###### Abstract  
Underwater acoustic (UWA) biomimicking communications have been developed for covert communications. For the UWA covert communications, it is difficult to achieve the bit error rate (BER) and the degree of mimic (DoM) performances at the same time. This paper proposes a biomimicking covert communication method to increase both BER and DoM (degree of mimic) performances based on the Time Frequency Shift Keying (TFSK). To increase DoM and BER performances, the orthogonality requirements of the time- and frequency-shifting units of the TFSK are theoretically derived, and the whistles are multiplied by the sequence with a large correlation. Two-step DoM assessments are also developed for the long-term whistle signals. Computer simulations and practical lake and ocean experiments demonstrate that the proposed method increases the DoM by 35% and attains a zero BER at \(-6\) dB of Signal to Noise Ratio (SNR).  
court communication; bio-mimetic; signal processing; underwater communication; MOS test +
Footnote †: journal: _Sensors_  
0000-0002-0001-9999-2284-3/10/0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-000000-000000-000000-000  
the low BER need to be simultaneously achieved and to be evaluated according to various parameters of the real dolphin sounds, e.g., long-term signal duration, bandwidth, etc. [8; 9; 10; 11; 12; 13; 14]. In general, the time duration and the frequency bandwidth of the dolphin whistles vary from several hundred milliseconds to two seconds and from several hundred Hz to tens of kHz, respectively [15; 16; 17; 18; 19]. Thus, the DoM evaluation needs to be performed for a long-term period.  
This paper proposes a TFSK-based biomimetic communication method increasing the DoM and BER performances. We theoretically derive the orthogonality requirements in the time- and frequency-domains and utilizes various whistle patterns with sequences with the large autocorrelation to increases the DoM and BER performances. To evaluate the long-term DoM of the proposed method, a two-step DoM assessment is developed. The computer simulation and the ocean experiments were executed to show that the proposed method demonstrated better DoM and BER performances than the conventional convert communications.  
The main contributions of the paper are summarized as follows:  
1. The time- and frequency-shifting unit requirements of the TFSK are theoretically derived for the orthogonality in the time- and frequency-domains. The requirements guarantee the low BER.
2. For the large DoM and the low BER, the sequence with a large correlation is multiplied to the whistles, which enables to use of various dolphin whistles without any restrictions. In addition, the orthogonality requirements for the proposed method are also derived.
3. Since the sequence makes the whistle spread in the frequency domain, the DoM assessments are conducted to find the unrecognizable spreading parameter. Thus, a two-step DoM assessment is proposed: The 1 st step is conducted to find the best length of the sequence. The 2 nd step is executed to confirm whether the long-term whistles signal with the selected sequence length is acceptable for the covert communication.
4. The computer simulations and the practical lake and ocean experiments were conducted and demonstrated the proposed method had the large DoM and the lower BER compared with the conventional covert communication methods.  
This paper is organized as follows. In Section 2, the orthogonal requirement of the TFSK according to a whistle pattern is derived, and the proposed biomimetic communication method is described. Section 3 explains the DoM assessment method for the proposed biomimetic communication signals. In Section 4, the BER and DoM performances of the proposed method are analyzed. In Section 5, the proposed biomimetic communication method demonstrated the large DoM and the low BER through computer simulations and practical lake and ocean experiments. Section 6 concludes the paper.