## 7 System Simulation Model
Finally, it returns the average energy consumption, the proportion of free channels, successful transmissions, and collisions over the simulated iterations. This simulation provides insights into the efficiency and reliability of different network configurations in terms of energy usage and communication success rates. The overall complexity of the algorithm is the product of the complexities of the loops, the outer loop is \(O(N^{3})\), the middle loop is \(O(1)\) as we know that it runs a fixed number (100,000), and the inner loop is \(O(N)\). Thus, the overall time complexity of the algorithm is \(O(N^{3})\times O(1)\times O(N)=O(N^{4})\). After validating the behavior of the system, the objective is to determine the efficiency and reliability of the birdsong-based communication system in real-world scenarios. By analyzing the previous simulation and the analytic results of the network metrics: throughput, collision rates, and free slot rates. The efficiency of the system is measured by evaluating the lifespan and throughput capabilities, given the transmission probability (\(\tau\)) and the number of nodes (\(N\)). This is represented as \(lifespan(\tau,N)\times Throughput(\tau,N)\). Furthermore, energy consumption tests are conducted to evaluate the power efficiency of the proposed method. By measuring the energy consumption of the sensor nodes that has intermittence compared to a system that remains constantly in the \(On\) state. However, we have to emphasize that a system that is always turned on, implies that the nodes are constantly emitting the bird sound, which we believe would be very suspicious to people in the surroundings effectively weakening the concealment of the network. Additionally, comparative tests are conducted to analyze the throughput capability of the birdsong-based communication system against the ZigBee protocol, which is a short-range wireless communication protocol. This test aims to highlight the difference of the proposed approach and provide insights for further improvements of the communication system. The inclusion of hidden information in the analysis is achieved by considering the maximum amount of bps that can be concealed in each audio file, as reported in Table 1. This value is then multiplied by the system's throughput, which is determined by its specific transmission probability (\(\tau\)) and the number of nodes (\(N\)). ## 8 Numerical Results

In this section we present the main results obtained through the analytical model developed in this work. First, we validate our analytic results comparing them to simulation results. Then, we obtain the main system performance parameters, such as throughput, time slot collision, and idle probabilities. Figure 10a-c, show the system throughput, idle and collision time slot probabilities respectively for both analytical and simulation results. We can observe a very good match between these results providing a validation of the mathematical model. To validate the differences that exist between both representations of the system, the figures presented in Figure 11 show the mean square error (MSE) for each of the graphs previously displayed. The maximum error reported is 13% in the Idle Slot graph (Figure 11b). For the Collision MSE, at a probability of \(\tau=0.9\), there is a 10.5% error between both analyses. The Throughput MSE is the measure that fits best, with only a 0.17% difference between the simulation and the analytical solution of the model. Figure 10: Comparison between analytical and simulation results for (**a**) Throughput, (**b**) Idle time slot probability, and (**c**) Collision probability. Now, we analyze the behavior of the proposed system where nodes turn \(On\) and \(Off\) according to the statistical characteristics of the bird's sounds. Figure 11(a), shows the throughput behavior when varying the number of nodes over the network or the transmission probability.