Covert underwater communication through cepstrum modulation mimicking Pseudorca crassidens whistles using machine learning

Abstract

The increasing demand for clandestine communication in underwater acoustic environment reflects the remarkable growth of research in underwater acoustic communication and networking. Mariners are driven to transmit information covertly in the ocean keeping it hidden from unfriendly users and intruders. This research introduces a novel technique of covert underwater acoustic communication that mimics false killer whale whistles. The secret information is embedded using cepstrum transform to imitate Pseudorca crassidens whistles. This covert communication can be achieved even in the presence of eavesdroppers, who are unable to recognize the communication signal due to unique watermarking characteristics. The proposed model uses machine learning to assess imperceptibility and demonstrates exceptional robustness and improved capacity. To validate the model for secure communication and networks, underwater experiments were conducted, resulting in superior bit error rate and high watermark capacity with a perfect low probability of recognition constraint covert communication.

Introduction

In the rapidly evolving global landscape, data security has become a paramount concern^1,2. As a result, the demand for Covert Underwater Acoustic Communication (CUAC) has seen a significant surge in marine and military applications driven by the increasing need for data security^3,4. Researchers are investigating novel and unique techniques that challenge conventional models and improve covert attributes of communication^5,6. The necessity for robust covert transmission in underwater environments has arisen as a critical area of research in this current decade^7,8. The mariners and oceanographers desire to covertly transmit their information to safeguard confidential data from unauthorized access and malicious intrusions^9,10. To protect sensitive information from eavesdroppers and unfriendly users, oceanographers must implement measures to conceal their communication channels^11,12. Despite limited research in this particular area, significant efforts are being made to investigate methods for achieving covert communication¹³.

The concept of Covert Underwater Acoustic Communication (CUAC) is not new¹⁴, researchers were already employing techniques to conceal information through the dispersion of waveforms more than four decades ago^15,16. In 1986, an experiment was done by J.H. Park to investigate the characteristics of an underwater acoustic channel, specifically focusing on a transmission distance of 20,000 yards¹⁷. Until the previous decade, it is achieved through the reduction of the Signal to Noise Ratio (SNR) and the dispersion of the waveform utilizing Direct Sequence Spread Spectrum (DSSS)^18,19, Orthogonal Frequency Division Multiplexing (OFDM)^20,21, and several other modulation techniques²². The communication signal is not detected by an intruder due to significantly low SNR. However, if the eavesdropper approaches closer to the transmitter, the signal can be readily detected by a radiometer²³. The limitations of this technique are that it has a low data rate and covert communication is not possible at all communication distance²⁴, their effectiveness is contingent upon the specific operational area²⁵.

To overcome these challenges, bionic CUAC was introduced^8,26. The biologically inspired CUAC system is the most effective technique to secure the transmission of classified information in the vast oceanic environment. Using natural underwater sounds, it encodes data in variations of frequency, amplitude, or time intervals²⁷. Concealed data is watermarked within the natural sea carrier, achieving commendable Low Probability of Recognition (LPR) characteristics^28,29. Eavesdroppers may identify the mimicked signal but perceive it as natural sound, ensuring information secrecy. This approach enables high SNR communication and extended transmission distances in underwater acoustic channels^30,31. The perfect LPR constraint covert communication can be achieved by successfully deceiving the adversary’s overall communication ranges in underwater acoustic channels in the presence of intruders^32,33.

Very sparse research has been conducted for mimicry CUAC however it has a high demand for research for transmitting covert communication in the vast ocean. The first covert experiment of mimicry communication to the best of my knowledge was done by H.S. Dol by mimicking whistles of dolphin sound³⁴. Liu et al. gave the concept of mimicking dolphin clicks and whistles^35,36 which is suitable for short-range communication. Data is carried in the time interval between the clicks and mapped on 6 bits of covert information. Sea piling sounds are mimicked by a researcher using Pulse Position Modulation³⁷ suitable for CUAC in shallow waters. Jiang et al. researched on detection of mimicry communication^38,39. Qiao et al. designed a CUAC MODEM for underwater communication⁴⁰. It can handle various sea natural sound databases for covert communication. The frequency hopping technique is used for mimicry communication⁴¹. For long-range covert operations in the sea frequency Megaptera novaeangliae songs are imitated and tested^42–44. One character per second covert capacity is achieved using this technique. All these researches gave a nice concept of mimicry communication using different sea natural noises, however, they have very little covert capacity with perfect imperceptibility.

In this research, a novel model for bionic CUAC employing Pseudorca crassidens whistles has been proposed which enhances the capacity for perfect LPR covert prospective. It is a highly robust and imperceptible technique for mimicry CUAC. False killer whales emit whistles for social interaction in the frequency range of 8–16 kHz⁴⁵. These whistles have been researched for the first time for mimicry communication in the published literature. The initial step involves denoising false killer whale signals through discrete wavelet transform to eliminate the ocean ambient noise present in the recordings. Subsequently, the cepstrum transform is used as a modulation technique to watermark covert information in real whistles. An innovative method is employed to embed covert information within the whistles. The mimicked signal closely resembles authentic whistles, and its imperceptibility is rigorously confirmed through correlation and Convolution Neural Networks (CNN)⁴⁶. The proposed innovative technique exhibits a notable covert capacity and remains virtually indistinguishable from natural noise. Further, the innovative technique has been validated in AWGN and multipath underwater acoustic channels using bellhop ray tracing algorithm to make it feasible for covert operations in the ocean. The proposed method gave excellent results making it perfect to use for clandestine communication for underwater medium for short-range communication up to 1 km.

The paper is organized as follows. Section 2 describes the methodology and details of cetacean noise focusing on the properties of Pseudorca crassidens whistles which is used as a carrier in this research. Section 3 demonstrates the modulation and demodulation process of proposed bionic covert communication using cepstrum transform with watermarking capacity. Results of imperceptibility analysis using correlation and CNN are shown in Sect. 4. Feasibility analysis of the proposed novel model in underwater acoustic channel has been validated in Sect. 5 and finally, Sect. 6 concludes the paper.

Methodology

In this section, the system model of the proposed technique for mimicry CUAC using cepstrum transform mimicking false killer whistles is briefly elaborated. Figure 1 shows the flowchart of LPR constraint bionic communication with respect to this novel procedure used in this research. The first step is to analyze the characteristics of ocean noise. The ocean noise is briefly elaborated in the next subsection. In this research, we have opted for Pseudorca crassidens whistles as a carrier for mimicry communication due to its presence in all regions of the ocean and its frequency characteristics^47,48. These whistles are used for the first time for establishing mimicry covert communication. After the selection of whistles, the acoustic data of whistles is denoised to eliminate the other noises present in the signal. Ocean environment adds various noises such as shipping noise⁴⁹ and other noises present in the sea. The vocals other than false killer whales act as a noise in this research. We have opted wavelet denoising method as it allows the smoothing of data. It is effective for isolating acoustic signals from variable underwater noise without distorting their temporal or spectral features. This approach improves the SNR of False killer whale calls preserving the fine scale acoustic structure necessary for accurate detection and analysis.

Fig. 1.

Proposed model of mimicry LPR constraint covert communication.

The next step is the unique method to embed covert information in false killer whale whistles with perfect imperceptibility. We have used cepstrum transform to embed data. The modulation and demodulation process for this novel technique is briefly elaborated in Sect. 3. After the modulation process, the imperceptibility analysis is done which is the key parameter for mimicry LPR constraint communication. In this research, two techniques are analyzed for imperceptibility analysis of real and mimicked signals. The mimicked signal is analyzed by time correlation and classification method using CNN. Both method validates it to be perfectly LPR constraint signal which can be witnessed in Sect. 5.

Ocean Noise.

Underwater visibility is severely limited, ranging from a few meters in clear daylight to less than a foot in muddy waters⁵⁰. Cetaceans rely on acoustic communication due to less visibility in the oceans. They produce a variety of acoustic signals for detecting prey, localization, and social interaction⁵¹. These sounds, serving various purposes for marine mammals, act as unwanted noise for underwater acoustic communication^52,53. This benefits to perform covert communication mimicking these natural sounds. The acoustic properties of the commonly emitted vocals of cetaceans are elaborated underneath:

• Echo localizing clicks: These are broadband signals, predominantly in the ultrasonic range with highly directional beam patterns. Typically lasting for microseconds, cetaceans emit multiple clicks at varying rates, ranging from 0.5 to 2 clicks per second⁵⁴. Such clicks are usually used by Toothed whales during foraging—a series of short, intense, and highly directional pulses to locate food in the dark oceans. Emitted clicks bounce back as echoes, enabling cetaceans to detect, and estimate the location, range, and direction of objects. While all odontocetes possess echolocation capabilities, baleen whales, except a very broad sense, do not echolocate, relying on listening to sound reflections off the ocean bottom, sea mounts, underwater canyon walls, and large objects⁵⁵.

• Whistle: Utilizes Frequency Modulated (FM) signals, serves as intercommunication tool among cetaceans. These signals typically have a fundamental frequency below 30 kHz with higher-order harmonics⁵⁶. Cetaceans, including dolphins and baleen whales, produce varied-frequency whistles as common communication signs. These signals, whether tonal or pulsed, exhibit spectral fluctuation and may have low directionality. In this research, false killer whale whistles are used as carrier signals. The properties of the whistle are discussed in detail in the next sub-section.

• Songs: Songs are intricate, long-duration signals produced by selected sea mammals like humpback^57,58, bowhead, blue, and fin whales³¹. These sequences exhibit a distinct hierarchical structure, with base units of single, uninterrupted sound emissions lasting seconds. The sounds vary from 20 Hz to over 24 kHz, involving frequency or amplitude modulation as amplitude fluctuates⁵⁹.

Pseudorca crassidens characteristics

This subsection briefly describes the acoustic vocalization properties of Pseudorca Crassidens. They are globally distributed oceanic dolphins and the sole living member of the Pseudorca genus. They are highly social and emit variety of vocals within the same species and other species. They emit clicks, whistles, and calls for various purposes which include localization, detecting prey and predators, and social interaction⁶⁰. They are distributed almost all over the ocean which benefits us to perform covert communication mimicking their sound in the entire region of the sea. Generally, they are found in tropical, subtropical, and warm waters in the oceans⁶¹.

False killer whale vocalizations include ascending whistles and have low sound pressure levels, low and high frequency pulse trains, and echolocation clicks. Fundamental frequencies of whistles range from 2 to 17 kHz with the duration of 0.03 to 3 s^61,62. Their distinct whistles, characterized by 5 kHz upsweeps lasting half a second, allow for individual identification based on acoustics. Research on the whistle repertoire of Pseudorca crassidens has revealed a variety of whistle types, with differences observed between feeding and traveling whales. These whistles have been further characterized by their acoustic features, such as frequency and duration. Studies have also found that the prevalence of ascending contour types in these whistles contradicts previous assumptions about their production. The source levels of these whistles have been estimated, with peak power spectral density levels ranging from 115 to 130 dB re 1 µPa2/Hz @ 1 m⁶³.

Figure 2 shows the false killer whale whistles sequence in the time and frequency domain. The acoustic data recordings are depicted from Wood Hole Oceanographic Institution’s Watkins Marine Mammal Sound database library⁶⁴. The recordings are done in Western North Atlantic and Dominica. Whistles of False killer whales are extracted from the recordings and they are used for mimicry covert communication as a carrier which will be discussed in Sect. 3.

Fig. 2.

False killer whale whistles sequence in (a) time domain (b) frequency domain.

A series of whistles of false killer whales is depicted in Fig. 2. It can be noticed that the frequency range of the whistle lies under 12 kHz and there is a variable time interval between the whistles. The variable time variable benefits us to make a bionic frame structure based on whistles which will be discussed later. Additionally, it is noticed that there is a lot of noise of low SNR in the recordings. To eliminate the noise, we processed the acoustic signal through wavelet transform. Figure 3 (a) and (b) shows a single whistle and its denoised version. From Fig. 3 (b) we can see that the noise is effectively reduced. In this research, we have used 60 samples of whistles for watermarking the covert information using the cepstrum domain. The methodology of this novel technique is elaborated in detail in the next section.

Fig. 3.

Spectrogram of False Killer Whale Whistle (a) original (b) denoised using wavelets.

Watermarking information in false killer whale whistles

This section briefly describes the novel method of watermarking covert information mimicking Pseudorca crassidens whistles using cepstrum modulation. Covert data is watermarked in the false killer whale whistle keeping the perfect imperceptibility. The process of watermarking the information is elaborated on step by step.

Frame structure

In mimicry CUAC, the whole frame should be akin to the sea’s natural noise to achieve the LPR constraint prospective. When the eavesdropper perceives the communication signal, it must recognize it as an ocean noise. Figure 4 shows the frame structure of mimicry covert communication. It consists of a synchronization signal and the communication frame with a guard interval between them which limits multipath and ISI interference in the underwater acoustic channels.

Fig. 4.

The frame structure of proposed mimicry model.

The synchronization signal incorporates a segment of a unique false killer whale whistle along with a checksum of bits, serving as a verification mechanism for the receiver to distinguish between the mimicked signal and the genuine whistles. There are plenty of false killer whales emitting whistles in the ocean, therefore, the checksum becomes crucial in the identification process. The receiver follows a two-step procedure:

1. Identification of the mimicked signal through the defined signal properties of the synchronization sequence.

2. Verification of the mimicked signal’s presence by calculating the checksum of bits. A correct checksum confirms it as the mimicked signal, while a mismatch leads the receiver to consider the signal as sea natural noise, assuming it to be a real false killer whale’s whistle.

The communication frame comprises of mimicked false killer whale whistle with watermarked covert information. The process of watermarking the covert information through the cepstrum modulation technique is discussed in the next subsection.

Modulation process

In this subsection, the modulation process of covert information in a false killer whale’s whistle using cepstrum transform is elaborated in detail. The cepstrum domain technique converts the signal into the cepstral domain and embeds data into cepstrum coefficients through statistical mean calculation. This modulation process has high computational complexity, however, it has the advantage of high embedding rates. It is also resistant to common signal attacks which is a benefit for underwater multipath channels. Its gives extremely high imperceptibility in mimicking underwater noise which is the key for underwater mimicry communications. It is robust against frequency distortions, such as Doppler shifts and dispersion, while also enabling better concealment of covert signals within natural ocean noise. Unlike amplitude or frequency modulation, cepstrum-based techniques do not introduce obvious spectral anomalies, making them harder to detect via conventional signal analysis. Additionally, cepstrum modulation can preserve signal integrity in non-stationary noise (e.g., from ships or marine life), offering superior performance for low-probability-of-detection (LPD) communications compared to simpler modulation schemes. Despite its computational complexity, these benefits make cepstrum a powerful tool for secure and reliable underwater data transmission. The pros and cons of using different modulation schemes for mimicry communication are shown in Table 1.

Table 1.

Comparison of different modulation schemes used for mimicry communication.

Modulation technique	Advantages	Disadvantages
Cepstrum65	Robust to multi-path in underwater environment  High data hiding capacity with perfect imperceptibility	Computationally complex due to multiple transformations
Frequency Hopping Spread Spectrum (FHSS)41	Resilient to narrowband interference  Hard to intercept	Poor performance in mobile environment due to Doppler
Direct Sequence Spread Spectrum (DSSS)66,67	Resistant to jamming  Good multi user capability	Suffers from underwater multipath interference  High processing gain needed
Amplitude modulation (AM) / frequency modulation (FM)	Simple to implement	Easily detectable  Poor performance in underwater noisy and multipath environments

Cepstrum transformation is computed by the process shown in Fig. 5. It consists of three steps. The first step computes the Fast Fourier Transform (FFT) and subsequently takes the natural logarithm. The final step which results in transforming into the cepstrum domain is computing the Inverse Fast Fourier Transform (IFFT) of the logarithm of FFT.

Fig. 5.

Time to cepstrum domain transform.

Let us suppose a sequence has the Fourier transform. Then mathematically Cepstrum⁶⁵ transform can be written as

1

where is the sequence obtained by the inverse fourier transform of . The advantage of the cepstrum coefficient is that they are de-correlated. It shows less variance against the most common signal processing. Cepstrum transformation has wide applications in speech analysis and audio signals. It is used in this research for information hiding in Pseudorca Crassidens whistle due to its high embedding characteristic which benefits to watermark covert data with increased capacity.

The flowchart of the modulation process using the cepstrum transform is depicted in Fig. 6. First, the covert information is transformed in cepstrum domain. The false killer whale whistle which is used as a carrier in this research is also converted to the cepstrum domain separately. The covert information in the cepstrum domain is added in the whistles at unique positions which acts as additional secrecy. In this research, these positions are known to the receiver for simplicity. The covert data is embedded in unique positions of the bionic sound, serving as essential demodulation points at the receiver and acting as a secret key.

Fig. 6.

Cepstrum modulation for watermarking covert data in false killer whale whistles.

After the insertion of the watermark, the mimicked signal is processed by inverse cepstrum to covert it in the time domain⁶⁸. The inverse cepstrum is the opposite of cepstrum which is discussed above. It consists of three steps which are IFFT, natural logarithm, and FFT respectively. After inverse cepstrum, the mimicked signal added is the frame with the synchronization signal to transmit in underwater acoustic channel.

Demodulation

In this subsection, the comprehensive process of extracting watermarked data from the mimicked signal, designed to mimic a false killer whale whistle, is outlined. Upon reaching the receiver, the watermarked imitated signal undergoes recovery facilitated by an energy detector, having traversed the underwater acoustic channel. The demodulation procedure, depicting the extraction of covert watermarked data, is visually represented in Fig. 7.

Fig. 7.

Extraction of covert information from the mimicked signal at the receiver.

The initial phase of extracting watermarked data from the signal frame begins with signal synchronization. The synchronization header, containing a known whistle for the receiver as discussed in Sect. 3.1, is correlated to verify it as the intended signal. Additional validation is performed through the checksum of bits. Following this, the watermarked mimicked communication signal is recovered and transformed into the cepstrum domain.

During the modulation process, covert information is strategically inserted into unique positions in the cepstrum domain. As previously explained, these positions of watermarked bits act as the secret key for information retrieval. For simplicity in this research, these positions are known to the receiver. The watermarked secret information is then extracted in the cepstrum domain as inversely performed in the modulation process. The covert data is restored in the cepstrum domain. The final step involves converting it back to the time domain through the inverse cepstrum technique.

Considering the signal degradation in the underwater channel caused by factors like absorption, multipath arrivals, and noise, the data undergoes supplementary processing involving equalization and error correction. Matching Pursuit (MP) estimation and Virtual Time Reversal Mirror (VTRM) equalization techniques are used in this research which enhances the Bit Error Rate (BER) effectively which will be shown in Sect. 5. MP estimation is chosen for its resilience to changing SNR and computational efficiency⁶⁹. The underwater channel is widely acknowledged as one of the most complex communication mediums^70,71 and degrades the signal due to factors such as large delays, multipath arrivals, doppler shift, frequency-selective fading, and limited bandwidth^39,72. The complexity of underwater acoustic channel is influenced by the characteristics of the ocean environment⁷³, necessitating continuous estimation of channel state information due to their time-varying nature^74,75. To compensate for the errors induced by the underwater acoustic channel and enhance the BER, the channel is estimated and equalized by MP estimation and VTRM equalization⁷⁶.

Covert capacity

This section delves into the capacity of covert information watermarking in the proposed technique. The quantity of hidden information within the communication frame is pivotal for enhancing the capacity of the proposed technique. However, it impacts the imperceptibility of the signal with the real false killer whale whistle, with imperceptibility being inversely proportional to capacity. This relationship can be expressed mathematically as:

2

where is represented as imperceptibility, is defined as capacity and k is constant. Capacity is defined as a number of covert data watermarked per unit time. Therefore,

3

where n, and are the number of covert bits, synchronization sequence time, and time of communication frame respectively. In this research, 100 bits of covert information are successfully watermarked with impeccable imperceptibility in the false killer whale whistle. The proposed cepstrum-based watermarking model exhibits the capability to transmit covert data at a rate of 55.5 bits per second, ensuring perfect LPR with flawless imperceptibility. The covert data capacity can be increased at the expense of imperceptibility.

Imperceptibility

Imperceptibility serves as a tool for gauging the similarity or likeness between signals⁷⁷. The mimicked signal, inclusive of the synchronization header, must closely resemble real oceanic sound. When an intruder intercepts the mimicked communication signal, it should recognize it as a cetacean vocal due to its analogy. In this research, the imperceptibility of the cepstrum-based watermarked mimicked signal and real false killer whale whistles are calculated using two major techniques and found to be perfectly imperceptible. The first is time correlation method and the second is a novel technique utilizing CNN is employed.

Time correlation method

In this section, the time correlation method is employed to quantify the similarity analyses between the real false killer whale whistle and the cepstrum-based watermarked mimicked signal. Correlation is a technique to compare how closely two signals align with each other⁷⁸. A higher correlation value indicates high imperceptibility which indicates that the two signals are similar to each other. Mathematically, correlation can be expressed as⁷⁹:

4

where is the correlation for all values of . and represents the acoustic signals of a real false killer whale whistle and the mimicked watermark signal respectively. The signal processing of this technique is achieved in the time domain. Figure 8 shows the correlation peak which ascertains the resemblances between the two signals. The peak value is divided by the summation of sub-bands, where a larger value indicates higher imperceptibility.

Fig. 8.

Imperceptibility analysis using time correlation.

The imperceptibility of the real Pseudorca crassidens whistle and the novel mimicked signal with covert watermarked data is proven by the time correlation method as witnessed by Fig. 8. The sharp peak of correlation proves that both signal are perfectly alike and similar. As imperceptibility is the key parameter for mimicry CUAC, it is also verified by the CNN method using machine learning which is elaborated in detail in the next sub-section.

Imperceptibility analysis using deep neural network

To assess the efficiency of the proposed mimicry CUAC model, a novel deep neural network architecture utilizing CNN is used to estimate the imperceptibility of the proposed method. CNN is trained to utilize false killer whale whistles and random noise. Following the training phase, the CNN undergoes testing utilizing three types of input: random noise, false killer whale whistles, and mimicked false killer whale whistles with embedded camouflage data using cestrum modulation⁸⁰. Figure 9 depicts the schematic representation of the proposed false killer whale whistle classifier. Initially, the dataset is generated by extracting samples from the false killer whale whistles and subsequently transforming them into a spectrogram through the use of the short-time Fourier transform. Next, the spectrogram of the killer whale and the noise spectrogram are fed into a CNN.

Fig. 9.

Proposed CNN model for Killer whale classification.

The fundamental component of a CNN is the convolutional layer^81,82. Convolution involves the process of systematically moving a small filter also referred to as a kernel across the input data^30,83, which in this research is the spectrogram of the false killer whale whistle to extract localized patterns and characteristics. Furthermore, the filter acquires the ability to identify distinct characteristics such as edges, corners, or textures by adjusting its weights throughout the training procedure. Several filters are employed to simultaneously capture distinct characteristics. Furthermore, more than one CNN layers are employed to acquire complicated attributes. Following the convolution operation, the resulting output is next processed to an activation function, typically a Rectified Linear Unit (ReLU)⁸⁴. The ReLU function gives non-linearity to the network, enabling it to establish and comprehend more detailed patterns^54,85. Pooling layers are employed to decrease the spatial dimensions of the input volume. Max pooling is a widely used approach that preserves the highest value inside a specific region, therefore retaining essential information while excluding less significant details. Pooling additionally benefits in decreasing the computational load and enhancing the network’s adaptability to input changes⁸⁶. The utilization of multiple convolutional layers with varying numbers of filters and sizes, in addition to pooling layers, is employed to extract increasingly complex features from the input data^87,88.

In the proposed model, two convolutional layers are utilized to categorize false killer whale whistles, as depicted in Fig. 9. Following multiple convolutional and pooling layers, the neural network reduces the high-level reasoning into a flattened vector. Subsequently, this vector is fed into one or more fully connected layers, which have characteristics of the layers observed in CNN⁸⁹. CNNs are trained by utilizing labeled data and employing a technique known as backpropagation. The network adapts its weights by minimizing a predetermined loss function, which is calculated based on the difference between the expected and actual outputs. Stochastic Gradient Descent (SGD) and ADAM are often employed optimization techniques for iteratively updating weights during training. The proposed model employs the ADAM optimizer to iteratively adjust the weights during the training process. Furthermore, dropout is a regularization method that involves briefly removing random neurons during training, thereby mitigating overfitting and enhancing the model’s generalization ability.

The training data is generated using the 58 false killer whale whistle samples. The data is augmented by initially introducing Additive White Gaussian Noise (AWGN) with a range of 0 dB to 30 dB, with steps of 5 dB. Subsequently, the whistle’s signal is transmitted through the underwater acoustic channel, resulting in a total of 1000 signals being generated. In addition, the data undergoes pre-processing and all signals are transformed into spectrograms using the STFT. A total of 1000 spectrograms were acquired for training purposes. Similarly, a spectrogram consisting of 1000 different types of signals, such as music, boat noise, and other mammal sounds, is generated for the noise category. The hyper-parameters utilized by the proposed CNN model for classifying false killer whale whistles are provided in Table 2.

Table 2.

Proposed CNN killer Whale classifier hyper-parameters.

Parameter	Optimal setting
Input layer	1
Number of convolution layer (s)	2
Kernel size of convolution layer (s)	[3 3]
Number of Kernel in convolution layer (s)	[4 8]
Max-pooling layer (s)	2
Flatten layer (s)	1
Fully connected layer neurons	100
Batch size	100
Hidden layer (s) Activation function	ReLU
Activation function in the output layer (s)	Softmax
Learning rate	0.001
Optimizer	Adam

The CNN is trained by dividing the data into three sets: training, validation, and test, with a ratio of 0.6:0.2:0.2. CNN is trained using spectrograms of false killer whale whistles and a dataset including random noise. It is then evaluated using the same sort of data. Figure 10 illustrates the training progress of the proposed model, indicating that as the number of epochs increases, the training accuracy also gets better and approaches a value close to 100%. Similarly, the validation accuracy also exceeds 99% and the cross-entropy loss decreases. The confusion matrix of the proposed classifier demonstrates a high level of accuracy on the test data, accurately predicting the killer whale with an accuracy rate of 99.5% as shown in Fig. 11. Moreover, the proposed approach is tested using a mimicked false killer whale whistle. Each whistle is encoded with a total of 100 bits of data employing cepstrum modulation. The encoded data is then transmitted through several UWA channels at varied SNR levels. Subsequently, a total of 950 spectrograms were utilized to evaluate the model. Figure 12 demonstrates that the proposed classifier, which achieved a high level of accuracy, successfully classified mimicked killer whale whistles as killer whale sounds 928 times while classifying into that category noise only 22 times. Hence, it can be concluded that the CNN classifier was able to detect the mimicked signal as a killer whale signal but not as a noise with high accuracy. It proves that the mimicked signal with covert information is highly imperceptible with the real false killer whistles.

Fig. 10.

Training diagram by CNN.

Fig. 11.

Confusion matrix.

Fig. 12.

Test results.

Imperceptibility analysis using ResNET-18

To further verify the imperceptibility of the proposed Cepstrum modulation for watermarking covert data in false killer whale whistles, the widely used model namely ResNET-18 is utilized. The architecture used for simulation is given in the Table 3. The input layer of ResNet-18 is replaced to accept spectrograms having dimensions 656 × 875 × 3. On the other hand, the output layer is also replace to classify only two classes that is killer whale and noise. The ResNET model is trained using the noise and killer whale spectrograms. The details of the training data are same as mentioned in above section. The training progress is shown in Fig. 13.

Table 3.

ResNET-18 killer Whale classifier hyper-parameters.

Layer / stage	Size	Kernel size / stride	Number of filters	Comments
Input layer	656 × 845 ×  3	NA	NA	Input spectrograms
Conv1	328 × 423 ×  64	7 × 7 / 2	64	Padding = 3
MaxPool	164 × 212 ×  64	3 × 3 / 2	NA	Padding = 1
Conv2_x	164 × 212 ×  64	3 × 3 / 1	64	2 BasicBlocks (each has 2 × Conv3 × 3)
Conv3_x	82 × 106 × 128	3 × 3 / 2	128	2 BasicBlocks
Conv4_x	41 × 53 ×  256	3 × 3 / 2	256	2 BasicBlocks
Conv5_x	21 × 27 × 512	3 × 3 / 2	512	2 BasicBlocks
Average Pool	1 × 1 × 512	Global AvgPool	NA	Averages over spatial dimensions
FC (Output)	1 × 1 × 2	NA	2	Fully connected, softmax for 2 classes

Fig. 13.

Training diagram by ResNET-18.

The training process show that the ResNET-18 depicts a rapidly converging model such that within just the first few iterations, training accuracy shoots up from about 50% to almost 100% and then stays at this maximal level for the remaining epochs out of the total 20 epochs considered. In response, training loss quickly falls from a value as high as around 15 to near zero within just a few initial iterations and then stays at a value that seems perfectly constant. The rapid convergence is an indication that the model has already memorized well enough all of the training data quite early in its learning process; therefore, it can be said that network capacity is better set against dataset complexity. Similarly, the confusion matrix in Fig. 14 show no errors on the training and testing dataset which depicts the accuracy of the ResNET-18 model. After training the ResNET-18 model using killer whale data and noise spectrograms the model was tested using mimicked spectrograms. A total of 950 spectrogram of mimicked spectrogram were input to the trained model. The results in Fig. 15 shows that 938 the mimicked whale data was classified as the actual whale click. This further verifies the robustness of the proposed scheme.

Fig. 14.

Confusion matrix of ResNET-18.

Fig. 15.

Test results of ResNET-18.

Robustness analysis by simulation experiment

Robustness refers to the capability of successfully extracting watermarks when the watermarked signal undergoes the effects of an underwater acoustic channel⁹⁰. This proves to be the most complex feature for an audio watermarking system, given the diverse range of potential attacks. To verify the effectiveness of the proposed scheme, the novel model is verified in AWGN and underwater multipath channel using the Bellhop ray tracing algorithm using real sound speed profile depicted from the National Oceanic and Atmospheric Administration (NOAA) World Ocean Atlas⁹¹. The underwater experiment is performed where the vocal of a false killer whale is present. In this research, we opted South China Sea near Hong Kong as tremendous Pseudorca crassidens are spotted in this region. The longitude and latitude of the site are 22.159 and 114.168 respectively. The simulation experiment is performed in shallow water whose depth is 100 m. The transmitter and receiver are positioned at 15 m and 18 m respectively. The detailed parameters are listed in Table 4.

Table 4.

Experimental parameters.

Parameter	Value
Sea bottom	100 m
Transmitter depth	15 m
Receiver depth	18 m
No. of Transmitter/Receiver	01 each
Frequency	48,000 Hz
Transmission distance	1 km
Angle beam	-30 ° to 30 °

The sound velocity profile (SVP) and the channel impulse response (CIR) based on SVP are graphed in Fig. 16a and b respectively. Bellhop ray tracing algorithm is used to generate CIR based of the parameters listed in Table 4. Short-range communication of 1 km is performed in shallow water. The channel is estimated using MP estimation as briefly discussed in Sect. 3.4 in demodulation process. Figure 17 displays the estimated CIR. It can be noticed from Fig. 17 that multipath have been efficiently reduced which enhances the BER significantly. The BER curve of the proposed cepstrum-based watermarking scheme mimicking false killer whales is shown in Fig. 18.

Fig. 16.

(a) Sound velocity profile (b) channel impulse response.

Fig. 17.

Estimated channel impulse response.

Fig. 18.

BER curve in AWGN and multipath channel with MP estimation.

First, we analyze the BER curve through the AWGN channel. The red curve in Fig. 18 shows the BER achieved through AWGN. It is evident from the Fig. 18 that zero error is achieved at 0 dB SNR. In multipath channel based on CIR shown in Fig. 16b, errorless covert communication is possible above 10 dB SNR without channel estimation. 10^− 2 BER which is almost a 1% error is achieved at 6 dB SNR.

To reduce the errors induced by the channel, the mimicked received signal is passed through an estimated channel shown in Fig. 17. The green curve in Fig. 18 shows the BER after MP estimation and VTRM equalization. More than 2 dB gain is achieved by this technique which can be witnessed from the graph. 10^− 3 BER is achieved at 3 dB SNR which is less than 0.1% error. Zero error is achieved for SNR greater than 4dB. Using SNR greater than 3dB we can perform perfect covert mimicry communication using the novel technique. The BER results proves that our proposed innovative model is suitable for covert communication with LPR characteristics in underwater acoustic channels.

Results and discussion

This section presents a comprehensive evaluation of the innovated proposed Cepstrum based mimicry covert communication and compares its performance against published biologically inspired CUAC methods. The analysis focuses on the key defining performance metrics for mimicry based covert communication systems which are robustness and covert capacity.

Robustness (BER) comparison

The robustness of the proposed method was assessed in both AWGN and realistic 1 km shallow water multipath channels simulated using the Bellhop ray tracing model. Table 5 compares the robustness of the proposed method with existing biologically inspired CUAC techniques under realistic shallow water multipath channels. The results clearly shows that the proposed method delivers the best performance, achieving a BER of 10^-2 at SNR down to 3 dB due to the inherent multipath resilience of cepstral coefficients, which effectively decorrelate phase distortion. This allows the proposed method to achieve high robustness at significantly lower SNR with high imperceptibility. Key robustness of the proposed mimicry communication using cepstrum modulation includes:

Table 5.

Comparison of robustness of mimicry communication methods.

Method	BER performance in multipath	SNR Required for BER < 10-2	Comments
Proposed cepstrum based mimicry	10-3 at 3 dB	3 dB	Best performance, cepstral decorrelation improves robustness
Dolphin click interval coding26	10-2 to 10-3	8–10 dB	Sensitive to interval distortion
Humpback song bionic Morse coding92	10-2	≥ 10 dB	Long-duration harmonics accumulate multipath distortion
DSSS masking66	10-2	6–8 dB	Robust but detectable under LPR constraints
FHSS mimicry93	10-2	6–8 dB	Doppler-sensitive

• BER = 0 at 0 dB SNR (AWGN).

• BER ≈ 10⁻³ at 3 dB SNR in shallow-water multipath after MP + VTRM equalization.

• ≥ 2 dB performance gain over DSSS and FHSS spread-spectrum methods.

• 4–6 dB gain over dolphin- and humpback-song-based mimicry approaches.

These results clearly indicate that the proposed method maintains reliable bit recovery even under harsh multipath conditions and at significantly lower SNR.

Covert data capacity comparison

Covert data capacity is the key factor which tells the amount of data watermarked in the mimicked signal. In mimicry based covert systems increasing the covert data capacity reduces imperceptibility of the mimicked signal. The covert data capacity is measured keeping the mimicked signal highly imperceptible. The proposed method achieves a significant increase in covert data rate without compromising similarity to the natural whistle. In our proposed cepstrum based mimicry communication 55.5 bits/s covert data rate is achived embedding 100 bits per whistle of false killer whales maintaining the imperceptibility greater than 97% which was verified by CNN and ResNet-18 classifiers.

The covert data rate comparison in Table 6 shows that the innovative proposed cepstrum based mimicry technique provides the highest data capacity achieving 55.5 bits/s substantially outperforming all biologically inspired communication techniques. Its superior rate is enabled by embedding covert information in cepstral coefficients which allow denser and more reliable symbol packing. In contrast, dolphin click interval coding gives only 6 bits per frame while humpback song mimicry using bionic Morse codes achieves an even lower covert rate of about one character per second. DSSS and FHSS mimicry methods for CUAC provide moderate capacities of 10–20 bits/s, however DSSS suffers from increased detectability under LPR constraints and FHSS is prone to Doppler sensitivity and synchronization challenges. Thus, the proposed method delivers significantly higher covert capacity while maintaining perfect robustness and high imperceptibility.

Table 6.

Comparison of Covert data capacity of mimicry communication methods.

Method	Covert rate	Limitations
Proposed cepstrum-based mimicry	55.5 bits/s	Highest capacity; more computational complexity
Dolphin click interval coding26	~ 6 bits/frame	Very low data rate
Humpback song bionic Morse coding92	~ 1 char/s	Long tonal structure limits rate
DSSS masking66	10–20 bits/s	Higher detectability under LPR constraints
FHSS mimicry93	10–20 bits/s	Doppler-sensitive; requires synchronization

The proposed cepstrum based watermarking embedding scheme therefore provides two to five times higher covert throughput than the best existing biologically inspired CUAC methods.

The expanded simulations and comparative analyses clearly demonstrate that the proposed cepstrum based mimicry model for CUAC delivers substantial gains in imperceptibility, robustness and covert data capacity over existing state of the art biologically inspired communication techniques. These advances stem from several key design advantages i.e. cepstral coefficients naturally decorrelate the spectral envelope which preserves the harmonic structure of the whistle and prevent multipath induced distortions. The embedding data within stable quefrency regions enhances resilience to Doppler shifts and phase rotations. The carrier signal false killer whale whistles offers richer spectral content in the 8–16 kHz band providing a wider embedding space which gives higher covert data capacity than dolphin clicks or humpback songs. As a result, the proposed method achieves near perfect imperceptibility, reliable performance at low SNR and significantly elevated data throughput. The proposed cepstrum based mimicry communication is the most effective biologically inspired covert underwater communication schemes reported to date.

Conclusion

A novel method for mimicry of covert underwater communication mimicking false killer whale whistles using cepstrum modulation is presented in this research. The novel model gives perfect LPR constraint communication and its performance is analyzed by researching its imperceptibility, covert data rate, and robustness. This innovative technique can watermark 55.5 covert bits per second. 100% imperceptibility which is verified through CNN using machine learning. The mimicked signal is passed through the underwater acoustic channel at the South China Sea near Hong Kong to verify the robustness of the proposed scheme. Zero error is achieved at the AWGN channel at SNR down to 0 dB. Less than 1% error is achieved in multipath channel which is diminished to zero error by using MP estimation and VTRM equalization with a gain of 2 dB. The proposed model proves to be perfect to use for LPR constraints covert operations in the vast ocean. Further research includes the enhancement of covert data capacity in LPR constraint communication.

Author contributions

The concept of the research was initiated by all authors. M.B. wrote the main manuscript. The methodology was drafted by M.B., S.L. and H.H.Z which resulted in preparation of Figs. 1, 2 and 3. Watermarking experiment was conducted by A.A, A.J and A.M where the Figs. 4, 5, 6 and 7 were prepared. The imperceptibility analysis experiment and results are extracted by H.H.Z and M.A.K. which results for Figs. 8, 9, 10, 11 and 12. The robustness of the proposed method was verified by M.B. and W.R. which resulted in preparation of Figs. 13, 14 and 15. All authors reviewed the manuscript.

Funding

This research work was funded by Umm Al-Qura University, Saudi Arabia under grant number: 25UQU4290339GSSR10.

Data availability

The research data is extracted from WHOI Marine Mammal Database website https://cis.whoi.edu/science/B/whalesounds/index.cfm.

Declarations

Competing interests

The authors declare no competing interests.