## 1 Introduction
In this sense, using a novel technique by applying the wavelet transform, the audio signal is decomposed into coefficients [21], in which a modification is made over the detail coefficients. Then, the signal is reconstructed by using the inverse wavelet transform. After these, by using the statistical variables of the song and silence times of the previously modified audios, we associate them to a phase distribution, which are based on the exponential distribution, hence they have memoryless properties, which means that the current state depends uniquely on the previous state. This distribution accurately model the behavior of the nodes in the sensor network system determined to reproduce a bio-inspired behavior. Random medium access protocols involve \(N\) nodes transmitting data on a single channel, with potential signal distortions from simultaneous transmissions. Timing can be continuous or slotted. Detection of ongoing transmissions may or may not be possible. The simplest protocols are Pure ALOHA, allowing transmission at any time, and its variant, Slotted ALOHA, which aligns transmissions with timed slots for increased efficiency. More complex protocols like Carrier Sense are not here. The S-ALOHA protocol is simple and widely used in Ad hoc networks and sensor networks. It is also used in competing 802.11 hotspots where they cannot sense each other's presence. This protocol is well-studied, with the purpose of identifying critical processes such as collision rates, free slots, throughput, and estimation of energy consumption. It is used for system analysis and to consider new alternatives for communication. Building on this, the performance of the system is evaluated considering that the nodes transmit their data packets using the S-ALOHA protocol, which functions as a MAC protocol where the shared channel is slotted, i.e., nodes can only transmit at the beginning of the slot [22]. In our case, it provides communication capabilities over a hidden channel, providing a different form of communication than radio frequency. The system evaluation transmission rates above the rates reported in previous works that make use of bio-inspired audios; additionally, the proposed analysis allows the system administrator to predict the system's behavior under different conditions, such as different number of nodes and transmission rates. Summarizing, this work introduces an innovative approach to wireless sensor network (WSN) communications by utilizing bird song audio for covert communication through audio steganography techniques, thus offering a unique alternative to traditional radio communication methods. Diverging from existing methods that focus on specific insertion points in natural sounds, our project stands out by altering the entire spectrum of bird song audios for embedding secret messages. This strategy not only diversifies the communication mediums used in WSNs but also provides a solution for combating electromagnetic jamming attacks, a prevalent issue in wireless networks. Additionally, the project proposes a method based on statistical behavior for energy efficiency in the Medium Access Control (MAC) layer. This method, inspired by the sound and silence patterns in bird songs, alignsthe sleep/awake cycles of network nodes with these natural patterns. By integrating the unique properties of natural sounds into technological applications, our approach marks a distinct departure from conventional techniques in covert communication and WSN functionality. Building on this, the main contributions of this work are as follows:  
* We conduct a comprehensive statistical analysis of bird sounds to determine the Coefficient of Variation (CoV) of active and inactive periods. This allows us to accurately model and account for effective data transmission within a covert channel communication system. * We perform a teletraffic analysis to calculate the optimal number of nodes that can transmit simultaneously.