UAV-BS Site Planning Based on Circular Coverage Strategy

Abstract

Future mobile communication technology will be used to build an integrated global coverage network. Unmanned aerial vehicles (UAVs) are the first choice for low-altitude networks due to their low cost, flexibility, and ease of operation. The characteristics of UAVs also bring new challenges to communication networks, such as short flight time, complex networking, and unstable communication quality. Therefore, it has become an urgent problem to reasonably plan the location of UAV Base Stations (UAV-BSs), reduce communication power consumption, optimize network performance, and build an efficient and stable UAV communication network (UAVCN). The traditional strategy only pays attention to the signal coverage, and ignores the influence of system transmission power on the network, which reduces the performance of the communication system. In this study, a circular coverage power optimization strategy (CCPO) based on system transmit power is proposed. The mathematical model of the circular coverage problem is used to describe the full coverage process of the UAV base station to ground users, and the deployment optimization is carried out with the goal of minimizing system transmit power, so as to obtain an efficient and reliable site planning scheme. In this paper, the binomial power function is used to continuously fit the discrete solution of the circle covering problem, and the circle covering power optimization formula is rearranged. By analyzing the convexity of the objective function under the circular coverage model, the convex optimization theory is used to solve the objective problem, and the optimal deployment number of UAVs and site planning scheme under the circular coverage power optimization strategy are given. Simulation verifies the superiority of the proposed method. Compared with the traditional hexagon strategy and the minimum power loss strategy, the circular coverage power optimization station location planning strategy can save 14.75% and 6.52% of power resources, providing a valuable reference for the design and optimization of UAV communication systems. It provides a promising solution for further improving the performance and efficiency of UAVCNs.

1. Introduction

With the development of Mobile Communication Technology from its inception to 5th Generation Mobile Communication Technology (5G), its communication characteristics have changed greatly. The first generation of communication could only provide phone service, and the quality of the communication signal was poor. The data transmission rate was improved from the era of text communication to the era of MMS. It then entered the era of video. 5G opened the door for the integration of communication technology and Internet technology; thus, there have been a variety of new wireless access technologies and evolution technologies. However, for people’s increasingly rich demands, there are still plenty of deficiencies.inally, 6th Generation Mobile Communication Technology (6G) has become a key research and development project in many countries [1,2,3].

At present, most of the base stations in 5G networks are deployed on land. This static and single-dimensional communication network may not meet the communication needs of users in the face of special communication scenarios or sudden network paralysis. The 6G communication network will be an unprecedented ultra-flexible and dense network with full dimension and full coverage. It will combine the traditional ground local area network, air network, satellite constellation network and underwater network to realize the global coverage and integration of air, ground, and sea. Especially with the increase in the types and numbers of aerial vehicles with strong mobility and easy deployment, such as helicopters, high-altitude flying boats, and unmanned aerial vehicle (UAVs), the establishment of low-altitude networks with aerial flight base stations as communication nodes to supplement the static network architecture will play a more important role.

Compared with other communication networks, the UAV Communication Network (UAVCN) has the advantages of convenience, controllability, and flexibility, which can be used for emergency communication scenarios such as disaster detection and rapid rescue, and can also provide effective communication services for high-density business scenarios such as important conferences and large-scale events. At the same time, UAV technology has also developed rapidly in recent years, with great improvement in manufacturing cost, operational controllability, and body size, which expands the application space of UAV communication in the public and civil field; it is now widely used in smart city traffic management, water conservancy project management, battlefield military information reconnaissance, agricultural and forestry resource management, etc. [4]. Generally, UAVs can be divided into two categories: fixed-wing UAVs and rotorcraft UAVs based on wing configuration [5,6]. Rotorcraft UAVs have the advantages of fast takeoff speed, flexible landing, and the ability to hover at any position in the air. However, they also have the problems of low flight altitude, limited maximum flight speed, small carrying capacity, and short flight distance. Fixed-wing UAVs have a long wingspan and large models, as well as superior flight performance and payload. The disadvantage is that they cannot take off and land vertically, and can only hover but not in the air. In the actual application process, different UAV types are used in the face of different scene requirements.

Energy consumption is an important factor affecting the results of site planning. The energy consumption of traditional base stations includes two parts: communication power consumption and cooling system power consumption, among which the communication power consumption, such as radio frequency and baseband processing, is the main consumer. Therefore, greater attention is paid to the optimization of communication energy consumption during the site planning process. Addressing these issues in UAV Base Station (UAV-BS) site planning, this paper proposes a solution based on UAV communication power consumption and employs a geometric method to tackle the problem. This ensures full coverage of the target area by UAV-BS while minimizing coverage redundancy. Subsequently, with the goal of minimizing system transmission power, the number of UAV-BS deployments and the site planning are optimized. This study integrates a multi-UAV coverage model with the Coverage and Connectivity Problem (CCP) to guarantee that any point can complete communication. On this basis, a function to minimize system transmission power is constructed, and site planning strategies for different target areas under full coverage are provided. The method uses a circular coverage strategy to establish a coverage model, which can maximize the reduction in overlap in UAV coverage areas and enhance deployment efficiency. In future UAV communication scenarios, this strategy can provide a reference for the planning and deployment of UAV-BS and also support the development of UAV communication technology.

2. Background and Related Work

The development of UAV communication is inseparable from research on UAV communication system models and their performance. In UAVCNs, the UAV can be used as an air user to receive ground information, and can also be equipped with communication equipment as a wireless relay or air base station to expand network coverage. Relevant research is shown in

Table 1. Research status of UAV communication.

Role in UAVCN	Effect	Application Scenario	Research Progress
Air subscriber	Directly connected to the ground network to communicate with other users and accessible worldwide; operators can remotely direct UAV behavior, thereby reducing human resource investment and improving network efficiency.	Emergency communications, agricultural environmental protection, logistics, urban security, construction engineering, military reconnaissance	[9,10,11,12]
Wireless relay	The UAV acts as an intermediate node to transmit communication signals from the sender to the receiver to expand the range and improve the quality of communication.	Emergency communications, battlefield communications, traffic monitoring, large public events, urban peak hours, crowded places	[13]
Aerial base station	It undertakes the communication function of the space-based network layer and provides communication services to ground users and air users. Interconnection with satellite constellations and sea-based networks to achieve global coverage is an important link in the future network.	Emergency communication, earthquake mitigation, field exploration, Marine QoS guarantee, logistics distribution, ground network supplement	[14,15,16,17,18,19,20,21,22,23,24,25]

. As aerial users, UAVs are used in the Internet of Things on a large scale to collect sensor data from ground equipment [7]. UAVs equipped with base stations as relays are used in ultra-dense scenarios, which can strengthen the signal of mobile users and provide long-distance communication. UAV-BSs are more used to assist the ground network in unloading data volume and emergency communication direction [8]. UAV communication is the first choice for low-altitude network composition due to its convenience and low environmental impact.

2.1. UAV Air Subscriber

The multi-rotor “Bee” UAV developed at the Beijing Institute of Technology is used for agricultural plant protection, urban planning, mine surveying, and other work [26]. In the field of logistics, UAVs are used for tasks such as express delivery and material transportation [9]. In the field of environmental protection, UAVs are used for tasks such as environmental monitoring and waste disposal. In the security field, UAVs can be used for patrolling, surveillance, and other tasks. The “Rainbow” series UAV, jointly developed by the Chinese Air Force, Aerospace Science and Technology Corporation, and other units, can perform reconnaissance, listening, intelligence collection, communication relay, electronic jamming, and other tasks in the air [10]. In the field of construction engineering, UAVs can perform inspection, measurement, and monitoring of buildings and infrastructure. For example, they can perform exterior wall inspection at high altitudes, or perform on-site monitoring and building surveying on construction sites [11]. In the field of emergency communication, UAVs can be used for search and rescue, fire monitoring, etc. [12]. UAVs can enter dangerous areas to search and monitor them, and provide real-time data and intelligence to rescue workers; for example, the Philo UAV developed by the Italian National Research Council can provide real-time image and video data at the scene of a fire to assist firefighters in fighting the blaze.

2.2. UAV Wireless Relay

As a communication relay, a UAV can transmit communication signals from the sender to the receiver to expand the communication range and improve communication quality [13]. In disaster response missions, UAVs can relay communication signals to first responders and rescue organizations. This can speed up response times for rescue operations while providing real-time data and information to support decision making. In the military domain, UAVs can be used as relay stations for battlefield communications. UAVs can transmit data, video, and images to support military decision-making and combat operations. In urban traffic monitoring, UAVs can be used as relay stations to transmit videos and images to the monitoring center. This can strengthen the ability of urban traffic monitoring and improve urban safety. With the development of UAV technology and the continuous iteration of wireless devices, UAV relay is an effective means to expand the communication coverage, improve the Quality of Service (QoS) of communication, and meet the communication needs of users.

2.3. UAV Aerial Base Station

Due to the good flexibility and adaptability of UAV-BSs, they can be strategically deployed to any location to provide communication services. After completing their service, UAV-BSs can quickly be repositioned to the next mission point. Moreover, UAV formations can be dynamically expanded to improve coverage efficiency, making UAV-BSs an essential component of modern communication networks. Most scholarly research on UAV-BSs focuses on three aspects: UAV-BS flight path planning, UAV-BS autonomous control, and UAV-BS network topology.

2.3.1. Research on UAV-BS Flight Path Planning

Jin et al. proposed a low-profile dual-frequency directional antenna for UAV applications [14]. The antenna has an octahedral structure, dual bandwidth, and directional radiation characteristics. By designing a suitable feed structure and adjusting the octahedral structure, the dual-frequency bandwidth of the antenna can be realized, and high gain and directional radiation can be achieved in the horizontal and vertical polarization directions. Maeng et al. proposed a linear precoding design scheme to achieve the reliable transmission of data and artificial noise [15]. At the same time, the proposed scheme was applied to fingerprint embedding authentication framework to minimize the probability of eavesdropping detecting authentication marks. Johannsen et al. proposed a channel model that meets the requirements of MIMO communication and can estimate the direction of arrival [16]. In order to achieve an approximate omnidirectional radiation pattern, a description based on a manifold matrix is used to optimize UAVs. Xiao et al. gave an overview of relevant technologies in the field of UAV millimeter wave communication, and predicted the future research direction of millimeter wave beamforming technology in the field of UAVCNs [17].

2.3.2. Research on UAV-BS Autonomous Control

Zeng et al., aiming at the scenario in which UAVs act as aerial base stations to provide wireless communication services, studied a scheme for the joint optimization of user scheduling, multi-resource coordination, and UAV travel path, so as to meet the requirements of user experience quality while improving energy efficiency as much as possible [18]. On this basis, an iterative optimization algorithm based on the Dinkelbach algorithm and block coordinate descent was proposed, and the problem was divided into four sub-problems for gradual optimization. Yu et al. proposed a UAV-enabled mobile edge computing system that ensures interaction between UAVs, Internet devices, and edge clouds. At the same time, they use successive convex approximations to jointly optimize UAV position, trajectory, and computational resources to provide the best service [19]. Nguyen et al. proposed a technique based on deep reinforcement learning to find the best trajectory and throughput in a specific coverage area. After training, the UAV is able to autonomously collect all data from the user node at a significant summation rate while minimizing the associated resources used [20]. Guo et al. proposed a new general UAV trajectory and communication co-design framework, which has a flexible number of node optimization variables to reduce the computational complexity of path planning for long period/distance UAV flight [21].

2.3.3. Research on UAV-BS Network Topology

Dou et al. proposed an adaptive dynamic programming method to design a UAV formation controller. By combining the event triggering mechanism with a neural network, the calculation and action amount of the multi-UAV system were reduced, thus reducing the communication overhead of the system. Meanwhile, combining the control accuracy of the continuous controller, the UAV can be effectively and accurately controlled [22]. Sergeev et al. studied the automatic control of UAV landing in bad weather. By using the principle of “flexible” motion trajectory and the method of the dynamic inverse problem, they studied the control algorithm of the UAV terminal landing maneuver and controlled the target point [23]. Zhang et al. proposed a sliding mode active anti-jamming control scheme that utilizes a differential tracker and state extender controller design process and compensates the total disturbance of the system in real time in the controller, thereby improving the robustness and anti-jamming ability of the system [24]. Hu et al. proposed a UAV cooperative positioning method based on the flight information of UAVs in different periods. By constructing a different number of beacon nodes together, the number of unknown variables to be solved for UAVs is reduced, and the accuracy and speed of the positioning optimization algorithm are effectively improved [25].

The above research has not only continuously broken through the technical bottleneck, but also emphasizes the important role of UAV-BSs in the future communication network. Therefore, this paper also takes UAV-BSs as its research object, analyzes its problems in site planning and auxiliary communication, and thus contributes to making some progress.

3. Theory

Convex optimization theory has a wide range of applications in the field of communications and can be used to improve the reliability, performance, and efficiency of communication systems.

3.1. Basic Concepts

(1) Convex Set: If for any two points $x_1,x_2$ in the set S and for any parameter $t\in [0,1]$, Equation (1) is satisfied, then S is called a convex set.

$$t{x}_1+(1-t)x_2\in S.$$

(1)

(2) Convex Function: If the domain of the function $f\left(x\right)$ is a convex set, and for any two points $x_1,x_2$ and any parameter $t\in [0,1]$ that lies between them, Equation (2) is satisfied, then $f\left(x\right)$ is called a convex function.

$$f(t{x}_1+(1-t)x_2)\le tf\left(x_1\right)+(1-t)f\left(x_2\right).$$

(2)

(3) Gradient: The rate of change of a scalar function at a particular point. It is a vector, where each component is the partial derivative of the function in the corresponding coordinate direction. The function value rises rapidly in the direction of the gradient; hence, gradient information is often used to guide the search direction and step size in optimization.

For a univariate function $f\left(x\right)$, its gradient is a scalar, denoted as $f^{\prime }\left(x\right)$.

For a multivariate function $f\left(\mathbf{x}\right)$, its gradient is a vector, that is, the following:

$$\nabla f\left(\mathbf{x}\right)=\left({\displaystyle \frac{\partial f}{\partial x_1}}{\displaystyle \frac{\partial f}{\partial x_2}}⋮{\displaystyle \frac{\partial f}{\partial x_n}}\right),$$

(3)

where ${\displaystyle \frac{\partial f}{\partial x_i}}$ represents the partial derivative of the function f with respect to the variable $x_i$.

(4) Hessian Matrix: It describes the second-order partial derivative information of a scalar function and is a second-order tensor. It describes the local curvature and shape of the function at a certain point. For an n-dimensional function $f\left(\mathbf{x}\right)$, its Hessian matrix $\mathbf{H}\left(\mathbf{x}\right)$ is an $n\times n$ matrix, where the element in the i-th row and j-th column is ${\displaystyle \frac{{\partial }^{2}f\left(\mathbf{x}\right)}{\partial x_i\partial x_j}}$. The determinant and eigenvalues of the Hessian matrix can be used to determine the nature of the local extremum and inflection points of the function, such as whether it is a local minimum or a saddle point. If $\mathbf{H}\left(\mathbf{x}\right)$ is positive definite, then the function $f\left(\mathbf{x}\right)$ has a local minimum at $\mathbf{x}$. In optimization, the Hessian matrix is also used to guide the search direction and step size; for example, Newton’s method is an optimization algorithm that utilizes the Hessian matrix information.

3.2. Optimization Problem

The formal representation of an optimization problem typically consists of two parts: the objective function and the constraints. The objective function is the function that needs to be optimized, while the constraints are the limiting conditions on the variables. The general form is as follows:

Objective function: ${min}_{x}f\left(x\right)$

Subject to constraints:

$$\begin{array}{cc}\hfill & g_i\left(x\right)\le 0,i=1,\dots ,m\hfill \\ \hfill & h_j\left(x\right)=0,j=1,\dots ,p,\hfill \end{array}$$

where x is the variable that needs to be optimized, and $f\left(x\right)$ is the objective function that needs to be minimized. $g_i\left(x\right)\le 0$ are the inequality constraints, and $h_j\left(x\right)=0$ are the equality constraints. m and p are the number of inequality and equality constraints, respectively. The solution to the optimization problem is the value of the variable that makes the objective function achieve its minimum value.

3.3. Optimality Conditions

(1) Lagrange Dual Problem: This involves incorporating the constraints into the objective function of the original problem, allowing the problem to be solved by minimizing a new function. Specifically, suppose we want to minimize the objective function $f\left(x\right)$, subject to some inequality constraints $g\left(x\right)\le 0$ and equality constraints $h\left(x\right)=0$. Then, we can introduce the following Lagrangian function:

$$L(x,\lambda ,\nu )=f\left(x\right)+\sum _{i=1}^m{\lambda }_i{g}_i\left(x\right)+\sum _{j=1}^p{\nu }_j{h}_j\left(x\right),$$

(4)

where $\lambda$ and $\upsilon$ are the Lagrange multipliers associated with the inequality and equality constraints, respectively.

Among them, ${\lambda }_i$ and ${\nu }_j$ are the Lagrange multipliers. Subsequently, the original problem can be solved by minimizing the Lagrangian function, that is, the following:

$$\underset{x}{min}\underset{\lambda ,\nu :{\lambda }_i\ge 0}{max}L(x,\lambda ,\nu ),$$

(5)

The solution to this problem is known as the Lagrangian dual problem of the original problem. If both the original problem and the dual problem have solutions and their optimal values are equal, then the problem is said to satisfy strong duality.

(2) Saddle Point Theorem: Let $L(x,\lambda ,\nu )$ be the Lagrangian function, and suppose $x^{*}\in {\mathbb{R}}^n$, ${\lambda }^{*}\in {\mathbb{R}}^m$, ${\lambda }^{*}\ge 0$, and ${\nu }^{*}\in {\mathbb{R}}^p$. If for every $x\in {\mathbb{R}}^n$, $\lambda \in {\mathbb{R}}^m$, $\lambda \ge 0$, and $\nu \in {\mathbb{R}}^p$, the conditions

$$L(x,\lambda ,\nu )\le L(x^{*},{\lambda }^{*},{\nu }^{*})\le L(x,{\lambda }^{*},{\nu }^{*}),$$

(6)

are satisfied, it is said that $(x^{*},{\lambda }^{*},{\nu }^{*})$ is a saddle point of $L(x,\lambda ,\nu )$.

Assume $(x^{*},{\lambda }^{*},{\nu }^{*})$ is a saddle point of the Lagrangian function $L(x,\lambda ,\nu )$ for the original problem. Then, $x^{*}$ is the optimal solution of the original problem, and $({\lambda }^{*},{\nu }^{*})$ is the optimal solution of its dual problem. Conversely, suppose $f\left(x\right)$ is a convex function, the inequality constraints are convex functions, and the equality constraints are all linear functions—i.e., $h\left(x\right)=Ax-b$, where A is a full-rank coefficient matrix. Suppose there exists $\widehat{x}$ such that $g\left(\widehat{x}\right)>0$ and $h\left(\widehat{x}\right)=0$. If x is the optimal solution of the original problem, then there exist $({\lambda }^{*},{\nu }^{*})$ with ${\lambda }^{*}\ge 0$ such that $(x^{*},{\lambda }^{*},{\nu }^{*})$ is a saddle point of the Lagrangian function of the original problem.

The Saddle Point Theorem provides a sufficient condition for the optimal solution and, in the latter part, illustrates a necessary condition for convex programming. It is important to note that the existence of an optimal solution for the original problem does not imply that the corresponding Lagrangian function necessarily has a saddle point. That is, the existence of a saddle point is not a necessary condition for the original problem to have an optimal solution.

(3) KKT Conditions: If an optimal solution of a convex optimization problem satisfies certain constraints, then this optimal solution must also satisfy the following requirements:

• The inequality constraints of the original problem must be satisfied: $g_i\left(x^{*}\right)\le 0$.
• The equality constraints of the original problem must be satisfied: $h_j\left(x^{*}\right)=0$,.
• The Lagrange multipliers must be non-negative: ${\lambda }_i\ge 0$.
• KKT Conditions: ${\lambda }_i{g}_i\left(x^{*}\right)=0$, meaning that the corresponding Lagrange multipliers are non-zero only when the constraints are active.

The conditions A, B, C, and D are necessary but not sufficient conditions for determining whether a solution is optimal. In practice, KKT conditions can be used to solve optimization problems with constraints and to verify whether the solutions satisfy the optimality conditions.

3.4. Optimization Algorithms

(1) Interior Point Method: The interior point method transforms a linear programming problem into a nonlinear programming problem with a convex objective function. The constraints of this problem include the constraints of the original linear programming problem and an additional “interior point constraint”, which restricts the solution set to a specific convex set.

The interior point method solves this nonlinear programming problem iteratively. Each iteration solves an “interior point problem”, whose solution is close to the solution of the previous iteration. The closer the solution of the interior point problem is to the optimal solution, the closer the interior point method is to the optimal solution of the linear programming problem. Suppose the linear programming problem is as follows:

$$\begin{array}{cc}\hfill \underset{x}{min}& c^{T}x\hfill \\ \hfill \mathrm{s}.\mathrm{t}.& Ax\le b,\hfill \end{array}$$

(7)

Let $x\in {\mathbb{R}}^n$ be the decision variable, $c\in {\mathbb{R}}^n$ be the coefficients of the objective function, $A\in {\mathbb{R}}^{m\times n}$ be the coefficient matrix of dimensions $m\times n$, and $b\in {\mathbb{R}}^m$ be the vector on the right-hand side of the constraints.

The iterative formula for the interior point method is as follows:

$$\begin{array}{cc}\hfill \underset{x}{min}& c^{T}x-\mu \sum _{i=1}^{m}ln(b_i-a_i^{T}x)\hfill \\ \hfill \mathrm{s}.\mathrm{t}.& Ax\le b,\hfill \end{array}$$

(8)

Here, $\mu$ is a parameter greater than zero, known as the “central path parameter”. In each iteration, the value of $\mu$ is gradually decreased, causing the interior point to approach the feasible region of the linear programming problem. As $\mu$ approaches zero, the solution of the interior point method gradually converges to the optimal solution of the linear programming problem.

(2) Gradient Descent Method: The gradient descent method minimizes the value of the objective function by continuously performing gradient iterations. Specifically, the algorithm calculates the gradient of the objective function at the current point and moves the current point a certain step length in the opposite direction of the gradient, causing the objective function to gradually approach its optimal value. The general formula for the gradient descent method is as follows:

$${\theta }_{i+1}={\theta }_i-\alpha \nabla J\left({\theta }_i\right),$$

(9)

Here, ${\theta }_i$ represents the parameter value at the i-th iteration, $\alpha$ is the learning rate, and $\nabla J\left({\theta }_i\right)$ denotes the gradient of the loss function at ${\theta }_i$.

The gradient descent method can also be divided into two forms: batch gradient descent and stochastic gradient descent. Batch gradient descent calculates the gradient using all training data in each iteration, which is slower but yields more accurate results. Stochastic gradient descent, on the other hand, randomly selects sample data to calculate the gradient during iterations, consuming fewer computational resources. However, the issue is that the optimal result may not be a global optimum but a local one.

The convergence rate and final outcome of the gradient descent method largely depend on the choice of step size. If the step size is too large, it may lead to the algorithm failing to converge or converging to an unstable result. If the step size is too small, the convergence speed of the algorithm will slow down. Therefore, it is often necessary to choose an appropriate step size strategy based on the actual problem, such as a fixed step size or a dynamic step size.

(3) Newton’s Method: Newton’s method is an iterative algorithm used to solve unconstrained optimization problems. Its basic idea is to approximate the objective function using a second-order Taylor expansion and then solve the equation where the first derivative is zero to obtain the direction of descent. Specifically, the iterative formula for Newton’s method is as follows:

$$x_{k+1}=x_k-{\displaystyle \frac{f^{\prime }\left(x_k\right)}{f^{″}\left(x_k\right)}},$$

(10)

Here, $f\left(x\right)$ is the objective function to be optimized, and $f^{\prime }\left(x\right)$ and $f^{″}\left(x\right)$ are the first and second derivatives of $f\left(x\right)$, respectively. $x_k$ is the solution at the k-th iteration, and $x_{k+1}$ is the solution at the next iteration.

Compared to first-order optimization algorithms such as gradient descent, Newton’s method can converge more quickly. However, it requires the computation of the first and second derivatives of the variables during the iterative process, which consumes a significant amount of computational resources. Therefore, in practical applications, it is necessary to choose the appropriate optimization algorithm based on the specific characteristics of the problem.

(4) Subgradient Method: This algorithm is an iterative method used to solve non-smooth convex optimization problems and is suitable for situations where the objective function is convex but not smooth. It is an extension of the gradient descent method for non-smooth cases.

For a non-differentiable convex function $f\left(x\right)$, at some points x, $f\left(x\right)$ may not have a gradient, but it has a subgradient. A subgradient is a lower bound on the subdifferentials in any direction at that point. Therefore, the subgradient method uses the subgradient in place of the gradient to optimize in the direction of function decrease.

The iterative formula for the subgradient method is as follows:

$$x^{k+1}=x^k-{\alpha }_k{g}_k,$$

(11)

Here, $x^{*}$ is the approximate solution at the k-th iteration, ${\alpha }_k$ is the step size, and $g_k$ is the subgradient of $f\left(x\right)$ at $x^{*}$. When $f\left(x\right)$ is differentiable, the subgradient method degenerates into the gradient descent method.

The subgradient method has convergence properties, but it converges slowly because it only uses subgradient information. Therefore, to accelerate the convergence rate, other optimization algorithms such as the quasi-Newton method can be employed.

4. Methodology

This study focuses on UAVCN communication energy consumption and the full coverage of users in the target area. The circle coverage strategy is used for modeling, and the proportional relationship between the small circle radius and the number of small circle radii is fitted by a power function under the given large circle radius. The goal is to minimize power loss under the condition of ensuring full coverage. Newton iteration is used to give the number of UAV-BS deployed to meet the target and the optimal coverage radius to determine the optimal UAV-BS site planning strategy.

4.1. UAV-BS Full Coverage Network Model

Considering the site planning of an aerial base station in a target area with radius R, this paper adopts a UAV equipped with aerial base stations to deploy over the target area to achieve full coverage of ground users in the target area, as shown in Figure 1. The flight altitude is H, and the UAV-BS forms a forward link with ground users. The Aircraft Control Center (ACC) forms a return link. Considering computing power and cost, it is assumed that a maximum of N UAVs can be accommodated in ACC.

4.2. Air-to-Ground Channel Model

Assume that the UAV-BS is equipped with an omnidirectional antenna for communication. Considering that the communication process between the UAV-BS and ground users is subject to multipath propagation, signal fading, and other effects, the UAV-BS ground communication link includes Non-Line-of-Sight (NLoS) links. The signal propagation in free space follows the shadow fading model. The channel model between the UAV-BS and ground users can be represented as follows:

$$PL(d,f)=P{L}_{FS}\left(f\right)+10\alpha lg\left(d\right)+\xi ,$$

(12)

where f is the carrier frequency, c is the speed of light, d is the signal transmission distance, $\alpha$ is the attenuation exponent with $\alpha \ge 2$, and $\xi$ is the shadowing component, which follows a normal distribution with a mean of 0 and variance ${\sigma }^2$. The first term of Equation (12), related to f, can be calculated using the Friis transmission equation at a reference distance of 1 meter in free space, given by $P{L}_{FS}\left(f\right)=20{log}_{10}\left({\displaystyle \frac{4\pi f}{c}}\right)$. The second term provides the logarithmic relationship between d and path loss, where $d=\sqrt{r^2+H^2}$, with r being the horizontal distance between the projection of the UAV-BS on the ground and the target user.

4.3. UAV-BS Full Coverage Network Energy Consumption Model

In the UAV-BS network, there are two types of downlink channels: the communication link between the central UAV-BS and other UAV-BSs, and the communication link between the UAV-BS and ground users. It is assumed that the communication links between the central UAV-BS and other UAV-BSs, as well as between the UAV-BS and users, all utilize Orthogonal Frequency-Division Multiple Access (OFDMA) technology for channel multiplexing to avoid severe co-channel interference. Considering the need for site planning for n UAV-BSs, the total communication energy consumption of the system is the sum of the total transmission power of the UAV-BSs to the ground and the communication power between UAV-BSs, that is, the following:

$$P_s(n,d)=\sum _{i=1}^n{P}_{\mathrm{g},i}\left(d\right)+\sum _{i=1}^{n-1}{P}_{u,i},$$

(13)

where $P_{g,i}\left(d\right)$ represents the transmission power required by the i-th UAV-BS when n UAV-BSs provide full coverage to ground users. $P_{u,i}$ is the channel allocation power between the central UAV-BS and the i-th UAV-BS. It is assumed that all UAV-BSs are identical rotary-wing UAVs, equipped with the same type of base station, and have the same coverage capability. The signal propagation distance is d, and the transmission power required is $P_g\left(d\right)$. If the Signal-to-Noise Ratio (SNR) at any location within the target area is greater than the SNR threshold ${\gamma }_{th}$, it is considered that the UAV deployment can meet the user requirements and achieve full coverage. The SNR for ground users is as follows:

$$\gamma =P_g\left(d\right)-P_{\mathrm{noise}}-PL(d,f),$$

(14)

where $P_{\mathrm{noise}}$ is the noise power. The minimum transmission power required for each UAV to serve ground users under full coverage is $P_g\left(d\right)$.

$$P_g\left(d_n\right)={10}^{{\displaystyle \frac{\gamma +P_{\mathrm{noise}}+PL\left(d_n\right)}{10}}},0<P_g\left(d_n\right)<P_{max},$$

(15)

where $d_n$ is the maximum distance over which each UAV can connect when n UAVs are deployed. By combining Equations (12), (13), and (15), the transmission power of the UAV communication system required to ensure full coverage is the following:

$$P_s=n{P}_g\left(d_n\right)+(n-1)P_u.$$

(16)

The objective is to ensure full coverage of the network while minimizing the power consumption of the UAV communication system. This problem can be described mathematically as follows:

P1:

$$\underset{n}{min}{P}_s=n{P}_g\left(\sqrt{r{\left(n\right)}^2+H^2}\right)+(n-1)P_u$$

subject to:

$$\begin{array}{cc}\hfill \mathrm{C}1:& 0<P_g<P_{max};\hfill \\ \hfill \mathrm{C}2:& S_c\left(n\right)-S\ge 0;\hfill \\ \hfill \mathrm{C}3:& n\le N;\hfill \\ \hfill \mathrm{C}4:& n\in {\mathbb{N}}^{+};\hfill \end{array}$$

where $r\left(n\right)$ represents the maximum coverage radius of each base station when n UAV-BSs are deployed. $P_{max}$ denotes the maximum transmission power that a UAV-BS can use when communicating with ground users. $S_c\left(n\right)$ is the area that can be covered by the planned deployment of n UAV-BSs, and S represents the total area of the target region. Constraints $C3$ and $C4$ ensure that under the condition where the transmission power of each UAV-BS is limited, deploying fewer than N UAV-BSs can still achieve full coverage of the target area.

4.4. Circle Coverage Power Optimization Strategy

To effectively solve the problem P1, this study employs a site planning strategy based on the Cooperative Coverage and Power Optimization (CCPO) approach, taking into account the number of deployed UAV-BSs and the system transmission power. A power function is utilized to fit the relationship between the coverage radius and the number of small circles. To minimize the system’s communication power consumption, an optimal UAV-BS site planning strategy is determined through Newton’s iteration method, establishing the optimal number of UAV-BSs and coverage radius.

Equation (16) shows that the system transmit power is affected by the SNR threshold, the communication distance between UAV-BSs and users, and the number of UAV-BSs. Due to unknown user location information, UAV-BS site planning is a challenge in the case of power constraints. The ground radiation coverage area of a UAV-BS equipped with an omnidirectional antenna can be modeled as a conical area, and its ground projection is positive circle.

In the above modeling process, the covering problem can be regarded as a kind of geometric problem, similar to the disk placement problem in the position problem [27]. Disk placement problems are divided into two categories: one is the Circle Packing Problem (CPP), such as shown in Figure 2a, where a container is packed with a number of circles, each with a maximum radius—these smaller circles do not need to be exactly the same. The other is CCP, which is the question of how much the area of a container can be completely covered by a given circle. The shape of the container can be a simple circle, square, rectangle, or a combination of lines and arcs [28]. Figure 2b shows the optimal placement of 5 equal circles within a larger circle.

Assume the radius of the large circle is 1. The radius of the small circles in the CCP and the number of circles required to completely cover the large circle satisfy

Table 2. Existing solutions for CCP problem.

Number of Small Circles (n)	Radius of Small Circle (${\mathit{r}}_{\mathbf{0}}\mathbf{\left(}\mathit{n}\mathbf{\right)}$)	Number of Small Circles (n)	Radius of Small Circle (${\mathit{r}}_{\mathbf{0}}\mathbf{\left(}\mathit{n}\mathbf{\right)}$)
$n=1,2$	1	$n=14$	0.3318
$n=3$	$\sqrt{3}/2$	$n=15$	0.3182
$n=4$	$\sqrt{2}/2$	$n=16$	0.3083
$n=5$	0.61	$n=17$	0.2986
$n=6$	0.556	$n=18$	0.2902
$n=7$	0.5	$n=19$	0.2774
$n=8$	0.437	$n=20$	0.2709
$n=9$	0.422	$n=21$	0.2629
$n=10$	0.398	$n=22$	0.2533
$n=11$	0.38	$n=23$	0.2500
$n=12$	0.361	$n=24$	0.2453
$n=13$	0.3467	$n=25$	0.2392

[28]. It can be seen from the table that the radius $r_0\left(n\right)$ of each circle decreases as the number of circles n increases. There is a specific placement strategy for the small circles for each value of n. It is challenging in mathematics to find a generally optimal placement strategy for any n, which means that a specific coverage strategy needs to be provided for each value of n.

In the full coverage scenario, the coverage area of each UAV-BS is considered a small circle, and the target area is the large circle that needs to be covered without distinction. Since multiple UAVs of the same type are used, the coverage range of each UAV is indistinguishable. Therefore, the UAV-BS site planning problem in this scenario can be solved using the CCP geometric model. Based on the CCP, this chapter describes the UAV-BS site planning problem as the mathematical problem shown in P2.

P2:

$$\underset{n}{min}{P}_s\left(n\right)=n{P}_g\left(\sqrt{{\left(R{r}_0\left(n\right)\right)}^2+H^2}\right)+(n-1)P_u$$

subject to

$$\begin{array}{cc}\hfill \mathrm{C}1:& 0<P_g<P_{max};\hfill \\ \hfill \mathrm{C}2:& S_c\left(n\right)-S\ge 0;\hfill \\ \hfill \mathrm{C}3:& n\le N;\hfill \\ \hfill \mathrm{C}4:& n\in {\mathbb{N}}^{+};\hfill \end{array}$$

where R represents the radius of the target area, and $r_0\left(n\right)$ represents the proportional relationship between the coverage radius of each UAV-BS and the radius of the target area when n UAV-BSs are deployed. The value of $r_0\left(n\right)$ satisfies Table 2. Due to the integer constraint included in the problem, the objective function becomes an equation with integer variables, which makes the problem difficult to solve. To address this, this paper attempts to use curve fitting to relax the integer constraints of the problem, thus finding a continuous solution. This solution is then rounded and compared to obtain the optimal number of UAV-BSs for the target area.

This paper utilizes nonlinear least squares to fit the data in Table 2 and employs a binomial power function for approximation. The fitting function for the relationship between the number of small circles and the radius of small circles under the CCP model is given as follows:

$$r_0\left(n\right)=a{n}^{-b}+c,$$

(17)

where a, b, and c are constants. Under a 95% confidence level, the confidence intervals for a, b, and c are $\left\{\right(1.725,1.851),(-0.8055,-0.7105),(0.06404,0.1085\left)\right\}$, and the values are taken as $(1.788,0.758,0.08626)$. For the deployment of n UAVs, the maximum distance each UAV can connect to is as follows:

$$d_n=\sqrt{r{\left(n\right)}^2+H^2}.$$

(18)

The maximum radius of the projection circle covered by each UAV-BS is as follows:

$$r\left(n\right)=R{r}_0\left(n\right).$$

(19)

Equation (16) can be replaced with the following:

$$P_s\left(n\right)=An{(r_0{\left(n\right)}^2+{\displaystyle \frac{H^2}{R^2}})}^{\alpha /2}+(n-1)P_u,$$

(20)

where,

$$A=R^{\alpha }{10}^{{\displaystyle \frac{\gamma +P_{\mathrm{noise}}+20{log}_{10}\left(\frac{4\pi f}{c}\right)+\xi }{10}}}.$$

(21)

Considering the optimization problem for the minimum communication energy consumption required for the UAV-BS to provide full coverage to the ground, it can be expressed as follows:

P3:

$$n^{*}=argmin\left(P_s\left(n\right)\right)$$

subject to:

$$\begin{array}{cc}\hfill \mathrm{C}1:& 0<P_g<P_{max};\hfill \\ \hfill \mathrm{C}2:& S_c\left(n\right)-S\ge 0;\hfill \\ \hfill \mathrm{C}3:& n\le N.\hfill \end{array}$$

Theorem 1.

The total transmission power $P_s\left(n\right)$ is a convex function with respect to n.

Proof of Theorem 1.

The second part of the objective function $P_s\left(n\right)$ is convex for $n>0$. If the first part is also convex, then the objective function, being a weighted sum of convex functions, maintains convexity.

To prove that $A·n{\left(r_0{\left(n\right)}^2+{\displaystyle \frac{H^2}{R^2}}\right)}^{\alpha /2}$ is a convex function, we consider the general form $f\left(x\right)=x{(g{\left(x\right)}^2+k)}^{\alpha /2}$.

The first and second derivatives are given by the following:

$$\begin{array}{c}\hfill f^{\prime }\left(x\right)={\left(g{\left(x\right)}^2+k\right)}^{{\displaystyle \frac{\alpha }{2}}}+\alpha xg\left(x\right)g^{\prime }\left(x\right){\left(g{\left(x\right)}^2+k\right)}^{{\displaystyle \frac{\alpha }{2}}-1}.\end{array}$$

(22)

$$\begin{array}{cc}\hfill f^{″}\left(x\right)=& 2\alpha g\left(x\right)g^{\prime }\left(x\right){\left(g{\left(x\right)}^2+k\right)}^{{\displaystyle \frac{\alpha }{2}}-1}\hfill \\ \hfill & +\alpha x{g}^{\prime }{\left(x\right)}^2{\left(g{\left(x\right)}^2+k\right)}^{{\displaystyle \frac{\alpha }{2}}-1}\hfill \\ \hfill & +\alpha xg\left(x\right)g^{″}\left(x\right){\left(g{\left(x\right)}^2+k\right)}^{{\displaystyle \frac{\alpha }{2}}-1}\hfill \\ \hfill & +2\alpha xg{\left(x\right)}^2{g}^{″}{\left(x\right)}^2{\left(g{\left(x\right)}^2+k\right)}^{{\displaystyle \frac{\alpha }{2}}-1}\hfill \end{array}$$

(23)

where

$$\begin{array}{c}\hfill g\left(x\right)=x^{-a}+b>0;\end{array}$$

(24)

$$\begin{array}{c}\hfill g^{\prime }\left(x\right)=-a{x}^{-(a+1)}<0;\end{array}$$

(25)

$$\begin{array}{c}\hfill g^{″}\left(x\right)=a(a+1)x^{-(a+2)}>0.\end{array}$$

(26)

To ensure that $f^{″}\left(x\right)\ge 0$, the value of x must satisfy

$$\begin{array}{c}\hfill x\ge {\displaystyle \frac{1}{-\left(\frac{g^{\prime }\left(x\right)}{2g\left(x\right)}+\frac{g^{″}\left(x\right)}{2g^{\prime }\left(x\right)}+\frac{g\left(x\right)g^{\prime }\left(x\right)}{g{\left(x\right)}^2+k}\right)}}.\end{array}$$

(27)

When $\alpha \ge 2$, $a=0.785$, $b=0.08626$, and $0<k<1$, using mathematical solving tools, it can be determined that x is within $(0,50]$ and the second derivative holds true. Therefore, it is known that $An{\left(r_0{\left(n\right)}^2+H^2\right)}^{\alpha /2}$ is convex, meaning $P_s\left(n\right)$ is a convex function. All the above constraints are convex sets. According to the definition of convex optimization problems, the UAV deployment optimization problem modeled in this paper is a convex problem, and there exists an optimal solution $n^{*}$ that minimizes the total transmission power required by the system.    □

P3 is reformulated into a standard convex problem:

P4:

$$n^{*}=arg\underset{n}{min}\left(P_s\left(n\right)\right)$$

subject to

$$\begin{array}{cc}\hfill & -P_g<0\hfill \\ \hfill & P_g-P_{max}\le 0\hfill \\ \hfill & S-S_c\le 0\hfill \\ \hfill & n-N\le 0\hfill \\ \hfill & C\left(i\right)\le 0\mathrm{for}i=1,2,3,4\hfill \end{array}$$

This paper uses the method of Lagrange multipliers to transform the above problem into an unconstrained optimization problem to solve for the solution that satisfies the inequality constraints. The Lagrange function for the above problem is constructed as follows:

$$\begin{array}{cc}\hfill L(n,{\lambda }_1,{\lambda }_2,{\lambda }_3,{\lambda }_4)& =P_s+\sum _{i=1}^{i=4}{\lambda }_i\mathrm{C}\left(i\right)\hfill \\ \hfill & =P_s-{\lambda }_1{P}_g+{\lambda }_2(P_g-P_{max})+{\lambda }_3(S-S_c)+{\lambda }_4(n-N)\hfill \end{array}$$

(28)

In order to facilitate the subsequent calculation, the above formula is simplified:

$$\begin{array}{cc}\hfill L(n,k_i)& =\mathrm{A}·n{(r_0{\left(n\right)}^2+{\displaystyle \frac{H^2}{R^2}})}^{\alpha /2}\hfill \\ \hfill & +(n-1)P_u-k_{1}n{(r_0{\left(n\right)}^2+{\displaystyle \frac{H^2}{R^2}})}^{\alpha /2}\hfill \\ \hfill & +k_2(n{(r_0{\left(n\right)}^2+{\displaystyle \frac{H^2}{R^2}})}^{\alpha /2}-{\displaystyle \frac{P_{max}}{A}})\hfill \\ \hfill & +k_3(1-r_0{\left(n\right)}^2)+k_4(n-N),\hfill \end{array}$$

(29)

where $k_1,k_2,k_3,\mathrm{and}{k}_4$ are non-negative Lagrange multipliers. For Equation (28) to have an optimal solution, it must satisfy the KKT conditions in optimization theory. That is,

$$\begin{array}{cc}\hfill & C\left(i\right)\le 0\hfill \\ \hfill & k_i\ge 0\hfill \\ \hfill & k_i{C}_i\left(x\right)=0\hfill \\ \hfill & {\displaystyle \frac{\partial L(n,k_1,k_2,k_3,k_4)}{\partial n}}=0.\hfill \\ & \mathrm{for}i=1,2,3,4.\hfill \end{array}$$

(30)

To solve Equation (30) using Newton’s method, let the i-th iteration value be denoted as $n_i$, and the $(i+1)$-th iteration value be the following:

$$\begin{array}{c}\hfill n_{i+1}=n_i-{\displaystyle \frac{L^{\prime }\left(n_i\right)}{L^{″}\left(n_i\right)}}.\end{array}$$

(31)

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill L\left(n_i\right)& =\mathrm{A}·n_i{(r_0{\left(n_i\right)}^2+{\displaystyle \frac{H^2}{R^2}})}^{\alpha /2}\hfill \\ \hfill & +(n_i-1)P_{uu}-k_1{n}_i{(r_0{\left(n_i\right)}^2+{\displaystyle \frac{H^2}{R^2}})}^{\alpha /2}\hfill \\ \hfill & +k_2(n_i{(r_0{\left(n_i\right)}^2+{\displaystyle \frac{H^2}{R^2}})}^{\alpha /2}-{\displaystyle \frac{P_{max}}{A}})\hfill \\ \hfill & +k_3(1-r_0{\left(n_i\right)}^2)+k_4(n_i-N).\hfill \end{array}\end{array}$$

(32)

$$\begin{array}{c}\hfill \begin{array}{c}\hfill L\left(n_i\right)=(\mathrm{A}-k_1+k_2)D\left(n_i\right)-2k_3{r}_0\left(n_i\right)r_0^{\prime }\left(n_i\right)+P_{uu}+k_4,\end{array}\end{array}$$

(33)

where,

$$\begin{array}{c}\hfill \begin{array}{c}\hfill D\left(n_i\right)=(1+{\displaystyle \frac{2\alpha n{r}_0\left(n_i\right)r_0\left(n_i\right)}{r_0{\left(n_i\right)}^2+\frac{H^2}{R^2}}})\times {(r_0{\left(n_i\right)}^2+{\displaystyle \frac{H^2}{R^2}})}^{\alpha /2}.\end{array}\end{array}$$

(34)

Then, n conforming to P2 can be obtained by solving Equation (31), and the minimum total transmit power of the system required to cover the target area with the proposed base station site planning strategy can be obtained by inserting Equation (19). Considering that the number of UAV-BSs is an integer value, the optimal number is rounded down and up at the same time, and the system transmit power required to cover the target area under the corresponding circular coverage strategy is calculated. Comparing the two calculation results, the UAV-BS site planning corresponding to the smaller value is selected.

In summary, the specific steps for UAV-BS site planning using CCPO are in Algorithm 1:

Algorithm 1: Circular Coverage Power Optimization Strategy

Require: SNR threshold ${\gamma }_{th}$, maximum transmission power of the base station $P_{max}$ Ensure: Optimal number of UAV-BSs $n^{*}$ under CCPO, minimum system transmission power $P^{*}$, and corresponding UAV-BS site planning    1: Initialize: Bandwidth B, frequency f, attenuation exponent $\alpha$, target area radius R, flight altitude H, and the relationship between the number of small circles and their radius as shown in Table 2    2: Use Equation (17) to fit the relationship between the number of small circles and their radius in the CCP solution, and calculate the coverage radius of each base station in the target area according to Equation (18)    3: Based on the initialized parameters, calculate the transmission power of a single UAV-BS under the circular coverage strategy, and find the minimum number of UAV-BS deployments $n_{min}$ that meet the power constraint     4: Optimal number of UAV-BS deployments and minimum system transmission power Set the initial value of the iteration $n_0=n_{min}$ and the error limit $\eta$. Calculate $n_{i+1}=n_i-{\displaystyle \frac{L^{\prime }\left(n_i\right)}{L^{″}\left(n_i\right)}}$ using Newton’s method. Determine if the result from (b) satisfies $|n_{i+1}-n_i|<\eta$. If it does, terminate the iteration and output $n^{*}=n_{i+1}$. Otherwise, return to step (b) and continue the iteration. Perform ceiling and floor operations on the optimal number of UAV-BSs obtained in step 4, recalculate the system transmission power, and compare to determine the minimum value. Update and output $n^{*}$, $P^{*}$, and the corresponding circular coverage strategy with the positions of the small circles as the site planning.

5. Experimental Results

The above methods are simulated, and the key parameters used in the simulation system are shown in

Table 3. Simulation parameter value.

Parameter	Value
Target area radius R	1000 m
UAV-BS deployment height H	100 m
Number of UAVs in control center N	50
Noise spectral density ${\eta }_0$	−174 dBm/Hz
A2G channel attenuation exponent ${\alpha }_1$	2
Maximum transmission power of single UAV-BS $P_{max}$	5 W
Reception SNR threshold ${\gamma }_{th}$	5 dB

. The flight control center contains 50 rotary-wing UAVs equipped with wireless communication base stations for arbitrary use, and the target area is a circular scene with a radius of $R=1000$ m. The UAV’s flight altitude is $H=100$ m, with a maximum transmission power of $P_{max}=5$ W for each UAV-BS. The channel attenuation exponent is $\alpha =4$, the channel noise is $P_{\mathrm{noise}}$ = −174 dBm/Hz, and the receiving SNR threshold is ${\gamma }_{th}=5$ dB.

In the above scenario, using the CCPO strategy, at least 20 UAVs need to be deployed to ensure full coverage of the target area. The corresponding site planning is shown in Figure 3.

Figure 4 illustrates the impact of UAV flight altitude H on system power consumption, with all other parameters held constant. The horizontal line segment indicates that under the condition of limited transmission power of UAV-BS, the corresponding deployment scheme cannot meet the full coverage requirement of the target area and will be discarded when selecting the optimal deployment scheme. After the horizontal line, it can be seen that the total transmit power function of the system is convex, which is consistent with Equation (21) and the results obtained by P4. Obviously, as the UAV flight altitude increases, the minimum number of UAV-BS required to achieve full coverage increases, and the total transmission power of the system increases, but the number of UAVs required for the optimal deployment decreases. This is because as the flight altitude increases, the distance between UAV-BS and ground users increases, and the transmission power required to achieve coverage also increases accordingly.

Figure 5 illustrates the impact of the attenuation exponent $\alpha$ on the site planning results under the condition that all other parameters are the same. As shown in the figure, as the attenuation exponent increases, the number of UAVs required to meet full coverage requirements using the CCPO strategy also increases. According to Equation (12), an increased attenuation exponent means that more transmission power is needed to provide communication services to ground users at the same distance. Additionally, the minimum point of the system power curve shifts to the right, increasing the optimal number of UAV-BSs. In scenarios where signal degradation is severe, we ensure that the system can still achieve full coverage by increasing both the transmission power and the number of UAV-BSs deployed. This approach is necessary to compensate for the power loss due to channel attenuation, especially in special scenarios where the attenuation exponent $\alpha$ significantly impacts the site planning results. By appropriately increasing the transmission power of the UAV-BSs, we can effectively counteract the increased attenuation and maintain the desired level of service coverage.

Under the condition that all other parameters are the same, this paper discusses the impact of the target area size and SNR threshold on site planning. As shown in Figure 6, with the same target area radius, ${\gamma }_{th}$ takes 0dB, 2.5 dB, and 5 dB respectively. Figure 6b is a magnification of a part of Figure 6a. As the SNR threshold increases, the optimal number of UAV-BSs deployed using the circular coverage method increases significantly. This is because as SNR increases, the area covered by a fixed power decreases, and thus the number of UAV-BSs required to achieve full coverage also increases.

Additionally, under the same SNR threshold, the number of UAV-BSs required by the optimal site planning solution overall shows a trend of increasing first, then remaining constant, and then decreasing as the target area radius increases, with local step-like growth. As can be seen in Figure 6a, when the SNR threshold is 5 dB, the optimal number of UAV-BSs increases with the target area radius within the range of 1000 m to 1800 m, remains constant between 1800 m and 2200 m, and then decreases. This trend occurs because, with the CCPO site planning proposed in this paper, the coverage radius of the UAV-BS increases with the target area radius, and the transmission power of a single UAV-BS also increases. However, the power of the UAV-BS is limited, and the coverage radius is constrained. The balance between these two is achieved by increasing the number of UAV-BSs to meet the full coverage requirement. The platform section appears because the maximum number of UAV-BSs is affected by the ACC capacity. Comparatively, deploying 50 UAVs results in the minimum system power consumption; as the target area radius continues to increase, the transmission power of the UAV-BSs deployed using circular coverage power optimization will exceed the maximum transmission power. With 50 UAVs, it is impossible to achieve full coverage of the target area under the maximum transmission power constraint. At this point, it is necessary to increase the number of UAV-BSs that the control center can accommodate or raise the transmission power limit to solve this problem, indicating that the size of the target area has guiding significance for the control center capacity planning.

Figure 6b describes the impact of minor variations in the target area radius on the UAV-BS site planning solution. When R takes values between 1120 m and 1136 m, the number of UAVs required is consistently 24, with a total system power consumption of 444.37 W. This is because the CCPO strategy adopted in this paper is a geometric coverage strategy, where minor increases in the target radius have a negligible impact on the coverage range of the UAV-BSs, and the optimal number of UAV-BS deployments does not change significantly. This result meets the requirements for the CCPO problem’s decentralized solution, and also indicates that the CCPO strategy does not require a new site plan when the target area is slightly adjusted. In practical applications, this feature can effectively reduce the investment in labor and computational resources.

Under the condition that the target area radius ranges from 1000 to 2000 m, and with other parameters as shown in Table 3, this paper compares the performance of the proposed site planning solution with the hexagonal coverage solution and the minimum power consumption coverage solution. All three methods can achieve full coverage of the target area. As can be seen in Figure 7, the traditional hexagonal coverage method places the center of the target area as the center of the first regular hexagon, using the property of two adjacent regular hexagons to achieve complete overlap to ensure no coverage gaps, expanding outward until the entire target area is covered, as shown in Figure 8. This method is simple to deploy, but due to severe overlapping, it requires a higher system transmission power to achieve full coverage. The minimum power consumption coverage method reduces the coverage radius of the small circles at the boundary of the target area, which, to some extent, reduces the transmission power of the outermost base stations, thus reducing power resource waste. However, this coverage method still has significant overlapping in certain areas within the target area, increasing power consumption and also intensifying signal interference. The CCPO strategy is also a feasible method, characterized by guaranteed full coverage and minimal overlapping area. Compared to the previous two methods, the system transmission power of the UAV-BS is reduced by an average of 14.75% and 6.52%, respectively. The results indicate that the CCPO strategy proposed in this paper can effectively solve the site planning and deployment problems of UAV-BSs, and also provide support for the development of UAVCN technology.

6. Discussion

In the process of communication network development, UAVs, as a new communication carrier, bring more possibilities for future network expansion. Meanwhile, their flexible mobility, deployability in the air, and other characteristics also make the network structure and its characteristics more complex, as well as the network design more challenging. In UAVCNs, as the channel complexity of UAV is higher, the power consumption is greater. UAV-BS station site planning has attracted much attention. This study focuses on UAVCN communication energy consumption and the full coverage of users in the target area. The circle coverage strategy is used for modeling, and the proportional relationship between the small circle radius and number is fitted by a power function with a given large circle radius, aiming to minimize power loss under the condition of full coverage. Newton iteration is used to give the number of UAV-BSs required to meet the target and the optimal coverage radius to determine the optimal UAV-BS site planning strategy.

The traditional hexagon strategy and the minimum power loss strategy can also achieve full coverage. However, due to its own limitations, the hexagon strategy can achieve full coverage while the power increases sharply. However, its simple deployment is also worth considering. In contrast, the method proposed in this paper can fully cover ground users and ensure the minimum communication power consumption under the same number of systems, but there are still some limitations to be considered. First, the method proposed in this paper requires each UAV-BS to provide omnidirectional and undifferentiated signal coverage to ground users, without considering the service differences of different users and their individual requirements on network performance. Second, this study does not involve dynamic environments, such as changes in UAV-BS position or user mobility, which may affect the coverage effect and system performance. The strategy primarily aims at optimizing power consumption, yet it does not encompass the allocation and management of spectrum resources. We recognize the significance of additional parameters including user experience quality, throughput, resource utilization, and computational complexity, which could offer a more thorough assessment of the strategies.

However, it should not be ignored that the method proposed in this paper can cover all points in the target area without discrimination, ensure that users at any location can access the network, meet the UAV network transmission power target, and effectively reduce the system transmission power, which has a lot of reference value for solving UAV-BS site planning problems.

7. Conclusions

This study discusses the status quo of UAV communication and UAV-BSs, focusing on the site planning of UAV-BSs. Aiming at its power consumption problem, a site planning strategy based on circular coverage power optimization is proposed. Simulation experiments show that the site planning strategy proposed in this paper can effectively reduce the system’s transmit power and achieve full coverage of the target area. It provides a valuable reference for the planning and deployment of UAV-BSs, and supports the development of UAV-BS communication technology. Subsequent studies will model the UAV-BS site planning process as a large circle covered by ellipses of different sizes to simulate the process of UAV-BS equipped with directional antennas to provide communication services for a specified area. Then, the UAVCN signal coverage performance will be improved by optimizing the number of UAV-BSs and the coverage area size to further meet the needs of different users. At the same time, we will focus on the challenges brought on by the flight characteristics of UAVs, and deeply study dynamic UAVCNs to find more reliable and efficient ways to improve network performance.