A Study on Performance Improvement of Maritime Wireless Communication Using Dynamic Power Control with Tethered Balloons

Abstract

In recent years, the demand for maritime wireless communication has been increasing, particularly in areas such as ship operations management, marine resource utilization, and safety assurance. However, due to the difficulty of deploying base stations(BSs), maritime communication still faces challenges in terms of limited coverage and unreliable communication quality. As the number of users on ships and offshore platforms increases, along with the growing demand for mobile communication at sea, conventional terrestrial base stations struggle to provide stable connectivity. Therefore, existing maritime communication primarily relies on satellite communication and long-range Wi-Fi. However, these solutions still have limitations in terms of cost, stability, and communication efficiency. Satellite communication solutions, such as Starlink and Iridium, provide global coverage and high reliability, making them essential for deep-sea and offshore communication. However, these systems have high operational costs and limited bandwidth per user, making them impractical for cost-sensitive nearshore communication. Additionally, geostationary satellites suffer from high latency, while low Earth orbit (LEO) satellite networks require specialized and expensive terminals, increasing hardware costs and limiting compatibility with existing maritime communication systems. On the other hand, 5G-based maritime communication offers high data rates and low latency, but its infrastructure deployment is demanding, requiring offshore base stations, relay networks, and high-frequency mmWave (millimeter-wave) technology. The high costs of deployment and maintenance restrict the feasibility of 5G networks for large-scale nearshore environments. Furthermore, in dynamic maritime environments, maintaining stable backhaul connections presents a significant challenge. To address these issues, this paper proposes a low-cost nearshore wireless communication solution utilizing tethered balloons as coastal base stations. Unlike satellite communication, which relies on expensive global infrastructure, or 5G networks, which require extensive offshore base station deployment, the proposed method provides a more economical and flexible nearshore communication alternative. The tethered balloon is physically connected to the coast, ensuring stable power supply and data backhaul while providing wide-area coverage to support communication for ships and offshore platforms. Compared to short-range communication solutions, this method reduces operational costs while significantly improving communication efficiency, making it suitable for scenarios where global satellite coverage is unnecessary and 5G infrastructure is impractical. Additionally, conventional uniform power allocation or channel-gain-based amplification methods often fail to meet the communication demands of dynamic maritime environments. This paper introduces a nonlinear dynamic power allocation method based on channel gain information to maximize downlink communication efficiency. Simulation results demonstrate that, compared to conventional methods, the proposed approach significantly improves downlink communication performance, verifying its feasibility in achieving efficient and stable communication in nearshore environments.

1. Introduction

In recent years, the importance of wireless communication at sea has increased, particularly in areas such as managing ship operations, utilizing marine resources, and ensuring safety. A stable communication network is essential for these purposes [1,2]. However, maritime communication faces unique challenges, as radio waves from terrestrial base stations have difficulty reaching offshore areas, making it challenging to establish a stable and wide-range communication network [3]. Ships are constantly moving, and fluctuations on the sea surface cause irregular positional changes, making it difficult to maintain a stable communication environment. Consequently, there is a growing demand for low-cost and highly efficient communication methods, which has become a significant challenge in maritime wireless communication today [4].

Traditional mainstream solutions include satellite communication, long-range Wi-Fi, and offshore base stations. Satellite communication offers wide coverage and high reliability. However, it is costly to operate, and communication latency is often an issue, especially with high-altitude geostationary satellites [5]. However, long-range Wi-Fi systems are relatively cost-effective but have limited signal coverage, making them insufficient for vast maritime areas [6]. Offshore base stations, such as antennas mounted on ships, are effective in specific areas but require significant installation and maintenance efforts, limiting their applicability to wide-area coverage [1,7].

To address these challenges, this paper proposes the use of tethered balloons deployed at altitudes of several hundred meters, serving as low- to mid-altitude aerostat (LMA) base stations [8]. By deploying these aerostats at high altitudes over the sea, they can achieve wider communication coverage compared to terrestrial base stations, while offering lower operational costs than satellite communication [9]. Furthermore, they provide a more efficient and wider coverage solution compared to short-range wireless technologies [8]. This study focuses on downlink communication from the tethered balloon to maritime users, aiming to optimize the communication to improve both cost efficiency and reliability.

Downlink communication is the process of directly transmitting signals from the base station (tethered balloon) to ships and maritime users, playing a crucial role in improving network performance. However, in dynamic and unstable environments, the quality of downlink signals is significantly affected [10]. This paper focuses on the instability of the tethered balloon’s position due to weather conditions and maritime environmental factors, as well as the continuous movement of maritime users influenced by both their own motion and sea surface fluctuations [11]. To address these issues, this study proposes a communication method leveraging active beamforming (ABF) technology. ABF enables the real-time tracking of receiver positions and focuses the signal on the optimal direction, thereby extending the communication range and improving signal quality [12].

Specifically, in the Multiple-Input–Multiple-Output (MIMO) system, this study explores an optimized power allocation strategy for transmitting antennas. Conventional power allocation methods, such as equal power allocation and proportional allocation based on channel state information (CSI), are commonly used in static communication environments. However, in dynamic maritime environments, these traditional approaches face significant limitations, making it difficult to guarantee optimal communication quality under constant movement and unpredictable fluctuations [13].

To overcome these challenges, this paper proposes a nonlinear power allocation method based on CSI. This approach nonlinearly allocates transmission power according to the channel gain of each antenna, assigning more power to antennas with higher gains while suppressing power to those with lower gains. This method enables efficient power utilization in dynamic environments, maintaining high communication quality even in non-uniform channel conditions, and significantly improving overall energy efficiency.

Finally, the effectiveness of the proposed method was verified by simulations. Compared to conventional equal power allocation and CSI-based proportional allocation methods, the proposed method demonstrated superior performance in reducing the Bit Error Rate (BER) and improving throughput. Moreover, the proposed approach significantly reduced power consumption while maintaining stable communication quality in dynamic environments. The results also showed that by adjusting the power distribution concentration parameter, optimal communication balance could be achieved. In particular, the proposed method outperformed conventional methods, particularly in scenarios with highly uneven channel conditions. These findings suggest that the proposed method is a promising approach to improve the efficiency and reliability of communication systems in dynamic and unstable maritime environments.

The organization of this thesis is as follows. Section 2 describes the system model assumed in this study. In Section 3, the conventional methods, the equal power allocation method, and the CSI-based proportional allocation method, as well as the proposed method, are explained in detail. Furthermore, to demonstrate the superiority of the proposed method, an analysis is conducted in terms of bit error rate (BER), throughput, and power consumption. Section 4 presents a performance comparison based on computational simulations. Finally, Section 5 provides a summary and conclusion of this thesis.

2. System Model

2.1. Network Model

The network model considered in this thesis is illustrated in Figure 1. The transmitter is positioned at the upper left, represented by a tethered balloon at an altitude of 500 m. The balloon is tethered to the ground via a cable, which also supplies power. To account for wind effects, the three-dimensional coordinates of the balloon, initially set at $(0,0,500)$, are allowed to vary within a range of $[-50,50]$ m, corresponding to a cubic space of $100\times 100\times 100$ m. The balloon moves randomly within this range at a velocity of 0 to 5 m/s to simulate typical balloon movements [14].

The receiver is located at the lower right, representing a ship. The ship travels at a constant speed of $V_s$, and due to ocean waves, it experiences vertical displacement, introducing a vertical velocity component. The wave-induced movement of the ship is modeled as a sinusoidal function to simulate realistic sea conditions. The amplitude of the wave is set to 5 meters, and the frequency is set to $0.1$ Hz.

2.2. Position Estimation

2.2.1. Transmitter Mobility Model

The following describes a model representing the random movement of a balloon. In this model, the balloon undergoes random drift and fluctuations in the x, y, and z directions due to environmental factors such as air currents and sea breezes.

$$\begin{array}{cc}\hfill x_s\left(t\right)& =x_{s0}+{\mu }_{x}t+{\sigma }_x{W}_x\left(t\right),\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill y_s\left(t\right)& =y_{s0}+{\mu }_{y}t+{\sigma }_y{W}_y\left(t\right),\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill z_s\left(t\right)& =z_{s0}+{\mu }_{z}t+{\sigma }_z{W}_z\left(t\right).\hfill \end{array}$$

(3)

In this context, ${\mu }_x$, ${\mu }_y$, and ${\mu }_z$ represent the drift coefficients in the x, y, and z directions, respectively, while ${\sigma }_x$, ${\sigma }_y$, and ${\sigma }_z$ denote the intensity of Brownian motion in each direction. The terms $W_x\left(t\right)$, $W_y\left(t\right)$, and $W_z\left(t\right)$ represent independent standard Brownian motions, which account for the random components of the balloon’s movement [15].

2.2.2. Receiver Mobility Model

The following describes a model representing the movement of a ship. It is assumed that the ship moves at a constant velocity $V_r$ in the horizontal plane. The vertical movement represents the up-and-down fluctuations caused by ocean waves, which are expressed as a superposition of three sinusoidal waves. This approach enables a more realistic simulation of wave undulations. Accordingly, the ship’s position $x_r\left(t\right)$, $y_r\left(t\right)$, and $z_r\left(t\right)$ can be expressed by the following equations.

$$\begin{array}{cc}\hfill x_r\left(t\right)& =x_{r0}+V_{rx}t,\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill y_r\left(t\right)& =y_{r0}+V_{ry}t,\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill z_r\left(t\right)& =A_{1}sin({\omega }_{1}t+{\varphi }_1)+A_{2}sin({\omega }_{2}t+{\varphi }_2)+A_{3}sin({\omega }_{3}t+{\varphi }_3).\hfill \end{array}$$

(6)

In this context, the initial position of the ship is given as $(x_{r0},y_{r0},z_{r0})$, where $V_{rx}$ and $V_{ry}$ represent the velocities in the x and y directions, respectively. The parameters $A_i$, ${\omega }_i$, and ${\varphi }_i$ denote the amplitude, angular frequency, and phase of the sinusoidal components, respectively.

2.2.3. Propagation Distance

The positions of the balloon (transmitter) and the ship (receiver) are denoted as $(x_s\left(t\right),y_s\left(t\right),z_s\left(t\right))$ and $(x_r\left(t\right),y_r\left(t\right),z_r\left(t\right))$, respectively. The propagation distance $d\left(t\right)$ between them at time t is given by the following equation [16].

$$\begin{array}{c}\hfill d\left(t\right)=\sqrt{{(x_s\left(t\right)-x_r\left(t\right))}^2+{(y_s\left(t\right)-y_r\left(t\right))}^2+{(z_s\left(t\right)-z_r\left(t\right))}^2},\end{array}$$

(7)

The azimuth and zenith angles of the ship as observed from the balloon are expressed by the following equations.

$$\begin{array}{c}\hfill \theta \left(t\right)={tan}^{-1}\left({\displaystyle \frac{y_r\left(t\right)-y_s\left(t\right)}{x_r\left(t\right)-x_s\left(t\right)}}\right),\end{array}$$

(8)

$$\begin{array}{c}\hfill \varphi \left(t\right)={cos}^{-1}\left({\displaystyle \frac{z_r\left(t\right)-z_s\left(t\right)}{d\left(t\right)}}\right).\end{array}$$

(9)

In this context, $\theta \left(t\right)$ and $\varphi \left(t\right)$ represent the azimuth and zenith angles, respectively. By substituting Equations (1) to (6), Equations (8) and (9) can be expressed as follows.

$$\begin{array}{c}\hfill \theta \left(t\right)={tan}^{-1}\left({\displaystyle \frac{y_{r0}+V_{ry}t-(y_{s0}+u_{y}t+{\sigma }_y{W}_y\left(t\right))}{x_{r0}+V_{rx}t-(x_{s0}+u_{x}t+{\sigma }_x{W}_x\left(t\right))}}\right),\end{array}$$

(10)

$$\begin{array}{c}\hfill \varphi \left(t\right)={cos}^{-1}\left({\displaystyle \frac{A_{1}sin({\omega }_{1}t+{\varphi }_1)+A_{2}sin({\omega }_{2}t+{\varphi }_2)+A_{3}sin({\omega }_{3}t+{\varphi }_3)-(x_{s0}+u_{z}t+{\sigma }_z{W}_z\left(t\right))}{\sqrt{{(x_s\left(t\right)-x_r\left(t\right))}^2+{(y_s\left(t\right)-y_r\left(t\right))}^2+{(z_s\left(t\right)-z_r\left(t\right))}^2}}}\right).\end{array}$$

(11)

2.3. Communication Model

As shown in Figure 2, this study employs a communication model based on a MIMO system utilizing hybrid beamforming. On the transmission side, signals are weighted through baseband precoding and dynamically adjusted in direction using digital signal processing, followed by digital-to-analog conversion (DAC) to convert the signals into analog form. Subsequently, further directional adjustments are made via radio frequency (RF) precoding, and the beamformed signals are transmitted into space through an antenna array. On the reception side, the received signals from each antenna are combined using RF combined and converted into digital signals through analog-to-digital conversion (ADC). Subsequently, baseband combining is performed to eliminate noise and equalize the channel, thereby improving communication quality. Furthermore, by applying the Multiple Signal Classification (MUSIC) algorithm for direction of arrival (DOA) estimation, the arrival direction of received signals can be efficiently calculated, achieving high-precision beamforming. This approach, which integrates both digital and analog layers, enables the construction of a communication system that excels in flexibility and efficiency [12,17].

2.3.1. Rician Fading Model and Path Loss

To accurately represent the maritime wireless environment, we adopt a Rician fading model, which captures the presence of both Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) components due to sea surface reflections and ship movements. The received signal is modeled as

$$h=\sqrt{{\displaystyle \frac{K}{K+1}}}{h}_{\mathrm{LoS}}+\sqrt{{\displaystyle \frac{1}{K+1}}}{h}_{\mathrm{NLoS}},$$

(12)

where

$h_{\mathrm{LoS}}$ represents the direct wave component, $h_{\mathrm{NLoS}}$ denotes the Rayleigh-distributed scattered component, K is the Rician K-factor, representing the ratio of LoS to NLoS power, defined as

$$K={\displaystyle \frac{A^2}{2{\sigma }^2}}.$$

(13)

Here, A is the LoS amplitude, and ${\sigma }^2$ represents the average power of the scattered multipath components.

The large-scale path loss is modeled using the log-distance path loss model:

$$L\left(d\right)={\left({\displaystyle \frac{4\pi d{f}_c}{c}}\right)}^2,$$

(14)

where d is the transmission distance, $f_c$ is the carrier frequency, and c is the speed of light. This formulation accounts for the attenuation of signals over a distance, a key consideration for maritime links.

2.3.2. Channel Estimation Using MMSE

Accurate channel estimation is essential for beamforming and adaptive power allocation. We employ the Minimum Mean Square Error (MMSE) method, which estimates the channel matrix $\widehat{H}$ as follows:

$$\widehat{H}=R_{HH}{X}^H{\left(X{R}_{HH}{X}^H+{\sigma }^{2}I\right)}^{-1}Y,$$

(15)

where $R_{HH}$ is the channel correlation matrix, X is the transmitted signal matrix, ${\sigma }^2$ is the noise variance, I is the identity matrix, Y is the received signal matrix.

This method reduces channel estimation error by considering the statistical properties of the channel and noise, leading to improved performance in dynamic environments.

2.3.3. Beamforming Strategy Using MUSIC Algorithm

To enhance communication efficiency, we apply hybrid beamforming based on the MUSIC (Multiple Signal Classification) algorithm. The estimated Direction of Arrival (DOA) is used to compute the beamforming weights. The MUSIC spectrum is given by

$$P_{\mathrm{MUSIC}}(\theta ,\varphi )={\displaystyle \frac{1}{a^H(\theta ,\varphi )E_n{E}_n^{H}a(\theta ,\varphi )}},$$

(16)

where $a(\theta ,\varphi )$ is the steering vector for azimuth angle $\varphi$ and elevation angle $\theta$, $E_n$ is the eigenvector matrix of the noise subspace.

The estimated DOA $(\widehat{\theta },\widehat{\varphi })$ determines the beamforming weight vector:

$$w=a^H(\widehat{\theta },\widehat{\varphi }).$$

(17)

Applying the beamforming weight to the received signal X, the output signal is

$$y=w^{H}X.$$

(18)

This process enables high-precision beamforming, effectively focusing transmission energy toward intended users, thereby improving signal quality and system capacity.

3. Conventional and Proposed Methods

3.1. Conventional Methods

3.1.1. Equal Power Allocation Method

The equal power allocation method is a simple approach in which each transmitting antenna transmits signals with equal power. This method does not consider channel state information (CSI), and the same power is allocated to all antennas.

When the total transmission power $P_{\mathrm{total}}$ is equally distributed among all antenna elements, the transmission power of each antenna $P_i$ is expressed as follows:

$$\begin{array}{c}\hfill P_i={\displaystyle \frac{P_{\mathrm{total}}}{N}}.\end{array}$$

(19)

When each element of the $M\times N$ planar array antenna transmits signals to the receiving end, a phase shift is required depending on the position of each antenna element. When the signals from each antenna element $(m,n)$ interfere and combine at the receiving end, the received signal power $R_{\mathrm{rec},\mathrm{equal}}$ is expressed as follows:

$$\begin{array}{c}\hfill R_{\mathrm{rec},\mathrm{equal}}={\left|\sum _{m=1}^M\sum _{n=1}^N\sqrt{{\displaystyle \frac{P_{\mathrm{total}}}{N}}}·h_{m,n}·e^{j{\theta }_{m,n}}\right|}^2.\end{array}$$

(20)

In this context, $h_{m,n}$ represents the channel gain of the antenna element $(m,n)$, and $e^{j{\theta }_{m,n}}$ denotes the phase shift term for beamforming, which is determined based on the position of each antenna element and the transmission angle. Further details are provided in Section 3.2.2 regarding the adaptive selection method of $\beta$.

3.1.2. CSI-Based Proportional Allocation Method

In the CSI-based proportional allocation method, the transmission power of each antenna is allocated in proportion to the CSI gain $g_{m,n}$. As a result, more power is allocated to antennas with better channel conditions, while power distribution to antennas with poorer channel conditions is suppressed.

The CSI gain $g_{m,n}$ represents the squared magnitude of the complex channel coefficient $h_{m,n}$, which characterizes the channel conditions between the $(m,n)$-th transmit antenna and the receiver. Mathematically, it is defined as

$$g_{m,n}={\left|h_{m,n}\right|}^2.$$

(21)

Here, $h_{m,n}$ is the complex channel coefficient, which is influenced by path loss, shadow fading, and multipath effects. A higher $g_{m,n}$ value indicates stronger received signal strength, whereas a lower $g_{m,n}$ suggests higher attenuation due to poor channel conditions.

The transmission power of each antenna element $P_{m,n}$ is then expressed as

$$\begin{array}{c}\hfill P_{m,n}=P_{\mathrm{total}}·{\displaystyle \frac{g_{m,n}}{{\displaystyle \sum _{k=1}^M\sum _{l=1}^N}{g}_{k,l}}}.\end{array}$$

(22)

Based on the transmission power allocated to each antenna element, the total received signal power at the receiving end, $R_{\mathrm{rec},\mathrm{proportion}}$, is expressed as follows:

$$\begin{array}{c}\hfill R_{\mathrm{rec},\mathrm{proportion}}={\left|\sum _{m=1}^M\sum _{n=1}^N\sqrt{P_{\mathrm{total}}·{\displaystyle \frac{g_{m,n}}{{\displaystyle \sum _{k=1}^M\sum _{l=1}^N}{g}_{k,l}}}}·h_{m,n}·e^{j{\theta }_{m,n}}\right|}^2.\end{array}$$

(23)

3.2. Proposed Method

3.2.1. CSI-Based Nonlinear Allocation Method

The objective of the CSI-based nonlinear allocation method is to efficiently distribute transmission power according to the CSI gain of each antenna. This method is specifically designed to maximize communication performance, particularly in environments with non-uniform channel conditions. By allocating more power to antennas with higher channel gains and reducing power allocation to antennas with lower channel gains, the limited power resources can be effectively utilized.

Based on the nonlinear allocation method, the transmission power of each antenna element $P_{m,n}$ is expressed as follows:

$$\begin{array}{c}\hfill P_{m,n}=P_{\mathrm{total}}·{\displaystyle \frac{g_{m,n}^{\beta }}{{\displaystyle \sum _{k=1}^M\sum _{l=1}^N}{g}_{k,l}^{\beta }}}.\end{array}$$

(24)

In this context, $P_{\mathrm{total}}$ represents the total transmission power, which signifies the overall power constraint of the system and corresponds to the sum of the transmission power allocated to each antenna. Within this constraint, optimal power allocation is performed based on the channel state. The parameter $g_{m,n}$ denotes the CSI gain of each antenna, which reflects the channel conditions between each antenna and the receiving end. A higher value of $g_{m,n}$ indicates better channel quality. Based on the channel conditions, more power is allocated to antennas with higher channel gains, while power distribution to antennas with lower channel gains is suppressed, ensuring the efficient utilization of transmission power. The parameter $\beta$ controls the concentration level of the power allocation. Specifically, as the value of $\beta$ increases, power becomes more concentrated on antennas with higher channel gains. Conversely, when $\beta$ is smaller, the power distribution approaches a more uniform allocation. However, an excessively high $\beta$ may lead to power over-concentration on a few antennas, reducing the overall communication robustness, while a too-low $\beta$ results in inefficient power utilization. Therefore, an appropriate range of $\beta$ is crucial for maintaining stable and efficient communication performance. Through simulation analysis (see Figure 6), we identified that an optimal range for $\beta$ lies between $1.4$ and $2.2$, with $1.8$ yielding the lowest bit error rate (BER). When $\beta$ is within this range, the system effectively balances power distribution and energy efficiency, achieving optimal performance under varying channel conditions. To further adapt to dynamic environments, our proposed method employs an adaptive adjustment mechanism based on CSI variation, ensuring $\beta$ remains within this optimal range in real-time operation.

By appropriately setting this parameter, it is possible to adapt to different channel environments and maximize communication performance. The selection of $\beta$ is dynamically adjusted based on the variation in CSI.

Based on the transmission power allocation using the nonlinear allocation method, the received signal power $R_{\mathrm{rec},\mathrm{nonlinear}}$ at the receiving end, where signals transmitted from each antenna are combined, is expressed as follows.

$$\begin{array}{c}\hfill R_{\mathrm{rec},\mathrm{nonlinear}}={\left|\sum _{m=1}^M\sum _{n=1}^N\sqrt{P_{\mathrm{total}}·{\displaystyle \frac{g_{m,n}^{\beta }}{{\displaystyle \sum _{k=1}^M\sum _{l=1}^N}{g}_{k,l}^{\beta }}}}·h_{m,n}·e^{j{\theta }_{m,n}}\right|}^2.\end{array}$$

(25)

In this context, $h_{m,n}$ represents the channel gain between each antenna and the receiving end, indicating the attenuation of the signal between the transmitter and receiver. The term $e^{j{\theta }_{m,n}}$ denotes the phase shift component for beamforming. Phase adjustments are applied to ensure that the signals from each antenna constructively interfere in the desired direction.

In beamforming with an $M\times N$ planar array antenna, an appropriate phase shift is required based on the position of each antenna element. The phase shift for each element, ${\theta }_{m,n}$, is expressed as follows:

$$\begin{array}{c}\hfill {\theta }_{m,n}={\displaystyle \frac{2\pi d}{\lambda }}(msin\theta cos\phi +nsin\theta sin\phi ).\end{array}$$

(26)

In this context, d, $\lambda$, $\theta$, and $\phi$ represent the distance between antenna elements, the signal wavelength, the azimuth angle, and the zenith angle, respectively.

3.2.2. Adaptive Selection Method for $\beta$

The parameter $\beta$ in the nonlinear allocation method is not a fixed value. Instead, it is more effective when dynamically adjusted according to the channel environment. In this context, the adaptive adjustment of $\beta$ is explained using the CSI standard deviation method, which adjusts $\beta$ based on the variation in channel gains.

$$\begin{array}{c}\hfill \overline{g}={\displaystyle \frac{1}{MN}}\sum _{m=1}^M\sum _{n=1}^N{g}_{m,n}.\end{array}$$

(27)

$$\begin{array}{c}\hfill \sigma =\sqrt{{\displaystyle \frac{1}{MN}}\sum _{m=1}^M\sum _{n=1}^N{(g_{m,n}-\overline{g})}^2}.\end{array}$$

(28)

In this context, $\overline{g}$ represents the average gain, and $\sigma$ denotes the standard deviation of the gains.

The parameter $\beta$ is dynamically determined by the following equation.

$$\begin{array}{c}\hfill \beta ={\beta }_{\min }+k·{\displaystyle \frac{\sigma }{\overline{g}}}.\end{array}$$

(29)

In this context, ${\beta }_{\min }$ and k represent the minimum value of $\beta$ and the sensitivity adjustment coefficient for the standard deviation, respectively. The term ${\displaystyle \frac{\sigma }{\overline{g}}}$ is the normalized value of the CSI gain standard deviation by its mean, which indicates the variation in channel quality.

When the channel quality is uniform (${\displaystyle \frac{\sigma }{\overline{g}}}$ is small), $\beta$ is set to a lower value to achieve a more uniform power distribution. Conversely, when the variation in channel quality is large (${\displaystyle \frac{\sigma }{\overline{g}}}$ is large), $\beta$ is set to a higher value to concentrate power on better channels. The adjustment coefficient k is expressed using linear regression in the following form:

$$\begin{array}{c}\hfill k=w_1·\overline{g}+w_2·\sigma +w_0.\end{array}$$

(30)

In this context, $w_1$, $w_2$, and $w_0$ are coefficients determined through regression analysis [18]. Linear regression utilizes the Least Squares Method (LSM) to learn the optimal coefficients by minimizing the following loss function:

$$\begin{array}{c}\hfill L(w_1,w_2,w_0)={\displaystyle \frac{1}{N}}\sum _{i=0}^N{\left(k_i-\left(w_1·{\overline{g}}_i+w_2·{\sigma }_i+w_0\right)\right)}^2.\end{array}$$

(31)

In this context, N represents the number of samples, while ${\overline{g}}_i$, ${\sigma }_i$, and $k_i$ denote the average gain, standard deviation, and target k value for each sample, respectively.

Through this approach, an adaptive estimation method for the adjustment coefficient k based on the statistical properties of the CSI is proposed, enabling the optimization of the power allocation parameter $\beta$.

4. Simulation

In this section, we compare the performance of the conventional and the proposed methods. The simulation parameters were selected based on practical considerations for maritime communication. 16-QAM was chosen as the modulation scheme to balance spectral efficiency and robustness against channel impairments, providing a higher data rate while maintaining a manageable BER in moderate SNR conditions. The carrier frequency of 2.4 GHz was selected due to its common use in wireless communication, offering a good balance between propagation characteristics and available bandwidth. Forty-eight subcarriers were used in the OFDM system to ensure sufficient frequency diversity while maintaining computational efficiency. The Doppler frequency of 5 Hz reflects the relative motion between the tethered balloon and maritime users, capturing realistic channel variations caused by ship movement. These choices ensure that the simulation accurately represents practical nearshore communication conditions while effectively evaluating the proposed method.

4.1. Comparison Between Conventional Methods

The simulation parameters are listed in

Table 1. Simulation parameter settings.

Parameter	Value
Transmission Power	5 W
Number of Antenna Elements	16
Transmission Gain	−8 dB
Modulation Method	16QAM
Carrier Frequency	2.4 GHz
Number of Subcarriers	48
Doppler Frequency	5 Hz
Number of Multipaths	5

. This section compares the simulation results of the two conventional methods introduced earlier, in which the transmission power of the CSI-based proportional allocation method is allocated according to the CSI gain ratio. In this method, the CSI gain is adjusted and controlled to simulate both uniform and non-uniform CSI conditions and is compared with the equal power allocation method.

Figure 3 shows the performance comparison between the CSI-based proportional allocation method and the equal power allocation method under a uniform channel environment. As can be seen from the figure, when the channel environment is relatively stable and uniform, there is no significant difference in BER between the CSI-based proportional allocation method and the equal power allocation method at various distances. This is because, in a uniform channel, there is little difference in CSI gains between the antennas, and the effect of power allocation based on the gain in the CSI-based proportional allocation method is not fully realized. As a result, the performance of both methods is almost identical, and no significant difference in BER is observed.

Figure 4 shows the performance comparison between the CSI-based proportional allocation method and the equal power allocation method under a non-uniform channel environment. As clearly seen in the figure, when the channel environment is non-uniform, meaning that there are differences in gain between the channels, the performance of the equal power allocation method deteriorates compared to the uniform channel environment shown in Figure 3.

On the other hand, the CSI-based proportional allocation method distributes the transmission power proportionally according to the gain ratio of each channel, which allows it to maintain relatively good performance even in such non-uniform channel environments. Specifically, since the CSI-based proportional allocation method distributes power according to the characteristics of each channel, it leads to an improvement in SNR, and a tendency to suppress BER is observed. As a result, in non-uniform channel environments, the CSI-based proportional allocation method exhibits better overall performance compared to the equal power allocation method.

4.2. Proposed Method

4.2.1. CSI-Based Nonlinear Allocation Method

From the results in Section 4.1, it was confirmed that power allocation according to the gain ratio between channels is effective in improving system performance under non-uniform channel environments. However, there are limitations to the CSI-based proportional allocation method. Specifically, in the proportional allocation method, power is simply distributed proportionally based on the gain ratio of each channel. When channel conditions fluctuate significantly or when excessive power is allocated to a particular channel, it may disrupt the overall SNR balance. In such environments, relying solely on proportional allocation may not yield optimal performance. Therefore, a more flexible and sophisticated power allocation method is required.

In this section, simulations using the CSI-based nonlinear allocation method proposed in Section 3.2 are performed, and the results are compared with those from the equal power allocation method and CSI proportional allocation method. This nonlinear allocation method aims to achieve higher performance by nonlinearly adjusting the power based on the channel state, as shown in Equations (24) and (28). By optimizing the allocation according to the channel characteristics, the method seeks to provide better performance. The simulation results suggest that the nonlinear allocation method can significantly reduce BER, especially in non-uniform channel environments compared to the conventional equal power allocation and proportional allocation methods.

Figure 5 shows the relationship between distance and BER for the equal power allocation method, CSI-based proportional allocation method, and the proposed CSI-based nonlinear allocation method. The results indicate that with the equal power allocation method, BER deteriorates sharply as the distance increases, with a significant degradation in communication quality, particularly for long-distance communication. On the other hand, the CSI-based proportional allocation method provides some BER improvement as the distance increases, but variability in BER due to channel non-uniformity is still observed. The proposed CSI-based nonlinear allocation method, compared to the conventional methods, achieves a generally lower BER, with particularly notable improvements for long-distance communication. This is due to the optimal power allocation achieved by the nonlinear distribution, where power is appropriately allocated to antennas with higher channel gains.

Even within the same proposed method, increasing the distribution concentration factor $\beta$ from 1.4 to 1.8 improved the concentration of power and resulted in a noticeable improvement in BER. However, when $\beta$ was further increased from 1.8 to 2.2, power became excessively concentrated on specific channels, leading to insufficient power distribution to other channels. As a result, the BER performance worsened again, returning to a level similar to that of $\beta =1.4$. This demonstrates that the distribution concentration factor $\beta$ has a significant impact on the performance of the proposed method. This trend is further detailed in the following Figure 6.

Figure 6 shows the relationship between the distribution concentration factor $\beta$ and BER at a propagation distance of 2 km. The simulation results indicate that when the distribution concentration factor is small ($\beta =1$), power is almost evenly allocated, which causes power to be spread to antennas with lower channel gains, resulting in a higher BER. On the other hand, increasing the distribution concentration factor to $\beta =1.8$ strengthens the power concentration on high-gain antennas, resulting in the minimum BER.

However, when the distribution concentration factor becomes excessively high, power becomes overly concentrated on a few antennas, disrupting the overall balance and causing BER to increase again. Notably, the minimum BER is achieved around $\beta =1.8$, suggesting that the proper selection of the distribution concentration factor is crucial for optimizing communication performance.

Additionally, the optimal distribution concentration factor calculated using the proposed method is $\beta =1.873$, which closely matches the optimal point shown in Figure 6. This result demonstrates that the proposed method can appropriately determine the optimal distribution concentration factor based on CSI, confirming its effectiveness. In particular, in dynamic environments, adapting the distribution concentration factor according to channel state variations is expected to maintain communication quality stability while maximizing energy efficiency.

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. Simulation parameter setting.

Parameter	Value
Transmission Power	5 W
Number of Antenna Elements	16
Transmission Gain	−8 dB
Modulation Method	16QAM
Carrier Frequency	2.4 GHz
Number of Subcarriers	48
Doppler Frequency	5 Hz
Number of Multipaths	5
Time Step	1 s
BER Threshold	$0.1\%$
Power Adjustment Step	0.5 W

.

Specifically, we assume that the transmitter and receiver do not displace in the y-axis direction and that $y_s\left(t\right)=0$. In addition, the balloon performs Brownian motion in the range of $[-50\mathrm{m},50\mathrm{m}]$ 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 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 effectiveness in reducing system total power consumption while maintaining performance in dynamically changing channel environments.

5. Conclusions

This study aims to improve communication quality and energy efficiency in wireless communication systems under dynamic channel environments. Traditional methods, such as equal power allocation and CSI-based proportional allocation, often struggle to optimize power distribution under uneven or rapidly changing channel conditions. These limitations lead to decreased communication stability and increased unnecessary energy consumption, constraining overall communication performance. To address this issue, this paper proposes a CSI-based nonlinear power allocation method. By dynamically adjusting power distribution according to channel conditions, the proposed method adapts to channel variations, ensuring more stable communication while enhancing throughput and energy efficiency. Experimental results demonstrate that, compared to conventional methods, the proposed approach significantly improves communication performance in dynamic environments and effectively reduces overall energy consumption. However, this study has certain limitations. Future research directions include verifying the applicability of the proposed method under more diverse mobility patterns and complex channel conditions, as well as improving its implementation efficiency in real-time environments. The findings of this study contribute to the advancement of next-generation wireless communication technologies and are expected to be further refined and enhanced in the future.