## 1 Introduction
To effectively conceal information in the bird's sounds, we first characterize the periods where birds remain silent (_Off_ period) and when they make sounds (_On_ periods) in such a way as for nodes to generate the previously recorded sounds closely following the statistical properties of these _On/Off_ periods and transmitting data packets only during the _On_ periods. At present, between the different proposals for creating a covert communication channel, there exists an approach that is focused on using bio-inspired sounds [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], in which they present the efficiency of the proposed communication schemes through computer simulations or physical prototypes. In these works, the authors often only consider a single sender and receiver without delving into how such a scheme would behave in a networked setting. Conversely, we develop a mathematical analysis of a communication system that not only considers a single sender and receiver but also provides network metrics such as the impact of the number of nodes in the system. Also, in our work, we consider the statistical main characteristics of the bird's specific sounds to hide the information better, i.e., to have the prerecorded sounds have the same statistical behavior as the birds. Specifically, we model these songs as an _On/Off_ process using phase-type distributions to vary the Coefficient of Variation accordingly, and we consider that the information from nodes is transmitted only during the _On_ periods while nodes remain silent during the _Off_ periods. The use of the phase-type distributions, such as the Erlang and Hyper-Exponential distributions, allows the use of Markov chains to model the system. This produces a covert channel that closely follows the specific patterns of the bird's songs, making the communication system imperceptible to potential attackers. Besides, this natural _On/Off_ process entails an important energy reduction in the system that we can measure using the derived mathematical model. In addition to closely matching the sound/silent (_On/Off_) periods to conceal the data transmission effectively, we also avoid distortion in the bird's sounds by means of steganographic techniques, which are a set of processes to hide a message in a container signal, such as text, images, audio, video, or in a specific protocol, and is employed to protect the exchanged data from malicious attacks [19]. In the majority of works mentioned before, they make use of synthetic sounds that closely resemble the original sounds to use as a carrier medium. However, in our case, we are using the original audio as a container of the message hidden on it. Within the techniques used to perform steganographic methods, there is a modification over the frequency domain using the discrete wavelet transform (DWT), which provides a resolution similar to the human ear time-frequency perception [19, 20]. The DWT produces 2 sets of coefficients: the approximation coefficients (\(cA\)) and the detail coefficients (\(cD\)), which are related to low and high frequencies, respectively. To hide the information sent by the nodes in the WSN, which in our case comprises a small number of bits to indicate the presence of unusual activity through the sound of shrill sounds like an electric saw or human detection sensors, we consider the time when birds are emitting their characteristic sounds (which we call songs throughout this work) inserting data in such a way as to modify them as less as possible. To this end, we develop a teletraffic analysis that captures the main dynamics of the system, such as system throughput, idle time probability, collision probability, and an energy consumption estimation. In this sense, a network model is developed below based on Continuous Time Markov chains where pre-recorded bird songs are used as carrier signals, which are modified with steganographic techniques for sharing messages using sound waves as the transmitting medium.