as:  
\[w_{l}(t)=\cos[\int f_{l}(t)dt]. \tag{1}\]  
Figure 3 shows an example of the proposed modulation technique when TFSK is applied to a single whistle. To achieve the modulation described in Equation (1) for the multiple whistles, phase modulation and time-frequency shift modulation are applied to the individual whistle signal, denoted as \(w_{l}(t)\). In Figure 3, it is assumed that one-time and one-frequency shift units are denoted as \(\Delta t\) and \(\Delta f\), respectively. The total numbers of time and frequency grids are assumed to be \(M\) and \(N\), respectively. If \(b_{M}\) and \(b_{N}\) are  
Figure 1: Whistle spectrogram of dolphins. Figure 2: The block diagram of the proposed method. calculated by \(log_{2}M\) and \(log_{2}N\), respectively, a sum of \(b_{M}\) and \(b_{N}\) bits is transmitted using the TFSK method. The arbitrary time-frequency modulated signal (\(x^{\prime}_{l}(t)\)) of the \(l\)-th whistle is obtained by shifting \(w_{l}(t)\) by \(m^{\prime}\Delta t\) and \(n^{\prime}\Delta f\), respectively.