## 7 System Simulation Model
As such, the practical implementation of this system should consider a hierarchical architecture such as clustered-based WSNs, where nodes only transmit to a near Cluster Head, while the cluster head transmits using RF signals to a further sink. Another alternative could consider the use of mobile sinks (motorized sinks such as terrestrial robots or drones) that recover the information using sound passing close to the nodes. However, these issues fall outside the scope of this work. Figure 12: Comparison between the system with nodes turning _On/Off_ and nodes always in _On/_ mode (**a**) Throughput, (**b**) Idle time slot, and (**c**) Collision. Figure 14: Transmission Rate comparison between modified audios and Zigbee minimum and maximum transition rates. (**a**) _Curve-billed Trasher_, and Zigbee minimum and maximum transition rates, (**b**) Birds’ audios, and Zigbee minimum transition rates. Figure 13: System Lifespan and efficiency of Nodes with _On/Off_ transitions, and nodes always _On_. (**a**) Lifespan, (**b**) Efficiency. ## 9 Conclusions

In this work, we proposed, analyzed, and studied a WSN using a covert channel based on bird sounds to hide the presence of the monitoring system. The proposed system closely follows the natural _On/Off_ behavior of bird's songs, effectively hiding the monitoring capabilities of the WSN by only transmitting when the sound is present while turning the nodes to the _Off_ mode when the bird's recording is silent. To achieve this, we propose the use of phase-type distributions to model these _On/Off_ periods. Also, information is inserted in the sound using the Wavelet transform in order to reduce the distortion of the original audio signal in such a way as to generate sounds with underlying data with almost no perceptible modifications compared to the original audio. This approach, however, imposes limitations on the transmission rate in three significant ways: sound operates at a much lower frequency than RF signals; nodes can only transmit when sound is present; and bits are only inserted as long as they do not cause significant distortion to the recorded audio. In view of this, our mathematical analysis provides important performance metrics, clearly demonstrating the system's capabilities in terms of throughput, transmission rate, and energy consumption. Specifically, the data hiding process is contingent on the audio coverage rather than the duration of the audio. For instance, a 10-s audio file could hide 2060 bps, a 13-s file could conceal 3980 bps, whereas a 55-s file might only conceal 57 bps. While all the stratums studied follow a hyper-exponential hypothetical distribution, further studies are necessary to determine if all bird species conform to this distribution. Moreover, the proposed _On/Off_ node scheme distributed across the network improves the system performance as the number of nodes and/or the probability of transmission (\(\tau\)) increases. For example, while at 1 node and a probability \(\tau=1\), the always _On_ scheme reaches 90% throughput, adding one more node (\(N=2\)) at the same transmission probability yields a maximum throughput rate of 49.9%, compared to 18% for the always _On_ scheme. This method conserves energy, extends the network's lifespan, and proves more effective in power consumption and network throughput analysis. Therefore, despite conventional RF systems achieving higher transmission rates, our proposal is robust against classical jamming attacks and operates imperceptibly to unauthorized intruders searching for RF transmissions. For future work, we plan to conduct practical tests to measure the transmission capacity in physical applications. We aim to verify the feasibility and limitations of this solution, which appears promising thus far, and to explore alternatives to address the significant reduction in transmission rates compared to RF transmissions. Methodology, A.I.R.-G., M.E.R.-A., I.Y.O.F. and G.G.-G.; Validation, A.I.R.-G.; Formal analysis, A.I.R.-G., M.E.R.-A., I.Y.O.F.