## 2 Proposed Method
### Proposed Bio-Mimetic TFSK Modulation Method
The block diagram of the proposed transmitter is shown in Figure 4.  
For the communication of the proposed method, transmission frames are utilized as in the conventional TPSK [13]. Every frame has a preamble which is made by a whistle with a large chirp rate, and the consecutive whistle patterns and the original time- and frequency-locations of the whistles in the frame are known to the transmitter and the receiver. Thus, the reference information of \(t=0\) and \(f=0\) for every whistle is known, too. What the receiver needs to detect is to estimate the time- and frequency-differences from the reference information. For the precise detection of the time- and frequency information from the received TPSK whistles, the maximum likelihood (ML) based receiver is proposed. Assume that the whistle is shifted by \(m^{*}\Delta t\) in frequency and \(n^{*}\Delta f\) in time for an arbitrary input. Then, the  
Figure 4: Block diagram of the proposed transmitter. modulated whistle (\(S_{m^{*},n^{*}}(t)\)) is transmitted. If \(S_{m^{*},n^{*}}(t)\) passes through the underwater acoustic (UWA) channel (\(h(t)\)), the received signal (\(r(t)\)) is modeled as:  
\[r(t)=h(t)\otimes S_{m^{*},n^{*}}(t)\ +n(t), \tag{11}\]  
where \(n(t)\) denotes AWGN. For the ML detection, the receiver generates the conjugate of the transmitted whistle (\(S_{m,n}^{*}(t)\)) for all available time-frequency shifts, in which \(m\) and \(n\) vary from \(-\Delta f\frac{N}{2}\) to \(\Delta f\frac{N}{2}\) and \(-\Delta t\frac{M}{2}\) to \(\Delta t\frac{M}{2}\), respectively. Then, all conjugate whistles are multiplied to  
to transmit many bits. Thus, for the more practical DoM assessment, the consecutive long-term biomimicking whistles need to be tested. In this paper, a two-step assessment method is performed to measure the DoM of the proposed biomimetic communication. For the 1 st step, the various sizes of the sequences are tested to find the sequence length (\(L_{c}\)) that humans do not recognize. For the 2 nd step, the long-term biomimicking whistles using the selected sequence length (\(L_{c}\)) are evaluated to check whether the size (\(L_{c}\)) is acceptable for the large DoM. If the evaluation fails, a smaller \(L_{c}\) is applied and the 2 nd step is executed again. The time of the consecutive whistle is set to 10 s for the 2 nd step. The DoM assessments of each step are based on the MOS test (BS1284) given by the International Telecommunication Union (ITU) [26; 27]. The DoM assessment procedure of the 1 st step is described in Table 1.  
If the MOS score of the modulated whistles by the sequence with \(L\) is close to that of the real dolphin whistle, the \(L\) is chosen for the sequence length that has unrecognizable frequency spreading. As a result of the 1 st step assessment, many \(L\)s are attained. Since the \(\Delta f\) is inversely proportional to the \(L\), the maximum \(L\) among the acceptable \(L\)s is selected to maximize the data rate and is set to \(L_{c}\). For the 2 nd step, whistles are modulated by the selected \(L_{c}\) and the consecutive long-term whistles with a 10-s duration are generated. Then, the 10-s long consecutive long-term whistles are evaluated for the similarity to the real dolphin whistles. The DoM assessment of the 2 nd step is described in Table 2.  
If the DoM of the proposed method is larger than or close to that of real dolphin whistles, we consider that people may be unable to distinguish the proposed biomimetic consecutive whistles from the real dolphin whistles. Since listeners have no prior information about the test set, the confidence of the evaluation is achieved. In the next section, the BER performance of the proposed method is analyzed, and \(L_{c}\) is selected through the 1 st step DoM assessment, and the selected \(L_{c}\) is evaluated through the 2 nd step DoM assessment.