1. Introduction
Underwater biomimetic communication ensures the covertness of communication signals by mimicking the communication signals with the sounds of underwater organisms. The underwater biomimetic communication method has been researched to overcome the large, low-probability detection problem of the conventional direct sequence spread spectrum method in underwater communication [
1,
2,
3,
4,
5,
6,
7].
Mimicking the dolphin whistles is commonly used for underwater biomimetic covert acoustic communications [
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23]. The dolphin whistles have chirp-like patterns varying in time and frequency with a usable frequency bandwidth of the projector, while whales and other animals generate the sounds with a low and wide bandwidth, respectively. Thus, dolphin whistles are more adequate than other ocean animal sounds for biomimetic underwater communication. Conventional biomimetic communications have been proposed using chirp spread spectrum, frequency shift keying, differential phase shift keying (DPSK), continuously varying carrier frequency modulation (CV-CFM), and time–frequency shift keying (TFSK) that transmit bits according to the time–frequency position of the whistle or the shape of the whistle pattern [
8,
9,
10,
11,
12,
13,
14,
15,
16,
17]. However, since most dolphins are social animals and live in groups, they produce multiple whistles. Mimicking the multiple dolphin group sounds is necessary to increase the covertness of underwater covert communication. Thus, the conventional whistle-mimicking method has a limitation of covertness by mimicking a single dolphin whistle, not a group of dolphins, which does not reflect the ecology of dolphins living in groups. When the group dolphin whistles are used for communication, the multiple whistles may increase the data rate but cause interference among the whistles, which decreases bit error rate (BER) performance.
In this paper, we propose a method to convey information by mimicking the multiple whistles produced by a group of dolphins to increase the covertness and the data rate. Multiple whistles can be generated by simultaneously transmitting the single dolphin sounds, but these have a problem in that interference occurs between the overlapped multiple whistles, resulting in low detection performance at the receiver.
The proposed method combines TFSK and CV-CFM to achieve high covertness and a high data rate by mimicking multiple dolphin whistles and mitigating the interference caused by overlapped multiple whistles. To obtain the high transmission rate, the proposed method for the multiple whistles sequentially modulates using TFSK followed by CV-CFM. When interference occurs at the overlapped multiple whistles, the CV-CFM method with phase modulation makes it difficult to demodulate the transmitted information at the interfered whistles. To solve the interference problem, we search the interference whistle locations and utilize spread orthogonal codes on the interfered whistles to mitigate the interference so that the interfered whistle can be decoded at the receiver. In addition, interleaving is applied to further reduce the effect of the remaining interference on the whistles. Since the proposed modulation method combines two modulation techniques, the complexity of the demodulation process is large and needs to be reduced. We propose a decoding algorithm in which the two modulation schemes do not interfere with each other’s decoding performance. Thus, TFSK is demodulated first to estimate the time–frequency position of the whistles, and the CV-CFM of individual whistles is demodulated.
To compare BER performance and the covertness of the proposed method, computational simulations, real ocean experiments, and mean opinion score (MOS) tests were conducted. Through computational simulations and ocean experiments, the proposed algorithm demonstrated lower BER and higher transmission rates compared to the conventional CV-CFM. The MOS test confirmed the high similarity of the proposed technique to actual dolphin whistle sounds.
The contributions of the proposed methods are as follows:
- 1.
This paper proposes an underwater biomimetic covert communication method that mimics multiple whistles produced by dolphin groups, which offers higher covertness and data rates compared to conventional underwater biomimetic communication methods.
- 2.
The proposed approach combines both TFSK and CV-CFM to generate multiple whistles and develops a mitigation method for interference when multiple whistles are overlapped.
- 3.
To achieve high transmission rates, a sequential decoding method is proposed to demodulate the multiple complex whistles resulting from the combination of the two modulation schemes.
- 4.
To evaluate the communication performance and degree of mimicking, this paper conducts computer simulations, ocean experiments, and MOS tests, and the superiority of the proposed method is proven.
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
-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
-th (
) whistle is denoted as
[
12], and the modeling of the
-th individual whistle is expressed as:
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
. In
Figure 3, it is assumed that one-time and one-frequency shift units are denoted as
and
, respectively. The total numbers of time and frequency grids are assumed to be
and
, respectively. If
and
are calculated by
and
, respectively, a sum of
and
bits is transmitted using the TFSK method. The arbitrary time–frequency modulated signal (
of the
l-th whistle is obtained by shifting
by
and
, respectively.
When TFSK and CV-CFM are combined, the
and
requirements of TFSK need to be derived to reduce detection errors during CV-CFM decoding. The one-frequency shift (
) of TFSK should be larger than the frequency spread (
) caused by CV-CFM to avoid overlapping frequency ranges between whistles and to ensure orthogonality. Thus, the value of
needs to be more than twice that of
, considering the overlapping intervals between whistles. This can be expressed as:
To determine the requirement of
for the TFSK modulation, the phase modulation of CV-CFM is considered. The requirement of
is derived based on the property that when two signals with different phases are demodulated at the receiver, their cross-correlation converges to zero [
25,
26]. In the case of CV-CFM applied to a whistle, the phase changes every
ts, which is a unit symbol for time of CV-CFM. For the overlapping intervals between whistles, if a time shift of two times
is applied, the whistle at the original position without time shift will have a different phase from the shifted whistle, resulting in a cross-correlation of zero. Therefore, the value of
that satisfies orthogonality between symbols during time shift modulation is given by the following equation:
The TFSK-modulated
-th whistle, denoted as
is shifted by the product of the arbitrary
and
values with
and
, respectively. Therefore,
is expressed as:
where
denotes a convolution operation. Using the single whistle in Equation (4),
whistles are shifted to their original positions by
and we add them together. Then, the TFSK-modulated whistles
with
whistles become the dolphin group sound and are expressed as:
where
includes interfered multiple whistles in the time–frequency domain.
The CV-CFM modulation method for individually modulated TFSK whistles is presented. Due to the characteristics of underwater acoustic communications, the frequency changes between symbols in a single whistle of CV-CFM are larger than the coherent bandwidth, and the conventional coherent modulation at the transmitter is inapplicable [
12,
21]. For simple demodulation, non-coherent modulation schemes such as differential binary phase shift keying (DBPSK) are used, which utilize the phase difference between two adjacent symbols.
In Equation (5), when interference occurs, the detection performance at the receiver decreases. This paper proposes a modulation method to detect interfered whistles and mitigate the interference by using the orthogonal codes during overlapped CV-CFM modulation. The orthogonal codes are used only for CV-CFM modulation in the interfered whistles, while they are not used for the non-interfered whistles.
For mitigating the interference when TFSK-generated whistles are overlapped, the proposed interference detection method utilizes energy detection in that the energy of the overlapping part of the contour of an individual whistle is larger than that of non-overlapped whistles. An example of energy when individual whistles are overlapped and interfered with by two dolphin whistles is shown in
Figure 4. In
Figure 4, the red line represents the
-th whistle, and the red rectangular background represents the energy of the
-th whistle. The blue line represents the
-th whistle, and the blue rectangular background represents the energy of the
-th whistle. The orange rectangular background shows the energy of the overlapped whistles.
For energy detection, assume that the two-dimensional value of time–frequency by STFT in Equation (4) is
, where τ represents a time and ω is a frequency, and the signal strength of a single signal
in Equation (4) is
. Assume that the time position of the
-th original whale whistle is
and the time length of each whistle is
. Then, by comparing the value of
with
, the location of the interfering signal can be easily found. If
is the interfered whistle and
is the non-interfered whistle, the interference detection criteria are expressed as follows:
If no interference
at the
-th whistle occurs, the whistle is modulated as the conventional CV-CFM.
information bits
) are transmitted. Note that the first bit
as a dummy bit for differential modulation is allocated to the first DBPSK symbol (
). The
-th symbol (
) is represented as in Equation (7) and the symbol transmitted at the
-th whistle is
.
If the -th whistle is overlapped, i.e., interfered , the proposed CV-CFM that mitigates the interference by interleaving with an orthogonal code is utilized. If the length of the orthogonal code is , the orthogonal code ( is used to modulate the -th whistle where the interference occurs. The spread symbol with is defined as .
When the interference occurs, the interference is concentrated on a part of a symbol. Since the overlapped length of the interfered whistles is short enough to mitigate the interference, the interference may not be completely erased. If the interleaving is applied to the symbols in an interfered whistle
, the effect of the interference is spread over, which improves the interference mitigation performance. Assume that the interleaved symbols are denoted by
. The
-th proposed modulated whistle
with the interference mitigated CV-CFM to the TFSK in Equation (4) is represented as:
If all
whistles are moved to the original whistle position
and added together, the multiple whistle signal that mimics the group dolphin whistles proposed in this paper is represented as:
The following section describes how to demodulate the proposed modulation signal consisting of TFSK and CV-CFM with interference mitigation methods.
3. Demodulation
In this section, the demodulation process of multiple whistles modulated by TFSK and interference-mitigated CV-CFM is described. To simultaneously demodulate the TFSK and CV-CFM, the complexity of the demodulation increases due to the numerous decoding possibilities. Thus, we propose a simple sequential demodulation approach.
To determine the decoding sequence of TFSK and CV-CFM, it is preferable to demodulate one method first in a way that is not influenced by the other decoding method. In the proposed dolphin whistle mimicking method, it is necessary to demodulate the TFSK signal first because the CV-CFM demodulation cannot be executed without knowledge of the time–frequency shifted positions of the whistles. When two modulation techniques are simultaneously demodulated, the searching space of the demodulation is given as M × N × K, while the sequential detection provides only (M × N) + K.
If the whistle information modulated by TFSK is obtained, the phase-modulated bits of CV-CFM can be detected. The structure of the proposed receiver demodulation block is shown in
Figure 5.
First, the method for TFSK-modulated bits is described. The conventional TFSK demodulation method used a maximum likelihood (ML) detection approach in that the conjugates of all possible TFSK-modulated whistles are multiplied by the received whistles. The detection rule is to select the largest energy at a point in the time–frequency shift. However, since the received whistles are modulated by the PSK in CV-CFM, the conventional demodulation method cannot be utilized.
Therefore, this paper proposes a time–frequency energy detection method that is not affected by the phase modulation of CV-CFM. In the proposed approach, the received signal is transformed into the 2D time–frequency domain using the short-time Fourier transform (STFT), and the value of each bin in the time–frequency domain is squared to obtain the energy. As a result of the energy calculation, the values of the bins are not affected by the phase modulation. By comparing the whistle contour energy of the generated whistle at the receiver with that of the received signal, the TFSK-modulated whistle that has the closest energy contour to that of the generated whistle is determined.
The received dolphin signal (
is obtained by assuming that the transmitted signal
passes through the underwater channel (
This can be represented by:
where
denotes the underwater background noise.
Let the energy values of the received whistle (
) be
and let the energy values of the whistle
) generated at the receiver based on
be
. The time interval resolution of the STFT is assumed to be
and the frequency resolution is assumed to be
. The window length and the discrete Fourier transform shift interval are set accordingly to ensure that both
and
have the same intervals in the time–frequency bins [
27]. Then,
is shifted by the time–frequency modulation,
and
, with
and
, respectively. The TFSK modulation indices
and
can be found when the time–frequency contour energy distribution of the received
is the closest distribution of the
-th whistle
, which is given as:
After the TFSK demodulation, the receiver has the time–frequency shift information of each whistle and proceeds to decode the phase-modulated values of the CV-CFM. Since the spread and the non-spread CV-CFM to the whistle are used in the presence of interference, different demodulation schemes need to be used whether the interference exists or not.
For the detection of the interfered whistle at the receiver, the energy detection method in Equation (6) is used: If the TFSK modulated positions have been identified for
whistles, the
whistles are generated to reconfigure the received whistles. The time–-frequency domain energy of these generated whistles is then calculated. If the energy of the whistles is greater than others, the whistles are considered overlapped whistles, i.e., interfered whistles. For the interfered whistle demodulation, the despreading is executed using the known orthogonal code. For whistle demodulation without interference, conventional CV-CFM phase demodulation is applied. This process is shown in
Figure 6.
To demodulate the phase-modulated bits of CV-CFM at the receiver, the
-th individual whistle is extracted from the received dolphin whistle
using the TFSK demodulation results of Equation (10). This extraction process obtains the received individual whistle
as:
The received extracted single whistle is multiplied by the complex conjugate of the frequency-shifted
, denoted as
in Equation (12), and the low-pass filtering is executed. Then, the whistle signal modulated by CV-CFM becomes a conventional baseband phase-modulated signal. The phase information of CV-CFM can be obtained as follows:
In the case of whistles without interference the symbols are demodulated by a conventional differential detection method. in Equation (13) represents the phase information of the -th interval of the whistle. The phase values on the l-th th received whistle are calculated as Since the CV-CFM utilizes DBPSK, conventional differential detection can be used for detecting the K-1 transmitted bits.
For the interference case
, the transmitted signal is detected by deinterleaving and despreading the bits obtained by differential detection. The obtained phase value
from the interfered whistle is the result of the multiplication between the code (
) and the transmitted symbol (
). Therefore, the transmitted symbol (
is obtained by multiplying the deinterleaved symbol by
for despreading as:
Since takes a value of 1 or −1 in Equation (14), the value of is equal to . When spreading is used, an additional SNR gain of is obtained compared to the case without spreading. This gain helps to mitigate inter-symbol interference.
The data rate of the proposed technique without interference is calculated as follows: the transmission bits of TFSK by time-shifting and frequency-shifting are
and
, respectively. The total TFSK transmission bits per whistle are given as
. Let
be the maximum modulation bandwidth that preserves the DoM, and let the average length of a whistle be
. The maximum number of symbols in CV-CFM is calculated as
. Therefore, the transmission rate of the proposed method is obtained as follows:
However, if whistles are overlapped and a spreading code is used, the data rate needs to consider the data rate of the interfered whistle case. Since the spreading code length is , the maximum number of symbols by CV-CFM is calculated as .
Assume that the average number of whistles per hour in a dolphin whistle is
and the probability of whistles with interference is
. The number of whistles without interference is obtained as
and the number of whistles with interference is given as
. Therefore, the total transmission rate of the proposed method is attained as follows:
This section has described the method for detecting transmitted bits for TFSK and interference-mitigated CV-CFM.