## 3 Conventional and Proposed Methods
### Proposed Method
#### 4.2.2 Dynamic Power Control Mechanism  
In this section, we perform a dynamic simulation based on the system model in Section 2. This simulation reproduces the situation where both the transmitter and receiver are under dynamic conditions and compares the difference in BER and throughput performance between the uniform power distribution method, the CSI proportional distribution method, and the proposed method, the nonlinear distribution method based on CSI. We compared the power consumption within a certain period of time for each conventional method and the proposed method. In order to clearly show the results, the system model has been partially simplified. The simulation conditions are based on the parameters shown in Table 2.  
Specifically, we assume that the transmitter and receiver do not displace in the y-axis direction and that \(y_{s}(t)=0\). In addition, the balloon performs Brownian motion in the range of \([-50\) m, \(50\) m\(]\) in the x-axis and z-axis directions. To simulate ocean waves with an amplitude of 5 m and a period of 10 s in the z-axis direction, the ship is moved based on Equation (6). The ship is moved with the settings \(A_{1}=5\), \(\omega=0.628\), \(A_{2}=0\), \(A_{3}=0\) m. The x-axis direction is modeled by placing the values in Equation (4) with \(x_{r0}=5000\), \(V_{rx}=10\) m/s. This recreates a situation in which a ship moves toward the coast at a speed of 10 m/s from a point 5000 m horizontally away from the balloon. Furthermore, because the channel state changes in response to the movement of the ship, the distribution concentration degree \(\beta\) is dynamically adjusted in real time according to the proposed method and is always kept at an optimal value, thereby stabilizing communication performance. Figure 6: Distribution concentration factor \(\beta\)-BER characteristics at propagation distance = 2 km. Figure 7 shows the throughput variations of each method over 60 ms under constant output power conditions. Consistent with previous simulation results, in dynamically changing channel conditions, the proportional allocation method outperforms the equal power allocation method. The proposed nonlinear allocation method achieves channel-state-optimized allocation by dynamically adjusting the distribution concentration value, improving throughput and stability. Notably, the nonlinear allocation method maintains stable and high throughput against channel variations, demonstrating its superiority in dynamic channel environments. To further validate the effectiveness and practicality of the proposed method, energy consumption and output power were measured in a dynamic mobile environment under BER range-limited conditions, with results shown in Figure 8. This confirmed that the proposed method has high energy efficiency and low power consumption. Figure 8 shows the power consumption changes for each method as the ship moves from 5 km to 10 km horizontally from the balloon, following the same mobility model as in previous simulations, under conditions maintaining BER at or below 0.1%. Comparing the consumed energy results, the methods rank from highest to lowest as follows: the equal power allocation method, the proportional allocation method, and the proposed method. During the movement from 5 km to 10 km horizontally, the proposed method demonstrated superior energy efficiency in dynamic channel conditions. With a total energy consumption of 7.91 Wh and an average power consumption of 56.97 W, it achieved significant power savings of 4.2% compared to the CSI proportional method and 10.9% compared to the equal power allocation method. These results confirm the proposed method's effec